Accomplishments in Integrated Nonlinear

Optics using Silicon Microring CROWs

(Project Report 0642603-Y5)
SHAYAN MOOKHERJEA
Department of Electrical and Computer Engineering, University of California, San Diego, MC 0407 La
Jolla CA 92093-0407 USA
Email: smookher@ucsd.edu

1. Introduction and Goals

Coupled resonator optical waveguides (CROWs), proposed as a type of
integrated optics device in 1998-1999 by Yariv et al. [1] and Stefanou and
Modinos [2], are linear sequences of micro-resonators fabricated on a chip that
guide light from one end of the chain to the other by nearest-neighbor coupling.
Figure 1 shows the operating principle of the CROW. Two identical
microresonators when coupled show, under optical excitation, a split resonance
consisting of two supermodes. The separation between the modes is
proportional to the magnitude of the coupling coefficient κ (which appears in
the matrix formulation of the coupled-mode equations). A CROW consisting
of a chain of N coupled resonators shows an N-fold splitting of the transmission
spectrum. Whether the individual peaks are resolvable depends on the strength
of the inter-resonator coupling, the loss, and the exact distribution of coupling
coefficients along the chain (i.e., apodization).

Figure 1 (a) An optical system comprising two identical resonators with inter-resonator coupling
coefficient k exhibits a split transmission spectrum where the separation between the peaks is
directly proportional to κ. (b) A CROW consists of N coupled resonators and shows a
“miniband” transmission characteristic with N individual super-mode resonances. The
bandwidth is again proportional to κ but with a different coefficient.

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This NSF-funded project [0642603] is a five-year (60 months, 2007-2012)
CAREER (Faculty Early Career Development Program) unified research and
education development program. The project’s focus is the science, engineering
and applications of low-power (milliwatt class) nonlinear optics using CROWs.
In silicon photonics, the main nonlinear optical phenomenon which is relevant
at power levels used in optical communications is four-wave mixing (FWM).
Because wavelengths shorter than about 1.1 µm are absorbed, second-harmonic
generation in silicon CROWs [3] of telecommunications band signals is
infeasible. Using a strong chi-(3) nonlinearity (which also is the basis of spatial
soliton formation [4], [5]), optical pump beams and a signal beam can be made
to interact in a fairly short silicon waveguide or compact resonator to generate
one or more new frequencies with converted power levels in the tens to
hundreds of microwatts. In the traditional context of parametric amplification
(of the signal), these new frequencies are called “idlers” but here, they play a
central role since they generate a new frequency absent in the plurality of
signals at the input to the device. This is more conventionally known as
wavelength conversion. The CROW structure is suitable as the foundation of
this project because it offers a very high conversion efficiency based on the
triple resonance of the pump, signal and idler modes. The enhancement is due
to slow-light effects, i.e., a reduction in the group velocity of light. Therefore,
studying how the group velocity is affected by dispersion [6] and fabrication
disorder in real structures is an essential part of this project.

2. Activities and Accomplishments

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The first set of research activities, labeled Task Area A (Waveguides) in Fig. 1,
focuses on improvements and refinements to our knowledge of waveguiding in
CROWs. Previously, a tight-binding model of band-center propagation was
formulated [7], [8], and theoretical studies of nonlinear propagation were
developed on this basis [9], [10]. However, it was predicted that propagation in
the band-edge regions of high dispersion and high nonlinearity would be
sensitive to disorder [11]. An accurate modeling of waveguiding and dispersion
is also necessary for coupled-microring filters [12] or tunable dispersion
compensation devices [13].
The first set of activities in this project focused on realizing long CROW
structures. We focused on the coupled-microring CROW configuration which
was studied by Poon et al. [14] and by IBM [15]. Directional couplers are used
to achieve a well-defined coupling coefficient between adjacent unit cells. We
experimentally studied the dispersion of directional couplers using a microring
coupled to a waveguide [16]. To help in designing structures in silicon
photonics, we developed an extension of coupled-mode theory which is
applicable to directional couplers in high index contrast materials, in coupled-
waveguide structures [17] and coupled-resonator structures [18]. When the
optical power is increased, silicon microring resonators with directional
couplers can exhibit interesting behavior, such as bistability and nonlinear on-
off switching [19]. However, these effects are not very significant at lower
power levels.
Figure 2 shows images of sections of coupled-microring CROWs fabricated in
this project in collaboration with IBM with several loss-reduction processing
steps such as oxidation smoothening of sidewalls and hydrogen annealing.
CROWs of up to 235 coupled resonators were successfully fabricated and
measured, and a good agreement was achieved between experiments and theory
[20]–[22]. Propagation losses as low as 0.062 dB/ring were measured. Figure
2(b) compares the transmission spectrum of a 35-ring CROW and a 235-ring
CROW. The increased passband loss, ripple and band-narrowing are effects of
disorder in the CROW, which we studied in detail during this project [22]–[24].
Figure 3 shows an example of a
measurement of group delay
ripple (GDR) measured for a
35-ring CROW using a high-
resolution optical vector
analyzer. This shows that a
reasonably low value of GDR
was achieved, less than 3 ps
over the passband width of 125
Figure 3 High-resolution measurement of group delay showing
the ripple across the transmission band of a 35-ring CROW.
GHz. Consequently, high-
speed data modulated signals

