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Optics Express

  • Vol. 17, Iss. 7 — Mar. 30, 2009
  • pp: 5517–5525
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Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout

Yah Leng Lim, Milan Nikolic, Karl Bertling, Russell Kliese, and Aleksandar D. Rakić  »View Author Affiliations


Optics Express, Vol. 17, Issue 7, pp. 5517-5525 (2009)
http://dx.doi.org/10.1364/OE.17.005517


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Abstract

The advent of two-dimensional arrays of Vertical-Cavity Surface-Emitting Lasers (VCSELs) opened a range of potential sensing applications for nanotechnology and life-sciences. With each laser independently addressable, there is scope for the development of high-resolution full-field imaging systems with electronic scanning. We report on the first implementation of a self-mixing imaging system with parallel readout based on a monolithic VCSEL array. A self-mixing Doppler signal was acquired from the variation in VCSEL junction voltage rather than from a conventional variation in laser power, thus markedly reducing the system complexity. The sensor was validated by imaging the velocity distribution on the surface of a rotating disc. The results obtained demonstrate that monolithic arrays of Vertical-Cavity lasers present a powerful tool for the advancement of self-mixing sensors into parallel imaging paradigms and provide a stepping stone to the implementation of a full-field self-mixing sensor systems.

© 2009 Optical Society of America

1. Introduction

Self-mixing interferometry is a sensing technique used to detect small displacements, velocity, change in the refractive index of materials, and flow [1

1. T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical Feedback Interferometry,” in Encyclopedia of Sensors, C. A. Grimes and E. C. Dickey, eds., vol. X, pp. 1–20 (American Scientific Publishers, Valencia, CA, 2006).

, 2

2. D. M. Kane and K. A. Shore, eds., Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (John Wiley, Chichester, 2005). [CrossRef]

, 3

3. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4(6), 283–294 (2002). [CrossRef]

]. The self-mixing phenomenon occurs when the laser beam is partially reflected from an external target and injected back into the laser cavity. The reflected light interferes or ‘mixes’ with the light inside the laser cavity and produces variations to the threshold gain, emitted power, lasing spectrum and the laser junction voltage. The reflected light can be frequency shifted, by means of Doppler effect, before being mixed with the original laser emission. The resulting output power variations are usually monitored by the photodiode integrated within the laser package. This phenomenon allows the laser to be used as an interferometric sensor incorporating the light source and the interferometer in one device thus significantly reducing the cost and the complexity of the sensing system. The coherent detection nature of this sensing scheme inherently provides very high sensitivity, frequently at the quantum noise limit.

Self-mixing sensors based on semiconductor lasers have long been regarded as a low cost, compact and robust solution for velocity [1

1. T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical Feedback Interferometry,” in Encyclopedia of Sensors, C. A. Grimes and E. C. Dickey, eds., vol. X, pp. 1–20 (American Scientific Publishers, Valencia, CA, 2006).

] and displacement measurement [4

4. S. Donati, L. Falzoni, and S. Merlo, “PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–944 (1996). [CrossRef]

, 5

5. G. Giuliani, S. Bozzi-Pietra, and S. Donati, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14(1), 24–32 (2003). [CrossRef]

]. The self-mixing systems reported so far in the literature are essentially single beam systems where spatial variations in a measured quantity are obtained by mechanically scanning the laser beam over the area to be imaged in a raster fashion. The raster scanning technique has one serious limitation: the time required to complete a full scan. This effectively limits the applicability of the technique to sensing stationary phenomena. Studies on hybrid parallel sensing systems are scarce [6

6. P. de Groot, G. Gallatin, G. Gardopee, and R. Dixon, “Laser feedback metrology of optical systems,” Appl. Opt. 28(13), 2462–2464 (1989). [CrossRef] [PubMed]

, 7

7. J. R. Tucker, J. L. Baque, Y. L. Lim, A. V. Zvyagin, and A. D. Rakic, “Parallel self-mixing imaging system based on an array of vertical-cavity surface-emitting lasers,” Appl. Opt. 46(25), 6237–6246 (2007). [CrossRef] [PubMed]

] and to the best of the authors’ knowledge, there has been no report on multichannel velocity measurements using a monolithic laser array.

