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Optimizing wide-range laser frequency noise characterization via delayed self-heterodyne

Yiming Wang1, 2, Gang Zhao3, Ruchan Cai1, 2, Peng Chen1, 2, Jia Wang1, 2 and Liang Xie1, 2,

+ Author Affiliations

 Corresponding author: Liang Xie, xiel@semi.ac.cn

DOI: 10.1088/1674-4926/26030039CSTR: 32376.14.1674-4926.26030039

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Abstract: Systematic optimization of the delayed self-heterodyne method for laser frequency noise characterization is investigated across an extensive linewidth range (100 Hz to 10 MHz). By evaluating various fiber lengths, window functions, and five demodulation algorithms, we identify a critical trade-off: long fibers enhance sensitivity for narrow-linewidth lasers but exacerbate spectral leakage in broad-linewidth sources. Our findings demonstrate that Hanning and Blackman windows effectively suppress this leakage, ensuring measurement consistency across different delay lengths. Among the evaluated algorithms, the Hilbert transform offers the superior balance of high-frequency accuracy and computational efficiency. Validated under low-power conditions, this optimized framework provides a robust and power-independent methodology for precise FN analysis, offering significant guidance for high-performance laser development.

Key words: laser frequency noise, delayed self-heterodyne, spectral leakage suppression, demodulation algorithms



