Tarasov Laser Physics and Applications Mir
Tarasov Laser Physics and Applications Mir
Tarasov Laser Physics and Applications Mir
Tarasov
Laser Phisics
and
Applications
MIR PUBLISHERS
B. Tapacca
L. TARASOV
Laser Physics
and Applicctions
n-
pu1JI'shed 1986
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Alpha
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1983.
Contents
Preface
9
14
33
41
45
45
47
2.1
2.2
2.3
2.4
i8
22
27
53
55
57
65
70
73
76
79
81
89
94
P4
100
106
111
iiG
118
Content'
129
134
138
139
145
148
150
. .
. .
. .
.
. .
. .
. . .
. . .
.
157
16
168
173
178
181
184
Index . . . . .
188
Preface
Preface
variation of the regime of oscillation to produce radiation with the desired spatial, temporal, frequency and
power characteristics. All these topics are treated in
Chapter 3. Finally, Chapter 4 is concerned with diverse
applications of lasers in science and engineering.
Chapter 1
o
B
10
ci. 1
==
viA
(1.1)
==
cln
(1.2)
11
t2
ek.
(1.4)
hvlc = h/'A
(1.5)
Equations (1.4) and (1.5) reflect the dual nature of radiation. These relationships combine the characteristics of a
microparticle (corpuscle or quantum) E and p with the wave
characteristics v and 'A. Essentially, these are two models to
explain the phenomenon of light. According to Bohr, they
are complementary, and connected mathematically by
means of Planck's constant h.
Thus, a plane, [llonochromatic, polarized, light wave is
an ensemble of photons occupying the same state. To various
states of photons there correspond various plane monochromatic waves.
Fermions and bosons. All microparticles existent in
nature may be divided into two groups according to their
behaviour in the ensemble of the like, or, as physicists say,
according to their statistical properties. In one group, microparticles behave as extreme individuals-if one state is
occupied by one microparticle it is denied to all the other
particles of this ensemble. In other words, one state can be
populated by one such particle only.
In the other group, microparticles behave in the ensemble
differently-they not only populate one and the same state
in an unlimited number, but the probability of them occupying a state is the greater the more such particles are already
in this state. Stated another way, these microparticles tend
to accummulate in separate states.
The microparticleS of the first group are called [ermions
(in deference to E. Fermi, an outstanding I talian physicist),
13
14
"Disordered" light waves. Wave trains. Actual light consists of many photons in a variety of states. These are
emitted by various atoms of emitting substance, which
radiate independently so that the emitted photons differ in
their energy, direction of momentum, and polarization.
In loose terms, a radiation combined of such photons may be
Ilnln)/(I max
+ Iml n)
(1.7)
15
16
17
1/1:
(1.10b)
\------=~-------=~/D
"/
18
ci.
C a totally reflecting mirror, and D the interference planejust a white screen. Beamsplitter B splits a wave train, while
mirror C reflects the divergent train into the point where
the transmitted train is to arrive. In order that the portions
of the same train, rather than different trains, meet at the
interference screen, the condition must be satisfied
L~
(1.11)
~c
19
W = ENe 1 2
(1.12)
20
en.
whereby the atom falls into the lower level. The transition
causes an emission of a photon (Fig. 1.6). Both the inducing
and the induced photons have the energy 8 12 == E 2 - E 1
Moreover, both of them have identical direction of their
momenta and identical polarization. In other words, the
secondary photon finds itself in the same state as the primary photon. This result is a sequel of the bosonic behaviour
of photons-they tend to accumulate in the same state.
This is the phenomenon of stimulated emission of light.
The more primary photons are incident on our elementary
volume, the higher the probability that the atom lying in
level E 2 will be forced to undergo a transition to E 1 Here
we should recognize a certain similarity between the stimulated emission and stimulated absorption processes, namely,
the probabilities of both processes are proportional to the
0/ Light
21
Wst = BNE 1 2
(1.13)
22
en.
and is defined as
W SP = A
(1.14)
23
these may account for only a small fraction of all the atoms
(molecules). One cubic centimetre of gaseous media has
about 1016 to 1017 of such species, while that of solid and
liquid media 1019 to 1020
We shall consider only those levels of the active species
which are of consequence for laser action. First of all we
single out two levels whose transition produces radiation.
We shall call it the lasing transition. As before, one of them
is the upper level, while the other is the lower level. Let
Ct2 == E 2 E 1 be the energy difference of these levels, then
V 1 2 == E1 2 /h is the frequency of the transition, that is the
frequency of emitted radiation. Let n 1 and n 2 be the number
of active species (per unit volume) lying in the upper and
lower levels respectively. These quantities are known as the
populations of these levels.
Light amplification in an inverted active medium. As Wf:.
already know, a photon of energy e1 2 can, with an identical
probability, induce either the E 1 ~ E 2 transition or the
E 2 ~ E 1 transition. Which of them will result depends on
the energy level in which the active centre lies. If the lower
level of the medium is more populated than the upper level,
the absorption processes will dominate. Conversely, if the
upper level is more populated than the lower, the processes
of stimulated emission will prevail.
Under normal conditions, specifically in thermodynamic
equilibrium, the populations of energy levels decline as the
level energy increases, so that normally n 2 < nt, and the
processes of absorption of light are dominant.
To produce radiation, however, we need that the processes
of stimulated emission will be dominant. Consequently, we
should take care of the higher population of the upper level,
that is, to ensure that
(1.15)
When this condition is met we say that a population inversion takes place in the medium.
Let us assume that such an inverted active medium be
prepared. Let a collimated light beam of frequency "12 and
irradiance I be incident on the medium (Fig. 1.8).
We would like to dwell a bit on the notion of irradiance.
I t is measured as the energy of a light beam incident on
unit area per unit time, therefore, the dimension of this
24
cs.
==
(Bhv12/V) (n 2
n1 ) I
(1.18)
The quantity
012
==
BhvJ2/V
(1.19)
25
virtue of (1.19)
(1.20)
The methods of creating a population invertion. To produce a population inversion, we should take care of the upper
energy level being populated more intensely than the lower
level, or to provide a way for the lower level to be depopulated faster than the upper level. Each time our aim is to
create higher populated upper levels in the medium.
The physical mechanisms of populating and depopulating
energy levels are many and diverse. Accordingly, there
exist various means of rendering the medium active, collectively known as the processes of pumping.
In optical pumping, the predominant population of the
upper level is achieved by means of light energy delivered
from appropriately selected sources such as gaseous discharge
flashtubes, or continuously burning tubes. Electrical pumping is accomplished by means of a sufficiently intense
electrical discharge in the medium and is particularly suited
to gas media. The discharge converts the gas into a plasma
where active centres collide inelastically with free electrons
and cause the predominant population of the upper pumping level. Inelastic collisions of active centres with other
atoms and molecules purposefully introduced into the gas
are also of importance for pumping as they provide resonance energy exchange. Chemical pumping raises active centres into the higher level by means of suitable exothermal
chemical reactions in the active material. Of other methods
of pumping we may mention also heat pumping in which
the active material is at first brought to a high temperature
and then rapidly cooled down. In more detail the suitability
of the pumping methods to....various active media will be
taken up in Chapter 2.
The principal pumping schemes. Atoms, ions, or molecules used as active centres often 'exhibit rather complicated
systems of energy levels. However, for all the variety of
these structures, the actual pumping schemes may be boiled
down to a few rather simple diagrams correctly depicting
the pumping process although neglecting some minor details.
These diagrams involve three or four levels only. Fig. 1.9
showing these diagrams uses the following nomenclature:
(0) the ground level, (1) the lower lasing level, (2) the upper
26
3
2
2,3
0,1
o
(a)
(b) .
(c)
lasing level, and (3) the pumping level. The upward arrow
implies the pumping transition, the downward arrow the
lasing transition, and the slant arrows the auxiliary fast
decays.
Consider the three-level pumping scheme shown in
Fig. 1.9a. Active species excited by some pumping process,
say, by optical pumping, are raised from the ground level 0
to the pumping levelS. Assume that more than half the active
species undergo this transition. Then a very fast (during
about 10-8 s) decay follows from level S to the upper lasing
level 2. This is a nonradiative transition which gives its
energy to the crystal lattice, if the material is a solid. The
decayed atoms reside in level 2 (for about 10-4 to 10-2 s) and
because more active centres are now in this level than in
the ground state the inversion of the material takes place.
In the three-level laser scheme shown in this diagram,
the ground state is simultaneously the lower lasing level
and therefore is labelled 0 and 1. Such sharing of functions
is a disadvantage in the sense that the lower lasing level
should be depopulated, or better still, empty, which is not
the case with the ground level being populated rather densely under normal conditions. Since it can be depopulated
by the pumping process only, to produce an inversion more
than half the active centres should be raised from this level.
This disadvantage is circumvented in the three-level scheme
shown in Fig. 1.9b. This arrangement takes care of the lower
lasing level being always virtually empty, as a fast decay
27
From
learned
medium
ruinates
28
en.
29
30
ek.
=--=====~-==~~
j
________
#: -- __
_. _ _ u
__
~ .J'.~ ~
:: -- :: 3: 3=/~ t
~Jft'
---
\"~
~ ~
__ -- ; ~ == ~\,\ =; ~
~ ~ ~ ~ =: =E~" ~
i i~- :
:: :::: ::
~~,
'---'[1''----''-----,
31
= U
(0) e-t/'te
(1.22)
32
cu.
1/Q
(1.26)
== 'Act/2n
If the causes of loss are many, say, absorption and radiation through the side surface, we may associate with each
type of loss its own loss factor cti and its own Q-factor, Qh
so that
1/Qi == 'A ct i/2n
(1.27)
If these losses are independent of each other, then the resultant change in the field energy inside the cavity may be
presented as the sum of contributions due to various losses,
I1U == ~ ~Ui. With referen.
0 - ce
to (1.21), we then have
2
1/'t'c == ~ 1/'t C , i and by virtue
of (1.25) and (1.26)
L
(1.28)
1/Q
== ~
1/Qi
33
- 0400
en.
34
Hz)
~ ~
I(z) + 61
-.---F~
~f1Z
~I (Fig. 1.14). This increment of the flux is proportional to the initial irradiance I (z) and the thickness of
the amplifying layer
(1.33)
~I = ~I (z) ~z
I (z)
~z
(1.34)
~I
(z)
(1.35)
0'12
t -
nt )
(1.36)
35
(1 37)
n 2-nl= 1+(x/v)I
where x is a parameter accounting for the nonlinear behaviour of the transition, and v is the velocity of light in the
medium. Denoting ~o = 0'12 (n 2 0 - n 1 0 ) , referred to as the
initial gain coefficient, .we recast (1.36) by virtue of (1.37) as
~ = 1+(,,;:) I
(z)
(1.38)
Note. To avoid possible confusion, we would like to emphasize that it should be distinguished between the absorption of radiation by the lasing transitions of active species
and the absorption by other non-lasing atoms and molecules
inside the cavity. The first absorption is always considered
together with stimulated emission and is taken into account
in the small-signal gain coefficient ~. The second absorption
is related to losses and enters the respective loss coefficienta.