This article reports, for the first time to our knowledge, a full-field self-mixing interferometer with monolithic VCSEL array. It thereby proposes a sensing system incorporating a simultaneous readout from multiple sensors by using a monolithic VCSEL array as the sensor and the emitter array. A Self mixing signal was acquired by detecting the change in VCSEL junction voltage caused by the light scattered from the target and injected back into the laser, rather than using the signal from an associated photodetector array [8

8. Y. L. Lim, K Bertling, P. Rio, J. Tucker, and A. Rakic, “Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect,” in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE 6038, 60381O–1 (2006). [CrossRef]

]. Removing the need for the photodetector array integrated with the VCSEL array significantly reduces the complexity and the cost of the system.

This article is organised as follows: Sec. 2 provides a brief overview of the self-mixing effect in VCSELs and application to velocity measurement. Section 3 describes in detail the experimental setup used to validate the sensor, followed by the results obtained. Finally, conclusions are drawn in Sec. 4 where advantages and limitations of the technique in characterising velocity distributions are discussed.

2. Theory

To demonstrate the performance of the system we used a target with a known distribution of velocity on its surface — a rotating disc. Light back scattered from the target moving with velocity ν⃗ experiences a Doppler frequency shift fD given by [9

9. H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer Verlag, Berlin, 2003).

]

fD=(ksckinc)·ν2π
(1)

where k⃗inc and k⃗sc are the wave vectors of the incident and scattered light respectively, and λ is wavelength of light in the medium surrounding the target. In the self-mixing interferometer configuration used here, the scattered signal is collected by the same lens used to focus the beam on the target and (1) becomes

fD=2νcosθλ
(2)

where θ is the angle between the axis of the incident beam and the velocity vector. For light reflected from a rough moving surface the Doppler signal is amplitude modulated by a random speckle effect, since the illuminated part of the target is changing continuously.

The result of coherent mixing within the VCSEL resonant cavity between the lasing field and the Doppler-shifted light backscattered by a moving target is a fluctuation of photon density and consequently the output power. Doppler frequency is usually obtained by observing the laser power spectrum obtained from the time domain signal through the fast Fourier transform (FFT). In this study, fluctuations in VCSEL terminal voltage were used as the source of the self-mixing signal instead of the usual current signal from the external photodiode.

3. Experimental setup and results

To investigate the performance of the proposed architecture we designed a system schematically shown in Fig. 1, based on a commercial 1×12 monolithic VCSEL array (EMCORE Corporation, Gigalase 8185-1100 [16

16. Emcore Corporation, “Laser Products: Array VCSELs,” (2009). URL http://www.emcore.com/fiberoptics/lasercomponents/laserproducts?pid= 49.

]). The EMCORE VCSELs are AlGaAs planar, top-surface emitting devices with 15 μm circular apertures in the top mirror contact, and have a pitch of 250 μm. This particular VCSEL array can operate in both single mode and multimode regimes, depending on the laser driving current. The average threshold current of the VCSELs is about 6 mA and each laser has a peak wavelength at around 850 nm. A single Thorlabs C240 as-pheric lens with a clear aperture of 8 mm and NA of 0.5 was employed to image all 12 laser beams onto a rotating disc. The aluminium disc, 10 cm in diameter, was sandblasted to provide a moving diffuse target. The disc was driven by a DC servo motor with a 43:1 gear reduction controlled by an Elmo Whistle motor controller. The stability of the disc’s angular velocity for the duration of the experiments was better than 1%, as established by monitoring the frequency of the motor’s rotary encoder. A custom built 12-channel laser driver was used to individually bias each laser to just above its threshold in order to obtain maximum sensitivity to the self-mixing effect. The self-mixing signals were obtained through terminal voltage variations across individual VCSELs. Terminal voltage fluctuations were first amplified individually using an accoupled, single stage, low noise preamplifier with gain G = 100 located in the proximity of the laser array. The pre-amplified voltage signals were then fed to a computer controlled analog multiplexing module for addressing and switching of the laser signals. Additional amplification (G = 100) was applied to bring the signal to a level suitable for processing by a 16-bit Data Acquisition card and the total bandwidth of the multi-stage amplification system is 600 kHz. A sampling rate of 800k samples per second was used to acquire the self-mixing signals which gives an effective measuring bandwidth of 400 kHz. Even though the measuring bandwidth is smaller than the amplifier bandwidth, aliasing was not a problem as there is not much signal above 200 kHz. The acquisition time for each laser channel was 41 ms. The Fast Fourier Transform (FFT) of the time domain signal was performed in the LabVIEW programming environment to obtain the self-mixing signal spectrum and 8 consecutive spectra were averaged before extracting the Doppler frequency. Considering that the maximum Doppler frequency in this experiment was expected at fD = 27 kHz, the bandwidth of the system was more than adequate for the task.

