Abstract

This tutorial presents a guided tour of laser feedback interferometry, from its origin and early development through its implementation to a slew of sensing applications, including displacement, distance, velocity, flow, refractive index, and laser linewidth measurement. Along the way, we provide a step-by-step derivation of the basic rate equations for a laser experiencing optical feedback starting from the standard Lang and Kobayashi model and detail their subsequent reduction in steady state to the excess-phase equation. We construct a simple framework for interferometric sensing applications built around the laser under optical feedback and illustrate how this results in a series of straightforward models for many signals arising in laser feedback interferometry. Finally, we indicate promising directions for future work that harnesses the self-mixing effect for sensing applications.

© 2015 Optical Society of America

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2015 (8)

C. Chen, Y. Zhang, X. Wang, X. Wang, and W. Huang, “Refractive index measurement with high precision by a laser diode self-mixing interferometer,” IEEE Photon. J. 7, 2600506 (2015).

A. Mowla, M. Nikolić, T. Taimre, J. R. Tucker, Y. L. Lim, K. Bertling, and A. D. Rakić, “The effect of the optical system on the Doppler spectrum in laser feedback interferometry,” Appl. Opt. 54, 18–26 (2015).
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J. A. Roumy, J. Perchoux, Y. L. Lim, T. Taimre, A. D. Rakić, and T. Bosch, “The effect of injection current and temperature on signal strength in a laser diode optical feedback interferometer,” Appl. Opt. 54, 312–318 (2015).
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P. Dean, J. Keeley, A. Valavanis, K. Bertling, Y. L. Lim, T. Taimre, R. Alhathlool, L. H. Li, D. Indjin, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Active phase-nulling of the self-mixing phase in a terahertz frequency quantum cascade laser,” Opt. Lett. 40, 950–953 (2015).
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O. Jacquin, E. Lacot, O. Hugon, and H. G. de Chatellus, “Using the Doppler shift induced by a galvanometric mirrors scanning to reach the shot noise limit with the laser optical feedback imaging (LOFI) setup,” Appl. Opt. 54, 1978–1983 (2015).
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J. Keeley, P. Dean, A. Valavanis, K. Bertling, Y. L. Lim, R. Alhathlool, T. Taimre, L. H. Li, D. Indjin, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Three-dimensional terahertz imaging using swept-frequency feedback interferometry with a quantum cascade laser,” Opt. Lett. 40, 994–997 (2015).
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M. Nikolić, Y. L. Lim, K. Bertling, T. Taimre, and A. D. Rakić, “Multiple signal classification for self-mixing flowmetry,” Appl. Opt. 54, 2193–2198 (2015).
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Y. Gao, Y. Yu, J. Xi, Q. Guo, J. Tong, and S. Tong, “Improved method for estimation of multiple parameters in self-mixing interferometry,” Appl. Opt. 54, 2703–2709 (2015).
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2014 (23)

J. R. Tucker, A. Mowla, J. Herbert, M. A. Fuentes, C. S. Freakley, K. Bertling, Y. L. Lim, R. S. Matharu, J. Perchoux, T. Taimre, S. J. Wilson, and A. D. Rakić, “Self-mixing sensing system based on uncooled vertical-cavity surface-emitting laser array: linking multichannel operation and enhanced performance,” Opt. Lett. 39, 394–397 (2014).
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T. Taimre and A. D. Rakić, “On the nature of Acket’s characteristic parameter C in semiconductor lasers,” Appl. Opt. 53, 1001–1006 (2014).
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F. P. Mezzapesa, L. L. Columbo, M. Dabbicco, M. Brambilla, and G. Scamarcio, “QCL-based nonlinear sensing of independent targets dynamics,” Opt. Express 22, 5867–5874 (2014).
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H. S. Lui, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, E. H. Linfield, A. G. Davies, and A. D. Rakić, “Terahertz inverse synthetic aperture radar imaging using self-mixing interferometry with a quantum cascade laser,” Opt. Lett. 39, 2629–2632 (2014).
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R. Kliese, T. Taimre, A. A. A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
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Y. Gao, Y. Yu, J. Xi, and Q. Guo, “Simultaneous measurement of vibration and parameters of a semiconductor laser using self-mixing interferometry,” Appl. Opt. 53, 4256–4263 (2014).
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T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, and A. D. Rakić, “Methodology for materials analysis using swept-frequency feedback interferometry with terahertz frequency quantum cascade lasers,” Opt. Express 22, 18633–18647 (2014).
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K. Kou, X. Li, L. Li, and H. Xiang, “Injected current reshaping in distance measurement by laser self-mixing interferometry,” Appl. Opt. 53, 6280–6286 (2014).
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A. L. Arriaga, F. Bony, and T. Bosch, “Speckle-insensitive fringe detection method based on Hilbert transform for self-mixing interferometry,” Appl. Opt. 53, 6954–6962 (2014).
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Y. L. Lim, T. Taimre, K. Bertling, P. Dean, D. Indjin, A. Valavanis, S. P. Khanna, M. Lachab, H. Schaider, T. W. Prow, H. P. Soyer, S. J. Wilson, E. H. Linfield, A. G. Davies, and A. D. Rakić, “High-contrast coherent terahertz imaging of porcine tissue via swept-frequency feedback interferometry,” Biomed. Opt. Express 5, 3981–3989 (2014).
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F. Michel, C. Juretzka, M. Carras, and W. Elsäßer, “30% improvement in absorption spectroscopy detectivity achieved by the detuned loading of a quantum cascade laser,” Opt. Lett. 39, 6351–6354 (2014).
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K. Bertling, J. Perchoux, T. Taimre, R. Malkin, D. Robert, A. D. Rakić, and T. Bosch, “Imaging of acoustic fields using optical feedback interferometry,” Opt. Express 22, 30346–30356 (2014).
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A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, S. J. Wilson, M. Nikolić, A. Valavanis, D. Indjin, E. H. Linfield, A. G. Davies, B. Ferguson, G. Walker, H. Schaider, and H. P. Soyer, “THz QCL self-mixing interferometry for biomedical applications,” Proc. SPIE 9199, 91990M (2014).

