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12 pages, 1071 KiB  
Article
A Numerical Study of Microwave Frequency Comb Generation in a Semiconductor Laser Subject to Modulated Optical Injection and Optoelectronic Feedback
by Chenpeng Xue, Wei Chen, Beibei Zhu, Zuxing Zhang and Yanhua Hong
Photonics 2024, 11(8), 741; https://doi.org/10.3390/photonics11080741 - 8 Aug 2024
Viewed by 617
Abstract
This study presents a comprehensive numerical investigation on the generation of a microwave frequency comb (MFC) using a semiconductor laser subjected to periodic-modulated optical injection. To enhance performance, optoelectronic feedback is incorporated through a dual-drive Mach–Zehnder modulator. The results show that the first [...] Read more.
This study presents a comprehensive numerical investigation on the generation of a microwave frequency comb (MFC) using a semiconductor laser subjected to periodic-modulated optical injection. To enhance performance, optoelectronic feedback is incorporated through a dual-drive Mach–Zehnder modulator. The results show that the first optoelectronic feedback loop, with a delay time inversely proportional to the modulation frequency, can optimize MFC generation through a mode-locking effect and the second optoelectronic feedback loop with a multiple delay time of the first one can further enhance the performance of the MFC. The comb linewidth appears to decrease with the increase in the second-loop delay time in the power function. These results are consistent with experimental observations reported in the literature. We also explore the impact of the feedback index on comb contrast, the statistical characteristics of the central 128 lines within the MFC, and side peak suppression. The simulation results demonstrate the presence of an optimal feedback index. The study also reveals that linewidth reduction, through increasing the feedback index and delay time, comes at the cost of declining side peak suppression. These findings collectively contribute to a deeper understanding of the factors influencing MFC generation and pave the way for the design and optimization of high-performance MFC systems for various applications. Full article
(This article belongs to the Special Issue New Perspectives in Microwave Photonics)
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<p>Scheme diagram of the MFC based on the modulated optical injection and optoelectronic feedback. PD: photodetector, Att: attenuator, PC: polarization controller, SG: signal generator, Cir: optical circulator, Spl: splitter, DMZM: dual-drive Mach–Zehnder modulator, OSA: optical spectrum analyzer, PSA: power spectrum analyzer.</p>
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<p>Optical spectra (left column) and power spectra (right column) of the case with injection parameters (0.13, 7 GHz): (<b>a</b>,<b>b</b>) correspond to the case with conventional optical injection, (<b>c</b>,<b>d</b>) are for the case with modulated optical injection.</p>
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<p>Bandwidth of the MFC as a function of modulation index. The insets (<b>a</b>,<b>b</b>) show the MFC spectra with respect to the modulation index <span class="html-italic">m</span> = 0.05 and <span class="html-italic">m</span> = 0.12, respectively.</p>
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<p>Power spectra of the generated dense MFC signals when the single-loop feedback <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>1</mn> </msub> </semantics></math> = 61.53 ns: (<b>a</b>,<b>b</b>) with <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.04, (<b>c</b>,<b>d</b>) with <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.08, (<b>e</b>,<b>f</b>) with <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.10, and (<b>g</b>,<b>h</b>) with <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.12.</p>
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<p>(<b>a</b>) Boxplot of line power with extreme values and quartiles and (<b>b</b>) 3-dB linewidth of the MFC as a function of feedback index <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Boxplot of line power and linewidth of the MFC as a function of the second-loop feedback index <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>2</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>2</mn> </msub> </semantics></math> = 8<math display="inline"><semantics> <msub> <mi>τ</mi> <mn>1</mn> </msub> </semantics></math>: (<b>a</b>,<b>d</b>) are for the case with <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.08, (<b>b</b>,<b>e</b>) are for the case with <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.1, and (<b>c</b>,<b>f</b>) are for the case with <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.12.</p>
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<p>Power spectra of the MFC with (<b>a</b>) <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>2</mn> </msub> </semantics></math> = 0.04 and (<b>b</b>) <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>2</mn> </msub> </semantics></math> = 0.08, <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.10 and <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>2</mn> </msub> </semantics></math> = 8<math display="inline"><semantics> <msub> <mi>τ</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>SPSC as a function of feedback index in loop 2, <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>Power spectra of the MFC where (<b>a</b>) <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 32, (<b>b</b>) <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 128, (<b>c</b>), and linewidth and (<b>d</b>) SPSC are a function of the delay time ratio, <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>1</mn> </msub> </semantics></math> = 0.10, and <math display="inline"><semantics> <msub> <mi>κ</mi> <mn>2</mn> </msub> </semantics></math> = 0.02.</p>
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9 pages, 2039 KiB  
Article
Modulated Short-Time Fourier-Transform-Based Nonstationary Signal Decomposition for Dual-Comb Ranging Systems
by Ningning Han, Chao Wang, Zhiyang Wu, Xiaoyu Zhai, Yongzhen Pei, Haonan Shi and Xiaobo Li
Photonics 2024, 11(6), 560; https://doi.org/10.3390/photonics11060560 - 14 Jun 2024
Viewed by 677
Abstract
Analyzing and breaking down nonstationary signals into their primary components is significant in various optical applications. In this work, we design a direct, localized, and mathematically rigorous method for nonstationary signals by employing a modulated short-time Fourier transform (MSTFT) that can be implemented [...] Read more.
Analyzing and breaking down nonstationary signals into their primary components is significant in various optical applications. In this work, we design a direct, localized, and mathematically rigorous method for nonstationary signals by employing a modulated short-time Fourier transform (MSTFT) that can be implemented efficiently using fast Fourier transform, subsequently isolating energy-concentrated sets through an approximate threshold process, allowing us to directly retrieve instantaneous frequencies and signal components by determining the maximum frequency within each set. MSTFT provides a new insight into the time-frequency analysis in multicomponent signal separation and can be extended to other time-frequency transforms. Beyond the analysis of the synthetic, we also perform real dual-comb ranging signals under turbid water, and the results show an approximate 1.5 dB improvement in peak signal-to-noise ratio, further demonstrating the effectiveness of our method in challenging conditions. Full article
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<p>(<b>a</b>) Waveform of blind-source signal <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) Time-frequency spectrogram <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>ξ</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Recovered results: (<b>a</b>) instantaneous frequencies; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Experimental setup for underwater dual-comb LiDAR. SS, signal source; LO, local oscillator; Rb, rubidium clock; <math display="inline"><semantics> <msub> <mi>M</mi> <mi>R</mi> </msub> </semantics></math>, reference mirror; BPD, balanced photodetector.</p>
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<p>Original and reconstructed signals at turbid water with 2.1 NTU and 9.3 NTU. (<b>a</b>,<b>c</b>) Measurement interferograms. (<b>b</b>,<b>d</b>) Reference interferograms.</p>
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<p>Comparison of different algorithms for the measurement interferogram of dual-comb LiDAR.</p>
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<p>Enlarged comparison between WT and our results around the peak.</p>
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17 pages, 4721 KiB  
Article
A Microwave Photonic 2 × 2 IBFD–MIMO Communication System with Narrowband Self-Interference Cancellation
by Ying Ma, Fangjing Shi and Yangyu Fan
Micromachines 2024, 15(5), 593; https://doi.org/10.3390/mi15050593 - 29 Apr 2024
Viewed by 940
Abstract
Combined in-band full duplex-multiple input multiple output (IBFD–MIMO) technology can significantly improve spectrum efficiency and data throughput, and has broad application prospects in communications, radar, the Internet of Things (IoT), and other fields. Targeting the self-interference (SI) issue in microwave photonic-based IBFD–MIMO communication [...] Read more.
Combined in-band full duplex-multiple input multiple output (IBFD–MIMO) technology can significantly improve spectrum efficiency and data throughput, and has broad application prospects in communications, radar, the Internet of Things (IoT), and other fields. Targeting the self-interference (SI) issue in microwave photonic-based IBFD–MIMO communication systems, a microwave photonic self-interference cancellation (SIC) method applied to the narrowband 2 × 2 IBFD–MIMO communication system was proposed, simulated, and analyzed. An interleaver was used to construct a polarization multiplexing dual optical frequency comb with a frequency shifting effect, generating a dual-channel reference interference signal. The programmable spectrum processor was employed for filtering, attenuation, and phase-shifting operations, ensuring amplitude and phase matching to eliminate the two self-interference (SI) signals. The simulation results show that the single-frequency SIC depth exceeds 45.8 dB, and the narrowband SIC depth under 30 MHz bandwidth exceeds 32.7 dB. After SIC, the desired signal, employing a 4QAM modulation format, can be demodulated with an error vector magnitude (EVM) as low as 4.7%. Additionally, further channel expansion and system performance optimization are prospected. Full article
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<p>Schematic diagram of the microwave photonic SIC scheme applied to the narrowband 2 × 2 IBFD–MIMO communication system.</p>
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<p>The spectra of the five-line OFC.</p>
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<p>The spectra of the OFCs: (<b>a</b>) three-line; (<b>b</b>) two-line.</p>
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<p>The output single-tone spectra (<b>a</b>–<b>c</b>) without/with SIC at antenna 1; (<b>d</b>–<b>f</b>) without/with SIC at antenna 2; (<b>a</b>,<b>d</b>) without SIC; (<b>b</b>,<b>e</b>) with single-path SIC; and (<b>c</b>,<b>f</b>) with dual-path SIC.</p>
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<p>The output 30/60 MHz narrowband spectra (<b>a</b>–<b>c</b>) without/with SIC at antenna 1; (<b>d</b>–<b>f</b>) without/with SIC at antenna 2; (<b>a</b>,<b>d</b>) without SIC; (<b>b</b>,<b>e</b>) with single-path SIC; and (<b>c</b>,<b>f</b>) with dual-path SIC.</p>
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<p>The output 30/90 MHz narrowband spectra (<b>a</b>–<b>c</b>) without/with SIC at antenna 1; (<b>d</b>–<b>f</b>) without/with SIC at antenna 2; (<b>a</b>,<b>d</b>) without SIC; (<b>b</b>,<b>e</b>) with single-path SIC; and (<b>c</b>,<b>f</b>) with dual-path SIC.</p>
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<p>Antenna 1, after adding the desired signal (4QAM, 70 MHz). (<b>a</b>,<b>b</b>) Output narrowband spectrum without/with SIC; (<b>c</b>,<b>d</b>) demodulation constellation diagram without/with SIC.</p>
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<p>Antenna 2, after adding the desired signal (4QAM, 70 MHz). (<b>a</b>,<b>b</b>) Output narrowband spectrum without/with SIC; (<b>c</b>,<b>d</b>) demodulation constellation diagram without/with SIC.</p>
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<p>Schematic diagram of three SSB modulation structures based on lithium niobate modulators (<b>a</b>) based on DDMZM; (<b>b</b>) based on DPMZM; and (<b>c</b>) based on optical filter.</p>
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<p>Three SSB modulation spectra (<b>a</b>) based on DDMZM; (<b>b</b>) based on DPMZM; and (<b>c</b>) based on optical filter.</p>
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<p>Schematic diagram of the improved microwave photonic SIC scheme for the N × N IBFD–MIMO communication system.</p>
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17 pages, 10859 KiB  
Article
A Reconfigurable Local Oscillator Harmonic Mixer with Simultaneous Phase Shifting and Image Rejection
by Bin Wu, Chaoyue Zheng, Hao Zhang and Qingchun Zhao
Electronics 2024, 13(5), 971; https://doi.org/10.3390/electronics13050971 - 3 Mar 2024
Viewed by 978
Abstract
The multibeam high-throughput satellites (HTS) are regarded as a crucial component in the forthcoming space-based Internet of Things (S-IoT) network. The multi-band frequency conversion capability of HTS is essential for achieving high-capacity information interconnection in the S-IoT network. To enhance the frequency conversion [...] Read more.
The multibeam high-throughput satellites (HTS) are regarded as a crucial component in the forthcoming space-based Internet of Things (S-IoT) network. The multi-band frequency conversion capability of HTS is essential for achieving high-capacity information interconnection in the S-IoT network. To enhance the frequency conversion capability of the on-board payload, a reconfigurable local oscillator (LO) harmonic mixer with simultaneous phase shifting and image-rejection is proposed and demonstrated based on a polarization division multiplexing dual-parallel Mach–Zehnder modulator (PDM-DPMZM). By adjusting the input radio frequency (RF) signal and direct current (DC) bias voltage of the modulator, four different LO frequency-multiplication mixing functions can be achieved. The phase of the generated signal can be flexibly tuned over a full 360° range by controlling the angle α between the polarization direction of the polarizer and one axis of the modulator, and it has a flat amplitude response. When combined with an optical frequency comb, the scheme can be extended to a multi-channel multi-band frequency conversion system with an independent phase tuning capability. Additionally, by adjusting the phase difference between dual channel output signals, it can be reconfigured to implement in-phase/quadrature (I/Q) mixing, double-balanced mixing and image-reject mixing. Full article
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<p>Schematic diagram of the reconfigurable LO harmonic mixer.</p>
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<p>RF input and DC biases of PDM-DPMZM under different phase-shift functions. (<b>a</b>) ±first-order LO harmonic mixing; (<b>b</b>) ±second and ±fourth-order LO harmonic mixing; (<b>c</b>) ±third-order LO harmonic mixing.</p>
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<p>Setup diagram of the reconfigurable LO harmonic mixer. LD: laser diode; PC: polarization controller; SG: signal generator; LO: local oscillator; RF: radio frequency; HC: hybrid coupler; PDM-DPMZM: polarization division multiplexing dual-parallel Mach–Zehnder modulator; PBS: polarization beam splitter; WSS: wavelength selective switch; EDFA: erbium-doped fiber amplifier; PBC: polarization beam combiner; PMC: polarization-maintaining coupler; Pol: polarizer; PD: photodetector; ESA: electrical spectrum analyzer.</p>
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<p>Optical spectra at the output of PDM-DPMZM and electric spectra at the output of PD under different LO conditions. ±second-order LO harmonic (<b>a</b>,<b>c</b>,<b>e</b>); ±fourth-order LO harmonic (<b>b</b>,<b>d</b>,<b>f</b>).</p>
Full article ">Figure 4 Cont.
<p>Optical spectra at the output of PDM-DPMZM and electric spectra at the output of PD under different LO conditions. ±second-order LO harmonic (<b>a</b>,<b>c</b>,<b>e</b>); ±fourth-order LO harmonic (<b>b</b>,<b>d</b>,<b>f</b>).</p>
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<p>Optical spectra at the output of PDM-DPMZM (<b>a</b>) and electric spectra at the output of PD when RF signal is mixed with the +3rd-order sideband (<b>b</b>) or -3rd-order sideband (<b>c</b>) of 7-line LO OFC.</p>
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<p>Electrical spectra of the mixed electrical signal of the second-order LO harmonic mixer for (<b>a</b>) frequency up-conversion from 31 GHz to 40 GHz and (<b>b</b>) frequency down-conversion from 11 GHz to 20 GHz. Different colors indicate different RF signal frequencies, varying from 21 GHz to 30 GHz in 1 GHz steps.</p>
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<p>Conversion gain (<b>a</b>) and NF of the second-order LO harmonic mixer (<b>b</b>).</p>
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<p>Waveforms of signals after phase continuous tuning in the case of the second-order LO harmonic mixing operation. (<b>a</b>) Up-conversion signal (28 GHz); (<b>b</b>) down-conversion signal (8 GHz).</p>
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<p>Waveforms of I/Q mixing and double-balanced mixing in the case of the second-order LO harmonic down-conversion. (<b>a</b>) I/Q mixing; (<b>b</b>) double-balanced mixing.</p>
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<p>Waveforms of the IF signals at the outputs of PD1 and PD2 in the case of I/Q mixing. (<b>a</b>) The two RF-induced IF signals; (<b>b</b>) the two image-induced IF signals.</p>
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<p>Measured spectra and waveforms of the down-conversion IF and image IF signals from the image-reject mixer. (<b>a</b>) IF signal frequency spectrum; (<b>b</b>) IF signal waveform.</p>
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<p>The SFDR of the reconfigurable LO harmonic mixer. (<b>a</b>) Second-order LO harmonic up-conversion; (<b>b</b>) second-order LO harmonic down-conversion.</p>
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11 pages, 3992 KiB  
Article
Research on Optical Mutual Injection to Generate Tunable Microwave Frequency Combs
by Bin Wu and Qingchun Zhao
Photonics 2024, 11(3), 195; https://doi.org/10.3390/photonics11030195 - 22 Feb 2024
Cited by 2 | Viewed by 1129
Abstract
In this study, a scheme for generating tunable microwave frequency combs (MFCs) based on optical mutual injection is proposed and experimentally investigated. The scheme is based on the optical injection of lasers to generate MFCs, and constitutes a feedback loop by using dual-laser [...] Read more.
