OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 8 — Apr. 17, 2006
  • pp: 3312–3317
« Show journal navigation

Self-mixing speckle interference in DFB lasers

Daofu Han, Ming Wang, and Junping Zhou  »View Author Affiliations


Optics Express, Vol. 14, Issue 8, pp. 3312-3317 (2006)
http://dx.doi.org/10.1364/OE.14.003312


View Full Text Article

Acrobat PDF (113 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Theoretical analysis and experimental results of self-mixing speckle interference in a distributed feedback (DFB) laser are presented in this paper. Self-mixing speckle interference occurs when external optical feedback comes from a moving rough surface. Dynamic output variations in the DFB laser as well as their probability density functions (PDFs) are analyzed on the basis of speckle theory and self-mixing interference in the DFB laser. Numeric simulations and experiments are in agreement with each other. The both results show that self-mixing speckle interference in DFB laser can be used to measure velocity of target.

© 2006 Optical Society of America

1. Introduction

Laser self-mixing effects are attracting widespread attention. Speckle interference or Doppler Effect introduced the lasers cavity, which produces self-mixing effect, can be used in various industrial and scientific measurement systems. S. Shinohara, L. Scalise, S. Donati, and some other researchers, successively utilized Doppler self-mixing effect and self-mixing speckle effect to measure the velocity, vibration and length of objects [1–7

1. T. Shibata and S. Shinohara et al. “Laser speckle velocimeter using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 45, 499–503 (1996). [CrossRef]

]. Various lasers, such as the Laser diode, Er-Yb-doped phosphate glass fiber laser, CO2 laser and vertical-cavity surface-emitting laser (VCSEL) etc., were used. Speckle signals statistic properties analysis as well as some other analytical methods for the self-mixing signals was presented [8–10

8. T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, and M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode”, IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999). [CrossRef]

]. Self-mixing effects have been studied extensively, but all of the former researches were based on the Fabry-Perot (F-P) cavity.

In this paper, we analyze self-mixing speckle interference in theλ /4 phase-shifted DFB laser. Self-mixing speckle occurs when a portion of light emitted from the DFB laser is reflected by a rough surface and coupled into the DFB cavity. The reentered light mixes with the original light in the DFB cavity and changes the output gain and spectra of the laser. The variations of the output gain as well as their PDFs are analyzed by theoretical simulations and experiments when the rough surface is moving transversely across the laser beam.

2. Theoretic analysis

Theλ /4 phase-shifted DFB self-mixing speckle interference system is schematically shown in fig. 1. Uniform medium grating in the DFB cavity is replaced by two gratings shifted by Λ/4 from each other. M1 and M2, posited at Z=-L/2 and Z=L/2, are left facet and right facet of the DFB cavity respectively. The length of the DFB cavity is L. S, an external reflector with rough surface, as well as M2, form an external cavity. LE is the length of external cavity. We suppose that ρr = ρ̂r e +ψr , ρl = ρ̂l e +ψl are the reflection coefficient M1 and M2 respectively, and ψr(ψl) is the phase term depending on the position of the right (left) facet.

Fig. 1. the schematics of self-mixing speckle interference system

Light output from M2 projects onto S. The backscattered radiations from different elements of the rough surface reenter the cavity, generating random interference, which is known as speckle. Based on the theory of Fraunhofer diffraction [13

13. Max Born and Emil Worlf, Principles of Optics, Pergamon press, (1975).

], the speckles optical field at M2can be calculated in the following.

U(X,Y)=EreiωτtA(x,y)exp(i4πh(x,y)λ)exp(i2π(xX+yY)λLE)dxdy
(1)

Where Er is the original optical field at M2, t is the coupling coefficient of the laser coupled from laser cavity to external cavity, τ is the single trip time of the light in the external cavity, λ is the optical wavelength, (X, Y), (x, y) are the coordinates along the speckles field and the scattering area on the rough surface respectively, A(x, y) is the aperture function of scattering area, h(x, y) is the altitude function of a random surface. We can assume that the random rough surface profile function h(x, y) obeys the statistics [14

14. E. I. Thorsos, “The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acous. Soc. Am. 83, 78–92 (1988). [CrossRef]

, 15

15. A. K. Fung and M. F. Chen, “Numerical simulation of scattering from simple and composite random surfaces,” J. Opt. Soc. Am. A 2, 2274–2284 (1985). [CrossRef]

]:

  1. <h(x,y)>=0,
  2. w=[<h(x,y)h(x,y)>]1/2, where w is root-mean-square (RMS) height,
  3. The autocorrelation function 〈h(x,y)h(x + l,y + l)〉 = w 2 exp(-l 2 /T 2), here T is the correlation length along the surface, l is the distance between two successive points on the surface.

In the case of speckles coupling into the laser cavity, the optical field at M2 is a superposed field, which can be written as

Er=ρrEr+ξtU(X,Y)
(2)

Where t’ is the coupling coefficient of the laser coupled from external cavity to laser cavity, ξ is the feedback ratio of external optical field coupled into laser cavity, U(X, Y) is the complex amplitude of the speckles coupled into the laser cavity.

