Abstract

Feedback parameter (the C factor) is an important parameter for a semiconductor laser operating in the regime of external optical feedback. Self-mixing interferometry (SMI) has been proposed for the measurement of the parameter, based on the time-domain analysis of the output power waveforms (called SMI signals) in presence of feedback. However, the existing approaches only work for a limited range of C, below about 3.5. This paper presents a new method to measure C based on analysis of the phase signal of SMI signals in the frequency domain. The proposed method covers a large range of C values, up to about 10. Simulations and experimental results are presented for verification of the proposed method.

© 2011 OSA

1. Introduction

As an active area of research, semiconductor lasers (SLs) with external optical feedback has attracted extensive theoretical and experimental work during the past decades. A significant research outcome in this area is an emerging technology for sensing and measurement called optical feedback self-mixing interferometry (SMI) technique. The basic structure of the SMI is shown in Fig. 1 , consisting of an SL, a lens and a target. The optical feedback from the external cavity modulates the SL power, which then can be used to measure the movement of the external cavity or retrieve system parameters of an SMI [110].

The scenario behind SMI sensing is the theoretical model developed from Lang and Kobayashi equations [11]. The model consists of the following equations [19]:

ϕF=ϕ0Csin[ϕF+arctan(α)],
g(ϕ0)=cos(ϕF),
P(ϕ0)=P0[1+m×g(ϕ0)].

Definitions of the parameters and variables in Eqs. (1)-(3) are listed in Table 1 .

Tables Icon

Table 1. Definition of the variables in Eq. (1)(3)

From Eqs. (1)(3), we see that ϕ0 affects the emitted powerP(ϕ0), which can be easily measured with a photo detector placed on the rear mirror of the SL. As g(ϕ0)=P(ϕ0)P0mP0, we can obtain g(ϕ0) through data processing on P(ϕ0). Without loss of generality, in this paper we use g(ϕ0)to study the features of the SMI signal. Physical quantities associated with the external cavity (e.g. velocity, vibration or displacement, etc.) can be extracted from an SMI sensing signal through the phaseϕ0=4πυ0L/c .

It is seen that there are two parameters in Eqs. (1)(3), that is, optical feedback parameter denoted by C [12,13], and linewidth enhancement factor (or α-factor) of an SL. As a key parameter of an SL, α characterizes the linewidth, the chirp, the injection lock range in an SL, and also characterizes the response of the SL to optical feedback [14]. Measurement of α has attracted extensive research with various approaches proposed [14], such as linewidth methods [15,16], FM/AM methods [1719], optical injection [2022] and optical feedback [1,6,7,23,24]. These different approaches were compared systematically in [25,26].

The feedback parameter C is also an important parameter which tells the operational modes of an SL application system. An SL is considered to operate in weak optical feedback regime when0<C<1; it runs moderate feedback regime for 1<C<4.6and in strong feedback regime when C>4.6 [2,5,8]. Nonlinear dynamics, spectral behavior and chaos in an SL are also closely related to the C value [12,13,2729]. Therefore, the measurement of C is very important for studying the behaviors of an SL and its applications.

In recent years, a number of SMI-based approaches are proposed to measure α, which can also yield the C value [1,6,7]. However, these methods are only applicable to limited range of C, as discussed below.

The first SMI based technique for α measurement was reported in [1] where SMI operates in moderate optical feedback regime. When C>1, the optical feedback in an SL causes hysteresis phenomenon in the laser power [2,11,12]. In this case, the waveform is sawtooth like [1,2,8,12]. An example of the hysteresis is plot in Fig. 2 using Eq. (1) and Eq. (2), where C=2 and α=5. When ϕ0 increases, g(ϕ0) follows the path A1-B-B1, which is different from the path B1-A-A1 for decreasing ϕ0. The area A1-B-B1-A is called hysteresis area with the width represented as ϕ0,AB. ϕ0,AB has been found in [12] as:

 

Fig. 2 Hysteresis phenomenon of SMI signal and the measurement principle on αin [20] with C=2and α=5.

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ϕ0,AB=2{C21+arccos(1C)π}.

ϕ0,AB can be measured by ϕ0,AB=ϕ0,CBϕ0,AD. ϕ0,CB, ϕ0,AD are read from the SMI waveform [1]. However, when C increases to a certain value, the hysteresis area will cover ϕ0,CB and ϕ0,AD, and thus they will disappear from the SMI waveform. In this case, the approach in [1] is no longer valid. Our simulations show that the approach in [1] can only be used when 1<C<3.5.

An SMI signal at weak feedback regime is similar to a traditional interference signal containing sinusoidal fringe pattern. In this case a data fitting algorithm and its improved version were reported in [6,7] for the measurement of α and C . The algorithm utilizes the SMI model incorporates an optimal estimate of α and C to yield the best match for the observed signals. Obviously, the approaches presented in [6,7] are only valid for the case of C<1. Hence the existing SMI methods for C measurement can only be used for the cases of C<3.5.

For an SL with external optical feedback, the value of C is determined by the following [2]:

C=ηττSL(1R2)R3R21+α2,
where R2, R3, η and τSLare, respectively, the power reflectivity of the SL cavity, the power reflectivity of the external cavity, the coupling coefficient of the feedback power, and the round trip time in the SL cavity. Note that η and τ are not fixed values when a moving target is used to form the external cavity of an SL. It is obvious that the value of C varies in different SL systems and the value can be greater than 3.5. Hence measurement of C over a large range is required.

In this paper, we propose to estimate C over an extend range of its value (up to 10 and more). Compared to existing techniques which are based on waveform analysis in time domain, the proposed technique is in the frequency domain where the C value is determined by looking at the spectrum of the phase signals derived from the SMI signalg(ϕ0). With existing time-domain approaches [1,6,7], different algorithms must be employed in different regimes of optical feedback. In contrast, the proposed approach employs the same algorithm to determine C, which covers different optical feedback regimes.

2. The proposed method

2.1 Operation principle

Let us consider the case of an external target moving periodically, resulting in the external cavity length L(t)and thus ϕ0 also periodically changing with time. Equation (2) and Eq. (1) can be rewritten as:

g(t)=cos(ϕF(t)),
ϕF(t)=ϕ0(t)Csin{ϕF(t)+arctan(α)}.

Taking Fourier transform, denoted by F{}, on both sides of Eq. (7), we have

ΦF(f)=Φ0(f)CF{sin[ϕF(t)+arctan(α)]},
where ΦF(f)and Φ0(f)are the Fourier transforms of ϕF(t)and ϕ0(t)respectively. For ease of manipulation let us introduce a function
ϕ1(t)=sin{ϕF(t)+arctan(α)},
so that Eq. (8) becomes
ΦF(f)=Φ0(f)CF{ϕ1(t)}=Φ0(f)CΦ1(f),
where Φ1(f) is the Fourier transforms of ϕ1(t).

From the SMI setup, we are able to acquire the SMI signal g(t). Based on our previous work [9], ϕF(t) can be obtained from g(t) by applying inverse cosine operation and phase unwrapping. Thereafter, we calculate the spectrum of ϕF(t), that is ΦF(f). Meanwhile, when ϕF(t) is available, we are able to work out ϕ1(t) using Eq. (9) and compute its spectrum Φ1(f).

As ϕ0(t)=4πυ0L(t)/c, ϕ0(t) also describes the moving of the target. If the external target moves in a manner close to simple harmonic vibration, ϕ0(t) will be close to a sinusoidal, in which case it can be considered as of narrow band in frequency domain.

Given ϕ0(t)narrow band in nature, from Eqs. (7) and (8), ϕF(t) should exhibit a broader spectrum than ϕ0(t) because of the nonlinear mapping from ϕ0(t) to ϕF(t). In other words, ΦF(f) and Φ1(f) should spread over a wider frequency range than Φ0(f) does. Now, we can divide the frequency range of non-vanishing spectrum of ΦF(f) and Φ1(f) into two domains, denoted by Ω1 and Ω2respectively, in which the spectrum of Φ0(f) is non-vanishing or vanishing, i.e.:

Ω1:f{ΦF(f)0,Φ1(f)0,Φ0(f)0},  and
Ω2:f{ΦF(f)0,Φ1(f)0,Φ0(f)=0}.

Considering the frequency components of ΦF(f) and Φ1(f) in Ω2, from Eq. (10) we have

ΦF(f)=C×Φ1(f),fΩ2.

Therefore C can be calculated as:

C=|ΦF(f)||Φ1(f)|,fΩ2.

The above relation is valid for all the frequency components in Ω2. In practice, we can employ a summation over all frequency components in Ω2to increase the accuracy of the estimate:

C=fΩ2|ΦF(f)|fΩ2|Φ1(f)|.

To apply the method, we shall identify Ω1 and Ω2. In the cases of harmonic vibration, ϕ0(t) is a periodic function with a fundamental (vibration) frequency f0. Then Φ0(f) should exhibit a large fundamental component atf0, and some harmonic components. The highest harmonic component will in general depend on the actual waveform, and yet in practice we consider 15f0as the upper frequency necessary to cover well the spectrum details. This choice will be confirmed by simulations discussed in the next Section.

In terms of the upper bound of Ω2, as ΦF(f) and Φ1(f) are available, we simple choose fM as high as possible while observing ΦF(fM)0 and Φ1(f)0. In this paper we have taken Ω2 to be {15f0,fM}.

2.2 Verification of the proposed method by simulation

In order to verify the effectiveness of the formula presented in Eq. (12) and Eq. (13), let us first consider that the external target vibrates in two possible modes, simple harmonic vibration where L(t) is a sinusoidal function, and a more complicated case where L(t) is a triangular function. In this Section we present the results of computer simulation on these two cases.

In the first case, ϕ0(t) is given as follows:

ϕ0(t)=φ0+Δφsin(2πf0t),
where φ0 is the light phase at the equilibrium position of a vibrating target. Δφ is the maximum phase deviation caused by target vibration amplitude, and f 0 is the vibration frequency. In the numerical simulation, we setα=3, C=5,φ0=3.9×106(rad), Δφ=10π(rad), f0=200Hz, and take a sampling frequency fs=51200Hz. Using Eqs. (14), (9) and (7), we obtain ϕ0(t), ϕ1(t) andϕF(t)as shown on the left side of Fig. 3 . Applying Discrete Fourier Transform (DFT) on these three signals, we obtain their spectra (in modulus) as shown in the right side of Fig. 3. We can see that both ϕ1(t) and ϕF(t)exhibit many high frequency components in contrast to signal ϕ0(t). This enables us to determine the two frequency ranges Ω1 and Ω2.

 

Fig. 3 Waveforms and spectra of signals ϕ0(t), Cϕ1(t), and ϕF(t) for sinusoidal case with C=5 and α=3.

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In order to demonstrate the process of calculating C, we plot details of spectra ofϕ0(t), ϕ1(t), andϕF(t)on Fig. 4 . It is seen that Φ0(f)is zero but Φ0(f)0 when f>2000Hz . Hence we can set the lower band of Ω2as 2000Hz, or 10f0. Based on Fig. 4 we can also set the upper bound of Ω2 to be 25000Hz or 125f0. By looking at the spectra at 5800Hz (which is on Ω2) on Fig. 4, we observeΦF(5800)=0.3701 and Φ1(5800)=0.0740, and hence by Eq. (12) we can determine the C value asC=0.3701/0.0740=5.0001, which is very close to the true value used in the simulations. By using Eq. (13) over Ω2:f[2000Hz,25000Hz], the C value is obtained as C=0.3701/0.0740=5.0001, which is also very close to the true value.

 

Fig. 4 Detailed spectra of signals ϕ0(t), ϕ1(t), and ϕF(t) for the sinusoidal case.

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Let us consider the second case, where L(t) is a triangular function with fundamental frequency of 200 Hz. Figure 5 shows ϕ0(t), ϕ1(t), and ϕF(t)in time domain and frequency domains, respectively with C=5 and α=3. We noticed that ϕ0(t) only exhibit spectrum over the frequency range from 0Hz to 3000Hz, and that ϕF(t) and ϕ1(t) has a much broader range than ϕ0(t), that is, they still have frequency components in a wide range of f3000Hz.

 

Fig. 5 Waveforms and spectra of signals ϕ0(t), Cϕ1(t), and ϕF(t) for the triangular case.

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We plot detailed spectra for signalsϕ0(t), ϕ1(t) and ϕF(t) on Fig. 6 , based on which we can haveΩ2:f[3000Hz,25000Hz] . For example, using Eq. (12) at the frequency of 3800Hz we are able to obtain 5.0060 for C. Applying Eq. (13) to all the frequency components over [3000Hz, 25000Hz], we get C=5.0001which is closer to the true value.

 

Fig. 6 Detailed spectra of signals ϕ0(t), ϕ1(t), and ϕF(t) for triangular case.

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Extensive simulations have been done for verification of the proposed method. We generated SMI data using different sets of C and α shown in Table 2 . The estimated C values using the method in [1] and the proposed method in this paper are shown in Table 2. It is seen that the proposed method is more accurate than the one in [1].

Tables Icon

Table 2. Estimated C Values Using Method in [1] and Proposed Method in this Paper

Note that the results shown in Table 2 are obtained using an accurate α value. In practice, it is hard to obtain accurate α for an SL. In fact α is such a complex parameter in that for the same SL, different α values can be obtained by using different measurement technique [26]. However, α is usually considered between 3 and 7 [2]. Hence, we may simply choose an α value within the possible range to measure C using the proposed approach. This requires us to investigate the influence of using such an inaccurate α value on the performance of the proposed approach. To this end, we carried out a set of simulations with the results shown in Table 3 . In the simulations, the true value of α is assumed to be 5 and C takes different values from 0.5 to 6.5. For each C values, we choose different α values (that is, 3, 4, 5, 6 and 7) respectively to estimate C using Eq. (13). It is seen that the estimated C values are always close to the true values as shown by the small relative standard deviations in Table 3.

Tables Icon

Table 3. Influence of αon the Estimation of C

3. Verification using experimental data

In order to test the measuring approach described in Section 2, we implemented an experimental SMI system, which is the same as the one described in our previous work [8]. The optical set-up consists of a laser diode (LD), a focus lens and a loudspeaker as the external target. The electrical set-up consists of LD driving devices, an optical power detection circuit and a digital oscilloscope. In the experiment, the laser diode (LD) is a HL7851G laser diode emitting at λ0=785nm. The LD is biased with a DC current of 90 mA and operates in single longitudinal mode regime. The sinusoidal vibration is generated by a loudspeaker driven by a signal generator.

For the purpose of comparison, we use the same experimental data presented in [8]. We also preprocessed the signal in order to remove unwanted noise and slow time-varying fluctuation in its amplitude. The measurement procedure is summarized below:

  • ⁃ Step 1. Preprocess an SMI signal by means of digital filtering for spike-like noise removal [10];
  • ⁃ Step 2. Normalize the SMI signal to get g(t);
  • ⁃ Step 3. Determine the vibration frequency f 0 by auto-correlation [7];
  • ⁃ Step 4. Carry out inverse cosine function operation on g(t) and then phase-unwrapping to obtain ϕF(t) [9];
  • ⁃ Step 5. Calculate ϕ1(t) using Eq. (9) with assuming α=3 (or obtain a α value by the methods mentioned in [26]).
  • ⁃ Step 6. Apply DFT on ϕF(t) and ϕ1(t) and obtain their spectra;
  • ⁃ Step 7. Set Ω2[15f0,fM], where fMis chosen as half of the sampling frequency. Calculate C value using Eq. (13) over all the frequency components onΩ2.

The waveforms of the experimental data are shown in Fig. 7 , which are taken from [8]. Each C value shown on Fig. 7 was obtained in [8] by simulating waveforms with different C values to match the experimental ones (which is a tedious task). We applied the above procedure to the data and obtained C values for each of the waveforms depicted in Fig. 7, and the results are shown in Table 4 . For illustration purposes, Fig. 8 shows the details of applying the proposed method to the waveform in Fig. 7. (c), yielding C=0.2901/0.0444=6.534. For comparison, we also show the results of the C values provided by [8] and the results obtained by the method in [1]. It is seen that the C values obtained by the proposed method are consistent to the values provided in [8]. However, for most cases, the method in [1] is not able to determine the value of C.

 

Fig. 7 Experimental SMI signals with different C values [8].

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Tables Icon

Table 4. Estimated C Values Using Experimental Signals

 

Fig. 8 Measurement process for the experimental signal shown in Fig. 7(c) using the proposed method.

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4. Conclusion

The paper describes an SMI-based method for measuring feedback factor C in a semiconductor laser with external optical feedback. In contrast to existing methods, which are usually based on time-domain analysis of SMI signals, the proposed one is of frequency domain in nature, which is based on analysis of the magnitude spectra of two phase signals derived from an SMI signal. The proposed approach is advantageous in that it can be used for any optical feedback level, and hence lifts the limitation in existing SMI based methods for measuring C. Effectiveness of the proposed method has been confirmed by both simulations and experimental verifications.

References and links

1. Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004). [CrossRef]  

2. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995). [CrossRef]  

3. L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004). [CrossRef]  

4. N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998). [CrossRef]  

5. 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), S283–S294 (2002). [CrossRef]  

6. 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(8), 1058–1064 (2005). [CrossRef]  

7. 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(7), 527–534 (2007). [CrossRef]  

8. 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(7), 840–848 (2009). [CrossRef]  

9. Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010). [CrossRef]  

10. Y. Yu, J. Xi, and J. F. Chicharo, “Improving the Performance in an Optical feedback Self-mixing Interferometry System using Digital Signal Pre-processing,” in Proceedings of IEEE Conference on Intelligent Signal Processing (Institute of Electrical and Electronic Engineers, Alcala de Henares, 2007), pp. 1–6.

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

12. G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984). [CrossRef]  

13. K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1(2), 480–489 (1995). [CrossRef]  

14. M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–An overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987). [CrossRef]  

15. D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995). [CrossRef]  

16. Y. Arakawa and A. Yariv, “Fermi energy dependence of linewidth enhancement factor of GaAlAs buried heterostructure lasers,” Appl. Phys. Lett. 47(9), 905–907 (1985). [CrossRef]  

17. L. Hua, “RF-modulation measurement of linewidth enhancement factor and nonlinear gain of vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 8(12), 1594–1596 (1996). [CrossRef]  

18. H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004). [CrossRef]  

19. H. Nakajima and J. C. Bouley, “Observation of power dependent linewidth enhancement factor in 1.55 mu m strained quantum well lasers,” Electron. Lett. 27(20), 1840–1841 (1991). [CrossRef]  

20. G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001). [CrossRef]  

21. W.-H. Seo and J. F. Donegan, “Linewidth enhancement factor of lattice-matched InGaNAs/GaAs quantum wells,” Appl. Phys. Lett. 82(4), 505–507 (2003). [CrossRef]  

22. C. H. Shin, M. Teshima, and M. Ohtsu, “Novel measurement method of linewidth enhancement factor in semiconductor lasers by optical self-locking,” Electron. Lett. 25(1), 27–28 (1989). [CrossRef]  

23. Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000). [CrossRef]  

24. D. Fye, “Relationship between carrier-induced index change and feedback noise in diode lasers,” IEEE J. Quantum Electron. 18(10), 1675–1678 (1982). [CrossRef]  

25. T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43(1), 6–15 (2007). [CrossRef]  

26. T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008). [CrossRef]  

27. N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988). [CrossRef]  

28. H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986). [CrossRef]  

29. V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002). [CrossRef]  

References

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  1. Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
    [Crossref]
  2. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
    [Crossref]
  3. L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
    [Crossref]
  4. N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
    [Crossref]
  5. 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), S283–S294 (2002).
    [Crossref]
  6. 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(8), 1058–1064 (2005).
    [Crossref]
  7. 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(7), 527–534 (2007).
    [Crossref]
  8. 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(7), 840–848 (2009).
    [Crossref]
  9. Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
    [Crossref]
  10. Y. Yu, J. Xi, and J. F. Chicharo, “Improving the Performance in an Optical feedback Self-mixing Interferometry System using Digital Signal Pre-processing,” in Proceedings of IEEE Conference on Intelligent Signal Processing (Institute of Electrical and Electronic Engineers, Alcala de Henares, 2007), pp. 1–6.
  11. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [Crossref]
  12. G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984).
    [Crossref]
  13. K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1(2), 480–489 (1995).
    [Crossref]
  14. M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–An overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
    [Crossref]
  15. D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
    [Crossref]
  16. Y. Arakawa and A. Yariv, “Fermi energy dependence of linewidth enhancement factor of GaAlAs buried heterostructure lasers,” Appl. Phys. Lett. 47(9), 905–907 (1985).
    [Crossref]
  17. L. Hua, “RF-modulation measurement of linewidth enhancement factor and nonlinear gain of vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 8(12), 1594–1596 (1996).
    [Crossref]
  18. H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
    [Crossref]
  19. H. Nakajima and J. C. Bouley, “Observation of power dependent linewidth enhancement factor in 1.55 mu m strained quantum well lasers,” Electron. Lett. 27(20), 1840–1841 (1991).
    [Crossref]
  20. G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001).
    [Crossref]
  21. W.-H. Seo and J. F. Donegan, “Linewidth enhancement factor of lattice-matched InGaNAs/GaAs quantum wells,” Appl. Phys. Lett. 82(4), 505–507 (2003).
    [Crossref]
  22. C. H. Shin, M. Teshima, and M. Ohtsu, “Novel measurement method of linewidth enhancement factor in semiconductor lasers by optical self-locking,” Electron. Lett. 25(1), 27–28 (1989).
    [Crossref]
  23. Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000).
    [Crossref]
  24. D. Fye, “Relationship between carrier-induced index change and feedback noise in diode lasers,” IEEE J. Quantum Electron. 18(10), 1675–1678 (1982).
    [Crossref]
  25. T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43(1), 6–15 (2007).
    [Crossref]
  26. T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
    [Crossref]
  27. N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988).
    [Crossref]
  28. H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986).
    [Crossref]
  29. V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002).
    [Crossref]

2010 (1)

Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
[Crossref]

2009 (1)

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(7), 840–848 (2009).
[Crossref]

2008 (1)

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
[Crossref]

2007 (2)

T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43(1), 6–15 (2007).
[Crossref]

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(7), 527–534 (2007).
[Crossref]

2005 (1)

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(8), 1058–1064 (2005).
[Crossref]

2004 (3)

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
[Crossref]

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

2003 (1)

W.-H. Seo and J. F. Donegan, “Linewidth enhancement factor of lattice-matched InGaNAs/GaAs quantum wells,” Appl. Phys. Lett. 82(4), 505–507 (2003).
[Crossref]

2002 (2)

V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002).
[Crossref]

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), S283–S294 (2002).
[Crossref]

2001 (1)

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001).
[Crossref]

2000 (1)

Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000).
[Crossref]

1998 (1)

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

1996 (1)

L. Hua, “RF-modulation measurement of linewidth enhancement factor and nonlinear gain of vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 8(12), 1594–1596 (1996).
[Crossref]

1995 (3)

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1(2), 480–489 (1995).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

1991 (1)

H. Nakajima and J. C. Bouley, “Observation of power dependent linewidth enhancement factor in 1.55 mu m strained quantum well lasers,” Electron. Lett. 27(20), 1840–1841 (1991).
[Crossref]

1989 (1)

C. H. Shin, M. Teshima, and M. Ohtsu, “Novel measurement method of linewidth enhancement factor in semiconductor lasers by optical self-locking,” Electron. Lett. 25(1), 27–28 (1989).
[Crossref]

1988 (1)

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988).
[Crossref]

1987 (1)

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–An overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[Crossref]

1986 (1)

H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986).
[Crossref]

1985 (1)

Y. Arakawa and A. Yariv, “Fermi energy dependence of linewidth enhancement factor of GaAlAs buried heterostructure lasers,” Appl. Phys. Lett. 47(9), 905–907 (1985).
[Crossref]

1984 (1)

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984).
[Crossref]

1982 (1)

D. Fye, “Relationship between carrier-induced index change and feedback noise in diode lasers,” IEEE J. Quantum Electron. 18(10), 1675–1678 (1982).
[Crossref]

1980 (1)

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

Acket, G.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984).
[Crossref]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002).
[Crossref]

Arakawa, Y.

Y. Arakawa and A. Yariv, “Fermi energy dependence of linewidth enhancement factor of GaAlAs buried heterostructure lasers,” Appl. Phys. Lett. 47(9), 905–907 (1985).
[Crossref]

Bosch, T.

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(7), 527–534 (2007).
[Crossref]

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(8), 1058–1064 (2005).
[Crossref]

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
[Crossref]

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), S283–S294 (2002).
[Crossref]

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

Bosch, T. M.

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(7), 840–848 (2009).
[Crossref]

Bouley, J. C.

H. Nakajima and J. C. Bouley, “Observation of power dependent linewidth enhancement factor in 1.55 mu m strained quantum well lasers,” Electron. Lett. 27(20), 1840–1841 (1991).
[Crossref]

Buus, J.

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–An overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[Crossref]

Chicharo, J.

Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
[Crossref]

Chicharo, J. F.

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(7), 840–848 (2009).
[Crossref]

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(7), 527–534 (2007).
[Crossref]

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(8), 1058–1064 (2005).
[Crossref]

Chuang, S. L.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001).
[Crossref]

Den Boef, A.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984).
[Crossref]

Donati, S.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

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), S283–S294 (2002).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Donegan, J. F.

W.-H. Seo and J. F. Donegan, “Linewidth enhancement factor of lattice-matched InGaNAs/GaAs quantum wells,” Appl. Phys. Lett. 82(4), 505–507 (2003).
[Crossref]

Fan, Y.

Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
[Crossref]

Feld, S.

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

Fordell, T.

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
[Crossref]

T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43(1), 6–15 (2007).
[Crossref]

Fye, D.

D. Fye, “Relationship between carrier-induced index change and feedback noise in diode lasers,” IEEE J. Quantum Electron. 18(10), 1675–1678 (1982).
[Crossref]

Giuliani, G.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
[Crossref]

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), S283–S294 (2002).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Gouaux, F.

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

Halbritter, H.

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

Hua, L.

L. Hua, “RF-modulation measurement of linewidth enhancement factor and nonlinear gain of vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 8(12), 1594–1596 (1996).
[Crossref]

Jacquet, J.

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

Jin, X.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001).
[Crossref]

Kobayashi, K.

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

Kuksenkov, D.

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

Lang, R.

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

Leibenguth, R.

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

Lenstra, D.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984).
[Crossref]

Lindberg, A. M.

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
[Crossref]

T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43(1), 6–15 (2007).
[Crossref]

Liu, G.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001).
[Crossref]

Meissner, P.

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

Merlo, S.

V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Nakajima, H.

H. Nakajima and J. C. Bouley, “Observation of power dependent linewidth enhancement factor in 1.55 mu m strained quantum well lasers,” Electron. Lett. 27(20), 1840–1841 (1991).
[Crossref]

Nam, C. H.

Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000).
[Crossref]

Norgia, M.

V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002).
[Crossref]

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), S283–S294 (2002).
[Crossref]

Ohtsu, M.

C. H. Shin, M. Teshima, and M. Ohtsu, “Novel measurement method of linewidth enhancement factor in semiconductor lasers by optical self-locking,” Electron. Lett. 25(1), 27–28 (1989).
[Crossref]

Olesen, H.

H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986).
[Crossref]

Osinski, M.

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–An overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[Crossref]

Osmundsen, J.

H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986).
[Crossref]

Park, J. R.

Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000).
[Crossref]

Petermann, K.

K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1(2), 480–489 (1995).
[Crossref]

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988).
[Crossref]

Plantier, G.

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
[Crossref]

Provost, J. G.

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

Riemenschneider, F.

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

Sagnes, I.

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

Scalise, L.

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
[Crossref]

Schunk, N.

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988).
[Crossref]

Scire, A.

V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002).
[Crossref]

Seo, W.-H.

W.-H. Seo and J. F. Donegan, “Linewidth enhancement factor of lattice-matched InGaNAs/GaAs quantum wells,” Appl. Phys. Lett. 82(4), 505–507 (2003).
[Crossref]

Servagent, N.

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

Shin, C. H.

C. H. Shin, M. Teshima, and M. Ohtsu, “Novel measurement method of linewidth enhancement factor in semiconductor lasers by optical self-locking,” Electron. Lett. 25(1), 27–28 (1989).
[Crossref]

Shin, Y. S.

Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000).
[Crossref]

Swirhun, S.

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

Symonds, C.

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

Temkin, H.

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

Teshima, M.

C. H. Shin, M. Teshima, and M. Ohtsu, “Novel measurement method of linewidth enhancement factor in semiconductor lasers by optical self-locking,” Electron. Lett. 25(1), 27–28 (1989).
[Crossref]

Tromborg, B.

H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986).
[Crossref]

Verbeek, B.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984).
[Crossref]

Wilmsen, C.

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

Xi, J.

Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
[Crossref]

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(7), 840–848 (2009).
[Crossref]

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(7), 527–534 (2007).
[Crossref]

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(8), 1058–1064 (2005).
[Crossref]

Yariv, A.

Y. Arakawa and A. Yariv, “Fermi energy dependence of linewidth enhancement factor of GaAlAs buried heterostructure lasers,” Appl. Phys. Lett. 47(9), 905–907 (1985).
[Crossref]

Ye, H.

Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
[Crossref]

Yoon, T. H.

Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000).
[Crossref]

Yu, Y.

Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
[Crossref]

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(7), 840–848 (2009).
[Crossref]

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(7), 527–534 (2007).
[Crossref]

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(8), 1058–1064 (2005).
[Crossref]

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
[Crossref]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

Appl. Phys. Lett. (3)

D. Kuksenkov, S. Feld, C. Wilmsen, H. Temkin, S. Swirhun, and R. Leibenguth, “Linewidth and alpha-factor in AlGaAs/GaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 66(3), 277–279 (1995).
[Crossref]

Y. Arakawa and A. Yariv, “Fermi energy dependence of linewidth enhancement factor of GaAlAs buried heterostructure lasers,” Appl. Phys. Lett. 47(9), 905–907 (1985).
[Crossref]

W.-H. Seo and J. F. Donegan, “Linewidth enhancement factor of lattice-matched InGaNAs/GaAs quantum wells,” Appl. Phys. Lett. 82(4), 505–507 (2003).
[Crossref]

Electron. Lett. (3)

C. H. Shin, M. Teshima, and M. Ohtsu, “Novel measurement method of linewidth enhancement factor in semiconductor lasers by optical self-locking,” Electron. Lett. 25(1), 27–28 (1989).
[Crossref]

H. Halbritter, F. Riemenschneider, J. Jacquet, J. G. Provost, C. Symonds, I. Sagnes, and P. Meissner, “Chirp and linewidth enhancement factor of tunable, optically-pumped long wavelength VCSEL,” Electron. Lett. 40(4), 242–244 (2004).
[Crossref]

H. Nakajima and J. C. Bouley, “Observation of power dependent linewidth enhancement factor in 1.55 mu m strained quantum well lasers,” Electron. Lett. 27(20), 1840–1841 (1991).
[Crossref]

IEEE J. Quantum Electron. (12)

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

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20(10), 1163–1169 (1984).
[Crossref]

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–An overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

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(8), 1058–1064 (2005).
[Crossref]

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(7), 527–534 (2007).
[Crossref]

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(7), 840–848 (2009).
[Crossref]

D. Fye, “Relationship between carrier-induced index change and feedback noise in diode lasers,” IEEE J. Quantum Electron. 18(10), 1675–1678 (1982).
[Crossref]

T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43(1), 6–15 (2007).
[Crossref]

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988).
[Crossref]

H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986).
[Crossref]

V. Annovazzi-Lodi, S. Merlo, M. Norgia, and A. Scire, “Characterization of a chaotic telecommunication laser for different fiber cavity lengths,” IEEE J. Quantum Electron. 38(9), 1171–1177 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1(2), 480–489 (1995).
[Crossref]

