#### For citation:

Skripal A. V., Dobdin S. Y., Dzhafarov A. V., Sadchikova K. A., Feklistov V. B. Distance Measurement with Harmonic Modulation of Self-Mixing Laser Wavelength at External Optical Feedback. *Izvestiya of Saratov University. Physics *, 2020, vol. 20, iss. 2, pp. 84-91. DOI: 10.18500/1817-3020-2020-20-2-84-91

# Distance Measurement with Harmonic Modulation of Self-Mixing Laser Wavelength at External Optical Feedback

**Background and Objectives: **Self-mixing interferometry of absolute distances is currently well represented by the method of frequency modulation of the laser diode supply current (FMCW). In recent years a harmonic modulation of the power current of a self-mixing laser began to be used. The advantage of the harmonic modulation method is due to the absence of the need to adjust the deviation of the radiation wavelength when changing the distance to the reflector. In the laser systems, the level of external optical feedback is an important parameter during interference measurements. The feedback level also affects the type of the self-mixing signal generated by modulation of the wavelength of laser radiation. The aim of this work was to study the effect of the feedback level on the accuracy of absolute distance measurements at the harmonic frequency modulation of laser radiation. **Materials and Methods:** The article presents a method of measuring distances using a semiconductor laser with a harmonic modulation of the radiation wavelength. The technique allows taking into account the influence of the feedback level to improve the accuracy of the measurements. In particular, it is proposed to reduce the feedback level in order to eliminate mode jumps and reduce the frequency shift of the laser diode radiation caused by a change in the concentration of charge carriers in the active region. **Results: **The results of the influence of the feedback level on the shape of the self-mixing signal and on the accuracy of distance measurements have been described. **Conclusion: **Evaluation of the feedback level can be carried out on the basis of the method of decomposition of the self-mixing signal in the Fourier and Bessel series and analysis of sets of spectral harmonics. The feedback level is determined using the values of the RMS deviation calculated from sets of spectral harmonics of the self-mixing signal.

- Amann M. C., Bosch T., Lescure M., Myllyla R., Rioux M. Laser ranging: a critical review of usual technique for distance measurement. Optical Engineering, 2001, vol. 40, iss. 1, pp. 10–19.
- Donati S. Developing self-mixing interferometry for instrumentation and measurements. Laser Photonics Rev., 2012, vol. 6, no. 3, pp. 393–417.
- Berkovic G., Shafi r E. Optical methods for distance and displacement measurements. Adv. Opt. Photonics, 2012, vol. 4, no. 4, pp. 441–471.
- Norgia M., Giuliani G., Donati S. Absolute distance measurement with improved accuracy using laser diode self-mixing interferometry in a closed loop. IEEE Trans. Instrum. Meas., 2007, vol. 56, iss. 5, pp. 1894–1900.
- Zheng J. Analysis of optical frequency-modulated continuouswave interference. Appl. Opt., 2004, vol. 43, iss. 21, pp. 4189–4198.
- Usanov D. A., Skripal An. V., Dobdin S. Yu., Astahov E. I., Kostuchenko I. S., Dzhafarov A. V. Methods of Autodyne Interferometry of the Distance by Injected Current Modulation of a Semiconductor Laser. Izv. Saratov Univ. (N. S.), Ser. Physics, 2018, vol. 18, iss. 3, pp. 189–201 (in Russian). DOI: https://doi.org/10.18500/1817-3020-2018-18-3-189-201
- Sukharev A. G., Napartovich A. P. Harmonic modulation of radiation of an external-feedback semiconductor laser. Quant. Electron., 2007, vol. 37, iss. 2, pp. 149–153.
- Karikh E. D. Semiconductor laser with combined external optical feedback. Vestnik BGU, 2015, vol. 1, no. 2, pp. 35–39.
- Noskov V. Ya., Smolskiy S. M., Ignatkov K. A., Chupahin A. P. Calculation of autodyne parameters with the rigid characteristic of the active element conductance. Ural Radio Eng. J., 2019, vol. 3, no. 1, pp. 7–29. DOI: https://doi.org/10.15826/urej.2019.3.1.001
- Ju R., Spencer P. S. Dynamic regimes in semiconductor lasers subject to incoherent optical feedback. J. Lightwave Technol., 2005, vol. 23, no. 8, pp. 2513–2523.
- Ma J. S., Gu W. H. Simulation of chaotic synchronization system based on optical feedback and injection. Optoelectron. Lett., 2006, vol. 2, no. 3, pp. 0192–0194.
- Takeuchi Y., Shogenji R., Ohtsubo J. Chaotic dynamics in semiconductor lasers subjected to polarizationrotated optical feedback. Appl. Phys. Lett., 2008, vol. 93, pp. 181105-1–181105-3.
- Karikh E. D. Determination of the parameters of lowrefl ecting object microvibrations by cepstrum of selfmixing signal in semiconductor laser. J. Belarus. State Univ. Phys., 2017, no. 3, pp. 57–64.
- Olesen H., Osmundsen J. H., Tromborg B. Nonlinear dynamics and spectral behavior for an external cavity laser. IEEE J. Quant. Electron., 1986, vol. 22, no. 6, pp. 762–773.
- Usanov D. A., Skripal An. V., Avdeev K. S. Spectrum of semicondactor laser autodyne at focusing radiation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, no. 2, pp. 54–65.
- Schunk N., Petermann K. Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback. IEEE J. Quant. Electron., 1988, vol. 24, no. 7, pp. 1242–1247.
- Scalise L., Yu Y., Giuliani G., Plantier G., Bosch T. Selfmixing laser diode velocimetry: Application to vibration and velocity measurement. IEEE Trans. Instrum. Meas., 2004, vol. 53, iss. 1, pp. 223.
- Giuliani G., Norgia M., Donati S., Bosch T. Laser diode self-mixing technique for sensing application. J. Opt. A: Pure Appl. Opt., 2002, vol. 4, pp. S283–S294.
- Lang R., Kobayashi K. External optical feedback effects on semiconductor injection laser properties. IEEE J. Quant. Electron., 1980, vol. 16, no. 3, pp. 347.
- Usanov D. A., Skripal A. V., Kashchavtsev E. O., Dobdin S. Y. Acceleration measurements upon micro- and nanodisplacements of an object using the autodyne signal of a semiconductor laser with allowance for the external optical feedback. Tech. Phys., 2013, vol. 58, no. 7, pp. 1083–1085.
- Tromborg B., Osmundsen J. H., Olesen H. Stability analysis for a semi- conductor laser in an external cavity. IEEE J. Quant. Electron., 1984, vol. 20, pp. 1023–1032.
- Usanov D. A., Skripal An. V. Poluprovodnikovye lazernye avtodiny dlya izmereniya parametrov dvizheniya pri mikroi nanosmeshcheniyah [Semiconductor laser autodynes for measurement of motion parameters at micro-and nanoscale displacements]. Saratov, Izdatel’stvo Saratovskogo universiteta, 2014. 136 p. (in Russian).

- 1401 reads