[1]
Chen Z F, Wang K K, Chen Q A, et al. Nano-ITLA based on thermo-optically tuned multi-channel interference widely tunable laser. J Lightwave Technol, 2023, 41(16): 5405 doi: 10.1109/JLT.2023.3261897
[2]
Chauhan N, Isichenko A, Liu K K, et al. Visible light photonic integrated Brillouin laser. Nat Commun, 2021, 12(1): 4685 doi: 10.1038/s41467-021-24926-8
[3]
Chen J Q, Chen C, Guo Q, et al. Linear polarization and narrow-linewidth external-cavity semiconductor laser based on birefringent Bragg grating optical feedback. Opt Laser Technol, 2024, 170: 110211 doi: 10.1016/j.optlastec.2023.110211
[4]
Kikuchi K. Fundamentals of coherent optical fiber communications. J Lightwave Technol, 2016, 34(1): 157 doi: 10.1109/JLT.2015.2463719
[5]
Okoshi T, Kikuchi K, Nakayama A. Novel method for high resolution measurement of laser output spectrum. Electron Lett (UK), 1980, 16(16): 630
[6]
Di Domenico G, Schilt S, Thomann P. Simple approach to the relation between laser frequency noise and laser line shape. Appl Opt, 2010, 49(25): 4801 doi: 10.1364/AO.49.004801
[7]
Horak P, Loh W H. On the delayed self-heterodyne interferometric technique for determining the linewidth of fiber lasers. Opt Express, 2006, 14(9): 3923 doi: 10.1364/oe.14.003923
[8]
Mercer L B. 1/f frequency noise effects on self-heterodyne linewidth measurements. J Lightwave Technol, 1991, 9(4): 485 doi: 10.1109/50.76663
[9]
Ma W C, Xiong B, Sun C Z, et al. Laser frequency noise characterization by self-heterodyne with both long and short delay. Appl Opt, 2019, 58(13): 3555 doi: 10.1364/AO.58.003555
[10]
Zhao Z A, Bai Z X, Jin D, et al. Narrow laser-linewidth measurement using short delay self-heterodyne interferometry. Opt Express, 2022, 30(17): 30600 doi: 10.1364/OE.455028
[11]
Zhang C Z, Huang L G, Guan T Y, et al. Laser coherence linewidth measurement based on deterioration of coherent envelope. Opt Laser Technol, 2024, 172: 110498 doi: 10.1016/j.optlastec.2023.110498
[12]
Zhao Z A, Bai Z X, Jin D, et al. The influence of noise floor on the measurement of laser linewidth using short-delay-length self-heterodyne/homodyne techniques. Micromachines, 2022, 13(8): 1311 doi: 10.3390/mi13081311
[13]
Wang D D, Jiang Y F, Gu H, et al. Improvement and analysis of a recirculating delayed self-heterodyne interferometer for laser linewidth measurement. Opt Fiber Technol, 2022, 71: 102945 doi: 10.1016/j.yofte.2022.102945
[14]
Tsuchida H. Simple technique for improving the resolution of the delayed self-heterodyne method. Opt Lett, 1990, 15(11): 640 doi: 10.1364/OL.15.000640
[15]
Daino B, Spano P, Tamburrini M, et al. Phase noise and spectral line shape in semiconductor lasers. IEEE J Quantum Electron, 1983, 19(3): 266 doi: 10.1109/JQE.1983.1071842
[16]
Zhou Q, Qin J, Xie W L, et al. Dynamic frequency-noise spectrum measurement for a frequency-swept DFB laser with short-delayed self-heterodyne method. Opt Express, 2015, 23(22): 29245 doi: 10.1364/OE.23.029245
[17]
Shi H B, Chang P Y, Wang Z Y, et al. Frequency stabilization of a cesium faraday laser with a double-layer vapor cell as frequency reference. IEEE Photonics J, 2022, 14(6): 1561006 doi: 10.1109/jphot.2022.3221494
[18]
Tombez L, Schilt S, Di Francesco J, et al. Linewidth of a quantum-cascade laser assessed from its frequency noise spectrum and impact of the current driver. Appl Phys B, 2012, 109: 407 doi: 10.1007/s00340-012-5005-x
[19]
Li B H, Yuan Z Q, Jin W, et al. High-coherence hybrid-integrated 780 nm source by self-injection-locked second-harmonic generation in a high-Q silicon-nitride resonator. Optica, 2023, 10(9): 1241 doi: 10.1364/OPTICA.498391
[20]
Chen J Q, Chen C, Guo Q, et al. A 1-μm-band injection-locked semiconductor laser with a high side-mode suppression ratio and narrow linewidth. Sensors, 2022, 22(23): 9239 doi: 10.3390/s22239239
[21]
Yuan Z Q, Wang H M, Liu P, et al. Correlated self-heterodyne method for ultra-low-noise laser linewidth measurements. Opt Express, 2022, 30(14): 25147 doi: 10.1364/OE.458109
[22]
Mertenskötter L, Kantner M. Frequency noise characterization of narrow-linewidth semiconductor lasers: a bayesian approach. IEEE Photonics J, 2024, 16(3): 0601407 doi: 10.1109/jphot.2024.3385184
[23]
Yao P H, Zhang Z, Zhou J N, et al. Application of sine-cosine demodulation technology in linewidth measurement of narrow linewidth single frequency laser. AOPC 2023: Optic Fiber Gyro, 2023, 1296819
[24]
Camatel S, Ferrero V. Narrow linewidth CW laser phase noise characterization methods for coherent transmission system applications. J Lightwave Technol, 2008, 26(17): 3048 doi: 10.1109/JLT.2008.925046
[25]
Zhang Y H, Cao X H, Chen W, et al. Precise linewidths measurement using short delay self-heterodyne interferometry and multiple peak-to-valley differences. AOPC 2023: AI in Optics and Photonics, 2023, 129660Y
Fig. 1.  (Color online) Schematic diagram of the laser frequency noise measurement principle based on the delayed self-heterodyne (DSH) technique.

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Fig. 2.  (Color online) Theoretical analysis of delay self-heterodyne interferometer. (a) Gain induced by the transfer function as a function of fiber length, (b) Position of periodic interference peaks arising from the transfer function as a function of fiber length

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Fig. 3.  (Color online) (a) Time-domain characteristics of various window functions, (b) Frequency-domain characteristics of various window functions.

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Fig. 4.  (Color online) Experimental setup for laser frequency noise measurement based on the delayed self-heterodyne (DSH) method.

