Abstract

The high density intensity fringes and phase behavior in birefringent dual frequency laser with multiple feedback are studied for the first time. It was discovered that the fringes of output intensity are made of bipolar pulses with symmetric external cavity feedback and the fringe density is as high as compared to the conventional feedback. The high density cosine-like fringes are obtained with asymmetric external cavity feedback by adjusting the tilt angle of the feedback mirror and the fringe density is about 22 times higher compared to the conventional feedback. Moreover, there is a phase difference between the two cosine-like fringes and the phase difference is varied with the change of the external cavity length. The experimental results and a theoretical analysis are presented in this work. These results offer a large increase in the resolution for the optical feedback interferometer with the birefringence dual frequency laser.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2007 (2)

D. Guo and M. Wang, “Self-mixing interferometry based on a double-modulation technique for absolute distance measurement,” Appl. Opt. 46(9), 1486–1491 (2007).
[CrossRef] [PubMed]

Y. Tan, S. Zhang, W. Liu, and L. Fei, “Intensity modulation in single-mode microchip Nd:YAG lasers with asymmetric external cavity,” Chin. Phys. 16(4), 1020–1026 (2007).
[CrossRef]

2006 (1)

2004 (1)

2003 (1)

Y. Yu, H. Ye, and J. Yao, “Analysis for the self-mixing interference effects in a laser diode at high optical feedback levels,” J. Opt. A, Pure Appl. Opt. 5(2), 117–122 (2003).
[CrossRef]

2002 (2)

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]

K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27(15), 1339–1341 (2002).
[CrossRef] [PubMed]

2001 (1)

P. de Groot, “Unusual technique for absolute distance measurement,” Opt. Eng. 40(1), 28–32 (2001).
[CrossRef]

1999 (1)

1997 (1)

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[CrossRef]

1996 (2)

R. C. Addy, A. W. Palmer, K. Thomas, and V. Grattan, “Effects of external reflector alignment in sensing applications of optical feedback in laser diodes,” J. Lightwave Technol. 14(12), 2672–2676 (1996).
[CrossRef]

P. A. Roos, M. Stephens, and C. E. Wieman, “Laser vibrometer based on optical-feedback-induced frequency modulation of a single-mode laser diode,” Appl. Opt. 35(34), 6754–6761 (1996).
[CrossRef] [PubMed]

1995 (1)

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]

1994 (1)

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[CrossRef]

1993 (2)

1986 (1)

1984 (2)

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

D. Lenstra, M. Vanvaalen, and B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125(2), 255–264 (1984).
[CrossRef]

Abe, K.

Addy, R. C.

R. C. Addy, A. W. Palmer, K. Thomas, and V. Grattan, “Effects of external reflector alignment in sensing applications of optical feedback in laser diodes,” J. Lightwave Technol. 14(12), 2672–2676 (1996).
[CrossRef]

Bearden, A.

Bosch, T.

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]

Boyle, W. J. O.

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[CrossRef]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[CrossRef] [PubMed]

Churnside, J. H.

Day, R.

de Groot, P.

P. de Groot, “Unusual technique for absolute distance measurement,” Opt. Eng. 40(1), 28–32 (2001).
[CrossRef]

Donati, S.

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. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[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]

Fei, L.

Y. Tan, S. Zhang, W. Liu, and L. Fei, “Intensity modulation in single-mode microchip Nd:YAG lasers with asymmetric external cavity,” Chin. Phys. 16(4), 1020–1026 (2007).
[CrossRef]

L. Fei and S. Zhang, “Self-mixing interference effects of orthogonally polarized dual frequency laser,” Opt. Express 12(25), 6100–6105 (2004).
[CrossRef] [PubMed]

Giuliani, G.

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]

Grattan, K. T. V.

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[CrossRef]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[CrossRef] [PubMed]

Grattan, V.

R. C. Addy, A. W. Palmer, K. Thomas, and V. Grattan, “Effects of external reflector alignment in sensing applications of optical feedback in laser diodes,” J. Lightwave Technol. 14(12), 2672–2676 (1996).
[CrossRef]

Guo, D.

Jaskorzynska, B.

D. Lenstra, M. Vanvaalen, and B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125(2), 255–264 (1984).
[CrossRef]

Ko, J. Y.

Lacot, E.

Lenstra, D.

D. Lenstra, M. Vanvaalen, and B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125(2), 255–264 (1984).
[CrossRef]

Lim, T. S.

Liu, W.

Y. Tan, S. Zhang, W. Liu, and L. Fei, “Intensity modulation in single-mode microchip Nd:YAG lasers with asymmetric external cavity,” Chin. Phys. 16(4), 1020–1026 (2007).
[CrossRef]

Mao, W.

Merlo, S.

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[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]

Mochizuki, A.

Norgia, M.

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]

O’Neill, M. P.

Osborne, L. C.

Otsuka, K.

Palmer, A. W.

R. C. Addy, A. W. Palmer, K. Thomas, and V. Grattan, “Effects of external reflector alignment in sensing applications of optical feedback in laser diodes,” J. Lightwave Technol. 14(12), 2672–2676 (1996).
[CrossRef]

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[CrossRef]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[CrossRef] [PubMed]

Roos, P. A.

Shinohara, S.

Stephens, M.

Stoeckel, F.

Sumi, M.

Tan, Y.

Y. Tan, S. Zhang, W. Liu, and L. Fei, “Intensity modulation in single-mode microchip Nd:YAG lasers with asymmetric external cavity,” Chin. Phys. 16(4), 1020–1026 (2007).
[CrossRef]

Thomas, K.

R. C. Addy, A. W. Palmer, K. Thomas, and V. Grattan, “Effects of external reflector alignment in sensing applications of optical feedback in laser diodes,” J. Lightwave Technol. 14(12), 2672–2676 (1996).
[CrossRef]

Vanvaalen, M.

D. Lenstra, M. Vanvaalen, and B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125(2), 255–264 (1984).
[CrossRef]

Wang, M.

Wang, W. M.

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[CrossRef]

W. M. Wang, W. J. O. Boyle, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[CrossRef] [PubMed]

Wieman, C. E.

Wong, T. L.

Yao, J.

Y. Yu, H. Ye, and J. Yao, “Analysis for the self-mixing interference effects in a laser diode at high optical feedback levels,” J. Opt. A, Pure Appl. Opt. 5(2), 117–122 (2003).
[CrossRef]

Ye, H.

Y. Yu, H. Ye, and J. Yao, “Analysis for the self-mixing interference effects in a laser diode at high optical feedback levels,” J. Opt. A, Pure Appl. Opt. 5(2), 117–122 (2003).
[CrossRef]

Yoshida, H.

Yu, Y.

Y. Yu, H. Ye, and J. Yao, “Analysis for the self-mixing interference effects in a laser diode at high optical feedback levels,” J. Opt. A, Pure Appl. Opt. 5(2), 117–122 (2003).
[CrossRef]

Zhang, S.

Appl. Opt. (6)

Chin. Phys. (1)

Y. Tan, S. Zhang, W. Liu, and L. Fei, “Intensity modulation in single-mode microchip Nd:YAG lasers with asymmetric external cavity,” Chin. Phys. 16(4), 1020–1026 (2007).
[CrossRef]

IEEE J. Quantum Electron. (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]

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[CrossRef]

J. Lightwave Technol. (2)

W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode laser for optical sensing applications,” J. Lightwave Technol. 12(9), 1577–1587 (1994).
[CrossRef]

R. C. Addy, A. W. Palmer, K. Thomas, and V. Grattan, “Effects of external reflector alignment in sensing applications of optical feedback in laser diodes,” J. Lightwave Technol. 14(12), 2672–2676 (1996).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

Y. Yu, H. Ye, and J. Yao, “Analysis for the self-mixing interference effects in a laser diode at high optical feedback levels,” J. Opt. A, Pure Appl. Opt. 5(2), 117–122 (2003).
[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]

Opt. Eng. (1)

P. de Groot, “Unusual technique for absolute distance measurement,” Opt. Eng. 40(1), 28–32 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Physica C (1)

D. Lenstra, M. Vanvaalen, and B. Jaskorzynska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125(2), 255–264 (1984).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. M1, M2, M3: mirrors; Q: quartz crystal; PBS: Wollaston prism; D1, D2: photoelectric detectors; BS: beam splitter; SP: spectrum analyzer; P: polarizer; ATT: attenuator; OS: oscilloscope.

Fig. 2
Fig. 2

Intensity curves of the two orthogonally polarized lights. (a) Conventional feedback; (b) Strong feedback, θ = 0; (c) θ = 0.9′; (d) on an enlarged time scale of (c); (e) θ = 1.2′; (f) on an enlarged time scale of (e); (g) θ = 1.8′; (h) on an enlarged time scale of (g).

Fig. 3
Fig. 3

Phase difference curves of two orthogonally polarized lights with different external cavity length: (a) l = 110mm; (b) l = 112mm; (c) l = 114mm.

Fig. 4
Fig. 4

Simulation curves of feedback lights. (a) Symmetric feedback, trace-1: conventional feedback; trace-2: multiple feedback; (b) Strong feedback, trace-1: θ = 0.9′; trace-2: θ = 1.2′; trace-3: θ = 1.8′.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

I= I 0 { 1+ K 2L [ t 2 2 r 3 r 2 m=1 q ( r 2 r 3 ) m1 f m cos( mω 2l c + δ m ) ] }
I o = I o0 { 1+ K 2L m=1 q t 2 2 r 3 m r 2 m2 f m cos( m ω o 2l c + δ om ) } I e = I e 0 { 1+ K 2L m=1 q t 2 2 r 3 m r 2 m2 f m cos( m ω e 2l c + δ em ) }
I o = I o0 { 1+ η 1 f 1 cos( ω o 2l c + δ o1 ) } I e = I e 0 { 1+ η 1 f 1 cos( ω e 2l c + δ e1 ) }
I o = I o0 { 1+ m=1 q η m f m cos( m ω o 2l c + δ om ) } I e = I e 0 { 1+ m=1 q η m f m cos( m ω e 2l c + δ em ) }
f m = s π d 2
δ=m 2l c ( ω o ω e )+( δ om δ em )
δ=4πΔνm l c

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