IEEE Photon. Technol. Lett. (4)

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001).
[Crossref]

L. Hua, “RF-modulation measurement of linewidth enhancement factor and nonlinear gain of vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 8(12), 1594–1596 (1996).
[Crossref]

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, and T. Bosch, “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53(1), 223–232 (2004).
[Crossref]

J. Opt. (1)

N. Servagent, F. Gouaux, and T. Bosch, “Measurements of displacement using the self-mixing interference in a laser diode,” J. Opt. 29(3), 168–173 (1998).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

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), S283–S294 (2002).
[Crossref]

Opt. Commun. (1)

Y. S. Shin, T. H. Yoon, J. R. Park, and C. H. Nam, “Simple methods for measuring the linewidth enhancement factor in external cavity laser diodes,” Opt. Commun. 173(1–6), 303–309 (2000).
[Crossref]

Proc. SPIE (1)

Y. Fan, Y. Yu, J. Xi, J. Chicharo, and H. Ye, “A displacement reconstruction algorithm used for optical feedback self mixing interferometry system under different feedback levels,” Proc. SPIE 7855, 78550L, 78550L-7 (2010).
[Crossref]

Other (1)

Y. Yu, J. Xi, and J. F. Chicharo, “Improving the Performance in an Optical feedback Self-mixing Interferometry System using Digital Signal Pre-processing,” in Proceedings of IEEE Conference on Intelligent Signal Processing (Institute of Electrical and Electronic Engineers, Alcala de Henares, 2007), pp. 1–6.

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Figures (8)

Fig. 1
Fig. 1

Schematic SMI.

Fig. 2
Fig. 2

Hysteresis phenomenon of SMI signal and the measurement principle on αin [20] with C = 2 and α = 5 .

Fig. 3
Fig. 3

Waveforms and spectra of signals ϕ 0 ( t ) , C ϕ 1 ( t ) , and ϕ F ( t ) for sinusoidal case with C=5 and α=3.

Fig. 4
Fig. 4

Detailed spectra of signals ϕ 0 ( t ) , ϕ 1 ( t ) , and ϕ F ( t ) for the sinusoidal case.

Fig. 5
Fig. 5

Waveforms and spectra of signals ϕ 0 ( t ) , C ϕ 1 ( t ) , and ϕ F ( t ) for the triangular case.

Fig. 6
Fig. 6

Detailed spectra of signals ϕ 0 ( t ) , ϕ 1 ( t ) , and ϕ F ( t ) for triangular case.

Fig. 7
Fig. 7

Experimental SMI signals with different C values [8].

Fig. 8
Fig. 8

Measurement process for the experimental signal shown in Fig. 7(c) using the proposed method.

Tables (4)

Tables Icon

Table 1 Definition of the variables in Eq. (1)(3)

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Table 2 Estimated C Values Using Method in [1] and Proposed Method in this Paper

Tables Icon

Table 3 Influence of αon the Estimation of C

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Table 4 Estimated C Values Using Experimental Signals

Equations (16)

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ϕ F = ϕ 0 C s i n [ ϕ F + arctan ( α ) ] ,
g ( ϕ 0 ) = cos ( ϕ F ) ,
P ( ϕ 0 ) = P 0 [ 1 + m × g ( ϕ 0 ) ] .
ϕ 0 , A B = 2 { C 2 1 + arccos ( 1 C ) π } .
C = η τ τ S L ( 1 R 2 ) R 3 R 2 1 + α 2 ,
g ( t ) = cos ( ϕ F ( t ) ) ,
ϕ F ( t ) = ϕ 0 ( t ) C s i n { ϕ F ( t ) + arctan ( α ) } .
Φ F ( f ) = Φ 0 ( f ) C F { sin [ ϕ F ( t ) + arctan ( α ) ] } ,
ϕ 1 ( t ) = sin { ϕ F ( t ) + arctan ( α ) } ,
Φ F ( f ) = Φ 0 ( f ) C F { ϕ 1 ( t ) } = Φ 0 ( f ) C Φ 1 ( f ) ,
Ω 1 : f { Φ F ( f ) 0 , Φ 1 ( f ) 0 , Φ 0 ( f ) 0 } ,   and
Ω 2 : f { Φ F ( f ) 0 , Φ 1 ( f ) 0 , Φ 0 ( f ) = 0 } .
Φ F ( f ) = C × Φ 1 ( f ) , f Ω 2 .
C = | Φ F ( f ) | | Φ 1 ( f ) | , f Ω 2 .
C = f Ω 2 | Φ F ( f ) | f Ω 2 | Φ 1 ( f ) | .
ϕ 0 ( t ) = φ 0 + Δ φ sin ( 2 π f 0 t ) ,

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