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Fig. 5.  (Color online) Measured power spectral density (PSD) of five lasers with different linewidths obtained from the 5 km delayed self-heterodyne (DSH) measurement system. (a)100-Hz linewidth laser (5-km delay), (b) kHz-range laser (5-km delay), (c) 100-kHz laser (5-km delay), (d) MHz-range laser (5-km delay), (e) 10-MHz laser (5-km delay)

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Fig. 6.  (Color online) Phase demodulation results for lasers with different linewidths using four delay fiber lengths (5 km, 1 km, 10 m and 2 m). (a) Demodulated phase of a 100-Hz linewidth laser at various delay lengths, (b) Demodulated phase of a kHz-range linewidth laser at various delay lengths, (c) Demodulated phase of a 100-kHz linewidth laser at various delay lengths, (d) Demodulated phase of a MHz-range linewidth laser at various delay lengths, (e) Demodulated phase of a 10-MHz linewidth laser at various delay lengths.

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Fig. 7.  (Color online) Frequency noise power spectral density (FN-PSD) for various laser linewidths across four delay fiber lengths after transfer function calibration. (a) Directly reconstructed FN: 100-Hz linewidth laser, (b) Directly reconstructed FN: kHz-range laser, (c) Directly reconstructed FN: 100-kHz laser, (d) Directly reconstructed FN: MHz-range laser, (e) Directly reconstructed FN: 10-MHz laser.

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Fig. 8.  (Color online) Time-domain phase demodulation results after applying different window functions for various laser linewidths and fiber lengths. (a) Windowed phase: 100-Hz laser (various delay lengths), (b) Windowed phase: kHz-range laser (various delay lengths), (c) Windowed phase: 100-kHz laser (various delay lengths), (d) Windowed phase: MHz-range laser (various delay lengths), (e) Windowed phase: 10-MHz laser (various delay lengths).

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Fig. 9.  (Color online) Comparison of FN-PSD results using different window functions to evaluate their effectiveness in suppressing spectral leakage across various laser linewidths. (a) Windowed FN: 100-Hz laser (various delay lengths), (b) Windowed FN: kHz-range laser (various delay lengths), (c) Windowed FN: 100-kHz laser (various delay lengths), (d) Windowed FN: MHz-range laser (various delay lengths), (e) Windowed FN: 10-MHz laser (various delay lengths).

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Fig. 10.  (Color online) Stability of FN-PSD measurements under low input optical power (−6 dBm), confirming power-independent characterization. (a) Windowed FN (Low input power): 100-Hz laser, (b) Windowed FN (Low input power): kHz-range laser.(c) Windowed FN (Low input power): 100-kHz laser, (d) Windowed FN (Low input power): MHz-range laser, (e) Windowed FN (Low input power): 10-MHz laser.

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Fig. 11.  (Color online) Comparison of FN-PSD measurement results under low input optical power (−3 dBm vs.−6 dBm) for Hanning and Hamming windows, demonstrating the power-independence of the noise characterization. (a) FN-PSD of the 100-Hz laser: Hanning vs. Hamming windows under varying power and delay lengths, (b) FN-PSD of the kHz-range laser: Hanning vs. Hamming windows under varying power and delay lengths, (c) FN-PSD of the 100-kHz laser: Hanning vs. Hamming windows under varying power and delay lengths, (d) FN-PSD of the MHz-range laser: Hanning vs. Hamming windows under varying power and delay lengths, (e) FN-PSD of the 10-MHz laser: Hanning vs. Hamming windows under varying power and delay lengths.

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Fig. 12.  (Color online) Comparison of laser frequency noise spectra obtained via five different demodulation algorithms (HT, IQ, HT-DCM, IQ-DCM, and SPLL). (a) FN-PSD: 100-Hz laser (comparison of various demodulation algorithms), (b) FN-PSD: kHz-range laser (comparison of various demodulation algorithms), (c) FN-PSD: 100-kHz laser (comparison of various demodulation algorithms), (d) FN-PSD: MHz-range laser (comparison of various demodulation algorithms), (e) FN-PSD: 10-MHz laser (comparison of various demodulation algorithms).

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Fig. 13.  (Color online) Robustness evaluation of laser frequency noise spectra under extreme low-SNR conditions (−15 dBm input power) obtained via five different demodulation algorithms (HT phase, IQ Phase, HT-DCM, IQ-DCM, and SPLL). The high-power (−3 dBm) HT measurement is plotted in grey as the ground-truth baseline. (a) FN-PSD: narrow-linewidth laser (laser 2) across four delay fiber lengths (5 km, 1 km, 10 m, and 2 m). (b) FN-PSD: broad-linewidth laser (laser 5) across the corresponding four delay fiber lengths.