R. Ocaña and T. Molina, “Mapping a vibrating surface by using laser self-mixing interferometry,” Proc. SPIE 9132, 913213 (2014).

A. Magnani, A. Pesatori, and M. Norgia, “Real-time self-mixing interferometer for long distances,” IEEE Trans. Instrum. Meas. 63, 1804–1809 (2014).
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R. Atashkhooei, J.-C. Urresty, S. Royo, J.-R. Riba, and L. Romeral, “Runout tracking in electric motors using self-mixing interferometry,” IEEE/ASME Trans. Mechatronics 19, 184–190 (2014).
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F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104, 041112 (2014).
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S. Donati and M. Norgia, “Self-mixing interferometry for biomedical signals sensing,” IEEE J. Sel. Top. Quantum Electron. 20, 104–111 (2014).
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V. Y. Noskov and K. A. Ignatkov, “Peculiarities of noise characteristics of autodynes under strong external feedback,” Russ. Phys. J. 56, 1445–1460 (2014).
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M. Nikolić, T. Taimre, J. R. Tucker, Y. L. Lim, K. Bertling, and A. D. Rakić, “Laser dynamics under frequency-shifted optical feedback with random phase,” Electron. Lett. 50, 1380–1382 (2014).
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H. Hao, D. Guo, M. Wang, W. Xia, and X. Ni, “Micro-displace sensor based on self-mixing interference of the fiber laser with phase modulation,” Photon. Sens. 4, 379–384 (2014).

W. Zhang, R. Xiang, S. Wu, B. Yang, Y. Liu, J. Zhu, H. Gui, J. Liu, L. Lu, and B. Yu, “Self-mixing gas leakage detection of tank based on Er3+–Yb3+ codoped distributed Bragg reflector fiber laser,” Curr. Appl. Phys. 14, 838–842 (2014).
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A. Arasanz, F. J. Azcona, S. Royo, A. Jha, and J. Pladellorens, “A new method for the acquisition of arterial pulse wave using self-mixing interferometry,” Opt. Laser Technol. 63, 98–104 (2014).
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2013 (17)

S. Donati and R.-H. Horng, “The diagram of feedback regimes revisited,” IEEE J. Sel. Top. Quantum Electron. 19, 1500309 (2013).
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K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
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U. Zabit, O. D. Bernal, and T. Bosch, “Self-mixing laser sensor for large displacements: signal recovery in the presence of speckle,” IEEE Sens. J. 13, 824–831 (2013).
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L. Campagnolo, M. Nikolić, J. Perchoux, Y. L. Lim, K. Bertling, K. Loubière, L. Prat, A. D. Rakić, and T. Bosch, “Flow profile measurement in microchannel using the optical feedback interferometry sensing technique,” Microfluid. Nanofluid. 14, 113–119 (2013).