Fig. 1. Experimental setup for measuring the velocity distribution on the surface of a rotating disc. The disc rotates in anti-clockwise direction around a horizontal axes and is tilted around the vertical axis by 5° to provide a small velocity component in the direction of the laser beam (θ = 85°).

The target was located 26.7 cm away from the laser array in-order to obtain a series of beam spots with a pitch of 0.8 cm on the target. The laser array was oriented vertically (in the y-direction), with the VCSEL designated LD1 located at the bottom of the array. After imaging the array on the disc, LD1 forms the highest spot due to the image inversion characteristic of the single element lens used. The vertical positioning of the array was set to locate five beam spots on each half of the disc surface with the central beam (LD6) located on the centre of the disc. Figure 2(a) shows the self-mixing signal obtained from one of the VCSELs. The multiple harmonics in the Doppler spectrum of the self-mixing signal indicate strong feedback. Based on the measured reflectivity of the target and the geometry used we estimated the value for the feedback parameter C ≈ 6, which is commensurate with the signal shape obtained. We determined the optimal operating condition for each of the VCSELs by maximising the signal to noise ratio while the lasers are positioned along the vertical axis of the disc. This was obtained by fitting, in real time, the fundamental spectral feature of the signal to a combination of the Gaussian profile and the parabolic noise floor and by varying the driving current to maximise the Signal-to-noise ratio (SNR) [see Fig. 2(a)]. SNR obtained for all VCSELs was between 25 and 30 dB over the range of measured Doppler frequencies (approx. 5 – 27 kHz). To estimate the accuracy of the system we first measured the velocity on the vertical diameter of the disc. The magnitude of the velocity ν at a distance r from the centre of the disc is given by

Fig. 2. (a) Self-mixing Doppler signal (blue) with fitted curves (red) used to estimate the signal-to-noise ratio; SNR = 30 dB. (b) top-view of the system; tilt of the disc θ = 85° is indicated. (c) side-view of the system; α is the angle the VCSEL beam makes with the optic axis.
ν=ωr
(3)

where ω is the angular velocity of the disc. This provides a linear distribution of velocity as a function of distance from the centre of the disc, a perfect test bed to quantify the quality of the system. Clearly, substitution of (3) into (2), suggests a linear distribution of fD as a function of distance from the centre of the disc.

To investigate the spatial resolution and imaging characteristics of the system the spatial distribution of velocity was mapped across the surface of the disc. We utilised an interlaced broom sweep with mechanical scanning in a horizontal direction. This provided a 47 × 23 square grid of pixels on the rotating disc from which an image was generated. Unlike raster scan systems, vertical mechanical scanning was replaced by parallel acquisition. It should be noted that each laser beam corresponds to one spatial pixel in the target plane.

Fig. 3. (a) Plot of the measured Doppler frequencies (circles) and calculated values (stars) on the vertical diameter of the disc, (b) Single-frame excerpt from video recording of the experimental setup showing the VCSEL beams on the surface of the rotating disk (Media 1).