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Fig. 14.  (Color online) Power evolution of frequency noise spectra for the narrow-linewidth laser (laser 2) across a degenerated input optical power gradient (−3 dBm to −15 dBm) utilizing four different delay fiber lengths (5 km, 1 km, 10 m, and 2 m). (a) FN-PSD evolution: HT phase algorithm, (b) FN-PSD evolution: IQ Phase algorithm, (c) FN-PSD evolution: HT-DCM algorithm, (d) FN-PSD evolution: IQ-DCM algorithm, (e) FN-PSD evolution: SPLL algorithm.

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Fig. 15.  (Color online) Power evolution of frequency noise spectra for the broad-linewidth laser (laser 5) across a degenerated input optical power gradient (−3 dBm to −15 dBm) utilizing four different delay fiber lengths (5 km, 1 km, 10 m, and 2 m). (a) FN-PSD evolution: HT phase algorithm, (b) FN-PSD evolution: IQ Phase algorithm, (c) FN-PSD evolution: HT-DCM algorithm, (d) FN-PSD evolution: IQ-DCM algorithm, (e) FN-PSD evolution: SPLL algorithm.

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Fig. 16.  (Color online) Quantitative robustness evaluation and reconstruction error analysis of five different demodulation algorithms (HT phase, IQ Phase, HT-DCM, IQ-DCM, and SPLL) under varying input optical powers. The top equation defines the logarithmic root mean square error (RMSE) metric. (a) Reconstruction RMSE: narrow-linewidth laser (laser 2, 5 km fiber), (b) Reconstruction RMSE: broad-linewidth laser (laser 5, 5 km fiber).

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Fig. 17.  (Color online) Comparison of the computational processing time required for the five different demodulation algorithms.

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Table 1.   Detailed specifications of the lasers evaluated in this study.

ParameterLaser 1Laser 2Laser 3Laser4Laser5
Laser typeECDLECDLSantec TSLStandard DFBID Photonics
ModelWL-1550-1HzPHX-C-F-MTSL-550INP-DCH-1550CCoBrite Dx4
Wavelength1548 nm1550 nm1550 nm1549 nm1550 nm
Linewidth~100 HzkHz-range~100 kHz~MHz-range10 MHz-range
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Table 2.   Summary guidelines for optimal DSH frequency noise measurement configurations.