L. Mashal, R. Nguimdo, G. Van der Sande, M. Soriano, J. Danckaert, and G. Verschaffelt, “Low-frequency fluctuations in semiconductor ring lasers with optical feedback,” IEEE J. Quantum Electron. 49, 790–797 (2013).
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T. Inoue, K. Tsushima, S. Mori, and K. Kasahara, “Quantum cascade laser intensity noise under external feedback conditions estimated from self-mixing method,” Electron. Lett. 49, 407–409 (2013).
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C. Juretzka, S. Breuer, L. Drzewietzki, F. Schad, M. Carras, and W. Elsäßer, “9.5  dB relative intensity noise reduction in quantum cascade laser by detuned loading,” Electron. Lett. 49, 1548–1550 (2013).
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M. C. Phillips, I. M. Craig, and T. A. Blake, “Reflection-absorption infrared spectroscopy of thin films using an external cavity quantum cascade laser,” Proc. SPIE 8631, 86310C (2013).

M. C. Phillips and M. S. Taubman, “Trace-gas sensing using the compliance voltage of an external cavity quantum cascade laser,” Proc. SPIE 8726, 87260D (2013).

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolić, R. Kliese, S. P. Khanna, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sens. J. 13, 37–43 (2013).
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H. Moench, S. Gronenborn, X. Gu, J. Kolb, M. Miller, P. Pekarski, and U. Weichmann, “VCSEL arrays with integrated optics,” Proc. SPIE 8639, 86390M (2013).

F. J. Azcona, R. Atashkhooei, S. Royo, J. M. Astudillo, and A. Jha, “A nanometric displacement measurement system using differential optical feedback interferometry,” IEEE Photon. Technol. Lett. 25, 2074–2077 (2013).
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A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
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M. Nikolić, D. P. Jovanović, Y. L. Lim, K. Bertling, T. Taimre, and A. D. Rakić, “Approach to frequency estimation in self-mixing interferometry: multiple signal classification,” Appl. Opt. 52, 3345–3350 (2013).
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Y. Yu and J. Xi, “Influence of external optical feedback on the alpha factor of semiconductor lasers,” Opt. Lett. 38, 1781–1783 (2013).
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A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21, 22194–22205 (2013).
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M. Nikolić, E. Hicks, Y. L. Lim, K. Bertling, and A. D. Rakić, “Self-mixing laser Doppler flow sensor: an optofluidic implementation,” Appl. Opt. 52, 8128–8133 (2013).
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2012 (8)

A. N. Konovalov and V. A. Ul’yanov, “Self-mixing detection of backscattered radiation in single-mode pulse-periodic CO2 lasers,” Appl. Opt. 51, 3900–3906 (2012).
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M. C. Phillips and M. S. Taubman, “Intracavity sensing via compliance voltage in an external cavity quantum cascade laser,” Opt. Lett. 37, 2664–2666 (2012).
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R. Teysseyre, F. Bony, J. Perchoux, and T. Bosch, “Laser dynamics in sawtooth-like self-mixing signals,” Opt. Lett. 37, 3771–3773 (2012).
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G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photon. 4, 441–471 (2012).

S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photon. Rev. 6, 393–417 (2012).

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, and M. I. P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
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H. Wang and J. Shen, “Power spectral density of self-mixing signals from a flowing Brownian motion system,” Appl. Phys. B 106, 127–134 (2012).
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M. Norgia, A. Pesatori, and L. Rovati, “Self-mixing laser Doppler spectra of extracorporeal blood flow: a theoretical and experimental study,” IEEE Sens. J. 12, 552–557 (2012).
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2011 (7)

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
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D. Guo, “Quadrature demodulation technique for self-mixing interferometry displacement sensor,” Opt. Commun. 284, 5766–5769 (2011).
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O. Hugon, F. Joud, E. Lacot, O. Jacquin, and H. G. de Chatellus, “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” Ultramicroscopy 111, 1557–1563 (2011).
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M. Dabbicco, A. Intermite, and G. Scamarcio, “Laser-self-mixing fiber sensor for integral strain measurement,” J. Lightwave Technol. 29, 335–340 (2011).
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Y. Yu, J. Xi, and J. F. Chicharo, “Measuring the feedback parameter of a semiconductor laser with external optical feedback,” Opt. Express 19, 9582–9593 (2011).
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P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davis, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36, 2587–2589 (2011).
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Y. Fan, Y. Yu, J. Xi, and J. F. Chicharo, “Improving the measurement performance for a self-mixing interferometry-based displacement sensing system,” Appl. Opt. 50, 5064–5072 (2011).
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2010 (7)

U. Zabit, R. Atashkhooei, T. Bosch, S. Royo, F. Bony, and A. D. Rakić, “Adaptive self-mixing vibrometer based on a liquid lens,” Opt. Lett. 35, 1278–1280 (2010).
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F. De Lucia, M. Putignano, S. Ottonelli, M. di Vietro, M. Dabbicco, and G. Scamarcio, “Laser-self-mixing interferometry in the Gaussian beam approximation: experiments and theory,” Opt. Express 18, 10323–10333 (2010).
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Y. L. Lim, R. Kliese, K. Bertling, K. Tanimizu, P. A. Jacobs, and A. D. Rakić, “Self-mixing flow sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 18, 11720–11727 (2010).
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M. T. Fathi and S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35, 1844–1846 (2010).
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M. Norgia, A. Pesatori, and L. Rovati, “Low-cost optical flowmeter with analog front-end electronics for blood extracorporeal circulators,” IEEE Trans. Instrum. Meas. 59, 1233–1239 (2010).
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D. Larsson, K. Yvind, I.-S. Chung, and J. M. Hvam, “Optimization of VCSELs for self-mixing sensing,” IEEE Photon. Technol. Lett. 22, 667–669 (2010).
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L. Gelens, L. Mashal, S. Beri, W. Coomans, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Excitability in semiconductor microring lasers: experimental and theoretical pulse characterization,” Phys. Rev. A 82, 063841 (2010).
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2009 (9)

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
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D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94, 091103 (2009).
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Y. Yu, J. Xi, J. F. Chicharo, and T. M. Bosch, “Optical feedback self-mixing interferometry with a large feedback factor C: behavior studies,” IEEE J. Quantum Electron. 45, 840–848 (2009).
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S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. 282, 2367–2379 (2009).
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A. Pruijmboom, S. Booij, M. Schemmann, K. Werner, P. Hoeven, H. van Limpt, S. Intemann, R. Jordan, T. Fritzsch, H. Oppermann, and M. Barge, “A VCSEL-based miniature laser-self-mixing interferometer with integrated optical and electronic components,” Proc. SPIE 7221, 72210S (2009).

M. Ishihara, T. Morimoto, S. Furuta, K. Kasahara, N. Akikusa, K. Fujita, and T. Edamura, “Linewidth enhancement factor of quantum cascade lasers with single phonon resonance-continuum depopulation structure on Peltier cooler,” Electron. Lett. 45, 1168–1169 (2009).
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L. Wei, J. Xi, Y. Yu, and J. F. Chicharo, “Linewidth enhancement factor measurement based on optical feedback self-mixing effect: a genetic algorithm approach,” J. Opt. A 11, 045505 (2009).
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Y. L. Lim, M. Nikolić, K. Bertling, R. Kliese, and A. D. Rakić, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express 17, 5517–5525 (2009).
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X. Dai, M. Wang, Y. Zhao, and J. Zhou, “Self-mixing interference in fiber ring laser and its application for vibration measurement,” Opt. Express 17, 16543–16548 (2009).
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2008 (7)

S. Blaize, B. Bérenguier, I. Stéfanon, A. Bruyant, G. Lérondel, P. Royer, O. Hugon, O. Jacquin, and E. Lacot, “Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry,” Opt. Express 16, 11718–11726 (2008).
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N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Detuning characteristics of the linewidth enhancement factor of a midinfrared quantum cascade laser,” Appl. Phys. Lett. 92, 121104 (2008).
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M. Norgia and C. Svelto, “Novel measurement method for signal recovery in optical vibrometer,” IEEE Trans. Instrum. Meas. 57, 1703–1707 (2008).
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S. Ottonelli, F. De Lucia, M. di Vietro, M. Dabbicco, G. Scamarcio, and F. P. Mezzapesa, “A compact three degrees-of-freedom motion sensor based on the laser-self-mixing effect,” IEEE Photon. Technol. Lett. 20, 1360–1362 (2008).
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A. Pruijmboom, M. Schemmann, J. Hellmig, J. Schutte, H. Moench, and J. Pankert, “VCSEL-based miniature laser-Doppler interferometer,” Proc. SPIE 6908, 69080I (2008).

M. Suleiman, H. Seat, and T. Bosch, “Interrogation of fiber Bragg grating dynamic strain sensors by self-mixing interferometry,” IEEE Sens. J. 8, 1317–1323 (2008).
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R. P. Green, J.-H. Xu, L. Mahler, A. Tredicucci, F. Beltram, G. Giuliani, H. E. Beere, and D. A. Ritchie, “Linewidth enhancement factor of terahertz quantum cascade lasers,” Appl. Phys. Lett. 92, 077106 (2008).

2007 (7)

D. Han, M. Wang, and J. Zhou, “Self-mixing speckle in an erbium-doped fiber ring laser and its application to velocity sensing,” IEEE Photon. Technol. Lett. 19, 1398–1400 (2007).
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L. Fei and S. Zhang, “The discovery of nanometer fringes in laser self-mixing interference,” Opt. Commun. 273, 226–230 (2007).
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Y. Yu, J. Xi, J. F. Chicharo, and T. Bosch, “Toward automatic measurement of the linewidth-enhancement factor using optical feedback self-mixing interferometry with weak optical feedback,” IEEE J. Quantum Electron. 43, 527–534 (2007).
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D. Guo and M. Wang, “Self-mixing interferometry based on a double-modulation technique for absolute distance measurement,” Appl. Opt. 46, 1486–1491 (2007).
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Y. Tan and S. Zhang, “Self-mixing interference effects of microchip Nd:YAG laser with a wave plate in the external cavity,” Appl. Opt. 46, 6064–6068 (2007).
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J. R. Tucker, J. L. Baque, Y. L. Lim, A. V. Zvyagin, and A. D. Rakić, “Parallel self-mixing imaging system based on an array of vertical-cavity surface-emitting lasers,” Appl. Opt. 46, 6237–6246 (2007).
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O. Jacquin, E. Lacot, C. Felix, and O. Hugon, “Laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 46, 6779–6782 (2007).
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2006 (7)

2005 (9)

G. Plantier, C. Bès, and T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
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A. N. Lukashkin, M. E. Bashtanov, and I. J. Russell, “A self-mixing laser-diode interferometer for measuring basilar membrane vibrations without opening the cochlea,” J. Neurosci. Methods 148, 122–129 (2005).
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C. Zakian, M. Dickinson, and T. King, “Particle sizing and flow measurement using self-mixing interferometry with a laser diode,” J. Opt. A 7, S445–S452 (2005).
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J. Xi, Y. Yu, J. F. Chicharo, and T. Bosch, “Estimating the parameters of semiconductor lasers based on weak optical feedback self-mixing interferometry,” IEEE J. Quantum Electron. 41, 1058–1064 (2005).
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S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
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2004 (6)

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G. Plantier, N. Servagent, T. Bosch, and A. Sourice, “Real-time tracking of time-varying velocity using a self-mixing laser diode,” IEEE Trans. Instrum. Meas. 53, 109–115 (2004).
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2003 (3)

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2002 (4)

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2001 (4)

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2000 (2)

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1999 (4)

1998 (5)

F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37, 6684–6689 (1998).
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N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29, 168–173 (1998).
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1997 (3)

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N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Instrum. Meas. 46, 847–850 (1997).
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1996 (2)

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1995 (7)

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1994 (2)

1993 (1)

1992 (3)

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1990 (1)

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1988 (1)

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1987 (1)

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1986 (2)

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1984 (4)

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1982 (4)

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1981 (2)

R. Bonner and R. Nossal, “Model for laser Doppler measurements of blood flow in tissue,” Appl. Opt. 20, 2097–2107 (1981).
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1980 (2)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
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1978 (3)

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1976 (3)

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1975 (1)

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1972 (2)

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1968 (1)

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1967 (1)

1966 (1)

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1964 (2)

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1963 (4)

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1962 (4)

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1961 (3)

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1960 (2)

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1958 (1)

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J. Xu, T. Zhao, H. Ming, J. Xie, D. He, L. Lv, H. Gui, B. Yi, L. Guo, C. S. Ranta, and Y. Kong, “Self-mixing laser range sensor,” U.S. patent7,283,214 (October16, 2007).

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M. Grabherr, H. Moench, and A. Pruijmboom, “VCSELs for optical mice and sensing,” in VCSELs, R. Michalzik, ed., Vol. 166 of Springer Series in Optical Sciences (Springer, 2013), pp. 521–538.

Supplementary Material (4)

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» Visualization 1: MP4 (6766 KB)     
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» Visualization 3: MP4 (8751 KB)     
» Visualization 4: MP4 (1628 KB)     

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Figures (25)

Figure 1
Figure 1 Three-mirror model of LFI. The laser is represented as the “internal” cavity with length L in , refractive index n in , and round-trip propagation time τ in . Light leaves the internal cavity through the partially transmissive mirror M 2 and traverses the “external” cavity of length L ext , refractive index n ext , and round-trip propagation time τ ext . A portion of this light re-enters the laser through M 2 and mixes with the field inside the laser cavity, affecting the operating state of the laser.
Figure 2
Figure 2 Operating regimes of LFI, after [68,69]. Region I, weak feedback; region II, moderate feedback; region III, strong feedback; region IV, chaos with islands of stability; region V, external cavity. We restrict ourselves to regions I–III, where the system operates interferometrically, and does not exhibit chaotic behavior.
Figure 3
Figure 3 Model used in rate-equation analysis of a laser under feedback, modified with permission from Coldren et al., Diode Lasers and Photonic Integrated Circuits (2012) [74]. Copyright 2012 Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission. From the top, carriers are generated by current injection, and are lost via three processes—nonradiative recombination governed by the rate R nr , stimulated emission via the gain term G , and spontaneous emission (not considered in the current model, but shown for completeness). In our model, the carrier lifetime τ n = ( R nr + R sp ) 1 and accounts for carrier loss via spontaneous emission and nonradiative processes. A fraction of the emitted photons traverses the external cavity and is reinjected after time τ ext .
Figure 4
Figure 4 Path-dependent behavior of external cavity phase φ FB in response to sinusoidal phase stimulus φ s under strong feedback ( C = 8 ), adapted from [87]. (a) Sinusoidal phase stimulus φ s varying in time with 8 π peak-to-peak amplitude. (b) External cavity phase response φ FB when C = 8 and α = 5 dwells on one solution region between A and B until it no longer contains a valid solution, at which point it could jump to solutions at points C, D, or E. We assume that the solution jumps to the next closest solution C. Note the locus of solutions for the increasing and decreasing portions of the phase stimulus trace out two different paths.
Figure 5
Figure 5 Illustration of the relationship between the temporal evolution of the phase stimulus φ s and the LFI signal cos ( φ FB ) . Visualization 1 shows the change in the LFI signal morphology as feedback parameter C increases from 0.1 to 30 for α = 5 . Visualization 2 shows the change in the LFI signal morphology as feedback parameter C increases from 0.1 to 30 for α = 0.1 . Visualization 3 shows the change in the LFI signal morphology as α increases from 5 to 10, for fixed feedback parameter C = 1.5 .
Figure 6
Figure 6 Schematic diagram of the basic LFI apparatus with (a) an external PD and (b) an internal PD. The laser current is controlled with a laser driver, through which electrical modulation may be applied. In (a), the emitted beam is split, with a portion passing through external optical elements to and from the target and that may be mechanically modulated, and a portion transmitted to an external PD. Interferometric signals are acquired using a data acquisition card connected to a computer (PC) through (i) an external PD together with a trans-impedance amplifier (TIA), followed by a bandpass filter (BPF); and/or (ii) the laser terminal voltage together with a voltage amplifier (Volt. Amp), followed by a BPF. In (b), the system topology is simpler, as the internal PD obviates the need for a beam splitter.
Figure 7
Figure 7 Schematic diagram of (a) an in-plane laser and (b) a VCSEL packaged with a monitoring PD in a transistor outline can. For the in-plane laser, the rectangular aperture results in an elliptical profile of the emitted beam from both the front and rear facets. The PD responds to optical power emitted from the rear facet of the laser. For the VCSEL, the circular aperture results in a circular profile of the emitted beam. The PD responds to optical power backreflected from the glass window.
Figure 8
Figure 8 Measured vibration amplitude of a titanium tweeter membrane at 300, 500, 580, 700, 800, 900, 3200, 3500, 3600, 6600, and 6800 Hz, showing different nodal structures. Reproduced with permission from [118]. Copyright 2014 SPIE.
Figure 9
Figure 9 Displacement measurement behavior, adapted from [87]. (a), (b) Periodic target displacement (stimulus) of peak-to-peak amplitude 2 λ with λ = 850 nm , and L ext = 0.5 m. Linear displacement (blue); sinusoidal displacement (red). (c)–(j) LFI signals for C = 0.5 , 5, 8, 25, with α = 4.6 . Higher feedback levels exhibit loss of fringes, ultimately resulting in the replication of the stimulus.
Figure 10
Figure 10 Sinusoidal phase-stimulus–power-response transfer function, with C = 2.5 and α = 4.6 . Visualization 4 shows the dependence of the LFI signal on C .
Figure 11
Figure 11 Electrocardiographic phase-stimulus–power-response transfer function, with C = 2.5 and α = 4.6 .
Figure 12
Figure 12 Three-dimensional range image of a bottle of corrector fluid against a flat background acquired at a distance of 0.7 m. The bottle height is 71 mm, and its diameter is 27 mm. (c) IEEE. Reproduced, with permission, from Gagnon and Rivest, IEEE Trans. Instrum. Meas. 48, 693–699 (1999) [141].
Figure 13
Figure 13 LFI response to simultaneous linear displacement and frequency changes. (a) Linear displacement (constant velocity of 10 mm/s). (b) Triangular frequency sweep (2 GHz peak-to-peak on λ 0 = 850 nm ). (c) Typical LFI signal ( C = 0.9 and α = 4.6 )—note the presence of large power modulation as a consequence of laser current (and hence output power) modulation. (d) Numerically differentiated LFI signal, showing differing number of fringes over the increasing portion of the frequency sweep and the decreasing portion of the frequency sweep. Adapted from [87].