Equations (1.33) and (1.34) have been written for loss-free
active materials experiencing only stimulated emission and
absorption in the lasing transitions of the active centres.
For inverted materials with nonzero losses, (1.33) should be
replaced with
(1.39)
i11 === (~ - a) I (z) i1z
This expression is rather indicative of the fact that two conditions should be satisfied in order for the inverted medium
to amplify a light signal. First, the processes of stimulated
emission must dominate over those of absorption for lasing
transitions, so that ~ > O. Second, the gain must exceed
the losses, ~ > a.
Should we include the losses in our cons'ideration , we
would introduce the loss power density PI (z) and write in
~*
c.
36
place of (1.34)
~I =
(1.40)
+ aout
(1.44)
= ~ v(~o-(a+aout)]a~~:ut
(1.47)
37
>
cx
(1.48)
CXout
V;:rtJ'oa-a
(1.49)
(1.50)
a,0p --
out -
where
P~~X
=:-;
= e- 2L ('V (3oa - a )
(1.51)
ci: 1
Pout
pmax
out
Fig. 1.16 Gain curve and loss level superimposed. The higher the
loss threshold, the smaller the
amplitude of the net gain profile
~o (v) = C (V-~~~+i\i
(1.52)
where V o is the central or resonance frequency of the transition (consistent with the maximum of the function), ~o is
the halfwidth of the function measured as the full width at
half-maximum power (FWI-IM), and C a constant.
The line AA drawn in this figure indicates the cavity loss
level. The plot above this line confines the area of the net
39
than unity, and Aq are resonant wavelengths. This resonance condition may be recast in terms of resonant
frequencies by virtue of (1.1) and (1.2) as follows
v q = qc/2Ln
(1.54)
where n is the refractive index of the medium filling the
cavity.
As can be seen from (1.54) the lines in the resonant spectrum are equidistant, since the spacing between the neighbouring frequencies is constant and equal to
(1.55)
~'V' = c/2Ln
40
OeDED
TEM oo
TEM o2
Fig. 1.18 Low-order transverse-mode patterns in cylindrical symmetry. The first integer defining the mode number indicates the
number of nulls as one passes across the beam in a radial direction.
The second integer specifies half the number of nulls in an azimuthal
direction
by the notation
1.7
41
The first steps on the way to the laser. The name laser
is an acromim of Light Amplification by Stimulated Emission of Radiation. Thus the term reflects the crucial role
of the processes of stimulated emission for quantum generators and amplifiers of coherent light. Therefore, the history
of laser development should be traced as far back as 1917
when Albert Einstein showed that the process of stimulated
emission must exist.
This was the first step toward the laser. The next one was
due to the Soviet physicist V.A. Fabrikant who pointed out
in 1939 to the possibility of exploiting stimulated emission
to amplify e.m. radiation travelling through a medium.
More specifically, he come up with the idea of using microsystems with inverse population of levels. Later, after the
Second World War, he returned to this idea and summarized
his research in a patent, filed in 1951 together with
M.M. Vudynsky and F.A. Butayeva, for the invention of
a means to amplify radiation by stimulated emission. This
42
43
44
Chapter 2
Types of Lasers
The table in Fig. 2.1 lists the most commonly used types of
lasers together with their active media and pumping methods. Lasers are normally classed by their active media
and means employed for excitation (pumping). This chapter,
therefore, will be devoted to the physical properties of
media utilized as active materials and the methods of
pumping allowing laser action to occur. We will also discuss
the system of interconnections between various pumping
techniques illustrated in Fig. 2.1. I t might look sophisticated at first glance, but we recommend to return to this
figure after reading this chapter to see it again from the
angle of what is said in this chapter.
Of the pumping methods presented in the figure two are
of major consequence-optical pumping and electrical pumping. Optical pumping is the most versatile pumping process.
It suits to excite a variety of active media including dielectric crystals, glasses, semiconductor materials, liquids,
and gas mixtures. Other pumping processes may integrate
optical pumping as a component as well. Electrical pumping
is accomplished by means of a sufficiently intense selfsustained electrical discharge and is particularly suited to
gaseous active media at pressures of 1 to 10 torr (mm of
mercury). The pertinent types of laser, using atomic, ion,
or molecular transitions, are not infrequently joined by
the common name of gas-discharge laser. These lasers as well
as solid-state, liquid, and semiconductor lasers find their
way into various fields of science and engineering.
The pumping process may be continuous or pulsed. So,
optical pumping employs gaseous-discharge flashtubes and
continuously emitting lamps. In electrical pumping, the
discharge may be pulsed and stationary or quasistationary.
ci: 2
46
ACTIVE
MATERIALS
Types of Lasers
r _~Y~~.9~~SERS
----1 II
PUMPING
I
Dielectric crystals
and glasses
Sol id-state
co
(J
Liquids:
- organ ic dyes,
';:;
Liquid
c,
- chelates,
-aprotonic
Photodissociation
Gaseous mixtures
of atoms and
molecules
Gas atomic
Ion
Rarefied hot
plasma'
Molecular
Electroion ization
Gaseous
molecular
mixtures
Gas-dvnam ic
Chemical
Highly ionized
cold plasma
Plasma
Two different type
semiconductors
(p-n junction)
Intrinsic
semiconductors
-.l
47
~8
en. 2
Types of Lasers
49
Fig. 2.3 Practical configurations of pump cavities for optically pumped solid lasers
50
Ch, 2
Types
0/ Lasers
11
--
--
:L,-:L, I - - C")
<.0
<.0
(b)
Fig. 2.5 Absorption (a) and fluorescence (b) spectra'of the chromium
ion in ruby
51
hand). Each of the bands is about 0.1 t-tm wide. The optical
pump of this laser is effected by a gas discharge xenon lamp.
The emission spectrum of the radiation spontaneously
omitted by the chromium ions in lasing (the fluorescence
spectrum of the chromium ion in ruby) is presented in
Fig. 2.5b. It consists of two bands: one at 0.6943 t-tm (the
so-called R1-line), the other at O.G929 t-tm (R 2-line). The
laser action occurs practically on the R 1-1ine only.
N ole. In atomic spectroscopy, there exists certain nomenclature for succinct identification of the states of atoms,
ions and molecules. We have no room in this text to discuss
this nomenclature at length and invite the reader to treat
the term symbols, such as 4Fl and 4F2' as certain labels of
the atomic levels. We will return to this nomenclature in
Sec. 2.5.
The Nd:YAG laser. The neodymium-doped yttrium alurninium garnet laser is the most popular type of solid state
Jaser. It has a rather low excitation threshold and a high
thermal conductivity, therefore lends itself for generation of
light pulses at a high repetition rate or for continuous operation (called continuous wave or cw operation in the laser
jargon). The efficiency of this laser is also comparatively
high, running to a few percent.
The atomic levels of the neodymium ion in YAG crystal
are presented in Fig. 2.6. In fact, the figure shows energy
bands of various width rather than thin levels. Each of this
bands contains a group of energy levels identified each by
its own atomic term symbol.
The optical pumping raises the ground state Nd atoms
(the atomic term 4/ 9/ 2) to a few states identified by the
terms 4G7 / 2 , 2G7 / 2 , 48 3 / 2
4F7 / 2, 4}?5/2
2H9 / 2 , and 4F3 / 2.
These five groups of states give rise to five hands in the
Nd:Y AG absorption spectrum plotted in Fig. 2.7a. The
bands are seen to reveal fine structure which reflects the
fact that the energy bands consist of individual levels.
The upper laser level is the state 4F3 / 2 The laser action
occurs when the neodymium ions decay from this level
to the states 4/11/2, 4] 9/2' 4/]3/2' and 4/ t 5/2 Since each of
these terms is associated with a few energy levels, the total
number of lasing transitions runs into two decades. The
major portion of the energy is emitted in the 4F:i / 2 ~ 4/11/2
52
Ch. 2
Types of Lasers
transitions (about 60%), therefore the 4111 / 2 state is normally taken as the lower laser level.
Figure 2.7b shows the Nd:YAG fluorescence spectrum for
the 4F3/2 ~ 4111 / 2 transitions. The spectrum contains seven
-.
l \\\\\ 1I1~1
1,5
483 / 2 + 4 F7/ 2
4F5/ 2 f 2H9/2
4G 7/ 2
-,
'/1
- .- ,- ,- ,'\. J
\\.\.,,"
~,",
4F 3/ 2
1.0
4G /
7 2
............
<,
4115/ 2
0.5
41 13 / 2
~
-:
41 11/ 2
419/ 2
(b)
4/11 /s
(b) spectra
53
54
en. 2
Types of Lasers
_L.__
covered by various dyes ru ns from 0.3 to 1.3 ~lnl. J3y selecting a suitable dye, one may obtain coherent radiation of
any wavelength from this range.
Rhodamine 6G is a practically important lasing dye of
the xanthene group. Fig. 2.8a shows its structural Iormu la
based on a system of benzene rings. X anthene dyes absorb
pumping radiation and fluoresce in the visible portion of the
spectrum. Fig. 2.8b shows the absorption and emission
spectra of rhodamine 6G. Like solid-state lasers, the linewidth of the absorption band is about 0.1 f.1m for this dye.
The emission band of this dye has the same linewidth which
is about 10 to 100 times broader than the fluorescence Iiuewidth of the dopants in solid-state lasers. This unusually
large em.ission linewidth and, as a consequence the gain curve
Iiuewidth , is one of the most interesting features of orgnnic
dye molecules utilized as active centres.
Optical pumping of dye lasers. Auxiliary lasers and lamp
sources are used to excite dye lasers. Jn the laser pumping,
the pump radiation is at the frequency of the pumping laser
or at a frequency t\VO or three times as high. In the latter
case it is said thnt the second or third harmonic. of the auxiliary laser transition is used for excitation.
2.4
Photodissociation Lasers
55
of the resonant cavity is 100 % reflectant for the pump radiation which enters the cavity through the prism and strikes
the dye cell to excite the dye. The dye fluorescent output
leaves the cavity through the output mirror.
Continuous laser pumping is also employed to excite these
lasers. This is frequently done with the argon ion laser
(discussed in Sec. 2.5). Because this pumping would heat
the dye exceedingly if in an ordinary arrangement, the pump
beam this time is arranged transverse to the dye medium.