Conveniently, we consider the external cavity as an equivalent facet of the laser cavity, and then the reflection coefficient of the equivalent facet is

ρreq=ρr+ξtU(X,Y)Er
(3)

Under the assumption of weak feedback, supposed that the light back-scattered from S has an amplitude reflectivity R and phase change ϕ, we can get the equivalent reflection coefficient of the laser facet

ρreq=ρr+(1ρ̂r2)Rejϕ
(4)
Δρr=(1ρ̂r2)Rejϕ
(5)

ρr is the change of ρr due to the feedback light from S.

Comparing the Eq. (3) and Eq. (4) and utility Eq. (1), we get

Rejϕ=ξtU(X,Y)((1ρ̂2)Er)
(6)

In addition, from the former research [11

11. H. Huan, M. Wang, and D. Guo et al. “Self-mixing interference effect of DFB semiconductor lasers,” Appl. Phys. B 79, 1554–1559 (2004). [CrossRef]

], the eigenvalue equation of longitudinal mode in theλ /4 phase-shifted DFB is derived when the scattered light couple into the DFB cavity from the right facet.

(1ρreqρ)(1ρlρ)=(ρreqρ)(ρlρ)e2γL
(7)
ρ=γ+(ajδ)jκ
(8)

Here α denotes threshold loss, δ is the departure of the oscillation frequency from the Bragg frequency, κ is the couple coefficient, and γ is the complex propagation constant.

Due to change of ρr, we can define the deviations of α and δ in the same way as reference [16

16. F. Favre, “Theoretical analysis of external optical feedback on DFB semiconductor lasers,” IEEE J. Quantum Electron. 23, 81–88 (1987). [CrossRef]

], which denote the changes of gain and phase in the DFB cavity

ΔαrLjΔδrL=CrRejϕ
(9)

Deduced from Eq. (7), (8), and (9), the variation of output gain is obtained

ΔG=2cCrRηLcos(ϕarg(Cr)arg(R))
(10)

Where c is the velocity of light, η is the equivalent refractive index of the DFB cavity.

3. Simulations and experiments

The experimental arrangement used to study self-mixing speckle effect is shown in Fig. 2. Light beam, wavelength of which is 1550nm, emitted from a λ /4 phase-shifted DFB, after coupling into a 3dB optical fiber coupler, is split in two parts. One part beam transmitting through an optical attenuator and a fiber self-focusing lens, projects onto a rough surface. Another is coupled into a PD which connected with an amplifier, then a digital storage oscilloscope. The rough surface, we selected an aluminum plate, is set on an accurate platform which is driven by a direct current motor. The backscattered light from the rotated rough surface couples into the laser cavity, and mixes with the original light, causing a fluctuant power output, self-mixing speckle signal. This signal of self-mixing speckle is detected by the PD.

Fig. 2. Schematic configuration of experimental system

In order to understand the speckle signal waveform, the output variations of the DFB laser are obtained by numerical simulation with Eq. (10) and experiment as shown in Fig. 3, when the velocity of rough surface is 167mm/s. We notice that they are all random output power. In the simulations, the RMS height of the surface w is 1.5um, the correlation length l is 3um, the wavelength of laser λ is 1550 nm, the length of DFB cavity L is 0.04cm, the external cavity LE 1cm, κ is 2, ρl is 0, and ρr is 0.53.

Fig. 3. The waveform of output variations from (a) simulation and (b) experiment (v= 167mm/s)

The output variations of the DFB laser are statistically analyzed. We get the PDFs of the output variations from simulation and experiment as shown in Fig. 4. The PDFs is Gaussian-alike shape. The difference of the PDFs between simulation and experiment is small at the same velocity of surface, which proves that the result of theoretical analysis is close to that of experiment.

Fig. 4. The PDFs of output variations from experiment and simulation (v=167mm/s)

The external cavity length is an important parameter affecting the dynamics of the DFB with optical feedback. It affects the PDF of output variation. We simulate the output variations in the external cavity lengths of 1cm, 5cm, and 10cm, and get their PDFs as shown in Fig. 5. We find that the longer the external cavity length, the smaller the output variation. In terms of this finding, the external cavity length is taken into account in subsequent experiment.

Fig. 5. Simulation results showing the effect of external cavity length on the PDF of output variations from a DFB laser

The velocity versus the output variations in the DFB is also investigated. In experiments, we get the PDFs of output variations at velocities of 98mm/s, 167mm/s and 340mm/s. Figure 6 shows the result of experiments. It is evident that the shape of PDF becomes more Gaussian-alike with the velocity increasing.

Fig. 6. The results of experiment showing the PDFs of output variation vary with velocities of surface

Additionally, the fluctuations frequency in the DFB output variations are studied. For different velocities of 98mm/s, 167mm/s, 257mm/s, 340mm/s, 431mm/s and 579mm/s, the output variations are experimentally obtained and processed by the method of Fast Fourier Transform (FFT). A linear relation between mean speckle frequencies and velocities of surface is shown in Fig. 7. Mean speckle frequency is defined as the ratio of number of fluctuations in the detected signal to the measurement time.