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(20 Gb/s NRZ modulation) could be transmitted through CROWs (even as long
as 235 coupled resonators) without distortion (see Year 4 report).

Figure 4 (a) For a 35-ring CROW, TE-polarized transmission (insertion loss) spectrum, i.e., the
drop port response normalized to the input port (black), and the group delay spectrum (red). A
single CROW band is shown here. (b) Measured band-center group delay τbc for a single CROW
band increases linearly with the number of resonators, N

Figure 4 shows a measurement of a transmission band for a 35-ring CROW.

Despite some ripple, the band is well defined and has a flat top as is desirable.
A total of 600,000 measurements of group delay were analyzed statistically to
examine the group delay ripple (GDR) over the central portion of the band. The
average band-center group delay τbc was obtained by averaging the root-mean-
squared group delay, measured with 1.4 pm resolution, over the central one-
half region of each transmission band, which was about 3 nm wide. As shown
in Fig. 4(b), τbc increased linearly with N, the number of resonators.

Figure 5(a) Probability density functions (PDFs) of the normalized group delay ripple (GDR)
(shown for positive GDR, similar distributions for negative GDR). The PDFs have exponential
tails whose slope decreases linearly with the number of resonators. (b) Measured group delay
ripple (GDR): 2x standard deviation of the raw GDR data for CROWs is plotted with circles,

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 and for waveguides with squares. The dashed line is a L1/2 fit to the waveguide data. The solid
line is the predicted GDR for CROWs obtained from PDFs shown in panel (a).

There is valuable information that can be obtained from studying the group
delay ripple in more detail. We statistically analyzed measurements of the
normalized GDR metric (ps/ring), Θ=(∆τ/N)|κ| where ∆τ is the difference
between the measured group delay (avoiding the band-edges) and the
corresponding band’s averaged value, and |κ| is the coupling coefficient of that
band, derived from the measured bandwidth. As Fig. 2b shows, the distribution
of Θ is well-modeled by an exponential distribution, i.e., pdf(|Θ|) ~exp(-
ν∆τ|κ|/N). Therefore, GDR (amplitude) can be described by twice the standard
deviation of the distribution, i.e., by 2ν-1, which has units of (ps/ring). We have
measured that λ has a linear dependence on N, with slope η=0.012 ps-1. The
GDR amplitude in an N-ring CROW was therefore given by 2Nν-1(ps).
Figure 5(b) shows the group delay ripple amplitude (GDR) for different lengths
of CROWs, and also for different lengths of conventional silicon waveguides
(without resonators). Whereas the GDR in long CROWs approached an
asymptotic upper-bound value, the measured GDR in conventional
nanophotonic silicon waveguides (fabricated on the same chip as the CROW
devices) increased as L1/2, which is similar to the scaling of GDR in cascaded
fiber Bragg gratings. This latter behavior arises from incoherent addition of
group delay statistics. In contrast, the effective strength of disorder in CROWs
is divided by N1/2 which compensates the observed L1/2 scaling with length in
conventional waveguides. Thus, the GDR amplitude in an N-ring CROW, 2Nν-
1
, shown with a solid black line in Fig. 5(b), reached a constant value, in the
large N limit, equal to η-1 plus an offset for the other components in the
measurement path =198 ps (in this batch of devices). Therefore, CROW modes
were confirmed experimentally, for the first time, to be phase-coherent
collective excitations using high-resolution transmission measurements and a
statistic analysis of photon transport.

Figure 6 (top panel) simulated transmission spectrum (left axis) and group delay spectrum (right
axis) for a silicon microring CROW with disorder. (bottom panel) experimental measurement.

