Abstract

Fabry–Perot cavities made with photonic crystal (PC) mirrors and other resonant structures exhibit nontraditional characteristics due to the strong wavelength dependence of their reflected phase. This Letter describes how engineering the phase of PC mirrors enables sensors that are tolerant to variations in laser center frequency and line width. Reflection spectra measurements of Fabry–Perot cavities made with PC mirrors were collected as a function of wavelength and cavity length, providing experimental verification of theory and simulations.

© 2013 Optical Society of America

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  1. W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
    [CrossRef]
  2. V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, Opt. Express 12, 1575 (2004).
    [CrossRef]
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    [CrossRef]
  4. A. Kavokin, I. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
    [CrossRef]
  5. P. Pottier, L. Shi, and Y. A. Peter, J. Opt. Soc. Am. B 29, 2698 (2012).
    [CrossRef]
  6. D. Zhao, Z. Ma, and W. Zhou, Proc. SPIE 7756, 775610 (2010).
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    [CrossRef]
  8. M. C. Rechtsman, Y. V. Kartashov, F. Setzpfandt, H. Trompeter, L. Torner, T. Pertsch, U. Peschel, and A. Szameit, Opt. Lett. 36, 4446 (2011).
    [CrossRef]
  9. O. Solgaard, in Photonic Microsystems (Springer, 2009), pp. 461–462.
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    [CrossRef]
  11. L. A. Coldren, S. W. Corzine, and M. L. Mašanović, in Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), pp. 108–109.
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    [CrossRef]
  13. S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. 20, 569 (2003).
    [CrossRef]
  14. W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
    [CrossRef]
  15. S. Hadzialic, S. Kim, A. S. Sudbø, and O. Solgaard, IEEE Photon. Technol. Lett. 22, 67 (2010).
    [CrossRef]

2012 (1)

2011 (1)

2010 (2)

D. Zhao, Z. Ma, and W. Zhou, Proc. SPIE 7756, 775610 (2010).

S. Hadzialic, S. Kim, A. S. Sudbø, and O. Solgaard, IEEE Photon. Technol. Lett. 22, 67 (2010).
[CrossRef]

2005 (2)

W. Suh, O. Solgaard, and S. Fan, J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

A. Kavokin, I. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

2004 (3)

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, Opt. Express 12, 1575 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

2003 (2)

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. 20, 569 (2003).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

2002 (1)

S. Fan and J. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

1995 (1)

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

Bernage, P.

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

Boj, S.

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

Chang-Hasnain, C. J.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Coldren, L. A.

L. A. Coldren, S. W. Corzine, and M. L. Mašanović, in Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), pp. 108–109.

Corzine, S. W.

L. A. Coldren, S. W. Corzine, and M. L. Mašanović, in Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), pp. 108–109.

Delevaque, E.

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Douay, M.

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

Fan, S.

W. Suh, O. Solgaard, and S. Fan, J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, Opt. Express 12, 1575 (2004).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. 20, 569 (2003).
[CrossRef]

S. Fan and J. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Hadzialic, S.

S. Hadzialic, S. Kim, A. S. Sudbø, and O. Solgaard, IEEE Photon. Technol. Lett. 22, 67 (2010).
[CrossRef]

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Joannopoulos, J.

S. Fan and J. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Joannopoulos, J. D.

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. 20, 569 (2003).
[CrossRef]

Kartashov, Y. V.

Kavokin, A.

A. Kavokin, I. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Kilic, O.

Kim, S.

S. Hadzialic, S. Kim, A. S. Sudbø, and O. Solgaard, IEEE Photon. Technol. Lett. 22, 67 (2010).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, Opt. Express 12, 1575 (2004).
[CrossRef]

Legoubin, S.

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

Lousse, V.

Ma, Z.

D. Zhao, Z. Ma, and W. Zhou, Proc. SPIE 7756, 775610 (2010).

Malpuech, G.

A. Kavokin, I. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Mašanovic, M. L.

L. A. Coldren, S. W. Corzine, and M. L. Mašanović, in Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), pp. 108–109.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Niay, P.

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

Pertsch, T.

Peschel, U.

Peter, Y. A.

Pottier, P.

Rechtsman, M. C.