In this study, a scheme for generating tunable microwave frequency combs (MFCs) based on optical mutual injection is proposed and experimentally investigated. The scheme is based on the optical injection of lasers to generate MFCs, and constitutes a feedback loop by using dual-laser mutual injection to obtain MFCs with a large continuous bandwidth and tunable comb spacing. The experimental setup analyzes the effects of injected optical power, modulation frequency and amplitude, and wavelength detuning on the generated MFC signals. The experimental results indicate that when the single-frequency electrical signal is set to 2 GHz, flat MFCs with amplitude variations within 10 dB can be obtained by optimizing the injected power and the frequency detuning between the two semiconductor lasers. Furthermore, the comb spacing of the MFCs can be made tunable by varying the modulation frequency and selecting the matched operating parameters to adapt to different application scenarios. Full article
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<p>Experimental setup. SL: semiconductor laser; OC: optical circulator; PC: polarization controller; MZM: Mach–Zehnder modulator; SG: signal generator; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; OSA: optical spectrum analyzer; PD: photodetector; ESA: electrical spectrum analyzer.</p>
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<p>Comparison of MFCs generated by unidirectional injection (<b>a</b>) and mutual injection (<b>b</b>).</p>
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<p>Electrical spectrum of the MFC when the modulation frequency is 2 GHz and the attenuator coefficient of VOA1 is 3.5 dB (<b>a</b>) and 13.5 dB (<b>b</b>).</p>
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<p>Effect of the attenuation coefficient on the bandwidth and maximum power of the MFCs. The X-axis is represented by the attenuation coefficient of VOA1.</p>
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<p>Electrical spectrum of the MFC when the modulation frequency is 2 GHz (<b>a</b>) and 3 GHz (<b>b</b>).</p>
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<p>Effect of the modulation frequency on the bandwidth and maximum power of the MFCs.</p>
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<p>Electrical spectrum of the MFC when the modulation amplitude is 0.2 V (<b>a</b>) and 0.8 V (<b>b</b>).</p>
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<p>Effect of frequency detuning on the bandwidth and maximum power of the MFCs (<b>a</b>) and electrical spectrum of the MFC when the wavelength detuning is 0.222 nm (<b>b</b>).</p>
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14 pages, 4235 KiB  
Article
Calibration of Dual-Channel Raman Spectrometer via Optical Frequency Comb
by Shengyujie Lv, Xiaoping Lou, Qiaona Gai and Taotao Mu
Sensors 2024, 24(4), 1217; https://doi.org/10.3390/s24041217 - 14 Feb 2024
Viewed by 999
Abstract
The portable Raman spectrometer boasts portability, rapid analysis, and high flexibility. It stands as a crucial and powerful technical tool for analyzing the chemical composition of samples, whether biological or non-biological, across diverse fields. To improve the resolution of grating spectrometers and ensure [...] Read more.
The portable Raman spectrometer boasts portability, rapid analysis, and high flexibility. It stands as a crucial and powerful technical tool for analyzing the chemical composition of samples, whether biological or non-biological, across diverse fields. To improve the resolution of grating spectrometers and ensure a wide spectral range, many spectrometer systems have been designed with double-grating structures. However, the impact of external forces, such as installation deviations and inevitable collisions, may cause differences between the actual state of the internal spectrometer components and their theoretical values. Therefore, spectrometers must be calibrated to establish the relationship between the wavelength and the pixel positions. The characteristic peaks of commonly used calibration substances are primarily distributed in the 200–2000 cm1 range. The distribution of characteristic peaks in other wavenumber ranges is sparse, especially for spectrometers with double-channel spectral structures and wide spectral ranges. This uneven distribution of spectral peaks generates significant errors in the polynomial fitting results used to calibrate spectrometers. Therefore, to satisfy the calibration requirements of a dual-channel portable Raman spectrometer with a wide spectral range, this study designed a calibration method based on an optical frequency comb, which generates dense and uniform comb-like spectral signals at equal intervals. The method was verified experimentally and compared to the traditional calibration method of using a mercury–argon lamp. The results showed that the error bandwidth of the calibration results of the proposed method was significantly smaller than that of the mercury–argon lamp method, thus demonstrating a substantial improvement in the calibration accuracy. Full article
(This article belongs to the Section Optical Sensors)
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<p>Diagram of the structure of the portable Raman spectrometer used in this study.</p>
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<p>Diagram of the optical path of the beam-splitting system in the Raman spectrometer used in this study.</p>
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<p>Raman spectrum of the optical frequency comb generated in this study.</p>
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<p>Flow chart of the dual-band calibration method.</p>
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<p>Standard Raman spectrum of acetaminophen.</p>
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<p>Original spectra of acetonitrile and the optical frequency comb in the high-wavenumber band.</p>
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<p>Relative positions of the spectral peaks of acetonitrile and those of the OFC.</p>
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<p>Peak-finding results for acetaminophen.</p>
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<p>Splicing of the high- and low-wavenumber bands was calibrated using acetaminophen.</p>
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<p>Benzoyl peroxide spectrum: (<b>a</b>) optical frequency comb calibration and (<b>b</b>) mercury–argon lamp calibration.</p>
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<p>Cyclohexane spectrum: (<b>a</b>) optical frequency comb calibration and (<b>b</b>) mercury–argon lamp calibration.</p>
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<p>Distribution of the residuals of the calibration curves for (<b>a</b>) benzoyl peroxide and (<b>b</b>) cyclohexane.</p>
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14 pages, 6746 KiB  
Article
Fully Phase-Locked Fiber Dual Comb Enables Accurate Frequency and Phase Detection in Multidimensional Coherent Spectroscopy
by Shiping Xiong, Zejiang Deng, Zhong Zuo, Jiayi Pan, Zilin Zhao, Gehui Xie and Wenxue Li
Photonics 2024, 11(2), 120; https://doi.org/10.3390/photonics11020120 - 28 Jan 2024
Viewed by 1280
Abstract
High-resolution optical multidimensional coherent spectroscopy (MDCS) requires frequency-stable laser sources and high-resolution heterodyne spectra. Fully phase-locked dual-comb spectroscopy (DCS) enables the achievement of high resolution, high accuracy, broad bandwidth, and a rapid multi-heterodyne spectrum, which results in the DCS’s potential to replace the [...] Read more.
High-resolution optical multidimensional coherent spectroscopy (MDCS) requires frequency-stable laser sources and high-resolution heterodyne spectra. Fully phase-locked dual-comb spectroscopy (DCS) enables the achievement of high resolution, high accuracy, broad bandwidth, and a rapid multi-heterodyne spectrum, which results in the DCS’s potential to replace the spectrometer and phase detection system in MDCS. We verified the phase measurement capability of the MDCS system based on fully phase-locked fiber DCS by studying phase-sensitive photon echoes and double-quantum processes. The accurate phase and frequency of linear and nonlinear signals were obtained simultaneously using a single detector without subsequent frequency drift correction. Subsequently, the acquisition of longtime quantum beat signals demonstrates the high phase coherence between excitation pulses. Additionally, the two-dimensional coherent spectrum (2DCS) with high signal-to-noise-ratio and 100 MHz resolution was obtained via the MDCS system based on fully phase-locked fiber DCS. These results exhibit that fully phase-locked fiber DCS is an effective method for high-resolution 2DCS measurement, which facilitates further research on cold atoms, higher-order nonlinear spectra, and molecular fingerprint vibrational spectroscopy. Full article
(This article belongs to the Special Issue Advanced Lasers and Their Applications)
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<p>Schematic diagram of the experimental setup. PPLN, periodically poled lithium niobate; HWP, half-wave plate; PBS, polarization beam splitter; AOM, acoustic–optic modulator; BS, beam splitter; BD, balanced detector.</p>
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<p>(<b>a</b>) Linear absorption spectrum, (<b>b</b>) the linewidth of individual comb tooth, (<b>c</b>) the coherent averaging absorption spectrum, and (<b>d</b>) the phase spectrum of DCS in Rb gas after FFT from a 1 s long recording. The absorption frequency is relative to a reference frequency, v<span class="html-italic"><sub>ref</sub></span> = 384.226348468 THz.</p>
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<p>(<b>a</b>) Single-quantum process and excitation pulse sequences and (<b>b</b>) double-sided Feynman diagrams. SE, stimulated emission; GSB, ground state bleach. (<b>c</b>) Double-quantum process and excitation pulse sequences and (<b>d</b>) double-sided Feynman diagrams. |f⟩, |e⟩, and |g⟩ are the doubly excited state, excited state, and ground state, respectively.</p>
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<p>(<b>a</b>) The single periodic linear and nonlinear DCS signals after RF down-conversion in 0 to half repetition frequency range. (<b>b</b>) Photon echo DCS and (<b>c</b>) the double-quantumDCS with comb teeth and coherent averaging after FFT one-second-long recording data. The reference frequency, v<span class="html-italic"><sub>ref</sub></span> = 384.226348468 THz.</p>
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<p>Experimental time-resolved photon echo dynamic process generated by (<b>a</b>) HHHH- and (<b>b</b>) HVVH-polarized excitation pulses (H, horizontal polarization; V, vertical polarizations). Photon echo beating dynamics of the amplitude for the four major peaks at emission frequencies (<b>c</b>) 8.24 GHz, (<b>d</b>) 5.92 GHz, (<b>e</b>) 2.98 GHz, and (<b>f</b>) 1.87 GHz. The reference frequency, v<span class="html-italic"><sub>ref</sub></span> = 384.226348468 THz.</p>
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<p>Experimental photon echo (<b>a</b>) amplitude 2DCS, (<b>b</b>) real-part 2DCS, simulated (<b>c</b>) amplitude 2DCS, and (<b>d</b>) real-part 2DCS generated by HHHH excitation pulses. Experimental photon echo (<b>e</b>) amplitude 2DCS, (<b>f</b>) real-part 2DCS, simulated (<b>g</b>) amplitude 2DCS, and (<b>h</b>) real-part 2DCS generated by HVVH excitation pulses. The reference frequency, v<span class="html-italic"><sub>ref</sub></span> = 384.226348468 THz.</p>
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<p>Experimental time-resolved double-quantum dynamic process generated by (<b>a</b>) HHHH- and (<b>b</b>) HVVH-polarized excitation pulses (H, horizontal polarization; V, vertical polarizations). Double-quantum beating dynamics of the amplitude for the four major peaks at emission frequencies (<b>c</b>) 8.24 GHz, (<b>d</b>) 5.92 GHz, (<b>e</b>) 2.98 GHz, and (<b>f</b>) 1.87 GHz. The reference frequency, v<span class="html-italic"><sub>ref</sub></span> = 384.226348468 THz.</p>
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<p>Experimental double-quantum (<b>a</b>) amplitude 2DCS, (<b>b</b>) real-part 2DCS, simulated (<b>c</b>) amplitude 2DCS, and (<b>d</b>) real-part 2DCS generated by HHHH excitation pulses. Experimental double-quantum (<b>e</b>) amplitude 2DCS, (<b>f</b>) real-part 2DCS, simulated (<b>g</b>) amplitude 2DCS, and (<b>h</b>) real-part 2DCS generated by HVVH excitation pulses. The reference frequency, v<span class="html-italic"><sub>ref</sub></span> = 384.226348468 THz.</p>
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11 pages, 11784 KiB  
Article
Generation of a Flat Optical Frequency Comb via a Cascaded Dual-Parallel Mach–Zehnder Modulator and Phase Modulator without Using the Fundamental Tone
by Shiyu Zhang, Zixiong Wang, Xunhe Zuo, Chuang Ma, Yang Jiang and Jinlong Yu
Photonics 2023, 10(12), 1340; https://doi.org/10.3390/photonics10121340 - 4 Dec 2023
Viewed by 1336
Abstract
Under the conventional scheme to generate an optical frequency comb (OFC) using an electro-optic modulator (EOM), the frequency interval of the OFC is determined via the frequency of the fundamental tone of the radio frequency (RF) driving signals. In this work, we use [...] Read more.
Under the conventional scheme to generate an optical frequency comb (OFC) using an electro-optic modulator (EOM), the frequency interval of the OFC is determined via the frequency of the fundamental tone of the radio frequency (RF) driving signals. In this work, we use two harmonics without the fundamental tone to drive two EOMs, where the frequency interval of the generated flat OFC is the frequency of the fundamental tone. The orders of the two harmonics are coprime. Specifically, one harmonic drives the first branch of the dual-parallel Mach–Zehnder modulator (DPMZM) only, and the other harmonic drives the phase modulator (PM). The flatness of the OFC is achieved by adjusting the amplitude and phase of the RF driving harmonics as well as the bias of the EOM. Both a simulation and an experiment were carried out to verify the effectiveness of the proposed scheme. When the second harmonic drives the DPMZM and the third harmonic drives the PM, an 11-comb line OFC is generated, where the flatness of the OFC was 0.63 dB and 0.65 dB under the simulation and experiment, respectively. When the third harmonic drives the DPMZM and the second harmonic drives the PM, a 13-comb line OFC is generated, where the flatness of the OFC was 0.62 dB and 0.95 dB under the simulation and experiment, respectively. We also investigate the performance of the generated OFC when one harmonic drives two branches of the DPMZM and the other harmonic drives the PM. The comparison of the OFCs’ performance demonstrates the effectiveness of the proposed scheme. Full article
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<p>The principle used to generate a flat OFC via cascaded DPMZM and PM without using the fundamental tone. <span class="html-italic">m</span> and <span class="html-italic">n</span> are the order of two harmonics that drive one branch of the DPMZM and PM, respectively, where <span class="html-italic">m</span> and <span class="html-italic">n</span> are coprime. LD: laser diode, MZM: Mach–Zehnder modulator, DPMZM: dual-parallel Mach–Zehnder modulator, PS: phase shifter, AMP: amplifier, PM: phase modulator, OSA: optical spectrum analyzer.</p>
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<p>The generated OFC in simulation under the scheme in <a href="#photonics-10-01340-f001" class="html-fig">Figure 1</a>, when (<b>a</b>) the second harmonic (12 GHz) and third harmonic (18 GHz) drive the DPMZM and PM, respectively; (<b>b</b>) the third harmonic (18 GHz) and second harmonic (12 GHz) drive the DPMZM and PM, respectively; (<b>c</b>) the second harmonic (12 GHz) and fifth harmonic (30 GHz) drive the DPMZM and PM, respectively.</p>
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<p>The experimental setup for OFC generation under the scheme in <a href="#photonics-10-01340-f001" class="html-fig">Figure 1</a>.</p>
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<p>The generated OFCs in the experiment under the scheme in <a href="#photonics-10-01340-f001" class="html-fig">Figure 1</a>, when (<b>a</b>) the second harmonic and third harmonic drove the DPMZM and PM, respectively; (<b>b</b>) the third harmonic and the second harmonic drove the DPMZM and PM, respectively.</p>
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<p>The principle used to generate a flat OFC via cascaded DPMZM and PM without using the fundamental tone. <span class="html-italic">m</span> and <span class="html-italic">n</span> are the orders of two harmonics that drive two branches of the DPMZM and PM, respectively, where <span class="html-italic">m</span> and <span class="html-italic">n</span> are coprime.</p>
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<p>The generated OFCs in simulation, (<b>a</b>) when the second harmonic (12 GHz) drove two branches of the DPMZM and third harmonic (18 GHz) drove PM; (<b>b</b>) when the third (18 GHz) harmonic drove two branches of the DPMZM and the second (12 GHz) harmonic drove the PM; (<b>c</b>) when the second harmonic (12 GHz) drove two branches of the DPMZM and fifth harmonic (30 GHz) drove PM.</p>
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13 pages, 2612 KiB  
Article
Tunable Optical Frequency Comb Generated Using Periodic Windows in a Laser and Its Application for Distance Measurement
by Zhuqiu Chen, Can Fang, Yuxi Ruan, Yanguang Yu, Qinghua Guo, Jun Tong and Jiangtao Xi
Sensors 2023, 23(21), 8872; https://doi.org/10.3390/s23218872 - 31 Oct 2023
Viewed by 1768
Abstract
A novel method for the generation of an optical frequency comb (OFC) is presented. The proposed approach uses a laser diode with optical feedback and operating at a specific nonlinear dynamic state named periodic window. In this case, the laser spectrum exhibits a [...] Read more.
A novel method for the generation of an optical frequency comb (OFC) is presented. The proposed approach uses a laser diode with optical feedback and operating at a specific nonlinear dynamic state named periodic window. In this case, the laser spectrum exhibits a feature with a series of discrete, equally spaced frequency components, and the repetition rate can be flexibly adjusted by varying the system parameters (e.g., external cavity length), which can provide many potential applications. As an application example, a dual-OFC system for distance measurement is presented. The results demonstrate the system’s ability to achieve target distance detection, underscoring its potential for real-world applications in this field. Full article
(This article belongs to the Special Issue Radar Remote Sensing and Applications)
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<p>Schematic diagram for an LD with EOF. LD, laser diode; BS, beam splitter; VA, variable attenuator; RM, reflection mirror; PZT, piezoelectric transducer; OI, optical isolator; OSA, optical spectrum analyzer; PD, photodiode; OSC, oscilloscope; PC, computer.</p>
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<p>Bifurcation diagram with a periodic window embedded in chaos.</p>
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<p>Time series (<b>a</b>) P3 region. (<b>b</b>) P6 region.</p>
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<p>Optical spectrum at <math display="inline"><semantics> <mrow> <mi>κ</mi> <mo>=</mo> <mn>0.041</mn> </mrow> </semantics></math>.</p>
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<p>Demonstration of the repetition rate changing with <span class="html-italic">L</span>.</p>
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<p>The relationship between <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Δ</mi> <mi>L</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>f</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Schematic setup of a dual-OFC system for distance measurement. OFC-EOF, external optical feedback-based OFC sources; OI, optical isolator; COL, collimator; FC, fiber coupler; EDFA, erbium-doped fiber application amplifier; PD, photodiodes; LF, low-pass filter; OSC, digital oscilloscopes; PC, computer for further processing.</p>
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<p>Measurement principle and processing diagram for distance measurement.</p>
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<p>(<b>a</b>) Beat spectrum of the <math display="inline"><semantics> <mrow> <mi>OF</mi> <msub> <mi mathvariant="normal">C</mi> <mrow> <mn>1</mn> <mspace width="4.pt"/> <mspace width="-0.166667em"/> <mspace width="-0.166667em"/> <mo>_</mo> <mspace width="-0.166667em"/> <mspace width="-0.166667em"/> <mspace width="4.pt"/> <mi>mea</mi> </mrow> </msub> </mrow> </semantics></math> beam, <math display="inline"><semantics> <mrow> <mi>OF</mi> <msub> <mi mathvariant="normal">C</mi> <mrow> <mn>1</mn> <mspace width="4.pt"/> <mspace width="-0.166667em"/> <mspace width="-0.166667em"/> <mo>_</mo> <mspace width="-0.166667em"/> <mspace width="-0.166667em"/> <mspace width="4.pt"/> <mi>ref</mi> </mrow> </msub> </mrow> </semantics></math> beam, and <math display="inline"><semantics> <mrow> <mi>OF</mi> <msub> <mi mathvariant="normal">C</mi> <mn>2</mn> </msub> </mrow> </semantics></math> beam after low-pass filtering. (<b>b</b>) Wrapped phase obtained by the Hilbert transform. (<b>c</b>) Unwrapped phase and the fit line. (<b>d</b>) The relationship between the varied <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mo>_</mo> <mi>r</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>d</mi> <msub> <mi>ϕ</mi> <mi>n</mi> </msub> <mo>/</mo> <mi>d</mi> <mi>n</mi> </mrow> </semantics></math> when <math display="inline"><semantics> <msub> <mi>D</mi> <mrow> <mi>p</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> </semantics></math> = 2,400,000.0 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m.</p>
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22 pages, 13671 KiB  
Article
Frequency Comb Generation Based on Brillouin Random Lasing Oscillation and Four-Wave Mixing Assisted with Nonlinear Optical Loop Mirror
by Yuxi Pang, Shaonian Ma, Qiang Ji, Xian Zhao, Yongfu Li, Zengguang Qin, Zhaojun Liu and Yanping Xu
Photonics 2023, 10(3), 296; https://doi.org/10.3390/photonics10030296 - 11 Mar 2023
Cited by 5 | Viewed by 1942
Abstract
A frequency comb generator (FCG) based on dual-cavity Brillouin random fiber lasing oscillation in the 1.5 μm telecon spectral window is established and experimentally demonstrated. In the half-open main cavity of the dual cavity, the stimulated Brillouin scattering in highly nonlinear fiber (HNLF) [...] Read more.