Laser linewidth regime Recommended delay fiber length Optimal window function Key physical rationale & pitfalls to avoid
Ultra-narrow-linewidth (sub-kHz, e.g., ~100 Hz) Ultra-long
(e.g., 5 km or longer)		 Hanning,
Blackman
 Requires maximum quadratic physical amplification ($ \propto {\tau }^{2} $) to boost extremely weak intrinsic phase drifts above the detector noise floor. Pitfall: short fibers will completely bury the true signal.
Narrow-linewidth
(1 kHz to ~100 kHz)		 Long
(e.g., 1 km−
5 km)		 Balances physical amplification for low-frequency $ 1/f $ noise with manageable high-frequency spectral leakage. Strong windowing is necessary to suppress sidelobes.
Broad-linewidth
(1 MHz to 10 MHz+)		 Short
(e.g., 2 m−10 m)		 Rapid phase fluctuations cause severe spectral leakage in long fibers, artificially elevating the high-frequency noise floor. Pitfall: strictly avoid rectangular and Hamming windows, as their non-zero boundaries fail to suppress leakage effectively.
DownLoad: CSV
[1]
Chen Z F, Wang K K, Chen Q A, et al. Nano-ITLA based on thermo-optically tuned multi-channel interference widely tunable laser. J Lightwave Technol, 2023, 41(16): 5405 doi: 10.1109/JLT.2023.3261897
[2]
Chauhan N, Isichenko A, Liu K K, et al. Visible light photonic integrated Brillouin laser. Nat Commun, 2021, 12(1): 4685 doi: 10.1038/s41467-021-24926-8
[3]
Chen J Q, Chen C, Guo Q, et al. Linear polarization and narrow-linewidth external-cavity semiconductor laser based on birefringent Bragg grating optical feedback. Opt Laser Technol, 2024, 170: 110211 doi: 10.1016/j.optlastec.2023.110211
[4]
Kikuchi K. Fundamentals of coherent optical fiber communications. J Lightwave Technol, 2016, 34(1): 157 doi: 10.1109/JLT.2015.2463719
[5]
Okoshi T, Kikuchi K, Nakayama A. Novel method for high resolution measurement of laser output spectrum. Electron Lett (UK), 1980, 16(16): 630
[6]
Di Domenico G, Schilt S, Thomann P. Simple approach to the relation between laser frequency noise and laser line shape. Appl Opt, 2010, 49(25): 4801 doi: 10.1364/AO.49.004801
[7]
Horak P, Loh W H. On the delayed self-heterodyne interferometric technique for determining the linewidth of fiber lasers. Opt Express, 2006, 14(9): 3923 doi: 10.1364/oe.14.003923
[8]
Mercer L B. 1/f frequency noise effects on self-heterodyne linewidth measurements. J Lightwave Technol, 1991, 9(4): 485 doi: 10.1109/50.76663
[9]
Ma W C, Xiong B, Sun C Z, et al. Laser frequency noise characterization by self-heterodyne with both long and short delay. Appl Opt, 2019, 58(13): 3555 doi: 10.1364/AO.58.003555
[10]
Zhao Z A, Bai Z X, Jin D, et al. Narrow laser-linewidth measurement using short delay self-heterodyne interferometry. Opt Express, 2022, 30(17): 30600 doi: 10.1364/OE.455028
[11]
Zhang C Z, Huang L G, Guan T Y, et al. Laser coherence linewidth measurement based on deterioration of coherent envelope. Opt Laser Technol, 2024, 172: 110498 doi: 10.1016/j.optlastec.2023.110498
[12]
Zhao Z A, Bai Z X, Jin D, et al. The influence of noise floor on the measurement of laser linewidth using short-delay-length self-heterodyne/homodyne techniques. Micromachines, 2022, 13(8): 1311 doi: 10.3390/mi13081311
[13]
Wang D D, Jiang Y F, Gu H, et al. Improvement and analysis of a recirculating delayed self-heterodyne interferometer for laser linewidth measurement. Opt Fiber Technol, 2022, 71: 102945 doi: 10.1016/j.yofte.2022.102945
[14]
Tsuchida H. Simple technique for improving the resolution of the delayed self-heterodyne method. Opt Lett, 1990, 15(11): 640 doi: 10.1364/OL.15.000640
[15]
Daino B, Spano P, Tamburrini M, et al. Phase noise and spectral line shape in semiconductor lasers. IEEE J Quantum Electron, 1983, 19(3): 266 doi: 10.1109/JQE.1983.1071842
[16]
Zhou Q, Qin J, Xie W L, et al. Dynamic frequency-noise spectrum measurement for a frequency-swept DFB laser with short-delayed self-heterodyne method. Opt Express, 2015, 23(22): 29245 doi: 10.1364/OE.23.029245
[17]
Shi H B, Chang P Y, Wang Z Y, et al. Frequency stabilization of a cesium faraday laser with a double-layer vapor cell as frequency reference. IEEE Photonics J, 2022, 14(6): 1561006 doi: 10.1109/jphot.2022.3221494
[18]
Tombez L, Schilt S, Di Francesco J, et al. Linewidth of a quantum-cascade laser assessed from its frequency noise spectrum and impact of the current driver. Appl Phys B, 2012, 109: 407 doi: 10.1007/s00340-012-5005-x
[19]
Li B H, Yuan Z Q, Jin W, et al. High-coherence hybrid-integrated 780 nm source by self-injection-locked second-harmonic generation in a high-Q silicon-nitride resonator. Optica, 2023, 10(9): 1241 doi: 10.1364/OPTICA.498391
[20]
Chen J Q, Chen C, Guo Q, et al. A 1-μm-band injection-locked semiconductor laser with a high side-mode suppression ratio and narrow linewidth. Sensors, 2022, 22(23): 9239 doi: 10.3390/s22239239
[21]
Yuan Z Q, Wang H M, Liu P, et al. Correlated self-heterodyne method for ultra-low-noise laser linewidth measurements. Opt Express, 2022, 30(14): 25147 doi: 10.1364/OE.458109
[22]
Mertenskötter L, Kantner M. Frequency noise characterization of narrow-linewidth semiconductor lasers: a bayesian approach. IEEE Photonics J, 2024, 16(3): 0601407 doi: 10.1109/jphot.2024.3385184
[23]
Yao P H, Zhang Z, Zhou J N, et al. Application of sine-cosine demodulation technology in linewidth measurement of narrow linewidth single frequency laser. AOPC 2023: Optic Fiber Gyro, 2023, 1296819
[24]
Camatel S, Ferrero V. Narrow linewidth CW laser phase noise characterization methods for coherent transmission system applications. J Lightwave Technol, 2008, 26(17): 3048 doi: 10.1109/JLT.2008.925046
[25]
Zhang Y H, Cao X H, Chen W, et al. Precise linewidths measurement using short delay self-heterodyne interferometry and multiple peak-to-valley differences. AOPC 2023: AI in Optics and Photonics, 2023, 129660Y