νksc(x,y)=ωycosθcosαxsinθsinαsin2θ+cos2θcos2θcos2α
(4)

where θ is the tilt angle of the disc [see Fig. 2(b)], α is the angle the individual beam makes with the optic axes of the system [see Fig. 2(c)], and x and y are the horizonal and vertical axes respectively. The calculated distribution of the velocity component parallel to the laser beam incident on the target is shown in Fig. 4(c). Agreement with the measured distribution shown in Fig. 4(d) is excellent. Along the horizontal diameter of the circle, the velocity vector has only the vertical (νy) component, and the detected signal should be zero (projection of the velocity vector on the laser beam is zero). Apart from this line, the recovery of the velocity distribution is simple; the distributions recovered from the calculated and experimental values are shown in Fig. 4(e) and (f) respectively. The agreement is strikingly good — both images represent a series of concentric circles. This demonstrates clearly that even with the ultimately simple and compact optical system, comprised of a single aspheric lens, less than three times the size of the laser array used, we could produce a virtually distortion free velocity distribution. Image distortion created by the lens system can be further corrected simply by pre-calculating the positions of the laser beams in the target plane in a lens design tool and by storing the beam positions in a lookup table. This would enable the use of a wide angle imaging lens and provide potentially a very short working distance. The said correction was implemented for the system used here but the improvement in the shape of the equi-velocity circles was not visually noticeable. The quality of the laser alignment on a monolithic array is evident from the perfect circular shape of the equal-velocity lines. All the problems usually encountered with raster scanning and hybrid arrays are completely absent in this implementation. This suggests that the lithographic alignment of lasers constituting the monolithic array is essential for expanding this concept to massively parallel Doppler imaging systems based on two-dimensional VCSEL arrays.

Fig. 4. Distribution of velocity on the rotating disc; rotation in anti-clockwise direction at a speed of 27.9 rpm. (a) The calculated contour plot of the velocity distribution on the disc; (b) Calculated Doppler signal distribution assuming all the laser beams are parallel to each other; (c) Calculated and (d) measured Doppler signal distribution obtained using the fanning out geometry explained in the text; (e) and (f) the velocity distributions recovered from the calculated and experimental values respectively. The agreement is strikingly good

4. Conclusion

In this article we proposed a full-field self-mixing sensor system for simultaneous readout from a plurality of lasers by using an array of VCSELs as both the light source array and the sensor array. The light emitted from one laser in the matrix illuminates one spot on the target, and is reflected back into the same laser to create the self-mixing signal. The s elf mixing signal is detected by sensing the change in VCSEL junction voltage caused by the light dynamically scattered from the target and injected back into the laser, rather than using the signal from a photodetector array. Removing the need for the photodetector array hybrid integrated with the VCSEL array significantly reduces the complexity and the cost of the proposed system. This coherent detection scheme provides not only for the high sensitivity and dynamic range usually associated with of the heterodyne detection, but also efficiently suppresses the optical crosstalk from the neighbouring lasers. In comparison with the spot-raster laser, the acquisition time is significantly shortened — the mechanical scanning process is replaced by concurrent acquisition at all channels/pixels. We have implemented a small scale prototype of the system, based on the 1×12 VCSEL array and validated the performance of the system by imaging the distribution of velocity on a rotating target. The results obtained resemble closely the calculated velocity distribution with error below 3% for the entire imaged surface. Results obtained suggest that the image quality improvement due to lithographic alignment of lasers constituting the monolithic array is essential for expanding this concept to massively parallel Doppler imaging systems based on two-dimensional VCSEL arrays.

References and links

1.

T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical Feedback Interferometry,” in Encyclopedia of Sensors, C. A. Grimes and E. C. Dickey, eds., vol. X, pp. 1–20 (American Scientific Publishers, Valencia, CA, 2006).

2.

D. M. Kane and K. A. Shore, eds., Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (John Wiley, Chichester, 2005). [CrossRef]

3.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4(6), 283–294 (2002). [CrossRef]

4.

S. Donati, L. Falzoni, and S. Merlo, “PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–944 (1996). [CrossRef]

5.

G. Giuliani, S. Bozzi-Pietra, and S. Donati, “Self-mixing laser diode vibrometer,” Meas. Sci. Technol. 14(1), 24–32 (2003). [CrossRef]

6.

P. de Groot, G. Gallatin, G. Gardopee, and R. Dixon, “Laser feedback metrology of optical systems,” Appl. Opt. 28(13), 2462–2464 (1989). [CrossRef] [PubMed]

7.

