Abstract

The self-mixing interference effects with a folding feedback cavity in a Zeeman-birefringence dual frequency laser have been investigated theoretically and experimentally. The fringe frequency of the self-mixing interference system can be doubled due to the hollow cube corner prism, with which a folding cavity is formed. The intensities of the two frequencies are changed periodically in the modulation of the external cavity length. When the phase difference between the two frequencies equals π/2, the intensity modulation curves can be divided into four zones with equal width in a period. Each zone corresponds to one polarization state. Based on the experimental results, a novel displacement sensor with a high resolution of λ/16, as well as functions of direction discrimination, is discussed.

© 2006 Optical Society of America

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References

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Appl. Opt. (5)

Chin. Phys. Lett. (1)

Y. Jin, and S, Zhang, "Zeeman-birefringence HeNe dual frequency lasers," Chin. Phys. Lett. 18, 533-536 (2001).
[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, 223-232 (2004).
[CrossRef]

IEEE Trans. Intrum. Meas. (1)

N. Servagent, T. Bosch and M. Lescure, "A laser displacement sensor using the self-mixing effect for modal analysis and defect detection," IEEE Trans. Intrum. Meas. 46, 847-850 (1997).
[CrossRef]

J. Lightwave Technol. (1)

R. C. Addy, A. W. Palmer, and K. T. V. Grattan, "Effects of external reflector alignment in sensing applications of optical feedback in laser diodes," J. Lightwave Technol. 14, 2672-2676 (1996).
[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, S283-S294 (2002).
[CrossRef]

Opt. Commun. (1)

G. Liu, S. Zhang, J. Zhu, and Y. Li, "A 450MHz frequency difference dual-frequency laser with optical feedback," Opt. Commun. 231, 349-356 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

(a) The configuration of M2; (b) The configuration of HCCP (unit: mm).

Fig. 3.
Fig. 3.

Simulation of the laser intensity versus the output voltage of the D/A card. (a) normal intensity modulation frequency; (b) doubled intensity modulation frequency with HCCP.

Fig. 4.
Fig. 4.

Simulation of the laser intensity variations of o-light and e-light. (a) without a threshold intensity; (b) with a threshold intensity

Fig. 5.
Fig. 5.

Observation of the laser intensity versus the output voltage of the D/A card. (a) normal intensity modulation frequency; (b) doubled intensity modulation frequency with HCCP.

Fig. 6.
Fig. 6.

Observation of the laser intensity variations of o-light and e-light.

Equations (17)

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E ( t ) = r 1 r 2 exp ( j 4 πv nL c + gL ) E 0 ( t ) + r 1 r 2 r 3 ξ exp ( j 4 πv nL + l + Δ l c + gL ) E 0 ( t ) ,
r 1 r 2 exp ( j 4 πv nL c + gL ) [ 1 + t 2 r 3 ζ r 2 exp ( j 4 πv l c + j 4 πv Δ 1 c ) ] = 1 .
r 1 r 2 exp ( gL ) { [ 1 + α cos ( φ + δ l ) ] 2 + [ α sin ( φ + δ l ) ] 2 } ½ exp [ j ( 4 πv nL c + θ ) ] = 1 ,
tan θ = α sin ( φ + δ l ) 1 + α cos ( φ + δ l ) .
r 1 r 2 exp ( gL ) [ 1 + α cos ( φ + δ l ) ] exp [ j ( 4 πv nL c + θ ) ] = 1 .
g = 1 L [ In ( r 1 r 2 ) + α cos ( φ + δ l ) ] .
4 πv nL c + θ = 2 .
g 0 = 1 L In ( r 1 r 2 ) .
Δ g = g g 0 = α L cos ( φ + δ l ) .
I = I 0 ( 1 K Δ g ) ,
I 1 = I 0 [ 1 + α K L cos ( 2 φ + δ l ) ] ,
φ H = 4 πv∙ 2 Δ l c = 2 φ .
I 2 = I 0 [ 1 + α K L cos ( 2 φ + δ l ) ] .
Δ g 0 = Δ g e .
I o = I 0 o [ 1 + α K L cos ( 2 φ + δ lo ) ] ,
I e = I 0 e [ 1 α K L cos ( 2 φ + δ le ) ] ,
δ = 4 π Δ v l c ,

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