It is focused into a 10 urn diameter spot on a dye stream
rapidly pumped through the excitation area. This flow
arrangement is not for cooling only, it is also essential for
removing photo-decay products from the generation zone.
2.4 Photodissociation Lasers
56
+ hv -+ A * + B
The process of molecular splitting as a result of light absorption is known as photodissociation. An interesting consequence of photodissociation that the absorption linewidth of the gas molecule turns out to be as wide as the absorption linewidths in solid and liquid active media. This
fact allows the use of wideband optical pumping. The excitation power is absorbed by dissociating molecules which
brings about an excited product to be used for lasing. This
type of gas lasers is termed photodissociation lasers.
Two classes of photodissociation lasers are known. One
uses the excited dissociation product as the active centre.
This excitation is said to have occurred in primary photoprocesses. The second class obtains excited active species
as a result of a series of chemical reactions with the products
of dissociation, that is, gets them from secondary chemical
reactions. Therefore, this type of laser is referred to as the
photochemical laser.
The iodine laser is an example of photodissociation laser.
A wideband optical pumping at 'A ~ 0.3 urn dissociates
CF 31 molecules
57
58
cs.
Types of Lasers
lasers) and of the flow discharge type (in atomic lasers and
molecular lasers). The arc discharge operates at high currents
and temperatures and produces high degrees of plasma ionization (measured as the ratio of free electrons to heavy particle concentrations in the plasma). The current density in
the discharge is as high as 100 to 1000 A/cm 2 , the discharge
temperature is 1000 K, and the degree of ionization is more
(a)
(b)
Fig. 2.10 Placement of electrodes for (a) high frequency and (b) de
vol tage exci ta ti on of discharge
59
3
I
............;,..
_----
lalo).
Note. As we noted in Sec. 1.5, the optical resonator selects
in space a direction in which laser action takes place. By
placing the output windows at the Brewster angle to the
resonator axis, we also select a certain polarization for the
lasing beam-in other words, we introduce a device to select
photons of certain polarization. Let an unpolarized light
wave be incident on a plane Brewster window of the laser
tube after travelling along the axis of this tube. The wave
may be represented as a combination of two polarized waves,
of which one is polarized in the plane of incidence and the
other perpendicular to this plane. The first wave will suffer
refraetion at the interface and enter the window, then will
be refracted again leaving the plate and will keep travelling
along the resonator axis. The second wave will undergo
reflection from the window and will be lost to the resonator.
Thus, the photon states with the polarization in the plane of
60
incidence turn out to be selected (in terms of Sec. 1.5), whereas the states with the perpendicular polarization do not.
It is an easy matter to see that the light wave reflected from
the window will not contribute to the oscillation in the
laser as it is lost to the cavity. The laser will take up for
oscillation the wave passing through the window, i.e., the
one polarized in the plane of incidence which includes the
resonator axis and the normal to the window. So, the Brewster windows help us to kill two birds with one stone. First,
we obtain a polarized laser output, and, second, exclude
losses suffered in the reflection from the tube windows.
Electronic configurations and atomic terms. Before we go
on discussing the processes causing inversion in gas-discharge
lasers a few words are in order on the state of active species
in a b . ~ous medium. Such a state includes a group of energy
levels defined in atomic spectroscopy by respective atomic
term symbols. These symbols, as we have already noted,
indicate the electronic state of the atom to which the contributions are made by the electrons orbiting this atom and
producing respective electronic configurations. Each stable
electronic energy state is described quantum-mechanically
by four quantum numbers and their specific symbols. More
specifically, these are the principal quantum number, n,
called so because the differences in energy are greatest for
electrons in quantum states with different n values, as it
defines the average distance of the electron from the nucleus;
the orbital quantum number, l, associated with different
amounts of orbital angular momentum (corresponds to much
smaller differences in energy than n does); the magnetic
quantum number, m, defining the z-component of angular
momentum (together with l this number determines the
extent to which the electronic orbit deviates from a perfect
sphere), and the spin quantum number, S, contributes to the
atom's energy when in a magnetic fi.eld.
In multi-electron atoms each electron is associated with
a set of quantum numbers. The quantum number n may
assume integer values 1,2,3, etc. The orbital quantum number l may take values from 0, 1, 2 ... to n - 1, hut for
historical reasons this quantum number is usually represented by a letter, as s, p, d, t, g, etc. The magnetic quantum
number m takes values from - l to l, and the spin s may be
61
62
14
12
Helium
atom
Neon atom
Fig. 2.12 Energy-level diagram of the He-Ne laser. The solid straight
arrows indicate the lasing transitions
the rest of the medium. Therefore, each atomic term represents a narrow energy level. Here, the energy band appears as the result of a few atomic states, identified' by the
term symbols of the same electronic configuration, tending
to unite into a single level of some energy spread.
The population inversion mechanism in the He-Ne laser.
Fig. 2.12 illustrates the basic transitions that occur in the
medium of a helium-neon laser. On the left, there are transitions of the helium atom, on the right those of the neon
atom. The excited states of the neon are shown by energy
bands identified according to the following table
designation
el. configuration
is
2p o3s
2s
2p o4s
3s
2p o5s
2p
2p&3p
3p
2p 64p
63
You may also come across a different (and a new one) notation for these states elsewhere, namely, by the quantum numbers of their single excited state electron -3s, 4s, 5s, 3p and
4p-which takes advantage of the fact that the other nine
electrons in the neon atom retain their ground-state quantum numbers.
Each s-band consists of four levels (four terms), while
each p-band, of ten levels. The 3s and 2s bands play the role
of the upper levels, whereas the 3p and 2p bands, that of the
lower laser levels. Laser action occurs on the three transitions: 3s -+ 3p at 3.39 f.1ID, 2s -+ 2p at 1.15 l-tm, and 3s ~
-+ 2p at 0.63 llm (red).
The inverted population in the He-Ne laser occurs as a
result of the population rate of the upper levels being considerably higher than that for the lower levels. Free electrons
of the gas discharge collide with the helium and neon atoms
to excite them by impact energy transfer. Absorptive transitions due to the electron impacts are shown by dashed arrows. The electrons excite the 1S 0 and 38 0 states in the
helium atoms and a variety of neon bands corresponding to
both the upper and lower lasing levels. The excited helium
atoms collide with the neon atoms and give up their energy
in the process known as resonant collision energy transfer.
This process is depicted by curved light arrows. The resonant transfer of energy from the helium to neon is crucial for
the more intense population build-up of the upper neon
levels than the lower levels. Three factors contribute favourably to this process. These are the close match, in energy,
of the pertinent helium and neon levels, the metastable
behaviour of the excited helium levels (their deactivation
through spontaneous emission is relatively slow), and a
higher partial pressure of the helium in the gas mixture,
that decreases the probability of energy transfer in the
reverse direction-from neon to helium.
The spontaneous emission in the lines 3s -+ is and 2s-+
-+ is proceeds slower than in the 3p -+ is and 2p -+ is
lines, therefore the lower lasing levels of the neon atoms
depopulate faster than the upper levels. The emptying of
the is-band levels is the bottleneck of the He-Ne lasing
process. The relaxation proceeds through electronic deexcitation, in which the excited neon atom gives up its energy
to free electrons, and through atomic collision of the Ne
64
65
66
ct: 2
types
01 Lasers
~-.-L. . . . . 2. . . ~ N2 --L
(~<3
4
---~-
-)
~
Fig. 2.t5 Two discharge tube configurations for the COs laser. (a) with
the discharge and laser volumes separated: 1 CO2 flow system, 2 N2
flow system, 3 hf glow discharge, 4 laser working volume, 5 output
mirror; (b) with the discharge and the laser in one chamber: A anode,.
C cathode
helium-neon laser; excited nitrogen molecules transfer energy to the CO2 molecules by resonant collisions. Carbon
dioxide lasers normally use a glow discharge for their excitation.
Figure 2.15a schematizes one of the first designs of the
CO2 laser using a high frequency glow discharge. The system
has two flow loops for pumping carbon dioxide and nitrogen.
The nitrogen molecules first enter the area of discharge and
become excited by collisions with the electrons of the discharge and then flow into the laser volume where they mix
up with the unexcited CO2 molecules. When these molecular
species collide, the nitrogen molecule imparts a proportion
of its energy to the CO2 molecule by resonant energy transfer. It is an important feature of this particular design that
the discharge electrons excite nitrogen molecules only, which
then transfer this energy to the active centres in another
area of the system.
Subsequent designs of the CO2 laser have fired a discharge
N 2 mixture. This has been as a rule a de
in the CO2
~.6
67
Molecu.lar Lasers
t.e1ow discharge. The arrangement of such a system is schemati zed in Pig. 2.15b. Similar to the previous arrangement,
this system employs pumping of the gas mixture through the
losing volume. This pumping is a way to avoid an undesired
change in the chemical composition of the active medium,
which could occur, in particular, as a result of the reaction
2(~02 ~ 2CO
02. Today, sealed-off CO2 lasers (with no
flow of the gas mixture) are in wide use. The life of such
devices could be as long as 1000 hours and more.
Vibrational modes of carbon dioxide. Thus far in OUI'
discussion, the energy levels of interest for laser transitions
~
(a)
M
(b)
~~
(c)
FII. 2.16 Vibrational modes of a COl molecule. (a) symmetric stretching, (b) bending, and (c) asymmetric stretching
,.
68
Carbon dioxide
Nitrogen
0.25
0.20
0.15
0.10
0.05
each mode. For example, the number (020) means that the
molecule in this energy state is in the pure bending mode
with two units of energy [i.e., no units of energy associated
with the symmetric and asymmetric stretch modes).
In addition to vibrational states, rotational states, associated with rotation of the molecule about the centre of
mass, are also possible. The energies associated with the rotational states, however, are generally small compared to
those of the vibrational states, and are observed as splittings
of the vibrational levels into a number of much finer sublevels. The separations between vibrational-rotational states
are usually much smaller on the energy scale than separations between electronic states.
The mechanism of population inversion in the CO 2 laser.
Fig. 2.17 shows the lowest vibrational levels of the ground
electronic state of a CO2 molecule and an N 2 molecule. In
the CO2 portion of the figure the levels correspond to vari-
2.6
Molecular Lasers
69
through inelastic collisions of the CO 2 molecules with elecI.IO(lS (electron impact) produced in the plasma of the discharge and with the excited nitrogen molecules (resonant
energy transfer).
States (020) and (100) decay into the ground state mainly
hy resonant energy transfer to the unexcited CO2 molecules
M.O that these accumulate in the (010) state
CO 2 (020)+C0 2 (000) ~ 2C0 2 (010)
CO 2 (100)
+CO
70
ct: 2
Types 01 Lasers
71
72
73
Thermodynamic methods of population Inversion. A sufficiently high population of the vibrational and rotational
states of a molecule may be achieved by thermal excitation.
To this end, a gas mixture should be heated to temperatures
in the range of 1000-2000 K. This simple rise of temperature
cannot, of course, produce a population inversion, as in
equilibrium the level is populated less, the higher its energy. In other words, whatever high the temperature of the
gas, the lower-lying levels of a molecule will be more populated than the higher-lying levels.
Now assume that the gas is heated to a temperature T 2 and
then rapidly cooled down to another temperature TI . Let 't
denote the time it takes the gas to be cooled from T 2 to T I'
and E 1 and E 2 be the lower and the upper level energy, respectively. Assume that the cooldown of the gas mixture
sweeps out level E 2 at a lower rate than level E I . Denote the
lifetimes of these levels by 'r 2 and 'ri Suppose that our cooldown is a rapid process and 't < 'r ~ 't? With this ~ilp.~
f
74
1(020)
J (
J
I \,
I
I
1 (001) I
~6
Fig. 2.20 Idea of the gas dynamic laser. 1 prechamber, 2 nozzle, 3 working volume of the resonator, 4 diffusor, 5 output
mirror, 6 laser output
75
76
Chemical compounds are able to store large amounts of energy that may be partially released in exothermal chemical
reactions, i.e. the ones proceeding with liberation of energy.
It has been rather attractive to convert this energy into coherent optical radiation. The chemical lasers are exactly
the srstems where such a conversion has been realized. Th e
77
78
ek.
2 Types 01
tassrs
When these chemically active species build up in a sufficiently large amount, the process will proceed rather fast
and the condition for lasing in some transitions of the HF*
species will occur. Since in a cyclic process the amount of
chemically active species remains unaltered, due to replenishment, there appears a possibility to involve, by chain
process, an enormous number of hydrogen and fluorine molecules into the reaction and build up the number of the
active centres HF*. The amount of chemical energy that can
in this way be converted into the coherent optical radiation
will by far exceed the energy expended in creating the chemically active centres.
An actual chain process is not endless of course. The chemically active species decrease in number by recombination
(H + H --+ H 2, F + F --+ F2). Therefore, the chemical reaction should be not only initiated but also maintained by
creating new chemically active species instead of those
~.10
79
Pldsma Lasers
II
80
81
82
2.11
Semiconductor tasers
83
ct: 2
Types
01 Lasers
~I
I
I
{a}
{b}
85
86
---.......
~f
.semiconductor
\ Semiconductor
\
(a)
"
Sernitransoarent
~~
liquid _
coolant -
~r]ro~
--Subs~ate~
~
-.-......
(b)
Electron
beam
Output
, coupler
\~
(c)
Fig. 2.24 Electron beam controlled semiconductor lasers. (a) transverse pumping, and (b, c) longitudinal pumping arrangements
87
energy level is seen to occur in the band gap, spaced ~E below the bottom of the conduction band. The energy separation ~E lis on the order of 0.01 eV which is about one hundredth of the band gap width E g. That ~E is small implies a
weak bonding of one of the electrons with the atom, there-
Eg
Valence ~
band /.
(a)
(b)
Fig. 2.25 Energy-band diagrams for (a) n-type and (b) p-type semiconductors
fore a small heat excitation would be enough for this electron to escape the atom and be raised from the donor level
into the conduction band.
Assume now that an n-type semiconductor is gradually
raised in temperature from 0 K. Since ~E < E g , the first
to occur will be the transitions from the donor energy level
to the conduction band, whereas the transitions of electrons
from the valence band to the conduction band will be virtually nonexistent. Normally, at around 20 to 50 K the donor
energy level is depleated, which means that all the donor
atoms have already donated their electrons into the conduction band. If the concentration of impurities in the material
is sufficiently high (at least 1018 atoms/em") the semiconductor is said to be heavily doped or highly degenerate n-type
material as already at the above temperatures it acquires a
degenerate situation in the conduction electrons.
The energy level situation with an acceptor-doped semiconductor is depicted in Fig. 2.25b. Here the acceptor atoms
are seen to produce the acceptor level ~E above the valence
hand. Now a small heat excitation is capable of raising electrons from the valence band onto the acceptor energy level.
Ch, 2
88
Types of Lasers
~-:
+
junction
Fig. 2.26 Injection laser. (a) schematic diagram and (b) device confi
guration: 1 p-type semiconductor, 2 n-type semiconductor, 3 meta
leads, 4 laser output
89
90
<,
AM
.>
~.
(a)
(b)-1J----
Fig. 2.27 Ring resonator. (a) three-mirror arrangement, (b) twomirror arrangement; A M active material, a, Brewster angle
9f
92
too) is
Wo
= (AL/2:rt)l,l2
(2.3)
w=(AL/n)1/2=woV2
(2.4)
The position of the beam waist may be controlled by choosing mirrors of different aperture or introducing a diaphragm
inside the cavity. We should also note that the light beam inside a cavity has no ideally confining side surface. The causrl
Laser
Active
medium
tic represents the volume filled with light in the sence that
outside this volume the light intensity of the beam rapidly
falls off away from the resonator axis.
The unstable confocal "telescopic" resonator. An example
of unstable resonator is shown in Fig. 2.30. This is the socalled "telescopic" resonator. For operation, it is filled with
an active medium. This resonator is formed by a concave mirror of r 1 = 3L and a convex mirror of r 2 = L. It is an easy
matter so see that both mirrors have a common focal point,
therefore this is also a confocal resonator. In the stability
diagram (see Fig. 2.28) this resonator is represented by point
B of gl = 2/3 and g2 = 2.
93
Chapter ~
Application purposes call for control of the laser output, including such common optical manipulations as deflecting
the beam in space, splitting it and focusing on a target. These
simple transformations are, however, far from~exhausting
the requirements for laser output control. On a wider scale,
laser output modification assumes that the output will possess a certain energy content or exhibit variable spectral,
temporal, and spatial characteristics.
Laser output can be modified in either of two ways inside the resonant cavity or beyond the cavity. In the first
case, the output is controlled by affecting the process of laser
oscillation, whereas in the last case, the output is transformed already when it has left the cavity. Sections 3.1 through
3.5 of this chapter will discuss the topics of intracavity
control, while the rest sections of the chapter will take up
modifications of laser radiation outside the cavity.
3. t Intracavify Control
of Spectral Charaderi'stics
As will be recalled, the spectral characteristics of laser radiation are decided by the active medium. The system of
energy levels of the active material gives rise to a specific
set of emission lines. By using various types of lasers one
may obtain, in principle, coherent output of any wavelength
within the range from 0.1 to 100 f.1m and even of longer wavelengths.
When we come to modifying the laser output we shall focus on the possibility of affecting the radiation frequency
for a particular type of laser and a certain -active material.
An obvious way of modifying the laser output by means of
diverse band filters passing specific bandwidths is of low
01
Spectral ~haracterlstlcs
~5
96
Ch,
path into the cavity, that is retained for laser action. The
other ray is lost. The mirror, however, may be shifted into a
position shown by the dashed plate in this figure to reflect
the other ray back into the cavity, therefore, a desired line
may be selected for laser oscillation. More often the configuration with a rotating mirror is used (Fig. 3.1b). For a given
eu
(1)
(J
~~
0QJ.-
"'C
~
co
..J
u..
(c)
(d)
orientation of the mirror only one wavelength incident normally on the mirror retraces its path back into the laser cavity, gets amplified by stimulated emission, and emitted as
the laser output. Other wavelengths fail to do so and no oscillation is sustained on these wavelengths. Gradually rotating
the mirror enables tuning the laser wavelength.
It was only for the sake of simplicity that we spoke above
about a selected wavelength. In fact this configuration with a
prism and a rotating mirror selects each time not a certain
wavelength but a spectral line of 10-4 to 10-3 J-tm Iinewidth.
This is about one hundredth the laser gain linewidth. Therefore, the rotating mirror selects for lasing one by one the
spectral lines from the laser emission linewidth.
Another configuration, shown in Fig. 3.1c, uses a diffraction grating which reflects back into the cavity rays incident on it at an angle of diffraction e related with the wave-
3.1
97
98
-,
I"
I
A
~!-
I
I
I
\
\
\
-
--
\!!-
90
following paragraphs after a short intermission for the analysis of linewidth achieved with such single-mode selection.
We recall that the linewidth measured in terms of frequency is given by equation (1.56). By assuming the resonator
quality factor Q = 106 , and Ao = 1 f.Lm (vo = ciAo = 3 X
X 1014 I-Iz) we obtain ~vc ~ 109 Hz. To convert this linewidth in wavelength units one may refer to the expression
~"Ac == -"A: ~vclc
(3.2)
It gives for the linewidth ~Ac of a single axial mode an order
of magnitude estimate of 10-5 to 10-6 um.
Another method for obtaining increased single axial-mode
output from a TEM oo laser is to introduce large losses for
.
SMI
Active
\:
SM'_1
~+~~a~rf'l
-I
(a)
(b)
additional mirror in
all but one of the modes. This can be done by introducing one
or a few additional mirrors within the laser cavity which
thereby is transformed essentially into a set of coupled resonators. The interference of light waves produced by these
resonators brings about a redistribution of light power between the oscillating longitudinal modes. A suitable choice
of reflectivity and position for the additional mirror builds
up the intensity of the desired axial mode and the losses for
the other axial modes. Collectively these methods of singlemoding may be referred to as interference techniques.
By way of illustration consider the resonant cavity shown
in Fig. 3.3a. Of the three mirrors involved only mirror M is
totally reflective (R s = 100%). The semitransparent mirror
8Ml is the output mirror of the resonator and 8M 2 is the
additional mirror. Fig. 3.3b shows the lineshape for the
longitudinal modes within the transition linewidth, as related to the modified resonator (solid lines) and to the initial
resonator without mirror 8M 2 (dashed lines). These results
are plotted for the specific case of llL = 3/4 and R t = 65%.
7*
ioO
ct:
"(b)
101
(d)
102
Ch, 9 Control
AI;
(3.3)
The refractive indices n 1 and n 2 linearly depend on the electric field strength in the cell (the Pockels effect)
n1
n2
=
=
no + n~rE/2
no - n:rE/2
(3.4)
n1
n 2 = ngrE
(3.5)
f03
= n2
grating produced by an ultrasound wave. This wave is launched in a medium (solid or liquid) by a piezoelectric transducer (PET). Due to the presence of the ultrasonic wave, the
material acts like a phase grating. In fact the strain induced
by the ultrasonic wave.results in local changes of the material refractive index (photoelastic effect). The grating has a
period equal to the acoustic wavelength A and an amplitude
proportional to the sound amplitude. A light beam incident
on such a three-dimensional grating partially undergoes
diffraction, i.e. is deflected in part from its previous direction. The proportion of the light being diffracted out may
be increased by increasing the high frequency driving voltage
applied to the PET.