J. R. Tucker, J. L. Baque, Y. L. Lim, A. V. Zvyagin, and A. D. Rakic, “Parallel self-mixing imaging system based on an array of vertical-cavity surface-emitting lasers,” Appl. Opt. 46(25), 6237–6246 (2007). [CrossRef] [PubMed]

8.

Y. L. Lim, K Bertling, P. Rio, J. Tucker, and A. Rakic, “Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect,” in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE 6038, 60381O–1 (2006). [CrossRef]

9.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer Verlag, Berlin, 2003).

10.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16(3), 347–55 (1980). [CrossRef]

11.

K. Petermann, Laser diode modulation and noise, Advances in Optoelectronics (Kluwer Academic Publishers, Dordrecht, 1991).

12.

Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, “Voltage change across the self-coupled semiconductor laser,” IEEE J. Quantum Electron. QE-17(7), 1216–1225 (1981). [CrossRef]

13.

G. Taylor and Q. Yang, “Optimization of the operating point of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. QE-32(8), 1441–1449 (1996).

14.

J. Katz, S. Margalit, C. Harder, D. Wilt, and A. Yariv, “Intrinsic electrical equivalent circuit of a laser diode,” IEEE J. Quantum Electron. QE-17(1), 4–7 (1981). [CrossRef]

15.

R. Juskaitis, N. Rea, and T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33(4), 578–584 (1994). [CrossRef] [PubMed]

16.

Emcore Corporation, “Laser Products: Array VCSELs,” (2009). URL http://www.emcore.com/fiberoptics/lasercomponents/laserproducts?pid= 49.

17.

P. J. de Groot and G. M. Gallatin, “Three-dimensional imaging coherent laser radar array,” Opt. Eng. 28(4), 456–460 (1989).

18.

J. H. Churnside, “Signal-to-noise in a backscatter-modulated Doppler velocimeter,” Appl. Opt. 23(13), 2097–2106 (1984). [CrossRef] [PubMed]

19.

C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection Locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1386–1393 (2003). [CrossRef]

20.

B. Luecke, G. Hergenhan, U. Brauch, M. Scholl, A. Giesen, H. Opower, and H. Huegel, “Autostable injection-locking of a 4×4 VCSEL-array with on chip master laser,” in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and L. Chun, eds., Proc. SPIE 3946, 240–245 (2000). [CrossRef]

21.

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of Vertical-Cavity Surface-Emitting Lasers,” IEEE J. Sel Top Quantum Electron. 3(2), 353–358 (1997). [CrossRef]

22.

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, “Observation of low-frequency fluctuations in Vertical-Cavity Surface-Emitting Lasers,” Opt. Lett. 28(11), 896–898 (2003). [CrossRef] [PubMed]

23.

R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, “Bistable polarization switching in mutually coupled Vertical-Cavity Surface-Emitting Lasers,” Opt. Lett. 31(7), 996–998 (2006). [CrossRef] [PubMed]

OCIS Codes
(250.7260) Optoelectronics : Vertical cavity surface emitting lasers
(280.3420) Remote sensing and sensors : Laser sensors
(280.4788) Remote sensing and sensors : Optical sensing and sensors

ToC Category:
Optical sensing and sensors

History
Original Manuscript: January 23, 2009
Revised Manuscript: March 11, 2009
Manuscript Accepted: March 11, 2009
Published: March 23, 2009

Citation
Yah Leng Lim, Milan Nikolic, Karl Bertling, Russell Kliese, and Aleksandar D. Rakic, "Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout," Opt. Express 17, 5517-5525 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5517