Fig. 7. The linear dependence between mean speckle frequencies and velocities of surface in experiment

4. Conclusion

We have investigated the speckle interference in the DFB lasers. Theoretical analysis and experiments results show that the PDF of speckle signal generated in a DFB laser is Gaussian distribution. The linear relationship between the mean speckle frequency and the velocity of rough surface has been obtained. It is promising to develop a new velocity sensor based on self-mixing speckle interference of the DFB laser.

Acknowledgments

This work was supported by the National Natural Science Foundation of China and the Specialized Research Fund for the Doctoral Program of Higher Education (20050319007) and Jiangsu province high-novel technology project (BG2003024).

References and Links

1.

T. Shibata and S. Shinohara et al. “Laser speckle velocimeter using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 45, 499–503 (1996). [CrossRef]

2.

P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers,” IEEE Photonics Technol. Lett. 14, 1717–1721 (2002). [CrossRef]

3.

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

4.

M. Norgia and S. Donati, “A displacement-measuring instrument utilizing self-mixing interferometry”, IEEE Trans. Instrum. Meas. 52, 1765–1770 (2003). [CrossRef]

5.

L. Scalise, Y. G. Yu, and G. Giuliani, et al. “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004). [CrossRef]

6.

J. W. Choi, M. J. Yu, and M. Kopica, “Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser,” Proc. Soc. Photo-Opt. Instrum. 5240, 230–234 (2004).

7.

M. Laroche, L. Kervevan, H. Gilles, S. Girard, and J.K. Sahu, “Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser,” Appl. Phys. B 80, 603–607 (2005). [CrossRef]

8.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, and M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode”, IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999). [CrossRef]

9.

Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, and M. Sumi, “Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode,” Appl. Opt. 38, 6859–6865(1999). [CrossRef]

10.

M. Norgi, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37, 800–806 (2001). [CrossRef]

11.

H. Huan, M. Wang, and D. Guo et al. “Self-mixing interference effect of DFB semiconductor lasers,” Appl. Phys. B 79, 1554–1559 (2004). [CrossRef]

12.

J. Zhou and M. Wang, “Effects of self-mixing interference on gain-coupled distributed-feedback lasers,” Opt. Express 13, 1848–1854 (2005). [CrossRef] [PubMed]

13.

Max Born and Emil Worlf, Principles of Optics, Pergamon press, (1975).

14.

E. I. Thorsos, “The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acous. Soc. Am. 83, 78–92 (1988). [CrossRef]

15.

A. K. Fung and M. F. Chen, “Numerical simulation of scattering from simple and composite random surfaces,” J. Opt. Soc. Am. A 2, 2274–2284 (1985). [CrossRef]

16.

F. Favre, “Theoretical analysis of external optical feedback on DFB semiconductor lasers,” IEEE J. Quantum Electron. 23, 81–88 (1987). [CrossRef]

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(260.3160) Physical optics : Interference

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 3, 2006
Revised Manuscript: April 6, 2006
Manuscript Accepted: April 6, 2006
Published: April 17, 2006

Citation
Daofu Han, Ming Wang, and Junping Zhou, "Self-mixing speckle interference in DFB lasers," Opt. Express 14, 3312-3317 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3312


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. Shibata, S. Shinohara et al. "Laser speckle velocimeter using self-mixing laser diode," IEEE Trans. Instrum. Meas. 45,499-503 (1996). [CrossRef]
  2. P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002). [CrossRef]
  3. G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003). [CrossRef]
  4. M. Norgia, S. Donati, "A displacement-measuring instrument utilizing self-mixing interferometry", IEEE Trans. Instrum. Meas. 52, 1765-1770 (2003). [CrossRef]
  5. L. Scalise, Y. G. Yu, G. Giuliani,  et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004). [CrossRef]
  6. J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).
  7. M. Laroche, L. Kervevan, H. Gilles, S. Girard, J.K. Sahu, "Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser," Appl. Phys. B 80, 603-607 (2005). [CrossRef]
  8. T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999). [CrossRef]
  9. Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, M . Sumi, "Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode," Appl. Opt. 38, 6859-6865(1999). [CrossRef]
  10. M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001). [CrossRef]
  11. H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004). [CrossRef]
  12. J. Zhou, M. Wang, "Effects of self-mixing interference on gain-coupled distributed-feedback lasers," Opt. Express 13,1848-1854 (2005). [CrossRef] [PubMed]
  13. Max Born and Emil Worlf, Principles of Optics, Pergamon press, (1975).
  14. E. I. Thorsos, "The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acous. Soc. Am. 83, 78-92 (1988). [CrossRef]
  15. A. K. Fung, M. F. Chen, "Numerical simulation of scattering from simple and composite random surfaces," J. Opt. Soc. Am. A 2, 2274-2284 (1985). [CrossRef]
  16. F. Favre, "Theoretical analysis of external optical feedback on DFB semiconductor lasers," IEEE J. Quantum Electron. 23, 81-88 (1987). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited