Abstract

We demonstrate experimentally how to harness quasi-periodic dynamics in a semiconductor laser with dual optical feedback for measuring subwavelength changes in each arm of the cavity simultaneously. We exploit the multifrequency spectrum of quasi-periodic dynamics and show that independent frequency shifts are mapped uniquely to two-dimensional displacements of the arms in the external cavity. Considering a laser diode operating at telecommunication wavelength λ1550nm, we achieve an average nanoscale resolution of approximately 9.8 nm (λ/160).

© 2013 Optical Society of America

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References

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2012

2011

S. Cohen, H. Cavalcante, and D. J. Gauthier, Phys. Rev. Lett. 107, 254103 (2011).
[CrossRef]

2010

2008

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

2005

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

2001

2000

1998

M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsäßer, Europhys. Lett. 42, 353 (1998).
[CrossRef]

1995

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

1994

1992

J. Mørk, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

1986

J. Mink and B. H. Verbeek, Appl. Phys. Lett. 48, 745 (1986).
[CrossRef]

Atashkhooei, R.

Bava, G. P.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

Becker, K.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

Blondel, M.

Bony, F.

Bosch, T.

Bunner, M. J.

M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsäßer, Europhys. Lett. 42, 353 (1998).
[CrossRef]

Cavalcante, H.

S. Cohen, H. Cavalcante, and D. J. Gauthier, Phys. Rev. Lett. 107, 254103 (2011).
[CrossRef]

Chau, L.-K.

Cohen, S.

S. Cohen, H. Cavalcante, and D. J. Gauthier, Phys. Rev. Lett. 107, 254103 (2011).
[CrossRef]

Cohen, S. D.

S. D. Cohen, “Subwavelength sensing using nonlinear feedback in a wave-chaotic cavity,” Ph.D. thesis (Duke University, 2013).

Day, R.

De Martini, B. E.

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

Debernardi, P.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

Degen, C.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

Deparis, O.

Donati, S.

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

Elsäßer, W.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsäßer, Europhys. Lett. 42, 353 (1998).
[CrossRef]

Fischer, I.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsäßer, Europhys. Lett. 42, 353 (1998).
[CrossRef]

Gauthier, D. J.

S. Cohen, H. Cavalcante, and D. J. Gauthier, Phys. Rev. Lett. 107, 254103 (2011).
[CrossRef]

Gavrielides, A.

Gensty, T.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

Giuliani, G.

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

Huang, C.-C.

Huang, C.-H.

Kane, D. M.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects in Semicondustor Lasers (Wiley, 2005), Chap. 7.

Kittel, A.

M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsäßer, Europhys. Lett. 42, 353 (1998).
[CrossRef]

Lacot, E.

Lin, H.-Y.

Liu, Y.

Liu, Y.-C.

Mark, J.

J. Mørk, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Masoller, C.

C. Masoller, Phys. Rev. A 50, 2569 (1994).
[CrossRef]

Mégret, P.

Merlo, S.

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

Mink, J.

J. Mink and B. H. Verbeek, Appl. Phys. Lett. 48, 745 (1986).
[CrossRef]

Mørk, J.

J. Mørk, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Ohtsubo, J.

Y. Liu and J. Ohtsubo, Opt. Lett. 19, 448 (1994).
[CrossRef]

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2006).

Owen, K. G.

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

Parisi, J.

M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsäßer, Europhys. Lett. 42, 353 (1998).
[CrossRef]

Pinel, J.

Rakic, A. D.

Rhoads, J. F.

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

Rogister, F.

Royo, S.

Shaw, S. W.

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

Shore, K. A.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects in Semicondustor Lasers (Wiley, 2005), Chap. 7.

Stoeckel, F.

Sukow, D. W.

Tromborg, B.

J. Mørk, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Turner, K. L.

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

Verbeek, B. H.

J. Mink and B. H. Verbeek, Appl. Phys. Lett. 48, 745 (1986).
[CrossRef]

Zabit, U.

Zielke, M. A.

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

Appl. Phys. Lett.

J. Mink and B. H. Verbeek, Appl. Phys. Lett. 48, 745 (1986).
[CrossRef]

B. E. De Martini, J. F. Rhoads, M. A. Zielke, K. G. Owen, S. W. Shaw, and K. L. Turner, Appl. Phys. Lett. 93, 054102 (2008).
[CrossRef]

Europhys. Lett.

M. J. Bunner, A. Kittel, J. Parisi, I. Fischer, and W. Elsäßer, Europhys. Lett. 42, 353 (1998).
[CrossRef]

IEEE J. Quantum Electron.

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

J. Mørk, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. A

C. Masoller, Phys. Rev. A 50, 2569 (1994).
[CrossRef]

Phys. Rev. Lett.

T. Gensty, K. Becker, I. Fischer, W. Elsäßer, C. Degen, P. Debernardi, and G. P. Bava, Phys. Rev. Lett. 94, 233901 (2005).
[CrossRef]

S. Cohen, H. Cavalcante, and D. J. Gauthier, Phys. Rev. Lett. 107, 254103 (2011).
[CrossRef]

Other

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects in Semicondustor Lasers (Wiley, 2005), Chap. 7.

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer, 2006).

S. D. Cohen, “Subwavelength sensing using nonlinear feedback in a wave-chaotic cavity,” Ph.D. thesis (Duke University, 2013).

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Figures (3)

Fig. 1.
Fig. 1.

Two-delay all-optical feedback system for multidimensional subwavelength sensing. The output of a laser diode (LD, Sumitomo SLT4416-DP) passes through a polarization control (PC), a 90/10 optical coupler (OC), and an optical attenuator (OA), and separates using a 50/50 beam splitter (BS). The feedback strength is set so that it reduces the laser threshold by 1%. The optical field propagates along two separate paths with time delays τx,y. Piezoelectric transducers (PZTx,y, Burleigh PZO-015) translate mirrors Mx,y by Δx,y and change feedback delay τx,y. After an optical isolator (OI), detection is performed using an ac-coupled 12 GHz photodetector (PD, New Focus 1544-B) and a 40GS/s, 8 GHz analog bandwidth, high-speed digital oscilloscope (OSC, Agilent DSO90804A).

Fig. 2.
Fig. 2.

Experimental quasi-periodic dynamics generated by a semiconductor laser with dual optical feedback. (a) Temporal evolution of v(t) generated by the photodetector and proportional to the intensity of the optical field. The pump current is I=23.6mA (the threshold is Ith8.0mA), τx55.5, τy55.6ns (corresponding to Δx,y=0), and 2% of optical intensity fed back in the laser cavity. (b) Power spectral density (PSD) of v(t) in the quasi-periodic regime showing four frequency clusters, each labeled by their central frequency fi, i=1,,4 (f1=1.07GHz, f2=2.13GHz, f3=5.42GHz, and f4=6.49GHz). (c), (d) Zooms on the structures of the second and fourth labeled frequency clusters later used for subwavelength sensing.

Fig. 3.
Fig. 3.

Experimental manifold associated with the quasi-periodic frequency shifts (a) Δf2 and (b) Δf4 as a function of Δx,y. The 2D manifolds are fitted with quadratic functions with coefficients for (a) a00|2=17.3784±1.0834kHz, a01|2=0.0691±0.0358kHz·nm1, a10|2=1.2458±0.0562kHz·nm1, a11|2=0.0058±0.0005kHz·nm2, a02|2=0.0041±0.0003kHz·nm2, and a20|2=0.0095±0.0009kHz·nm2; and (b) a00|4=67.7941±3.2683kHz, a01|4=1.2050±0.1079kHz·nm1, a10|4=1.8789±0.1694kHz·nm1, a11|4=0.0093±0.0014kHz·nm2, a02|4=0.0127±0.0010kHz·nm2, and a20|4=0.0140±0.0026kHz·nm2.

Equations (2)

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v¯(t)1i4Aisin[2π(fi+Δfi)(ttskew)],
Δf2,4(Δx,Δy)=0i+j2aij|2,4ΔxiΔyj,

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