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In addition to the experimental studies, we developed our modeling tools.
Traditional simulation methods such as finite-difference time-domain are not
well suited to modeling low CROWs with disorder. The length of the structure
can be several millimeters, and disorder is manifest at the nanoscale. Therefore,
efficient new methods for studying and modeling such structures were
developed [22]. An exponential tail of the distribution of time delay and the
distribution of GDR was confirmed by numerical simulations of intentionally
disordered microring CROWs. Our models were able to accurately reproduce
the free-spectral range, transmission band width and amplitude, group delay
and even the group delay ripple and amplitude ripple characteristics, as shown
in Figure 6.

Figure 7 Intra-band four-wave mixing in a 35-ring CROW with signal detuning from -0.2 to -
0.6 nm.

The second major set of research activities in this project focused on

wavelength conversion using four-wave mixing (FWM). Previously, FWM was
studied in silicon waveguides showing its potential for use in optical
communications [25]. Here, we studied FWM in silicon microring CROWs.
Figure 7 shows the spectra for a group of five measurements, in which a tunable
signal was mixed with a fixed-wavelength pump in a 35-ring CROW to
generate idlers on the long-wavelength side of the pump. All the wavelengths
are within a single passband. The variation in CROW conversion efficiency can
be correlated with ripples in the transmission spectrum of the as-fabricated
waveguide.
Figure 8 shows the spectra for inter-band FWM, in which the pump and the
signals are in different passbands, separated by one free-spectral range. Energy
transfer occurs to both higher and lower wavelengths. Once again, the ripples

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in the transmission spectrum of the waveguide lead to variations in the
conversion efficiency.
In order to extract the conversion enhancement due to the CROW from the
feeder and output waveguides, the conversion efficiency was measured for a
straight silicon waveguide (SWG) of the same geometric length. The results are
shown in Figure 9. Approximately +8dB and +5dB resonator-enhanced
conversion improvements over the straight waveguide were measured for the
inter-band and intra-band mixing cases. However, in absolute terms, these
conversion efficiencies are not high enough for practical use. In later research,
much higher FWM efficiencies were obtained using a single silicon microring
resonator [26].

Figure 8 Inter-band four-wave mixing in a 35-ring CROW with signal detuning with respect to
pump of -6.3 to -7.6 nm.

External Collaboration: A collaboration with IBM’s silicon photonics group

(Dr. W. M. J. Green) provided insights into silicon photonics fabrication and
also supported technical collaboration on fabricating the CROW structures
[23], [27], [20]. Dr. Ivan B. Divliansky (Research Scientist, CREOL, Florida)
collaborated with us for the electron-beam lithography of long waveguide
structures [28].

3. Progress and Impact

For several years, CROWs remained mainly a theoretical concept, with few
experimental demonstrations of more than a dozen or so coupled resonators
which showed high loss, lack of tunability and limited practical utility in optical

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communications or signal processing. Around 2007, silicon microring CROWs
were studied by IBM for applications in delay lines and optical buffers [15],
but were found to be significantly impacted by loss, disorder and dispersion
[29]. Since nonlinear optics is even more sensitive to these issues, there had
been no intensive study of nonlinear optics in CROWs.

Figure 9 a) Inter-band four-wave mixing: Conversion efficiency of the CROW was about +8 dB
higher than for a straight waveguide of equivalent geometric length. (b) Intra-band four-wave
mixing: Conversion efficiency of the CROW was about+5 dB higher than for a straight
waveguide of equivalent geometric length.

Prior to this project, there were few experimental reports on long CROWs even
in the linear propagation regime, and computational methods had not yet been
developed and validated which could calculate optical propagation realistically
in CROWs that comprise several hundred coupled resonators. We made
advances in all these areas by studying and modeling disorder effects,
improving fabrication technology and demonstrating four-wave mixing in
CROWs.
Once disorder, loss and dispersion are partially mitigated, the benefits of the
CROW device architecture for integrated nonlinear optics become apparent.
For example, for a typical silicon single-mode waveguide at 1550 nm, the four-
wave mixing nonlinear coefficient is γ = 200 W-1 m-1. A 35-ring CROW was
experimentally measured to have a slow-light enhanced value γeff = 4150 W-1