Figure 14
Figure 14 Propagation of the acoustic field with the ultrasonic transmitter propagating the field into free space. Left, measured; right, simulation. (a) Image at t = 0 s . (b) Amplitude of acoustic field. (c) Phase of acoustic field. Reproduced with permission from [154]. Copyright 2014 Optical Society of America.
Figure 15
Figure 15 Terahertz porcine tissue imaging using LFI. (a) Amplitude-like imaging modality based on a 101 × 101 array of LFI waveforms (inset: high-resolution image based on a 51 × 301 array), and (b) the phase-like imaging modality. (c)–(h) Heat maps of LFI waveforms for different tissue types associated with the color markers overlayed in (a). The tissue types are: (c) aluminum separator, (d) epidermis, (e) upper dermis, (f) lower dermis, (g) sub-dermal fat, and (h) muscle tissue. (i) Corresponding amplitude-like/phase-like plots of waveforms (c)–(h). The mark of each tissue type appears to form natural clusters. Reproduced with permission from [162]. Copyright 2014 Optical Society of America.
Figure 16
Figure 16 (a) Photograph of Egyptian doll head, reproduced with permission from [165]. Copyright 2001 Optical Society of America. (b) 3D image of the doll head from (a), obtained by imaging using an acousto-optic modulator, reproduced with permission from [165]. Copyright 2001 Optical Society of America. (c) Phase image of an isolated red blood cell on a glass slide, obtained by acousto-optic imaging, reprinted from Ultramicroscopy 111, Hugon et al., “Coherent microscopy by laser optical feedback imaging (LOFI) technique,” 1557–1563 (2011), with permission from Elsevier [166]. (d) Phase map of light propagating along the waveguide, reprinted with permission from [22]. Copyright 2008 Optical Society of America.
Figure 17
Figure 17 Apparatus for the simultaneous measurement of thickness and refractive index of a transparent material (adapted from [169]). The emitted beam is incident to the transparent sample at angle α and is refracted at angle θ to the partial reflector and second photodetector (PD2). A portion of the beam is reflected and subsequently returns to the laser diode, whose optical power is monitored by the first photodetector (PD1). A part of this returning beam undergoes reflection from the internal surface of the sample, resulting in double reflection. This double-reflected beam is observed only at PD2 and has negligible impact at PD1.
Figure 18
Figure 18 (a) Representative intensity distributions of the infrared pump laser by placing a charge-coupled device (CCD) camera at the sample position. The pattern was computer controlled by a spatial light modulator (SLM) and projected onto the silicon surface. Dark pixels of SLM liquid crystal maintain the polarization of the incident light and define the exposed area. (b) Terahertz imaging in reflection mode of photoexcited electron plasma on semiconductors. The spatial distribution of free carrier charges corresponds to the structured beam profile. Reprinted with permission from Mezzapesa et al., Appl. Phys. Lett. 104, 041112 (2014) [173]. Copyright 2014 American Institute of Physics.
Figure 19
Figure 19 (a), (b) Two specimen through-focus images of a semiconductor chip taken at 3 μm axial separation with a semiconductor laser confocal microscope. Field of view is 80 μm × 80 μm . Reprinted with permission from [78]. Copyright 1994 Optical Society of America.
Figure 20
Figure 20 Locating defective transistors using an optical-feedback thermographic microscope. (a) Thermal map of photodetector array sample superimposed on reference confocal image showing anomalous “hotspots” (yellow regions), which are possible defect sites. (b) Regions of increasing thermal activity reveal the integrity of the semiconductor architecture where thermal blooming on two regions is apparent. Image area is 180 μm × 180 μm . (c) Homogeneity of the localized quantum efficiency of regions across a silicon photodiode is evaluated at optical spatial resolution. Region 1 represents a substrate; 2, n -type semiconductor; 3, p n overlay; and 4, bonding pad. (d) Thermal map of the quantum efficiency of the photodiode revealing the nonuniform response on the boundaries and the n region. Image area is 270 μm × 270 μm . Reprinted with permission from [179]. Copyright 2006 Optical Society of America.
Figure 21
Figure 21 Intensity-based (chopped beam) LFI imaging of coins. (a) A British two-pence coin. (b) A high-resolution image of (a) using a THz QCL operating at 2.60 THz. (c) An Australian five-cent coin. (d) An image of (c) using a 3.57 μm mid-infrared DFB interband cascade laser. (e) An image of (c) using an 851 nm near-infrared VCSEL. Adapted from [21,180,181].
Figure 22
Figure 22 Visualization of Eq. (61). The vector ( k s k i ) is normal to the reflection surface. If the velocity vector v is in the plane tangent to the reflection surface, as pictured, there will be zero Doppler shift. A velocity vector outside this plane will give a non-zero Doppler shift, which means the surface is translating in such a way that it is changing the external cavity length. Therefore, the external cavity length must change for a Doppler shift to occur.
Figure 23
Figure 23 Morphology of Doppler flow spectra, adapted from [53,55]. (a) Doppler flow spectra for six flow rates ranging from 0 to 50 μL/min for the same scattering level of 2% wt. % milk diluted in water. (b) Doppler flow spectra for four scattering levels, ranging from 0.2% to 100% wt. % milk diluted in water, for the same maximum fluid velocity of 1.6 mm/s.
Figure 24
Figure 24 Simulated and measured distribution of velocity components along the lasing axes for a flow channel with inlet (at left) flow rate of 15 ml/min. Reprinted with permission from [104]. Copyright 2010 Optical Society of America.
Figure 25
Figure 25 Philips Twin-Eye Laser LFI sensor, adapted from [108]. (a) Sensor with integrated lenses. (b) System-in-package with lenses removed.

Tables (1)

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Table 1. List of Symbols

Equations (68)

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κ ˜ = κ 1 τ in = ε ( 1 R 2 ) R R 2 1 τ in ,
C = κ τ in τ ext 1 + α 2 ,
d d t ( E ( t ) e j ω t ) = { j ω m + 1 2 ( Γ G 1 τ p ) } E ( t ) e j ω t + κ ˜ E ( t τ ext ) e j ω ( t τ ext ) ,
d N ( t ) d t = η i I ( t ) q V N ( t ) τ n G S ( t ) ,
G = v g g = v g a ln ( N / N tr ) ( 1 + ε G S ) ,
G = v g a ( N N tr ) .
d E ( t ) d t = { j ( ω m ω ) + 1 2 ( Γ G 1 τ p ) } E ( t ) + κ ˜ E ( t τ ext ) e j ω τ ext .
S ( t ) = | E ( t ) | 2 = E ( t ) E * ( t ) ,
d S ( t ) d t = E ( t ) d E * ( t ) d t + E * ( t ) d E ( t ) d t ,
d S ( t ) d t = ( Γ G 1 τ p ) S ( t ) + 2 κ ˜ S ( t ) S ( t τ ext ) cos [ ω τ ext + φ ( t ) φ ( t τ ext ) ] .
φ ( t ) = arctan ( Im ( E ( t ) ) Re ( E ( t ) ) ) .
d φ ( t ) d t = 1 ( Re ( E ( t ) ) ) 2 + ( Im ( E ( t ) ) ) 2 [ Im ( d E ( t ) d t ) Re ( E ( t ) ) Re ( d E ( t ) d t ) Im ( E ( t ) ) ] .
d φ ( t ) d t = 1 S ( t ) [ Im ( E * ( t ) d E ( t ) d t ) ] ,
d φ ( t ) d t = ( ω m ω ) κ ˜ ( S ( t τ ext ) S ( t ) ) 1 2 sin [ ω τ ext + φ ( t ) φ ( t τ ext ) ] .
n in = n th + ( N N th ) n in N .
ω m ω th = m π c L in ( 1 n in 1 n th ) = m π c L in ( n th n in ) n th n in = m π c L in n th n in ( ( N N th ) n N ) = ω m n th ( ( N N th ) n N ) .
Γ G = Γ G th + Γ ( N N th ) G N = 1 τ p + Γ ( N N th ) G N ,
ω m ω th = ω m n th ( Γ G 1 τ p ) n in N / ( Γ G N ) .
ω m ω th = 1 2 α ( Γ G 1 τ p ) .
d φ ( t ) d t = 1 2 α ( Γ G 1 τ p ) κ ˜ ( S ( t τ ext ) S ( t ) ) 1 2 sin [ ω th τ ext + φ ( t ) φ ( t τ ext ) ] .
{ d S ( t ) d t = ( Γ G 1 τ p ) S ( t ) + 2 κ ˜ S ( t ) S ( t τ ext ) cos [ ω th τ ext + φ ( t ) φ ( t τ ext ) ] d φ ( t ) d t = 1 2 α ( Γ G 1 τ p ) κ ˜ ( S ( t τ ext ) S ( t ) ) 1 2 sin [ ω th τ ext + φ ( t ) φ ( t τ ext ) ] d N ( t ) d t = η i I ( t ) q V N ( t ) τ n G S ( t ) .
{ d S ˜ ( t ) d t = ( Γ G 1 τ p ) S ˜ ( t ) + 2 κ ˜ S ˜ ( t ) S ˜ ( t τ ext ) cos [ ω th τ ext + φ ( t ) φ ( t τ ext ) ] d φ ( t ) d t = 1 2 α ( Γ G 1 τ p ) κ ˜ ( S ˜ ( t τ ext ) S ˜ ( t ) ) 1 2 sin [ ω th τ ext + φ ( t ) φ ( t τ ext ) ]