Effect of external cavity length on self-mixingsignals in a multilongitudinal-mode Fabry–Perotlaser diode

Liang Lv, Huaqiao Gui, Jianping Xie, Tianpeng Zhao, Xiyao Chen, Anting Wang,Feng Li, DeYong He, Jun Xu, and Hai Ming

The effect of external-cavity length on self-mixing signals in a multilongitudinal-mode Fabry–Perot laserdiode (FP-LD) was investigated experimentally. It has been shown that the output waveforms of self-mixing signals vary periodically when the length of the external cavity changes. This result agrees wellwith our theoretical calculations for the self-mixing effect of two adjacent longitudinal modes in a FP-LD.Moreover, the time-averaged output intensities of self-mixing signals has also been measured andcompared with theoretical analysis. © 2005 Optical Society of America

OCIS codes: 140.5960, 280.3340, 280.3420.

1. Introduction

Laser Doppler velocimeters (LDVs) are elegant non-contact remote sensors with which to determine thespeed of a target by means of the Doppler shift ofoptical frequencies. To date, many kinds of LDVshave been developed and used to measure distance,displacement, alignment, and vibration of remoteobjects. One kind of LDV is based on the self-mixingeffect and utilizes laser diodes (LDs) because theyare highly sensitive to external optical injection.This LDV consists of a laser diode, a collimationlens, and a process circuit. When an external reflec-tor is moving toward or away from the laser diode,a portion of the laser output can be reflected into theinternal cavity. As a result, a beat note can be ob-tained in the laser output, and this is referred to asthe self-mixing effect.4 Much attention was drawnrecently to semiconductor laser interferometers be-cause of their simple structure, small size, and lowpower requirements.

The output characteristics of a LD are sensitive toexternal optical feedback, as was shown before.8,9

However, specific research on the external-feedback

effect in multilongitudinal-mode LDs has seldombeen reported.1 Multilongitudinal-mode LDs havebeen widely used because of their advanced technol-ogy and low cost compared with single-longitudinal-mode lasers.

In this paper we present experimental resultsand theoretical analyses with regard to the effect ofexternal cavity length (Lext) on self-mixing signals ina multilongitudinal-mode Fabry–Perot laser diode(FP-LD). First we introduce experimental results forthe waveform and time-averaged intensity of self-mixing signals in a FP-LD. Then theoretical calcula-tions are presented to explain the experimental data.

2. Experiment

The experimental setup that we used to study theself-mixing effect of a FP-LD is shown in Fig. 1. Thewavelength and operating current of the FP-LD(Samsung) were 0.65 �m and 31 mA, respectively.The actual power of was LD is 2.7 mW. The emissionlight was focused onto a moving target by a lens. Aphotodetector (PD) in the LD package was used tomonitor the output power emitted from the other sideof the LD.

The time-averaged intensity of self-mixing signalswas measured with a millivoltmeter, and the resultsare shown in Fig. 2. From Fig. 2(a) it can be seen thatthe time-averaged intensity changes periodicallywith peak spacing of 1.05 mm when Lext varies. Theenvelope line of their relation curve takes the shapeof Gaussian function because the light on the target isa Gaussian beam. The maximum intensity, at Lext

The authors are with the Department of Physics, University ofScience and Technology of China, Hefei, Anhui 230026, China. L.Liang’s email address is lvliang@mail.ustc.edu.cn.

Received 26 July 2004; revised manuscript received 10 October2004; accepted 19 October 2004.

0003-6935/05/040568-04$15.00/0© 2005 Optical Society of America

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� 48.9 mm, corresponds to the waist of the Gaussianbeam with the largest feedback. The intensity be-comes lower when the reflecting surface moves awayfrom this position. In Fig. 2(b), the time-averagedintensity of self-mixing signals is measured in detailfrom the left adjacent peak (A) to the maximum peak(B) in Fig. 2(a).

The waveforms of the self-mixing signals in themultilongitudinal-mode FP-LD at four values of Lextwere recorded with a two-channel oscilloscope (Tek-tronix TDS 3052B, 500 MHz), as shown in Fig. 3.

It can be seen from the results that the waveformsof the self-mixing signals also change periodicallywith the same period of 1.05 mm as the time-averaged intensity when Lext varies. The waveforms

take normal shapes (regular sawtoothlike wave-forms) at Lext � 43.95 mm and Lext � 45.0 mm andabnormal shapes (distorted waveforms, which arecombinations of two sawtoothlike waveforms) be-tween them. These abnormal waveforms may causeerrors when the multilongitudinal-mode FP-LD isused to measure Doppler frequency. The appearanceof abnormal waveforms results from the self-mixingeffect of the multilongitudinal-mode FP-LD withmultilongitudinal modes. Explanations follow.