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m-1. Since the wavelength-converted power (idler) in FWM is quadratically
proportional to γ, the improvement in γ by a factor of about 50 compared to a
conventional waveguide of the same length leads to a 34 dB improvement in
the converted power at the new wavelength. However, it is easier to make
conventional waveguides longer, since the length of CROWs has been difficult
to scale beyond a few hundred resonators.
In addition to classical FWM, we developed a model for spontaneous four-wave
mixing (SFWM) using the Collett-Gardiner approach [30]. This method
formulates the time-domain equations of motion in the Heisenberg picture. We
solved the equations in the case of a single resonator as well as for multiple
resonators, showing the potential advantages of the latter.
Impact on Human Resources: Three graduate students in the PI's group worked
on this topic as part of their education and training. A post-doctoral scholar,
although not directly supported by CAREER funds, has contributed to the
CROW measurements and is a co-author on the relevant papers. Students
presented papers at a number of major conferences including CLEO.
A graduate student interacted on a weekly basis with under-privileged children
of the Preuss School from disadvantaged families; these students must qualify
for Federal Lunch Programs and be from families that have no college
education. The mentorship was valuable in encouraging these students to enroll
for college in science and engineering majors.

4. Subsequent Extensions
Research in this project accomplished a significant improvement in the state-
of-the-art of CROW waveguides. Low-loss CROW waveguides of record
length were demonstrated in using coupled microrings in silicon photonics, and
four-wave mixing was demonstrated. Based on the outcomes of this CAREER
project, a wide range of subsequent projects were initiated on focused research
topics, including improved nonlinear mixers, harnessing disorder for
functionality, and quantum photonics. In some of these projects, we continued
to use CROWs. In some cases, single microring resonators with a higher quality
factor offered better performance in experiments.
Infrared imaging is another useful experimental tool which we developed
during this project, to study light propagation through the length of these
structures [28], [31]. Light from a tunable laser is transmitted through the
device and the device plane is imaged using a microscope with a high numerical
aperture objective and an InGaAs camera. Images are taken at different
wavelengths, and in principle, contain the same information that is obtained by
transmission measurements made using optical fibers. However, typical
infrared images of guided light at 1550 nm lack the quality and depth of

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information needed to perform quantitative analysis, such as extracting
propagation loss, or coupling coefficients. We developed an experimental
procedure which allows us to achieve high dynamic range infrared imaging of
light propagation by “bracketing” multiple image acquisitions made at different
exposure settings.
The CROW structures studied in this project are passive waveguide structures.
A tunable laser was used to study optical propagation at different points in the
dispersion relationship. In the future, we seek a control “knob” to tune the
waveguiding properties of the CROW structure without changing the
wavelength of the laser. The most practical way of tuning silicon microring
CROWs is to use biasing of a p-n junction [32]. Integrated electro-optic
modulators could be another way of achieving phase shifters with more than
100 GHz of bandwidth, as was demonstrated later [33]. The thermo-optic
effect, which we used for tunable filters, is also another option as a control knob
that can be used to control silicon photonics devices over a wide bandwidth
[34]. However, it is difficult to tune individual rings in a CROW structure using
this approach since heat spreading can lead to crosstalk.
The CROW structure can have other applications including generation of
quantum light [30], and developing amplifiers and lasers with novel properties
[35]. The resonator-enhanced nonlinearity benefits the generation of entangled
photon-pair and heralded single-photon generation using silicon photonics [36].
Unlike slow-light photonic crystal waveguides, a CROW provides enhanced
nonlinearity in several passbands simultaneously which can be useful for
multiplexed photon-pair generation [37] and tuning the entanglement properties
[38]. Our initial measurements of spontaneous four-wave mixing (SFWM)
were on correlated photon-pair generation and heralded single-photon
generation. An experimental measurement of entanglement was performed
later, using a two-photon interferometer constructed to verify time-energy
entanglement [36]. Going beyond what was achieved using CROWs, bright and
high quality photon-pair generation and heralded single-photon generation was
shown later using high-Q single silicon microring resonators [39].
Microring resonators are sensitive to disorder. We studied potential methods
for precisely tuning resonators without heaters. Our method is based on field-
induced local oxidation of Si to SiO2 via a chemical reaction near an
electrically-biased conducting atomic-force microscope tip [40], [41]. Scanning
probe lithography has previously been used to modify the resonance frequency
of a GaAs photonic crystal cavity. A single silicon microresonator can be
monitored and controlled more easily [42] than a long CROW device.

5. Open-Access Reporting Initiative

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PRAISE: This open-access document is provided in support of our PRAISE
(Public Report of Activities, Impact and Subsequent Extensions) initiative.
What is it? An open-access document shared with the public which describes
the research outcomes of publicly-funded projects. For us, these projects are
typically funded by the NSF (National Science Foundation).

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