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    Received: 24 March 2026 Revised: 23 April 2026 Online: Accepted Manuscript: 14 May 2026

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      Article Navigation >  Journal of Semiconductors  > 2026  > Accepted Manuscript
      Yiming Wang, Gang Zhao, Ruchan Cai, Peng Chen, Jia Wang, Liang Xie. Optimizing wide-range laser frequency noise characterization via delayed self-heterodyne[J]. Journal of Semiconductors, 2026, In Press. doi: 10.1088/1674-4926/26030039 ****Y M Wang, G Zhao, R C Cai, P Chen, J Wang, and L Xie, Optimizing wide-range laser frequency noise characterization via delayed self-heterodyne[J]. J. Semicond., 2026, accepted doi: 10.1088/1674-4926/26030039
      Citation:
      Yiming Wang, Gang Zhao, Ruchan Cai, Peng Chen, Jia Wang, Liang Xie. Optimizing wide-range laser frequency noise characterization via delayed self-heterodyne[J]. Journal of Semiconductors, 2026, In Press. doi: 10.1088/1674-4926/26030039 ****
      Y M Wang, G Zhao, R C Cai, P Chen, J Wang, and L Xie, Optimizing wide-range laser frequency noise characterization via delayed self-heterodyne[J]. J. Semicond., 2026, accepted doi: 10.1088/1674-4926/26030039
      shu

      Optimizing wide-range laser frequency noise characterization via delayed self-heterodyne

      DOI: 10.1088/1674-4926/26030039
      CSTR: 32376.14.1674-4926.26030039
      • 1.

        State Key Laboratory of Optoelectronic Materials and Devices, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

      • 2.

        College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China

      • 3.

        School of Physical Science and Technology, Key Laboratory of Special Functional Materials and Devices, Ministry of Education, Lanzhou University, Lanzhou, 730000, China

      More Information
      • Yiming Wang received his Bachelor of Science degree from the School of Physics and Electronic Engineering, Shanxi University in 2020. He is currently pursuing his Doctor of Philosophy degree at the Institute of Semiconductors, Chinese Academy of Sciences, under the supervision of Professor Liang Xie. His research focuses on laser noise and high-resolution spectroscopy measurement
      • Liang Xie received his Doctor of Philosophy degree from Lanzhou University in 1998.He is currently a Professor at the Institute of Semiconductors, Chinese Academy of Sciences. His research interests include high-speed optoelectronic device packaging and testing, instrument development based on optoelectronic technology, optical communication, and optical sensing technology
      • Corresponding author: xiel@semi.ac.cn
      • Received Date: 2026-03-24
      • Revised Date: 2026-04-23
        • Available Online: 2026-05-14

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