A frequency comb generator (FCG) based on dual-cavity Brillouin random fiber lasing oscillation in the 1.5 μm telecon spectral window is established and experimentally demonstrated. In the half-open main cavity of the dual cavity, the stimulated Brillouin scattering in highly nonlinear fiber (HNLF) and Rayleigh scattering in single-mode fiber are employed to provide sufficient Brillouin gain and the randomly distributed feedback, respectively, for random mode resonance. The sub-cavity includes an Er-doped fiber amplifier to couple back and boost lower-order Stokes and anti-Stokes light for the cascade of stimulated Brillouin scattering to generate multiple higher-order Stokes and anti-Stokes light. Meanwhile, efficient four-wave mixing is stimulated in the HNLF-based main cavity, further enhancing the number and intensity of the resonant Stokes and anti-Stokes light. By taking advantages of the unique transmission characteristics of nonlinear optical loop mirrors, the power deviation between Stokes and anti-Stokes lines is further optimized with 17 orders of stable Stokes lines and 15 orders of stable anti-Stokes lines achieved within the 10 dB power deviation, with maximum optical signal-to-noise ratio (OSNR) of ~22 dB and ~17 dB and minimum OSNR of ~10 dB and ~7.5 dB for Stokes and anti-Stokes lines, respectively. In addition, the dynamic characteristics of the proposed FCG have been experimentally investigated. Such an FCG with fixed frequency spacing will find promising applications in fields of optical communication, microwave, optical sensing, etc. Full article
(This article belongs to the Special Issue Fiber Laser and Their Applications)
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<p>Experimental setup of the proposed FCG. (ISO: isolator, OC: optical coupler (OC1 and OC2: 2 × 2 50:50, OC3: 2 × 2 70:30), EDFA: erbium-doped fiber amplifier, VOA: variable optical attenuator, PC: polarization controller, CIR: circulator, HNLF: highly nonlinear fiber, SMF: single-mode fiber, NOLM: nonlinear optical loop mirror).</p>
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<p>Simulation of the transmission characteristic of NOLM as a function of input power for different <span class="html-italic">θ</span> with (<b>a</b>) 75 km long and (<b>b</b>) 10 km long delay fiber, respectively.</p>
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<p>Simulation of the transmission characteristic of NOLM with different coupling ratios of OC3 as a function of input power for different <span class="html-italic">θ</span> of (<b>a</b>) 0.5π, (<b>b</b>) 0.667π, (<b>c</b>) π, (<b>d</b>) 1.333π and (<b>e</b>) 1.5π with 10 km long delay fiber.</p>
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<p>Optical spectrum of (<b>a</b>) forward-propagating frequency comb in 12 nm wavelength span, (<b>b</b>) forward-propagating frequency comb in 2.2 nm wavelength span, (<b>c</b>) backward-propagating frequency comb in 12 nm wavelength span and (<b>d</b>) backward-propagating frequency comb in 2.2 nm wavelength span.</p>
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<p>Optical spectrum of (<b>a</b>) forward-propagating frequency comb in 12 nm wavelength span, (<b>b</b>) forward-propagating frequency comb in 2.2 nm wavelength span, (<b>c</b>) backward-propagating frequency comb in 12 nm wavelength span and (<b>d</b>) backward-propagating frequency comb in 2.2 nm wavelength span.</p>
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<p>Optical spectrum evolution of (<b>a</b>) forward-propagating and (<b>b</b>) backward-propagating frequency combs in 2.6 nm wavelength span with the increase of EDFA output power from 150 mW to 850 mW.</p>
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<p>Optical spectrum comparison between (<b>a</b>) forward-propagating and backward-propagating frequency combs with EDFA output power of 900 mW; (<b>b</b>) forward-propagating frequency combs with or without NOLM.</p>
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<p>(<b>a</b>) DSH beating RF spectra of the pump laser and the 1st~7th order Stokes lines of the proposed FCG for comparison; (<b>b</b>–<b>h</b>) DSH beating RF spectra of the 1st~7th order Stokes lines of the proposed FCG, respectively.</p>
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<p>(<b>a</b>) DSH beating RF spectra of the pump laser and the 1st~7th order Stokes lines of the proposed FCG for comparison; (<b>b</b>–<b>h</b>) DSH beating RF spectra of the 1st~7th order Stokes lines of the proposed FCG, respectively.</p>
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<p>DSH beating RF spectra of (<b>a</b>) the pump laser and the 1st~4th order anti-Stokes lines of the proposed FCG for comparation; (<b>b</b>–<b>e</b>) DSH beating RF spectra of the 1st~4th order anti-Stokes lines of the proposed FCG; (<b>f</b>) comparison of the 1st-order-Stokes line and the 1st-order-anti-Stokes line.</p>
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<p>Relative intensity noise of (<b>a</b>) the Stokes random emissions of the first seven orders and the pump laser and (<b>b</b>) the anti-Stokes random emissions of the first four orders and the pump laser.</p>
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<p>Frequency noise of (<b>a</b>) Stokes light of the first five orders and the pump laser and (<b>b</b>) the anti-Stokes light of the first three orders and the pump laser.</p>
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<p>Temporal traces of 1st-order Stokes light in generated frequency combs at the EDFA output power of (<b>a</b>) 350 mW, (<b>b</b>) 375 mW, (<b>c</b>) 400 mW, (<b>d</b>) 425 mW and (<b>e</b>) 450 mW, and at the pump power of 3 mW.</p>
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<p>Temporal trace of first-order Stokes light in generated FCG at the pump power of (<b>a</b>) 3 mW, (<b>b</b>) 3.5 mW, (<b>c</b>) 4 mW, (<b>d</b>) 4.5 mW and (<b>e</b>) 5 mW, and at the EDFA output power of 450 mW.</p>
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<p>(<b>a-1</b>–<b>g-1</b>) Temporal trace and (<b>a-2</b>–<b>g-2</b>) intensity distribution of 1st-order~7th-order Stokes light in generated FCG.</p>
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<p>(<b>a-1</b>–<b>d-1</b>) Temporal trace and (<b>a-2</b>–<b>d-2</b>) intensity distribution of 1st-order~4th-order anti-Stokes lines in the proposed FCG.</p>
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10 pages, 10655 KiB  
Communication
Mode-Locked Fiber Laser Sensors with Orthogonally Polarized Pulses Circulating in the Cavity
by Hanieh Afkhamiardakani and Jean-Claude Diels
Sensors 2023, 23(5), 2531; https://doi.org/10.3390/s23052531 - 24 Feb 2023
Viewed by 1527
Abstract
Intracavity phase interferometry is a powerful phase sensing technique using two correlated, counter-propagating frequency combs (pulse trains) in mode-locked lasers. Generating dual frequency combs of the same repetition rate in fiber lasers is a new field with hitherto unanticipated challenges. The large intensity [...] Read more.
Intracavity phase interferometry is a powerful phase sensing technique using two correlated, counter-propagating frequency combs (pulse trains) in mode-locked lasers. Generating dual frequency combs of the same repetition rate in fiber lasers is a new field with hitherto unanticipated challenges. The large intensity in the fiber core, coupled with the nonlinear index of glass, result in a cumulative nonlinear index on axis that dwarfs the signal to be measured. The large saturable gain changes in an unpredictable way the repetition rate of the laser impeding the creation of frequency combs with identical repetition rate. The huge amount of phase coupling between pulses crossing at the saturable absorber eliminates the small signal response (deadband). Although there have been prior observation of gyroscopic response in mode-locked ring lasers, to our knowledge this is the first time that orthogonally polarized pulses were used to successfully eliminate the deadband and obtain a beat note. Full article
(This article belongs to the Special Issue Optical Sensors, Pushing the Limits)
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<p>Absorption spectrum of carbon nanotubes.</p>
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<p>Schematic of the PM fiber laser cavity generating two cross-polarized counter-circulating pulses. WDM: wavelength division multiplexer, G: gain fiber, OC: output coupler, Col: collimator, PBS: polarizing beam splitter, s: s-polarized, p: p-polarized.</p>
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<p>(<b>a</b>) The experimental setup of the free-space part of the orthogonally polarized ring fiber laser to separate the two orthogonal polarizations. Col: collimator, PBS: polarizing beam splitter. (<b>b</b>) The magnified picture of the PBS with the three optical faces labeled.</p>
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<p>Radio frequency spectrum of the pulse trains in opposite directions of the cross-polarized fiber laser with (<b>a</b>) different and (<b>b</b>) the same repetition rates. The scales on the x and y axes are the same in both graphs. CW: clockwise, CCW: counter-clockwise, bandwidth resolution: 100 Hz.</p>
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<p>(<b>a</b>) Oscilloscope trace of the clockwise (upper) and counter-clockwise (lower) pulse trains in cross-polarized fiber laser. (<b>b</b>) The envelope of the modulated pulse train due to the asymmetry in the ring cavity.</p>
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17 pages, 2978 KiB  
Review
Recent Advances and Outlook in Single-Cavity Dual Comb Lasers
by Chenghong Zhang, Fangrui Qu, Peiwen Ou, Haoqi Sun, Shi He and Bo Fu
Photonics 2023, 10(2), 221; https://doi.org/10.3390/photonics10020221 - 18 Feb 2023
Cited by 13 | Viewed by 3490
Abstract
Dual-comb spectroscopy as an emerging tool for spectral analysis has been investigated in a wide range of applications, including absorption spectroscopy, light detection and ranging, and nonlinear spectral imaging. Two mutually coherent combs facilitate high-precision, high-resolution, and broadband spectroscopy. Recently, dual combs generated [...] Read more.
Dual-comb spectroscopy as an emerging tool for spectral analysis has been investigated in a wide range of applications, including absorption spectroscopy, light detection and ranging, and nonlinear spectral imaging. Two mutually coherent combs facilitate high-precision, high-resolution, and broadband spectroscopy. Recently, dual combs generated from a single cavity have become compelling options for dual-comb spectroscopy, enabling huge simplification to measuring systems. Here, we review the progress of single-cavity dual comb lasers in recent years and summarize the distinctive advantages of single-cavity dual combs. First, the principles of optical frequency comb and dual-comb spectroscopy are introduced in time and frequency domains. Then, the implementation techniques and typical applications of single-cavity dual comb lasers are discussed, including directional multiplexing, wavelength multiplexing, polarization multiplexing, and space multiplexing. Finally, an outlook on the development of single-cavity dual combs is presented. Full article
(This article belongs to the Special Issue Mode Locked Fiber Laser)
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<p>The concept of the OFC. (<b>a</b>) Features in the time domain. (<b>b</b>) Comb teeth in the frequency domain.</p>
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<p>The concept of the DCS. (<b>a</b>) The asynchronous optical sampling. (<b>b</b>) The beat frequency produced by two OFCs.</p>
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<p>Experimental results of the DCS based on a bidirectional dual-comb laser. (<b>a</b>) Schematic diagram of the DCS system. (<b>b</b>) Absorption spectra of HCN calculated from single-shot (blue) and 200-times averaged (gray) interferograms, respectively. (<b>c</b>) Extracted absorption lines of 100 Torr, 16.5 cm HCN gas cell measured by proposed the DCS system and the deviations compared to the corresponding NIST SRM2519 data. Reproduced with permission [<a href="#B62-photonics-10-00221" class="html-bibr">62</a>]. Copyright 2016 authors, published by AIP Publishing.</p>
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<p>Experimental results of wavelength-multiplexed dual combs. (<b>a</b>) The schematic diagram of wavelength-multiplexed dual combs. Reproduced with permission [<a href="#B93-photonics-10-00221" class="html-bibr">93</a>]. Copyright 2021 Chinese Optics Letters. (<b>b</b>) The experimental setup of absolute distance measurement based on wavelength-multiplexed dual combs. (<b>c</b>) Top view of the gauge blocks being measured. (<b>d</b>) Measured heights and residuals of the gauge blocks. Reproduced with permission [<a href="#B65-photonics-10-00221" class="html-bibr">65</a>]. Copyright 2020 Elsevier.</p>
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<p>Device and application of laser based on polarization-multiplexing. (<b>a</b>) The setup of laser based on polarization-multiplexing. Reproduced with permission [<a href="#B104-photonics-10-00221" class="html-bibr">104</a>]. Copyright 2022 American Institute of Physics. (<b>b</b>) The experimental setup of wearable and skin-mountable fiber-optic strain sensors interrogated by a dual-comb fiber laser. (<b>c</b>) Profile display of the sensor attached to the volunteer’s neck. (<b>d</b>) Response of the sensor to deep inhalations and exhalations. Reproduced with permission [<a href="#B108-photonics-10-00221" class="html-bibr">108</a>]. Copyright 2019 Wiley.</p>
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<p>Experimental results of space-multiplexed dual combs. (<b>a</b>) The schematic diagram of space-multiplexed dual combs. (<b>b</b>) The absorption spectrum of HCN measured by the DCS. (<b>c</b>) The comparison between the measured P22 absorption line and the counterpart in the HITRAN database. Reproduced with permission [<a href="#B115-photonics-10-00221" class="html-bibr">115</a>]. Copyright 2022 American Institute of Physics.</p>
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20 pages, 8365 KiB  
Article
An Investigation of All Fiber Free-Running Dual-Comb Spectroscopy
by Fu Yang, Yanyu Lu, Guibin Liu, Shaowei Huang, Dijun Chen, Kang Ying, Weiao Qi and Jiaqi Zhou
Sensors 2023, 23(3), 1103; https://doi.org/10.3390/s23031103 - 18 Jan 2023
Cited by 1 | Viewed by 1616
Abstract
A dual-comb spectroscopy (DCS) system uses two phase-locked optical frequency combs with a slight difference in the repetition frequency. The spectrum can be sampled in the optical frequency (OF) domain and reproduces the characteristics in the radio frequency (RF) domain through asynchronous optical [...] Read more.
A dual-comb spectroscopy (DCS) system uses two phase-locked optical frequency combs with a slight difference in the repetition frequency. The spectrum can be sampled in the optical frequency (OF) domain and reproduces the characteristics in the radio frequency (RF) domain through asynchronous optical sampling. Therefore, the DCS system shows great advantages in achieving precision spectral measurement. During application, the question of how to reserve the mutual coherence between the two combs is the key issue affecting the application of the DCS system. This paper focuses on a software algorithm used to realize the mutual coherence of the two combs. Therefore, a pair of free-running large anomalous dispersion fiber combs, with a center wavelength of approximately 1064 nm, was used. After the signal process, the absorption spectra of multiple species were simultaneously obtained (simulated using the reflective spectra of narrow-bandwidth fiber Bragg gratings, abbreviated as FBG). The signal-to-noise ratio (SNR) could reach 13.97 dB (25) during the 100 ms sampling time. In this study, the feasibility of the system was first verified through the simulation system; then, a principal demonstration experiment was successfully executed. The whole system was connected by the optical fiber without additional phase-locking equipment, showing promise as a potential solution for the low-cost and practical application of DCS systems. Full article
(This article belongs to the Section Optical Sensors)
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<p>Principle of dual-comb interference [<a href="#B22-sensors-23-01103" class="html-bibr">22</a>]. (<b>a</b>) Time domain of the two combs’ periodic sequence; (<b>b</b>) time domain of the interference envelope diagram in the RF; (<b>c</b>) OF domains of the LO and SIG combs; (<b>d</b>) RF spectrum of SIG.</p>
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<p>Diagram of the DCS system.</p>
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<p>Optical spectra of the reference path (blue) and signal path (red).</p>
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<p>Simulation of the DCS system’s RF spectra with jitters. (<b>a</b>) Reference path spectrum, (<b>b</b>) signal path spectrum.</p>
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<p>Simulation of the reference path signal. (<b>a</b>) Raw time domain signal; (<b>b</b>) raw frequency domain signal; (<b>c</b>) corrected time domain signal; (<b>d</b>) corrected frequency domain signal; (<b>e</b>) Magnified view of red rectangle shown in (<b>b</b>); (<b>f</b>) Magnified view of red rectangle shown in (<b>d</b>).</p>
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<p>Simulation of the signal path signal. (<b>a</b>) Raw time domain signal; (<b>b</b>) raw frequency domain signal; (<b>c</b>) corrected time domain signal; (<b>d</b>) corrected frequency domain signal; (<b>e</b>) Magnified view of red rectangle shown in (<b>b</b>); (<b>f</b>) Magnified view of red rectangle shown in (<b>d</b>).</p>
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<p>(<b>a</b>) Normalized RF spectra of simulation signal; (<b>b</b>) Magnified view of the components.</p>
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<p>Transmittance spectrum of the simulation signal.</p>
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<p>Simulation inversion from the RF domain to the OF domain.</p>
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<p>Real experiment system schematic.</p>
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<p>Phase noise measurement of the large anomalous dispersion fiber comb used in this work and another typical dispersion-managed fiber comb [<a href="#B32-sensors-23-01103" class="html-bibr">32</a>].</p>
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<p>Experiment of the reference path signal. (<b>a</b>) Raw time domain signal; (<b>b</b>) raw frequency domain signal; (<b>c</b>) corrected time domain signal; (<b>d</b>) corrected frequency domain signal; (<b>e</b>) Magnified view of red rectangle shown in (<b>b</b>); (<b>f</b>) Magnified view of red rectangle shown in (<b>d</b>).</p>
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<p>Experiment of the signal path signal. (<b>a</b>) Raw time domain signal; (<b>b</b>) raw frequency domain signal; (<b>c</b>) corrected time domain signal; (<b>d</b>) corrected frequency domain signal; (<b>e</b>) Magnified view of red rectangle shown in (<b>b</b>); (<b>f</b>) Magnified view of red rectangle shown in (<b>d</b>).</p>
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<p>(<b>a</b>) Normalized spectrum of the experiment signal. (<b>b</b>) Magnified view of the components.</p>
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<p>Normalized transmittance spectrum of the experiment signal.</p>
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<p>Experiment inversion from the RF domain to the OF domain.</p>
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<p>Comb component after the signal process in the experiment: (<b>a</b>): around the absorption peak, (<b>b</b>): around the peak of the whole spectrum.</p>
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<p>Comb component after the signal process in the experiment: (<b>a</b>): around the absorption peak, (<b>b</b>): around the peak of the whole spectrum.</p>
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<p>SNR varies with the sampling time.</p>
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11 pages, 3288 KiB  
Article
Photonic Integrated Frequency Shifter Based on Double Side Band Modulation: Performance Analysis
by Andrés Betancur-Pérez, Cristina de Dios and Pablo Acedo
Photonics 2022, 9(11), 793; https://doi.org/10.3390/photonics9110793 - 25 Oct 2022
Viewed by 2264
Abstract
In this research, we present an analysis of a photonic integrated frequency shifter as a stage for a THz dual comb generator. We studied the performance of the PIC by simulating it with standard building blocks, and aimed toward an improvement of the [...] Read more.
In this research, we present an analysis of a photonic integrated frequency shifter as a stage for a THz dual comb generator. We studied the performance of the PIC by simulating it with standard building blocks, and aimed toward an improvement of the output signal quality. We revised two approaches of the PIC by simulating two modes of generating a double side band modulation suppressed carrier (DSB-SC) with a Mach Zehnder modulator structure (MZM). One approach was using a single Electro-Optic Phase Modulator (EOPM) on an MZM structure (SE-MZM), and the other one was using Double EOPM (DE-MZM). We found a cleaner spectrum with the DE-MZM, since this structure is usually applied to reduce the chirp effect in optical communication systems. We obtained 23 dB of side mode suppression ratio SMSR with one filter, and 44 dB of SMSR with a two-stage filter. In the case of DE-MZM, we obtained a clean tone on intermediate frequency (IF) free of spurious sidebands and comb in IF frequency with 10 dB more power compared to SE-MZM. Full article
(This article belongs to the Section Optical Communication and Network)
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<p>(<b>a</b>) Double EOPM-MZM architecture (DE-MZM). Adding one EOPM operated with a signal 180° degrees of phase difference to that of the other EOPM enables push-pull operation with proper bias. This operation mitigates the chirp effect induced when the beam is phase modulated. (<b>b</b>) Single EOPM-MZM architecture (SE-MZM). This is the simplest Mach-Zehnder modulator structure to build and operate with one EOPM, but the chirp is not controlled. For push-pull operation, both EOPM must be biased on different operative points of the characteristic curve as the EOPMs work only with negative voltage.</p>
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<p>(<b>a</b>) System architecture, including the comb generator stage using two phase modulators. (<b>b</b>) Zoom into Frequency shifter stage. The spectral behavior is described stage by stage. Both MZMs (Mach-Zehnder Modulators) are operated with RF driving frequencies equal to <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>s</mi> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>s</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>. The difference between these frequencies will be the IF frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>I</mi> <mi>F</mi> </mrow> </msub> </mrow> </semantics></math>, where the shrunken comb will be centered. These frequencies should be high enough to ease the filtering with the FSR (Free Spectral Range) of the AMZI (Asymmetric Mach-Zehnder Interferometer). The AMZIs are tuned with a DC voltage until it filters one of the sidebands that both MZMs deliver. The EOPMs (Electro-Optic Phase Modulator) on the comb generation stage are driven with RF voltages equal to <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>r</mi> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>r</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>. The difference between these two repetition frequencies will be the repetition of the shrunken comb equal to <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mi>r</mi> </msub> </mrow> </semantics></math>. Since we need to generate a dual comb, the phase modulators for comb generation should be just after the frequency shifter stage. If a simple electro-optic frequency shifter or an electro-optic modulator for telecommunications is required, we can disable one branch by tuning the TC (Tunable Coupler) to direct the beam through one of the optical paths and leave the EOPM free, with no modulation applied. SOAs (Semiconductor Optical Amplifiers) are utilized to compensate for losses and to absorb the power remaining of the disabled branch.</p>
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<p>AMZI: Asymmetric Mach-Zehnder Interferometer. EOPM: Phase Modulator. The FSR depends on the length difference between the two paths. By applying voltage on the EOPM, we can adjust the central frequency of the filter. This is an optical filter with a simplified structure and operation.</p>
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<p>(<b>a</b>) Characteristic curve of the SE-MZM structure. (<b>b</b>) Characteristic curve of the DE-MZM structure. (<b>c</b>) DSB-SC spectrum of the SE-MZM approach. (<b>d</b>) DSB-SC spectrum of the DE-MZM approach.</p>
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<p>Frequency shift effect. SMSR after filter. (<b>a</b>) SE-MZM output optical spectrum. (<b>b</b>) DE-MZM output optical spectrum. (<b>c</b>) DE-MZM output optical spectrum filtered with two cascaded AMZI filters. (<b>d</b>) SE-MZM electrical spectrum of <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>I</mi> <mi>F</mi> </mrow> </msub> </mrow> </semantics></math>, SMSR=36 dB. (<b>e</b>) DE-MZM electrical spectrum of <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>I</mi> <mi>F</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) Optical Dual-Comb with SE-MZM. (<b>b</b>) Optical Dual-Comb with DE-MZM. (<b>c</b>) Comb in IF frequency, centered at 1 MHz when operated with the SE-MZM approach. (<b>d</b>) Comb in IF frequency, centered at 1 MHz operated with the DE-MZM approach. Each one of the spurious sidebands obtained with DSB-SC modulation has a comb associated after they pass through the EOPM. In the case of DE-MZM, the combs are more separated than in the case of the SE-MZM. This means that all the mixing products are also far apart from the main set in the case of the DE-MZM approach. It can be observed that the DE-MZM structure offers an IF comb with more power (10 dB more than in the case of SE-MZM).</p>
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<p>On the black port, there will be DC signals. The electrical waveguides for the RF signals should have the same length on the respective MZM; otherwise, phase will need to be adjusted. (<b>Left</b>) Packaging of the DE-MZM FS. (<b>Right</b>) Packaging of the SE-MZM FS. In this representation, we are not including the RF ports for the EOPM used for comb generation.</p>
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<p>A radiography of the electrical spectrum after the dual comb is mixed. <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>s</mi> </msub> </mrow> </semantics></math> is the frequency shift applied in the FS stage, which is 1 MHz. <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mi>r</mi> </msub> </mrow> </semantics></math> is the repetition frequency difference between the two RF signals applied on the comb generation stage (the two EOPM after the FS). In this case, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>10</mn> <mo> </mo> <mi>kHz</mi> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>r</mi> </msub> </mrow> </semantics></math> is the repetition frequency of the RF signals applied in the comb generation stage. In this case, <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>500</mn> <mo> </mo> <mi>MHz</mi> </mrow> </semantics></math>.</p>
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8 pages, 3255 KiB  
Article
Dual Optical Frequency Comb Generation with Dual Cascaded Difference Frequency Generation
by Yanli Yin, Kaiwu Wang, Gege Zhang, Zhongyang Li, Pibin Bing, Sheng Yuan, Anfu Zhu, Degang Xu and Jianquan Yao
Crystals 2022, 12(10), 1392; https://doi.org/10.3390/cryst12101392 - 1 Oct 2022
Cited by 1 | Viewed by 1505
Abstract
In this work, we propose a novel dual optical frequency comb (DOFC) generation scheme based on dual cascaded difference frequency generation (DCDFG). Feasible designs are introduced that enable the two sets of cascaded optical waves, initially generated by DCDFG in an aperiodically periodically [...] Read more.
In this work, we propose a novel dual optical frequency comb (DOFC) generation scheme based on dual cascaded difference frequency generation (DCDFG). Feasible designs are introduced that enable the two sets of cascaded optical waves, initially generated by DCDFG in an aperiodically periodically poled lithium niobate (APPLN) crystal with a pump wave and two signal waves, then transferred to high-order Stokes waves by oscillations of cascaded Stokes waves and the optimization of phase mismatching of each-order DCDFG; finally, a DOFC was constructed. We demonstrate a high-performance DOFC with characteristics of high repetition frequency difference, tunable repetition frequency difference, high flatness, and a tunable spectral distribution range by providing a theoretical framework. We argue that the scheme proposed in this work is promising for achieving a high-quality DOFC. Full article
(This article belongs to the Special Issue Nonlinear Crystals for Terahertz Generation)
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<p>Schematic diagram of DOFC generation by DCDFG. <span class="html-italic">ω</span><sub>0</sub> and <span class="html-italic">ω</span><sub>a,1</sub> generate a set of cascaded optical waves <span class="html-italic">ω</span><sub>a,<span class="html-italic">m</span></sub> and THz wave <span class="html-italic">ω</span><sub>T1</sub>, respectively. <span class="html-italic">ω</span><sub>0</sub> and <span class="html-italic">ω</span><sub>b,1</sub> generate a set of cascaded optical waves <span class="html-italic">ω</span><sub>b,<span class="html-italic">m</span></sub> and THz wave <span class="html-italic">ω</span><sub>T2</sub>, respectively. (<b>a</b>) Schematic diagram of a bow-tie resonant cavity for cascaded optical Stokes waves; C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub>, and C<sub>4</sub> are resonant cavity mirrors, and APPLN is a nonlinear optical crystal. (<b>b</b>) The interaction of the two sets of <span class="html-italic">ω</span><sub>a,1</sub> and <span class="html-italic">ω</span><sub>b,<span class="html-italic">m</span></sub> generating DOFC; <span class="html-italic">N</span> is the number of oscillations of cascaded optical waves <span class="html-italic">ω</span><sub>a/b,<span class="html-italic">m</span></sub>.</p>
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<p>Evolution of DOFC generated by DCDFG within the OPO. <span class="html-italic">m</span> = 200, <span class="html-italic">L</span> = 6 cm, <span class="html-italic">I</span><sub>0</sub> = 100 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>1</sub> = 1 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>2</sub> = 1 MW/cm<sup>2</sup>. (<b>a</b>) Evolution of <span class="html-italic">ω</span><sub>a,<span class="html-italic">m</span></sub> and <span class="html-italic">ω</span><sub>b,<span class="html-italic">m</span></sub> with oscillation number <span class="html-italic">N</span>. (<b>b</b>) Spectral distribution of <span class="html-italic">ω</span><sub>a,<span class="html-italic">m</span></sub> and <span class="html-italic">ω</span><sub>b,<span class="html-italic">m</span></sub> with <span class="html-italic">N</span> = 200; the range covered by the dashed box was DOFC within 1 dB flatness. (<b>c</b>) Enlargement of the range covered by the dashed box in (<b>b</b>).</p>
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<p>Evolution of DOFC generated by DCDFG within the OPO. <span class="html-italic">m</span> = 200, <span class="html-italic">L</span> = 6 cm, <span class="html-italic">I</span><sub>0</sub> = 100 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>1</sub> = 1 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>2</sub> = 1 MW/cm<sup>2</sup>. (<b>a</b>) Evolution of <span class="html-italic">ω</span><sub>a,<span class="html-italic">m</span></sub> and <span class="html-italic">ω</span><sub>b,<span class="html-italic">m</span></sub> with oscillation number <span class="html-italic">N</span>. (<b>b</b>) Spectral distribution of <span class="html-italic">ω</span><sub>a,<span class="html-italic">m</span></sub> and <span class="html-italic">ω</span><sub>b,<span class="html-italic">m</span></sub> with <span class="html-italic">N</span> = 200; the range covered by the dashed box was DOFC within 1 dB flatness. (<b>c</b>) Enlargement of the range covered by the dashed box in (<b>b</b>).</p>
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<p>Spectral distribution of DOFC with different cascading order <span class="html-italic">m</span>, cascading order <span class="html-italic">m</span><sub>1</sub> = 50, <span class="html-italic">m</span><sub>2</sub> = 100, <span class="html-italic">m</span><sub>3</sub> = 150, <span class="html-italic">m</span><sub>4</sub> = 200, <span class="html-italic">m</span><sub>5</sub> = 250, <span class="html-italic">L</span> = 6 cm, <span class="html-italic">N</span> = 200, <span class="html-italic">I</span><sub>0</sub> = 100 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>1</sub> = 1 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>2</sub> = 1 MW/cm<sup>2</sup>. (<b>a</b>) Spectral distribution of DOFC with different cascading order <span class="html-italic">m</span>; the range covered by the dashed box was DOFC within 1 dB flatness. (<b>b</b>) Enlargement of the dashed box in (<b>a</b>).</p>
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<p>Spectral distribution of DOFC with different crystal lengths <span class="html-italic">L</span>. Crystal length <span class="html-italic">L</span><sub>1</sub> = 4.0 cm, <span class="html-italic">L</span><sub>2</sub> = 4.5 cm, <span class="html-italic">L</span><sub>3</sub> = 5.0 cm, <span class="html-italic">L</span><sub>4</sub> = 5.5 cm, <span class="html-italic">L</span><sub>5</sub> = 6.0 cm, <span class="html-italic">m</span> = 200, <span class="html-italic">N</span> = 200, <span class="html-italic">I</span><sub>0</sub> = 100 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>1</sub> = 1 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>2</sub> = 1 MW/cm<sup>2</sup>. (a) Spectral distribution of DOFC with different crystal lengths <span class="html-italic">L</span>; the range covered by the dashed box was DOFC within 1 dB flatness. (<b>b</b>) Enlargement of the dashed box in (<b>a</b>).</p>
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<p>Evolution process of DOFC generated by DCDFG within the OPO. <span class="html-italic">m</span> = 200, <span class="html-italic">L</span> = 6 cm, <span class="html-italic">I</span><sub>0</sub> = 100 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>1</sub> = 1 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>2</sub> = 1 MW/cm<sup>2</sup>; <span class="html-italic">ω</span><sub>0</sub> and <span class="html-italic">ω</span><sub>a,1</sub> are 281.9 THz and 281.8 THz, respectively. (<b>a</b>) Evolution of DOFC generated by DCDFG within the OPO with oscillation number <span class="html-italic">N</span>; <span class="html-italic">ω</span><sub>b,1</sub> = 281.7997 THz, Δ<span class="html-italic">f<sub>rep</sub></span> = 300 MHz. (<b>b</b>) Evolution of DOFC generated by DCDFG within the OPO with oscillation number <span class="html-italic">N</span>; <span class="html-italic">ω</span><sub>b,1</sub> = 281.7996 THz, Δ<span class="html-italic">f<sub>rep</sub></span> = 400 MHz. (<b>c</b>) Spectral distribution of DOFC with <span class="html-italic">N</span> = 200; the dashed box indicates Δ<span class="html-italic">f<sub>rep</sub></span> = 300 MHz within 1 dB flatness, and the solid box indicates Δ<span class="html-italic">f<sub>rep</sub></span> = 400 MHz within 1 dB flatness.</p>
Full article ">Figure 5 Cont.
<p>Evolution process of DOFC generated by DCDFG within the OPO. <span class="html-italic">m</span> = 200, <span class="html-italic">L</span> = 6 cm, <span class="html-italic">I</span><sub>0</sub> = 100 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>1</sub> = 1 MW/cm<sup>2</sup>, <span class="html-italic">I</span><sub>2</sub> = 1 MW/cm<sup>2</sup>; <span class="html-italic">ω</span><sub>0</sub> and <span class="html-italic">ω</span><sub>a,1</sub> are 281.9 THz and 281.8 THz, respectively. (<b>a</b>) Evolution of DOFC generated by DCDFG within the OPO with oscillation number <span class="html-italic">N</span>; <span class="html-italic">ω</span><sub>b,1</sub> = 281.7997 THz, Δ<span class="html-italic">f<sub>rep</sub></span> = 300 MHz. (<b>b</b>) Evolution of DOFC generated by DCDFG within the OPO with oscillation number <span class="html-italic">N</span>; <span class="html-italic">ω</span><sub>b,1</sub> = 281.7996 THz, Δ<span class="html-italic">f<sub>rep</sub></span> = 400 MHz. (<b>c</b>) Spectral distribution of DOFC with <span class="html-italic">N</span> = 200; the dashed box indicates Δ<span class="html-italic">f<sub>rep</sub></span> = 300 MHz within 1 dB flatness, and the solid box indicates Δ<span class="html-italic">f<sub>rep</sub></span> = 400 MHz within 1 dB flatness.</p>
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