3. Theory

For a multilongitudinal-mode FP-LD, the total out-put of self-mixing signals results from the linearcombination of self-mixing signals of each longitu-dinal mode. From the point of view of interferencetheory, laser light is a standing wave between twocavity mirrors. The standing wave consists of twolight waves with equal amplitudes and frequenciesbut with opposite propagation directions. If we as-sume that the intensities of the self-mixing signalsof the longitudinal modes are equal to one another,the total intensity of self-mixing signals can be de-duced as follows1:

I(t) � �I0 �j�1

P

exp i(2kjLext)�exp i(�dt) � c.c., (1)

where �d and kj represent the angular frequency thatcorresponds to the Doppler frequency shift of thescattered light and to the wave-number of a mode,respectively, and c.c. is the complex conjugate of theprevious terms:

2kjLext � 2(�0 � 2�jc � 2nL0)Lext

c , (2)

where �0 represents the angular frequency of thelight, n is the effective refractive index of the lasermedium, and L0 is the physical length of the lasercavity.

The phase delay between two self-mixing signalscaused by two adjacent longitudinal modes is theinteger number times 2� when Lext�nL0 is an inte-ger. As n � 3.5 and L0 � 300 �m, the period of thephase-delay difference mentioned above is 1.05 mm,which is equal to the period of time-averaged inten-sity and the waveform change of self-mixing signals.

Figure 4 shows simulation results of the wave-forms of self-mixing signals at four values of Lext fora multilongitudinal-mode FP-LD according to Eqs.(1) and (2). It can be seen that at Lext � 49.35 mm andLext � 50.4 mm, where Lext�nL0 is an integer, thewaveforms of self-mixing signals are normal (regularsawtoothlike waveforms) as in the case of single-mode lasers.2 If Lext�nL0 is not an integer, the wave-forms of total self-mixing signals are abnormal. Thesimulation curves agree well with the experimentalresults mentioned above. The abnormal waveformsmay introduce errors in velocity measurement. To

Fig. 1. Schematic diagram of a self-mixing interference system.

Fig. 2. (a) Changes in time-averaged intensity of a self-mixingsignal with different values of Lext and (b) the time-averaged in-tensity change of the self-mixing signal with different values of Lext

in one period.

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prevent this, it is required that the roughness (theundulation height) of the object’s surface not be big-ger than a quarter of a laser cavity’s optical length

(� 0.26 mm for a FP-LD). So, only when the object’smovement is perpendicular to the direction of thelaser beam (Lext is not varied), the abnormal wave-

Fig. 3. Waveforms of self-mixing signals for four external-cavity lengths: vertical axis, arbitrary units; horizontal axis,0.02 ms�division.

Fig. 4. Results of simulations of the waveforms of self-mixing signals for four external-cavity lengths.

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form is not created when a multilongitudinal-modeFP-LD used.

The results of calculation of the time-averaged in-tensities of self-mixing signals for several values ofLext are shown in Fig. 5 and also agree well with theexperimental data. The intensity peaks of the self-mixing signals are located at Lext � 49.35 mm andLext � 50.4 mm, where Lext � k�nL0� (k is a positiveinteger), and the intensity valley is located at Lext� 49.9 mm, where Lext � �k � 1�2��nL0� (k is a pos-itive integer).

To investigate this phenomenon further, we calcu-lated the waveforms of self-mixing signals of eightlongitudinal modes, as shown in Fig. 6. We also as-sume that the amplitudes of the self-mixing signals ofall longitudinal modes are equal to one another. Asshown in Fig. 6, the waveform is more complex for themultiple peaks that exist in one Doppler period. Butonly one peak existed in one Doppler period at a

certain value Lext in a previous experiment. So we caninfer that it is the combination of two adjacent lon-gitudinal modes of a multilongitudinal-mode FP-LDthat results in waveform distortion of self-mixing sig-nals.

4. Conclusions

The investigation of the influence of external-cavitylength on self-mixing signals in multilongitudinal-mode FP-LDs has shown that the amplitudes of self-mixing signals vary periodically with external-cavitylength, and the signal waveform changes too. Themain conclusion to be drawn from these investiga-tions is that the period of the phase delay betweentwo self-mixing signals caused by two adjacent lon-gitudinal modes is 1.05 mm, which is equal to theperiod of time-averaged intensity and changes inwaveform of self-mixing signals. So we conclude thatthe appearance of abnormal waveforms, which intro-duce error in velocity measurement, results from theself-mixing effect of a multilongitudinal-mode FP-LDwith two adjacent longitudinal modes when the ob-ject’s movement is not perpendicular to the directionof the laser beam. We can adopt single-mode lasers toprevent this undesirable phenomenon.

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Fig. 5. Time-averaged intensity of self-mixing signals for severalexternal-cavity lengths in one period.

Fig. 6. Result of the combination of eight longitudinal modes.

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