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References

  1. T. Bosch, C. Bes, L. Scalise, and G. Plantier, "Optical Feedback Interferometry," in Encyclopedia of Sensors, C. A. Grimes and E. C. Dickey, eds., vol. X, pp. 1-20 (American Scientific Publishers, Valencia, CA, 2006).
  2. D. M. Kane and K. A. Shore, eds., Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (John Wiley, Chichester, 2005). [CrossRef]
  3. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A, Pure Appl. Opt. 4, 283-294 (2002). [CrossRef]
  4. S. Donati, L. Falzoni, and S. Merlo, "PC-interfaced, compact laser-diode feedback interferometer for displacement measurements," IEEE Trans. Instrum. Meas. 45, 942-944 (1996). [CrossRef]
  5. G. Giuliani, S. Bozzi-Pietra, and S. Donati, "Self-mixing laser diode vibrometer," Meas. Sci. Technol. 14, 24-32 (2003). [CrossRef]
  6. P. de Groot, G. Gallatin, G. Gardopee, and R. Dixon, "Laser feedback metrology of optical systems," Appl. Opt. 28, 2462-2464 (1989). [CrossRef] [PubMed]
  7. J. R. Tucker, J. L. Baque, Y. L. Lim, A. V. Zvyagin, and A. D. Rakic, "Parallel self-mixing imaging system based on an array of vertical-cavity surface-emitting lasers," Appl. Opt. 46, 6237-6246 (2007). [CrossRef] [PubMed]
  8. Y. L. Lim, K. Bertling, P. Rio, J. Tucker, and A. Rakic, "Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect," in Photonics: Design, Technology, and Packaging II, D. Abbott, Y. S. Kivshar, H. H. Rubinsztein-Dunlop, and S. Fan, eds., Proc. SPIE 6038, 60381O-1 (2006). [CrossRef]
  9. H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer Verlag, Berlin, 2003).
  10. R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. QE-16, 347-55 (1980). [CrossRef]
  11. K. Petermann, Laser diode modulation and noise, Advances in Optoelectronics (Kluwer Academic Publishers, Dordrecht, 1991).
  12. Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, "Voltage change across the self-coupled semiconductor laser," IEEE J. Quantum Electron. QE-17, 1216-1225 (1981). [CrossRef]
  13. G. Taylor and Q. Yang, "Optimization of the operating point of a vertical-cavity surface-emitting laser," IEEE J. Quantum Electron. QE-32, 1441-1449 (1996).
  14. J. Katz, S. Margalit, C. Harder, D. Wilt, and A. Yariv, "Intrinsic electrical equivalent circuit of a laser diode," IEEE J. Quantum Electron. QE-17, 4-7 (1981). [CrossRef]
  15. R. Juskaitis, N. Rea, and T. Wilson, "Semiconductor laser confocal microscopy," Appl. Opt. 33, 578-584 (1994). [CrossRef] [PubMed]
  16. Emcore Corporation, "Laser Products: Array VCSELs," (2009). URL http : //www.emcore.com/fiber optics/laser components/laser products?pid = 49.
  17. P. J. de Groot and G. M. Gallatin, "Three-dimensional imaging coherent laser radar array," Opt. Eng. 28, 456-460 (1989).
  18. J. H. Churnside, "Signal-to-noise in a backscatter-modulated Doppler velocimeter," Appl. Opt. 23, 2097-2106 (1984). [CrossRef] [PubMed]
  19. C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, "Injection Locking of VCSELs," IEEE J. Sel. Top. Quantum Electron. 9, 1386-1393 (2003). [CrossRef]
  20. B. Luecke, G. Hergenhan, U. Brauch, M. Scholl, A. Giesen, H. Opower, and H. Huegel, "Autostable injectionlocking of a 4×4 VCSEL-array with on chip master laser," in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and L. Chun, eds., Proc. SPIE 3946, 240-245 (2000). [CrossRef]
  21. J. Y. Law and G. P. Agrawal, "Effects of optical feedback on static and dynamic characteristics of Vertical-Cavity Surface-Emitting Lasers," IEEE J. Sel Top Quantum Electron. 3, 353-358 (1997). [CrossRef]
  22. N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, "Observation of low-frequency fluctuations in Vertical-Cavity Surface-Emitting Lasers," Opt. Lett. 28, 896-898 (2003). [CrossRef] [PubMed]
  23. R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, "Bistable polarization switching in mutually coupled Vertical-Cavity Surface-Emitting Lasers," Opt. Lett. 31, 996-998 (2006). [CrossRef] [PubMed]

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