Setzpfandt, F.

Shelykh, I.

A. Kavokin, I. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

Shi, L.

Solgaard, O.

S. Hadzialic, S. Kim, A. S. Sudbø, and O. Solgaard, IEEE Photon. Technol. Lett. 22, 67 (2010).
[CrossRef]

W. Suh, O. Solgaard, and S. Fan, J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, Opt. Express 12, 1575 (2004).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

O. Solgaard, in Photonic Microsystems (Springer, 2009), pp. 461–462.

Sudbø, A. S.

S. Hadzialic, S. Kim, A. S. Sudbø, and O. Solgaard, IEEE Photon. Technol. Lett. 22, 67 (2010).
[CrossRef]

Suh, W.

W. Suh, O. Solgaard, and S. Fan, J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, Opt. Express 12, 1575 (2004).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. 20, 569 (2003).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

Szameit, A.

Torner, L.

Trompeter, H.

Wang, Z.

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

Yanik, M. F.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

Zhao, D.

D. Zhao, Z. Ma, and W. Zhou, Proc. SPIE 7756, 775610 (2010).

Zhou, W.

D. Zhao, Z. Ma, and W. Zhou, Proc. SPIE 7756, 775610 (2010).

Appl. Phys. Lett. (1)

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

S. Hadzialic, S. Kim, A. S. Sudbø, and O. Solgaard, IEEE Photon. Technol. Lett. 22, 67 (2010).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

J. Appl. Phys. (1)

W. Suh, O. Solgaard, and S. Fan, J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

J. Opt. Soc. Am. (2)

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. 20, 569 (2003).
[CrossRef]

S. Legoubin, M. Douay, P. Bernage, P. Niay, S. Boj, and E. Delevaque, J. Opt. Soc. Am. 12, 1687 (1995).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

A. Kavokin, I. Shelykh, and G. Malpuech, Phys. Rev. B 72, 233102 (2005).
[CrossRef]

S. Fan and J. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Proc. SPIE (1)

D. Zhao, Z. Ma, and W. Zhou, Proc. SPIE 7756, 775610 (2010).

Other (2)

O. Solgaard, in Photonic Microsystems (Springer, 2009), pp. 461–462.

L. A. Coldren, S. W. Corzine, and M. L. Mašanović, in Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), pp. 108–109.

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Figures (7)

Fig. 1.
Fig. 1.

Unit cell of the simulated PC mirror.

Fig. 2.
Fig. 2.

(a) Reflectance spectrum and reflected phase of the PC. (b) Effective thickness (teff).

Fig. 3.
Fig. 3.

(a) Simulated FP spectra with and without reflected phase included. (b) Reflectance responsivity.

Fig. 4.
Fig. 4.

(a) Experimental setup. (b) PC reflectance.

Fig. 5.
Fig. 5.

FP spectrum, spectral distance between maxima/minima and resulting phase at (a) (L=175μm) and (b) (L=155μm).

Fig. 6.
Fig. 6.

Reflected phase and effective thickness.

Fig. 7.
Fig. 7.

(a) Reflectance spectra. (b) Responsivity at L=30.8μm+100nm.

Equations (8)

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R(L,β)=r12+r222r1r2cos(β·2L+ϕ12(β))1+r12r222r1r2cos(β·2L+ϕ12(β)).
dRdL=4β0r1r2(r221)(r121)sin(β0·2L+ϕ12(β0))(1+r22r122r1r2cos(β0·2L+ϕ12(β0)))2.
dRdLmax=4β0[(r121)(r221)16r12r22γ2(2r12r22+γ+2)2]γ=r14r24+34r12r22+1+r12r22+1.
dβdL=βL+12dϕ12(β)dβ.
Leff=L+12dϕ12(β)dβ=L+teff.
δRδL=δRδβ·δβδL.
δRδβ=(dϕ12(β)2dβ+L)×4r1r2(r121)(r221)sin(ϕ12(β)+2Lβ)(r12r22+2r1r2cos(ϕ12(β)+2Lβ)+1)2.
[2β2L+ϕ12(β2)][2β1L+ϕ12(β1)]=2πFSR=(β2β1)=πL+Δϕ12(β)/2ΔβπLeff.

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