An arrangement with the laser Qbeing switched by an acoustooptic modulator is shown in Fig. 3.4d. Inside the acoustooptic modulator, also referred to as acoustooptic shutter, the
light wave forms with the diffraction grating, induced by
an acoustic wave an angle e which must satisfy the diffraction relationship:
(3.7)
2A sin e = 'A
where 'A is the wavelength of light in the graving's medium.
To meet this condition, the shutter is suitably oriented relative to the resonator axis. The angle e is referred to as the
Bragg angle. Note that the relation (3.7) is a modification
of (3.1).
When the PET is off, no ultrasound wave is launched into
the shutter medium, and the incident light beam traverses
it without any losses. When the PET is on, the modulator
will diffract a portion of the incident light beam of irradiance 1 0 into a diffracted beam of irradiance II' shown by a
dashed line in Fig. 3.4d. 1:4e closer the efficiency /1//9 of
t04
1.05
In the initial state, when laser oscillation has not yet commenced, all the absorbing species are in the lower level,
therefore n 2 = O. This state of the cell is unbleached, it is
characteristic of the maximum absorption. Assume that a
pumping pulse has excited the active centres in the active
material and has inverted the populations of the lasing levels. As yet laser action cannot occur in spite of the high
population inversion because of high losses introduced by
the unbleached cell. Some of the excited active centres can
meanwhile spontaneously fall to the lower laser level and
1/-=-=-+-U
Active
medium
Saturable
absorber
(a)
@
(b~..J,..J,
hv
.1
. J, ..)
(c)
106
Ch,
f07
place due to the unstable resonator behaviour and nonlinearities in the cavity.
Production of giant pulses. Short pulses of high peak
power can he produced in pulse pumped lasers by using active
or passive Q-switching. Consider first the case of active
Q-switching. By using one or another type of control for the
cavity Q, the level of cavity losses is deliberately driven rather
high to raise the threshold of oscillation. This builds up a considerable population inversion for
the lasing levels. Then the cavity
is switched into a low-Q state,
causing the oscillation threshold
to drop rapidly to the lowest possible level. As a result, the ini- Fig. 3.6 Structure of a light
pulse lased in the free osciltial population inversion turns
lation mode
out to be appreciably high above
this new low-loss threshold, and
a giant pulse is lased. Its peak power- is higher, the more
the initial buildup of inverted population, achieved under
the low-Q condition, exceeds the threshold inversion corresponding to the high-Q of the cavity. The duration of such
giant pulse of gigawatt range is from 10 to 50 nanoseconds,
although the minimum pulse length may be 1 to 3 ns.
Figure 3.7a shows the time evolution of a giant pulse in a
Q-switcl,1ed laser with a shutter which rapidly switches the
cavity Q from its minimal to the maximal value. The plots
shown in the figure represent four time-varying functions:
irradiance I(t), population inversion N(t), quality factor
Q(t), and threshold population inversion Nth(t). We note
in passing that Nth varies in inverse proportion to Q. At
t = 0, N(t) crosses Nth(t) to start the oscillation process.
Since this process begins, as have been already noted, from
spontaneous transitions that give rise to cavity noise, it
develops slowly. It can be readily seen that the irradiance
power increases at first slowly, linearly with time, the linear
portion, t 1 , being relatively long, on the order of 100 nanoseconds. Almost all the energy of the pulse is emitted during
the next, relatively short (about 10 ns) nonlinear interval,
t 2 Within the time interval t 1 , the population inversion of
the laser levels remains practically unaltered, whereas du-
fOB
(a )
,,-----N(t)
----
---Ht)
""
Q{t)
'--
Nth(t}
---..)
--(b)
N(t)
(c)
ring t 2 this function N (t) sharply falls off as all the population stored in the upper level during the low-Q condition is
emitted in one giant pulse.
Such pulses may also be produced with passive Q-switching
methods, employing saturable absorbers (bleaching dye cells)
with relatively high density of absorbing species and a relatively long relaxation time. In addition, the cross section
of stimulated transitions of the cell must appreciably exceed
that of stimulated transitions in the active material.
109
ftO
.ct: 3
tit
ft2
(b)
constructive interference pattern and the output becomes repetitive. Such a laser is then said to be "mode-locked" and its
emission is regularly spaced pulses of high peak power.
These pulses are of extremely short duration. The duration of an individual pulse, 't", is decided by the linewidth of
the gain curve, in other words, by the number of locked
modes which the transition line' can sustain
'T ~ 1/ Llv ~ 11m L\v'
(3.9)
The peak power of an individual ultrashort pulse is about
m times the output power without mode locking. The period
of the pulses may approximately be found as
T ~ 11Llv' = 2Lnlc
(3.10)
For solid state neodymium lasers, the linewidth of the
transition line is about 1010 Hz, and for organic dye lasers
it is about 1012 to 1013 Hz. Letting Llv' ~ 107 Hz yields that
the maximum possible number of axial modes these lines
can sustain equals 103 and 10 5 to 106 , respectively.
Figure 3.8a gives an approximate comparison of the profiles of a giant pulse (shadowed in the figure) and a modelocked pulse train produced in the same pulse pumped laser.
ii3
8-0l00
it4
Ch,
Fig. 3.9
it5
pulse that will pass through the bleaching dye cell and gets
amplified in its round trip through the active medium. If
the cell recovers fast, it will be shut immediately behind
this pulse and stay ready for being saturated by the next
fluctuations of the field. As these are less intense proportionally they will suffer greater
attenuation in the absorber.
(a)
Therefore, the strongest pulse will grow faster than the
others, and after many round
trips the situation depicted in
(b)
Fig. 3.9b will eventually result, where a single intense
mode-locked pulse remains.
Thus, a fast-recoverable saturable absorber inserted in
the cavity is able to select and
enhance the most intense fluctuations in the initial energy
density and, conversely, to
suppress the other, less intense, fluctuations. As a result Fig. 3.tO Trains cf ultrashort
the profile of the initial radia- pulses enveloped in the gain
tion field deforms with each profile at (a) complete and
next round trip. The energy (b, c) incomplete mode locking
contained in diverse fluctuations is redistributed, accumulating in one stronger pulse.
This pulse grows in power and becomes shorter in duration.
To summarize in loose terms, the presence of a rapidly
recoverable saturable absorber inside the cavity launches a
single light pulse bouncing back and forth (from one mirror
to another) within the cavity. At first the pulse grows in
magnitude, then, when the pump energy given to the active
material is exhausted, gradually declines in power. At regular intervals of time T this pulse arrives at the output mirror and is partially emitted. As a result, the laser output is
a regular train of pulses following each other with the pulse
repetition time T, as shown in Fig. 3.10a.
In actual conditions, however, the ideal pattern depicted
above may not take place. For one thing, the shutter may
not relax fast enough to "close" before a less intense pulse
trailing the major pulse. The result will be an output train
8*
116
Ch,
of pulses plotted in Fig. 3.10b. For the other thing, the initial noise may provide two or more identically intense initial pulses which the dye cell will enhance in the same extent.
Therefore, the resonator period will contain two or more intense pulses of short duration (Fig. 3.10c).
By way of a remark we note that the description given
above for the mode locking of ultrashort pulses in a laser
with a saturable absorber may be called a treatment in the
time domain. Indeed, this description presents the development of mode-locked pulse trains as the process of regular
(recurrent with a period T) lasing of a portion of an intense
fluctuation spike selected and enhanced from the stimulated
emission noise in the cavity by the bleachable dye cell. A similar pattern of an intense pulse bounced back and forth
within the cavity may be invoked in a treatment of active
mode locking. We recall that the losses incurred by the
acoustooptic modulator are modulated in time with period
T. In its round trips, the pulse will pass through the shutter
each time at the instant consistent with the lowest level of
losses.
In other texts, similar description but in the frequency
domain may be encountered. This treats the process of mode
locking as the result of interference of a large number of
modes uniformly spaced on the frequency scale and forced to
oscillate with synchronous phases.
3.5 Modifying the Spatial structure
of the Laser Output
3.5
117
ua
fi9
light powers. In practice it is realized owing to small divergence of laser beams and availability of pulsed outputs with
enormously high peak powers. Available lasers yield light
fields.with intensities as high as 101o to 1011 VIm. These electric field strength are comparable with those within the
atom. Now the dielectric susceptibility of the medium becomes a function of the light field intensity.
For high light powers, theory suggests that the susceptibility can be presented as a sum of rapidly diminishing terms
X (E) = Xo
XIE + 'X2 E 2 + . . .
(3.13)
p = 'X (E) E
'Xo E
+ 'XIE2
(3.14)
PNdz, t) =i-Xt E ;l +
~ XtE~l cos
r4nv (t- ~ ) ]
~ ==
(3.17)
t20
al" traversing the medium at velocity Vt. Under certain conditions this "aerial" may cause emission of a new light wave
at the frequency of the wave of polarization. We put the
equation for this generated wave as
E 2 (z, t) = E 0 2 cos [4nv (t - z/v 2 ) ]
(3.18)
The amplitude of this wave E 0 2 may be expressed in terms of
E 01' the nonlinear susceptibility Xl' and other parameters
of the medium. The velocity V 2 of the generated- wave differs
from the velocity of the incident wave VI because the refractive index is a function of frequency; in accord with (1.2)
VI
V2
= cln
= cln
[v)
(2v)
(3.19)
Hence, in a nonlinear medium, a strong light wave of frequency v can beat with itself by means of the nonlinear polarization and give rise to a new light wave at frequency 2v,
the so-called second harmonic, accordingly this process is
called second harmonic generation.
Consider now the case with two waves, one at frequency VI
and the other at frequency V 2 , being launched into the nonlinear medium. The superposition of these waves gives the
e.m. field
E (z, t)
E OI cos [2nvI (t -
+E
z/vl ) ]
02
cos [2nv 2 (t -
z/v 2 ) ]
(3.20)
x1Eg1cos" [2nvI
z/v1 ) ]
XIE~2 cos" [2nv 2 (t - z/v 2 )J
+
+ 2XIEOIE02 cos [2nv1 (t -
(t -
121
122
Oh,
(c)
Nonlinear crystal
refractive index normally increases with frequency. Therefore, the dimensions of the refractive-index sphere and
ellipsoid increase accordingly. Fig. 3.11b shows for comparison the sections through these surfaces plotted for a frequency v (solid lines) and the doubled frequency 2v (dashed
lines). The dashed ellipse is seen to intersect with the solid
circle; one of the points of intersection is point B. This
means that for light waves propagating in the OB direction
(i.e, close to the cone where OB is a generating element)
the phase-matching condition is satisfied
nO (v) = ne (2v)
(3.23)
The cone angle Om is obviously the phase-matching angle.
For all directions lying on this cone the ordinary refractive
index at frequency v equals the extraordinary refractive
index at frequency 2v.
123
2V
F
124
Material
Symbol
KDP
ADP
CDA
D-CDA
Formula
KH 2 P04
NH 4H2P04
CsH 2As0 4
CsD2 As0 4
LiNbO a
LiIO a
Ba~NaNb5015
125
2Jtvn(v)/c
(3.24)
fiG
Ch,
Control
0/ the
Laser Output
"1
"1
127
Glan
(a)
prism
Nonlinear
crystal
(b)
Fig. 3.13 (a) Singly resonant and (b) doubly resonant parametric
oscillators, (c) Glan-Foucault prism
128
Ch. 3 Control
0/ the
Laser Output
f2b
In this section we shall look at another application of nonlinear optics providing automatic correction of the laser
wavefront.
Problem formulation. Let us imagine a laser producing
highly coherent radiation with an almost plane wavefront
but of relatively low power. To boost this power, the laser
output is passed through a number of quantum amplifiers,
i.e., active components in which pumping creates a population inversion. As the laser output traverses these quantum
amplifiers, they build up its power but markedly degrade
the degree of coherence. The inhomogeneity of material
properties in these amplifiers and deformations induced
in these components by mechanical and heat stresses, to
name only the principal factors, introduce distortions in
the initially almost plane wavefront. As the number of
amplifying stages increases, the output receives ever higher
9-0~OO
ek.
aConlrol
fat
Suppose now that the plane mirror is replaced by a reflecting surface which is exactly the shape of the oncoming
wavefront, as shown in Fig. 3.14b. Such a mirror having
the surface which in each moment of time matches the
profile of the arriving wavefront may be called the adaptive
mirror. Upon the reflection from the adaptive mirror each
ray is backscattered in the same line-experiences a 1800
~--:w!
(a)
~--
(b)
Nonlinear medium
(e)
Fig. 3.14 Reflection from a plane (a), adaptive (b), and "nonlinear"
(c) mirror
t33
Nonlinear mirror
k2
(a)
Nonlinear
crystal
t34
ek.
8 Control
matching condition
k, - k,
ks
(3.26)
As an example of the system exploiting this principle consider a laser adaptive system capable of yielding high-power
outputs of highly coherent light. The optical configuration
of this system is depicted in Fig. 3.15b.
The prime source of radiation is a low-power laser emitting highly coherent beam at frequency 'V. The beamsplitter
BS1 splits the beam into two parts of different irradiance.
The more intense beam passes through, while the less intense
beam is reflected. The first beam is amplified in the amplifier
and then excites the second harmonic (at frequency 2v)
in the nonlinear crystal. The mirrors M 1 and M 2 are totally
reflective (R = 1) for the light at v but transmittive at 2".
As a result the second harmonic travels with almost no
losses into the nonlinear medium which here plays the part
of the nonlinear mirror. It is this wave that is denoted as
wave 1 (frequency 2", wavevector k l ) in Fig. 3.15a.
The second light beam reflected by BS l undergoes one
more splitting at the beamsplitter BS 2 , passes through the
amplifying stages and upon traversing once the nonlinear
medium it is reflected by mirror M 2 to this medium again.
This beam represents wave 2 (frequency v, wavevector k 2)
in diagram (a) of Fig. 3.15. Waves 1 and 2 interact in the
nonlinear medium to produce a new light wave 3 at frequency v, defined by wavevector k 3 connected with k l and k 2
by the relation (3.26). Wave 3 propagates counter to the
wave approaching from BS 2 through the amplifiers and has
the wavefront reversed with respect to the countercurrent
wave. As a result, the output leaving the system through
BS 2 is an amplified beam at frequency 'V with an almost
ideal wavefront.
3.8 Light Beam Manipulation
135
136
~~~~~~-..-...-~.
e=
arcsin ('A/2A)
(3.28)
137
Chapter 4
Applications of Lasers
are
ta9
ek.
fOO
4 Application, of Laser'
>:--
, . , Plasma
"
~--
(a)
(b)
(c)
i4i
Inert gas
Fig. 4.2 Inert gas laser welding for otherwise inaccessible locations
cs. 4:
Appiicatlons
01 taser.
143
i44
145
i46
ions are very fast and there is not enough time for the patient
to respond to the incision and sense pain.
It is now common for laser surgical units to fix the laser
scalpel in a facility which provides the possibility of certain movements of the beam and its rotation. Fibre optics
(see Sec. 4.6) has put the laser scalpel into the surgeon's
hand: flexible optic fibres lead the beam to the radiator in
the hand. The radiator contains a lens system for beam
focusing.
Laser radiation is efficient in haemorrhage control due
to cauterizing action of the laser beam on the blood vessels.
Therefore, 'Lasers are used for reduction of hematic losses,
which is especially important for patients with poor blood
coagulation. Laser surgery became a routine procedure in
the treatment of liver and lungs, and for elimination of moles
and tumors developing on the skin tissues. Most common
sources for these applications are CO2 and argon lasers.
A separate medical field for laser surgery is ophthalmology
where the laser (usually Ar+) has already been in use for
several years to treat the detachment of the retina. The beam
is focused on a certain point of the retina after it has passed
through the lens of the eye and the vitreous chamber without
being absorbed in them. The green beam of the laser is
strongly absorbed by the red blood cells of the retina and
the consequent thermal effect leads to re-attachment of the
retina. The operation is carried out by a 0.01-s pulse and,
being very short, is virtually painless. Of other illnesses
treated by the focused laser beam, mention should be made
of cataract, varied tumors, and glaucoma. In the last case
the laser pulse is used to destroy plugs in blood vessels
feeding the eye. Most popular ophthalmological systems
involve also neodymium and ruby lasers.
Lasers are now finding increasing use in therapy. The
He-Ne laser' has produced. curing effect on trophic ulcers,
poorly healing wounds, and bone fractures. Relatively rapid
healing effect has been observed for all these cases after
a few radiative treatments.
Stomatology is another field in medicine where the laser
has also been found useful. It has been proved capable of
destroying selectively those tissues of the tooth affected by
caries, that is, the laser can replace dental drills. In this
t41
Fig. 4.4 (a) Two views of the laser surgery unit Skalpel-1, (b) ophthalmologic surgery with the Yatagan-2 facility
f48
a 10-W CO2 laser. The unit is widely used for plastic surgery, including burns treatment, gynaecologic operations,
and treatment of festering wounds.
Figure 4.4b sllows the process of an ophthalmologic operation with the J atagan-2 facility (developed by the same
establishment). The facility is built around a Q-switched
ruby laser. It is designed for the microsurgery of the front
tissues of the eye.
4.3 Isotope Separation
Numerous applications in the industry, medicine, and research field require substances enriched in a certain isotope
(say deuterium against hydrogen). These needs stimulated
techniques of isotope separation, which are supposed to
separate the wanted isotope with the aim of its accumulation
or a higher proportion in the final product. These techniques
are of immense importance for nuclear power engineering.
The point is that natural uranium ore used to fuel nuclear
stations contains mainly the isotope 238U and only 0.7%
of 235U, whereas it is the latter isotope that fires nuclear
plants. It is essential that nuclear fuel contained about 3 %
of 235-uranium.
The most promising in the family of separation techniques
is that based on laser excitation or dissociation, feverishly
developed in recent years. Laser separation exploits the fact
that various isotopes of an element exhibit different absorption bands in their spectra, i.e., each isotope absorbs light
of its own wavelength. These absorption bands are fairly
narrow and lie close to each other in the spectrum. To excite
one isotope without "touching" the other, one has to irradiate
their mixture by a source of narrow bandwidth centered on
the wavelength of the wanted isotope. It is desirable also
that this source be tunable so that the radiation may be
tuned to the desired wavelength. This opportunity is offered
by tunable lasers.
Let us assume that we have a mixture of two isotopes one
of which is desired to be separated. To achieve the goal we
irradiate the mixture by a powerful output of a laser operating at the absorption wavelength of the wanted isotope. The
excited atoms of this isotope are raised to the upper level,
while the other isotope remains in the ground state. Now we
t49
--=-G
.z:-----2
o
(a)
6
(b)
1~
~v,GHz
separation) having first been selectively pumped to an excited (vibrational) level. This compound is subsequently dissociated as a result of further optical pumping. The dissociated
atoms enter then in a chemical reaction with purposefully
introduced molecules so that the product contains only the
wanted isotope. This product is separated for further treatment. Still another technique is such that the atoms or molecules containing the desired isotope enter in certain chemical
reactions upon laser excitation to form an easily separable
compound.
The two-step photo-ionization technique appears to hold
the greatest promise for uranium isotope separation. The
configuration of a system using this principle is shown in
Fig. 4.5a. The beam of uranium atoms emitted from a heated
uranium-rhenium alloy is pumped by a continuous dye laser
tuned to a desired wavelength (tv = 0.59154 um] and then is
additionally excited by ultraviolet radiation from a mercury
lamp (A = 0.21 to 0.31 11m) to be ionized. The beam of the
235U ions is separated from 238U in a mass spectrometer.
150
Fig. 4.5b shows the absorption bands for both uranium isotopes. The frequency spacing between the bands is seen
to be more than 5 GHz. Because the dye laser has a bandwidth of only 0.1 GHz, it readily tunes for pumping the
wanted isotope alone.
4.4 Holography
Holography is a revolutionary technique which allows threedimensional (i.e., complete) pictures to be taken of a given
object or scene. The word is derived from the Greek words
"holos" (complete) and "graphos" (writing). The technique
became a practical proposition and really demonstrated its
potential only after the invention of the laser. In this section
we shall look at the principles and uses of holography.
Suppose we wish to obtain an image of an object on a
screen. Then we must illuminate the object so that the reflected light entered the screen. Moreover, the reflection is to
be such that the rays reflected from different points on the
object surface come to different points on the screen; in
other words, the travel of rays from the object to the screen
must be "ordered" to produce a certain pattern. This is
achieved normally by lens systems. The result is the familiar
photographic method of imagery. The invention of laser
brought about a qualitatively new method of imagery without lens systems-optical holography.
The principle of holography. We place an object illuminated by a coherent source of light in front of a photodetector
(a screen covered with a photosensitive layer, most commonly a photographic emulsion, and therefore capable of permanent hold of images). The light wave incident on the
object is a component of a single monochromatic beam of
light split into two components, one of which is directed
toward the object while the other to the recording medium.
The component that is incident on the object is scattered
by it, and this scattered radiation, now called the object,
or signal, wave, impinges on the recording medium of the
photodetector. The wave that proceeds directly to the recording medium is called the reference wave. In Fig. 4.6a
it arrives at the photodetector at an angle a. Since the
object and reference waves originate from. the same source
they are mutually coherent and form a stable interference
pattern when they meet at the recording medium. The
4.4 Holography
t5t
(a)
(b)
f52
Thus, the holographic method of optical imagery is a twostep method. In the first step, the hologram of the object
is recorded, whereas in the second step the image is reconstructed from this hologram. The hologram recording is
based on interference of coherent waves, and the reconstruction relies 011 diffraction of waves. We note that the "ordering"
of light rays necessary for the reconstruction is provided
automatically by the reconstructing (illuminating) wave.
Holographic imagery requires highly coherent radiation.
If L is the maximum difference of pathlengths that the two
(4.1)
t53
4.4 Holograph,
plate a hologram cannot be erased to record another hologram. There exist also "reversible" recording media, for
example, photochromic materials, such as specially doped
g-lasses, or organic polymers capable of altering their colour
or transmittance when irradiated by certain wavelengths.
To conclude, we refer to Fig. 4.7 which shows an optical
arrangement for hologram recording. A single laser is here
2_
Ct
fa)
(b)
Fig. 4.8 (a) Interference of light waves in hologram recording, (b) diffraction of light in hologram reconstruction: 1 object beam, 2 reference beam, 3 reconstructing wave, 4 and 5 diffracted beams, 6 transmitted beam
.
'A/sin a
(4.2)
t54
Ch: 4 Applications
0/ Lasers
(4.3)
(a)
(b)
4.4 Holography
i55
readily seen, one of the beams in Fig. 4.9b is this very beam.
No object is present at A when the object beam is reconstructed, but one of the evolving light beams is identical
with the beam that would be reflected by the object. In
other words, when we reproduce the image we do it by reconstructing the object wave.
Holography of three-dimensional objects. The reconstruction of the object wave from a hologram is obviously independent of whether the object recorded has been a point or
three-dimensional one. If a 3-D object is recorded, then
upon reconstruction the viewer will see not a plane, photograph-like image of the object, but rather a realistic 3-D
image indiscernible from the object so as this could be seen
during the hologram recording. If the viewer shifts aside,
other objects hi.dden behind the first one will become visible
and new side features emerge. In other words, the viewer
will see an absolutely real 3-D scene.
It will be noted that in this arrangement it is the primary,
or virtual image, that exhibits the features of the real object.
The conjugated, or real, image will appear inverted in depth,
i.e., reversed front to back with the features being farther
from the viewer in the holographed object appearing closer.
This image is called pseudoscopic. The situation will reverse
in another reconstruction arrangement with the illuminating
wave travelling in the direction opposite to that of the
reference wave (the hologram is illuminated from the back
side), then the real image will have actual appearance,
while the virtual image becomes pseudoscopic.
A few words are in order on the types of holograms. We
have seen in Fig. 4.8b that when the hologram is illuminated
with a beam similar to the original reference wave the transmitted wave divides into three separate components, one of
which exactly duplicates the original object wave. If the two
interfering beams are travelling in substantially the same
direction, the recording of the interference pattern is said
to be a Gabor hologram or an in-line hologram. If the two
interfering beams arrive at the recording medium from substantially different directions, the recording produces a
Leith-Upatnieks or off-axis hologram. If the two interfering
beams are travelling in essentially opposite directions the
recorded hologram is referred to as reflection hologram first
invented by Y, N, Denisyuk, a Soviet researcher.
f56
i57
i58
ek.
4 Application. 0/ Laser,
i59
100
cs. 4:
Applications
0/ Lasers
t6t
t6Z
ing, the reference wave is passed through an encoding mask
to gain a special wavefront. Without this mask, even the
most skillful decoders will be unable to read (decode) this
hologram.
Pattern recognition. How can a wantedletter be recognized
in a text? a non-standard prod uct in a sequence of sim ilar
items? an expected signal among those arriving at the input?
All these problems are solved by a branch of science known
as pattern recognition theory. Holography is one of the
promising means for practically solving such problems.
We look at the pattern recognition procedure handled by
holoraphic means by taking a letter-and-text example. Let
")"~
"
~
~ ~.
>'
(a)c:J- 2
1
B
(b)
Fig. 4.t2 (a) Holographic matrix, (b) schematic diagram of a holographic memory system: 1 laser, 2 digital light deflector, 3 auxiliary
helographic matrix, 4 nondiffracted beam, 5 transparency imposing
spatial modulation (page composer), 6 holographic matrix store
4.5
163
~case
2
~/ s2
Case 1
A~A-'-~'181
i,
;2
./
18 ,
(a)
S,
'
8,/18 2
(b)
Fig. 4.13 (a) Double laser diode, (b) NOT logic exercised by optically
coupled injection lasers
fraction is deflected by the lens L I , traverses without deflection the central area of the lens L 2 (plaeed in the focal
plane of L I ) and impinges on one of the holograms in the
memory matrix. Here it interferes with the wave which
has been divergent and becomes convergent after L 2 The
latter wave on its path to the holographic matrix has passed
through the transparency, called page composer, and has
been converted into a carrier of the respective spatial signal.
The solid-line arrows in the figure correspond to the case
when the deflector directs the laser beam in position A,
and the dashed arrows show the situation with the beam in
position B. By making the deflector alter the initial position
of the beam and changing simultaneously the spatial signal
written in the transparency, one may gradually fill with
the desired information all the cells of the matrix memory.
Optically coupled injection lasers. These lasers are fabricated in a single chip with a common p-n junction but with
separate pumping circuits. Fig. 4.13a illustrates schematically two optically coupled injection lasers, often called dual
laser or strip diode. Here i l and i 2 designate the pumping
currents for the left and right diodes respectively, the dashed
line shows the common p-n junction, and the shadowed face
shows the diode end which cannot serve as a resonator
11
f64
Ch, 4
Applications of Lasers
We have already emphasized the large information capacity of optical communications channels. It will be recalled
that an increase in frequency of the carrier wave expands the
frequency bandwidth available for transmission. Additionally, higher carrier frequencies offer better directivity for
communications, higher powers being concentrated in the
signal, hence provide for higher efficiencies of communications systems. Finally, the use of light beams for transmission
purposes warrants the message best of all from interception
and makes it immune to distortions by interference.
The optical communication systems using lasers as light
sources divide naturally into two groups: those where signals
are transmitted through free (unguided) space, and those
where they are carried by light guides.
Communications through open space. Open space in which
optical signals propagate may be either in space beyond the
Earth or in the Earth's atmosphere and water. Schematically
this transmission line is illustrated in Fig. 4.14a. The laser
beam with a modulation impressed on it in the modulator
4.6
f65
Optical Communications
80
OJ'"
.~ 20
c
~"'
A,pm
0.72
15
I:b)
Fig. 4.14 (a) Components of a laser communication line, (b) atmospheric transmittance as a function of wavelength: 1 laser, 2 modulator,
3 directional beaming facility, 4 receiving "aerial" (telescope),:5 optical signal recei ver
t66
(a)
(c)
Fig. 4.15 Lens waveguide (a), dielectric fibre guide (b), and optical
cable (c)
4.6 Optical
Commu.~lcatl~lI~.
,
_t67
168
Cb. 4 Applications
0/ Lasers
169'
170
4.7
171
3~
(a)
(b)
172
Ch. 4
Applications of Lasers
t=
2v sin (0.,/2)/'A
(4.6)
where v is the velocity component in the direction perpendicular to the fringes. This frequency is measured to infer
the velocity component of the flow.
When the measuring system is installed near the flow
(within a few tens of centimetres), they depend for their
measurements on helium-neon lasers with output of about
10 m W. When velocity measurements are made for distant
flows, the system normally relies on argon lasers of about
1 W output.
It should be noted that equation (4.5) could be derived
from (4.2), observing that D = d cos (a/2). The geometrical
construction presented in Fig. 4.17b brings forth the difference between these expressions: (4.5) describes the distance
173
t74
17~
176
(a)
(b)
Fig. 4.18 Interferograms revealing the nature of internal stress occurTed in a deformed object (a), and the presence and location of internal
defects in an object (b)
177
178
+ +
179
(b)
fSO
cs. 4
Applications 0/ Lasers
Exercises
181
Exercises
Problems
1. What frequency range corresponds to the interval of
light wavelengths from 0.1 to 10 ~m?
2. What is the photon energy for a light wavelength of
0.6 urn?
3. The quality factor of an optical resonator is Q =
= 2 X 10 7 at 0.6 t-tm wavelength. Compute the loss coefficient for this Q.
4. Suppose we have doubled all the linear dimensions of
the resonator, i.e. cavity length and mirror curvature radii
and apertures. Will the new resonator be equivalent to the
original one?
5. Suppose we have increased two times the aperture of
the cavity mirrors. How should the other parameters of the
passive resonator be altered to make the new resonator equivalent to the original one?
6. Derive the optimal reflectivity for the output mirror
in an 0.5-m long cavity with the loss coefficient 0.081 m-1
(except radiative losses) and the initial gain coefficient
0.1 m -I.
7. Find the frequency spacing between two adj acent axial
modes for a ruby laser (a ruby rod with polished ends acting
as mirrors), given the rod length is 0.6 m and the ruby refractive index is 1.76.
8. Assume that all the pumping power of the pumping
lamp is being absorbed by the active species of the ruby
laser (chromium ions) which are raised to the 4FI state to fall
then to the upper laser level. Referring to Fig. 2.4, estimate
the efficiency of this laser.
9. The ruby lasers are known to possess efficiencies below
1 %, that is appreciably lower than the value obtained in
the previous problem. Why?
10. Prove that at the Brewster angle of incidence, the
reflected and refracted rays are mutually orthogonal.
11. Describe the geometry of the optical resonator, specified on the stability diagram (see Fig. 2.28) by gl = g2 =
= 2.
12. What is the geometry of the optical resonator producing the g-values gl = 1 and g2 = 1/2 on the stability
diagram (see Fig. 2.28)?
182
13. Referring to Fig. 2.29, estimate the angle of divergence for a light beam of 0.5 ~m wavelength leaving the
O.5-m long resonator.
14. Estimate the speed (switching rate) of a fused silica
acoustooptic shutter for a light beam of 1.2 mm diameter,
given the velocity of sound in the shutter material is 6 X
X 103 m/s.
15. Compute the peak power of a pulse, given that the
laser operates at a pulse repetition rate of f = 1 MHz (a cavity dumping mode) yielding pulses of L = 20 ns duration
with an average power of the train being P = 10 W,
16. The gain profile linewidth of a ruby laser is 6 GHz.
Use the result of problem 7 to compute the maximum possible number of longitudinal modes for this laser.
17. Estimate the pulse peak power for a laser operating
in a giant-pulse mode, given: pump pulse energy, 1 kJ;
laser efficiency, 0.5 %; giant pulse duration, 10 ns.
Answers
1. From 3 X 1013 to 3 X 1015 Hz.
2. 2 eVe
3. By virtue of (1.26) we get the loss coefficient of 0.5 m-I.
4. I t will not. For the new resonator, the Fresnel number
is twice as large as that of the original cavity; see (1.32).
5. The resonator length and mirror radii of curvature
should be increased four times; see (1.32).
6. From (1.49) the optimal coefficient of radiant losses
amounts to 0.009 m-I. By making use of (1.51), where for
x ~ 1 one may adopt eX = 1
x, the optimal reflectivity
of the output mirror is found to be 99% for this case.
7. According to (1.55), the frequency spacing in question
equals 1.4 X 10 8 Hz.
8. The photon efficiency for this situation is defined as
the ratio of emitted to pumping photon energies. Referring
to Fig. 2.4, this ratio is approximately 1.5/2.5 = 0.6.
Therefore, the efficiency in question amounts to 60 %.
9. In fact, not all of the pumping energy is absorbed by
the active species. Besides, a proportion of the excited ions
decays directly to the ground level without falling first
to the upper laser level.
10. Let ~ be the angle of refraction, and ex the angle of
incidence equal to the Brewster angle and to the angle of
Eeerctses
183
Appendix
Material
ms
Ruby
Ruby
rOP-1ooM
rOP-300
rOC-301
rOC-1oo0
JITH-4
100
300
Nd : glass
300
Nd : glass
1000
0.1
Nd:YAG
1
0.5
0.8
20
0.04
OfM-20
JITMIIq-1
JITH-1
JITM-3
JITM-5
Material
IPulse inergy,l
Ruby
0.42
Nd : glass
Nd:YAG
Nd:YAG
Nd:YAG
0.01
0.03
0.05
Pulse
duration, ns
20
15
10-12
10-12
8-12
I Peak power,
kW
2X104
105
103
3X103
5X10 3
Note: The JITH lasers operate in a single pulse mode, and in a repetitively
Q-switched mode with pulse repetition rates of 12.5, 25, 50, and
100 Hz.
185
Appendlz
Harmonic Generation
Soviet type
designat ton
Generated
harmonic
JITHnQ...3
JITMntI-4
JITMntI-5
JITMIIq-6
JITHnQ-7
JITHntI-8
2nd
3rd
4th
2nd
3rd
4th
PulsemJ
pnergy,
"',Ilm
3
0.45
0.16
5
1
0.5
0.53
0.35
0.26
0.53
0.35
0.26
Pulse
duration,
ns
Peak
power,kW
8-10
.8-9
7-9
8-10
8-9
300
50
20
500
100
7-9
50
Note: (I) the JITHllQ-3, 4, 5 models are based on the JITH-3 design; (U) the
JITHll"tl-6, 7, 8 models are based on the JITH-5 design; (iii) for the
frequency triplers and quadruplers a frequency doubler output is also
possible.
JITH-501
JITH-502
JITM-701
JITH-401
A, ).Lm
1.06
1.06
0.53
0.53
Pulse duraIpower,
PumpkW I Pulse
Average
rate, kr~1
z power,
W I tton,
Jl.S
~6
~8
~5
5-20
5-20
5-6
~4
~5
CW
1-2
~5
~5
0.3-0.6
0.3-0.6
0.3-0.4
Note: (1) all models operate on the fundamental mode; (it) 0.53 ).LID corres-
OKr-13
JIr-56
JIr-65
JIr-38
Type
He-Ne
He-Ne
He-Ne
He-Ne
Power, W
0.0002
0.002
0.02
0.05
Model
Type
JIr-109
JIr-30
JIr-25
JIr-43
CO2
CO2
CO2
Ar+
Power. W
1
5
25
40
186
Appendix
Tuning
range, um
Linewidtb,
nm
Pulse rep.
rate, PPS
Pulse
energy, J
JIllilI-404
JIiKlI-406
JIiKH-408
JIiKH-409
0.43-0.65
0.43-0.65
0.43-0.65
0.43-0.65
0.4
0.2
0.2
0.2
1/3
1/6
2/15
1/15
0.02
0.1
0.5
1
Nott. (i) the linewldth is given tor a selective resonator with a reflective
diffraction grating; (il) the pulse energy refers to A 0.59 J.Lm in a
non-selective cavity.
==
In Russian
L. V. Tarasov: Lasers-Reality and Hope (Prosveshchenie,
Moscow 1984)
L. V. Tarasov: Optics Born by the Laser (Prosveshchenie, Moscow
1977)
Yu. L. Klimontovich: Quantum Generators oj Light and N onlinear Optics (Prosveshchenie, Moscow 1966)
V. S. Letokhov, N. D. Ustinov: Power Lasers and Their Applications (Sovetskoye Radio, Moscow 1980)
G. V. Venikov: Optical Computing Systems (Znanie, Moscow 1976)
In English
o. Svelto:
Index
Band gap, 82
Beam
deflectors, 135
difraction limit, 117
manipulation, 134
spot size, 92
waist, 91
Beamsplitter, 17
Birefringence, 123
Bleachable cell, 104
Bosons, 12
Brewster angle, 59
c
Carbon dioxide laser, 65
gas-dynamic, 74
longitudinal flow, 66
Chemical laser, 77
Coherence, 14
degree of, 16
time, 17
CO2 laser, see Carbon dioxide
laser
Conduction band, 82
Conversion efficiency, 123
Cube corner reflector, 171
D
Deuterium fluoride chemical
transfer laser, 79
Diffraction limit, 117
Doppler
ranging, 168
velocimetry, 171
Doubly resonant parametric
oscillator, 127
Dye laser, 53
E
Einstein coefficients, 22
Electroionization lasers, 70
Electronic configurations, 60
Electrooptical shutter, 100
Emission line, 38
Eximer laser, 69
F
Fermi-Dirac statistics, 13
Fermions, 12
Fluorescent line, 38
Four-level laser, 27
Fourth harmonic generation, t23
Frequency multipliers, 125
Frequency tuning, 125
Fresnel number, 33
Fundamental wave, 123
G
Gain coefficient, 34
Gain curve, 37
Gain profile, 38
Giant pulse generation, 107
Glass laser, 53
G-parameters, 90
Ground level, 25
lndez
H
Harmonic generators, 124
Helium-neon laser, 58, 62
Hologram, 151
amplitude, 156
Gabor, 155
Leith-Upatnieks, 155
reflection, 155
thick, 156
Holography, 150
for coding, 161
for data storage, 160
for information search, 161
for pattern recognition, 162
I
Image, holographic
conjugate or real, 154
primary or virtual, 154
pseudoscopic, 155
Index ellipsoid, 121
Injection laser, 88
optically coupled, 163
Interference technique, 99
Interferometric distance measurements, 170
Intracavity elements, 95
Ion laser, 57
Irradiance, 15
K
Kerr effect, 100
L
Laser
applications, 138
basic principles, 9
beam waist, 91
dual, 163
effect, on materials, 139
gain curve, 37
historical review, 41
intracavity control, 94
oscillation, 27, 36
output control, 94
phase conjugation, 130
pulse, 106
schemes, 26
189
single mode, 97
spot size, 92
wavefront correction, 129
Laser, types
Ar", 64
chemical, 76
CO2 , 65
dye, 53
electron-beam, semiconductor,
85
eximer, 69
gas-discharge, 45
gas-dynamic, 73
glass, 53
He-Ne, 58
injection, 88
Nd: YAG, 51
photodissociation, 55
ruby, 49
semiconductor, 81
Soviet-made, commercial 184
Laser cutting, 143
Laser environmental monitoring,
173
Laser for information systems,
157
Laser for thermonuclear fusion,
178
Laser gyroscope, 173
Laser heat treatment, 142
Laser hole perforating, 144
Laser isotope separation, 148
Laser landing system, 178
Laser material working, 139
Laser rangefinder, 168
Laser surgery, 145
Laser welding, 141
Lasing level, 26
Level nomenclature, 25
LIDAR, 174
Light amplification, 23
Losses
cavity, 31
di ffraction, 32
radiant, 32, 37
M
Maser, 42
Mode
asymmetrical stretching, 67
axial, 40
190
Inde
Pulse trains, 110
Pumping
chemical, 25
electrical, 25, 45
electroionizing, 71
gas-dynamic, 73
heat, 25
level, 26
optical, 25, 45
schemes'. 25
bending, 67
cavity dumping, 110
fundamental, 40
longitudinal, 41
Q-switching, 100
symmetric stretch, 67
TEM, 40
transverse, 41
vibrational, 67
Mode locking, 111
active, 113
methods of, 113
passive, 113
Molecular laser, 65
Q
Q-switching
acoustooptic, 103
mechanical, 100
methods of, 100
passive, 104
saturable absorber, 104
Quality factor, defined, 30
Nd : YAG laser, 51
Neutral atom laser, 57
Nonlinear media, 118
Nonlinear mirror, 133
Nonlinear optics history,
128
o
Optical cavity, see Resonator
Optical communications, 164
Optical deflectors
analog acoustooptic, 135
analog electrooptic, 135
digital electrooptic, 136
prism, 135
Organic dye lasers, 53
p
Radiant losses, 32
Raman back scattering, 175
Resonant collision energy
transfer, 63
Resonator, 29
confocal, 91
equivalent, 33
.Ilnear, 89
modes, 40
ring, 89
stable, 90
unstable, 117
Ruby laser, 49
S
191
Spontaneous emission, 21
Spot size, 92
Stability of optical resonator, 90
Stimulated Brillouin scattering,
132
Stimulated emission, 20
Stimulated emission cross section, 24
Stokes satellites, 132
T
Transition line, 38
Transitions, 18
in semiconductors, 83
lasing, 23
sluppression of, 95
v
Valence band, 82
Visibility of fringes, 14
w
Wave
extraordinary, 121
idler, 126
object, 150
ordinary, 121
pump, 126
reconstructing, 152
reference, 150
signal, 126, 150
Wavefront correction, 129
Waveguides, 166
Wave trains, 14
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