Abstract

Fabry–Perot interferometers (FPIs) with multilayer dielectric mirrors and mirror spacings as low as 0.7% of the operating wavelength are studied. It is shown how these low-order FPIs are affected by the phase dispersion characteristics of multilayer dielectric mirrors. Because experimental results in the optical regime are extremely difficult to obtain, radio frequency experiments are performed with coaxial cable FPI structures. Experimental results show excellent agreement with theory. These phase effects in FPIs with ultrathin mirror spacings are of great interest in the design of tunable microcavities with possible applications in optical communications.

© 2007 Optical Society of America

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  1. J. T. Knudtson, D. S. Levy, and K. C. Herr, "Electronically tunable, first-order Fabry-Perot infrared filter," Opt. Eng. 35, 2313-2320 (1996).
    [CrossRef]
  2. S. L. Mielke, R. E. Ryan, T. Hilgeman, L. Lesyna, R. G. Madonna, and W. C. Van Nostrand, "Measurements of the phase shift on reflection for low-order infrared Fabry-Perot interferometer dielectric stack mirrors," Appl. Opt. 36, 8139-8144 (1997).
    [CrossRef]
  3. M. Xiang, Y. M. Cai, Y. M. Yu, J. Y. Yang, and Y. L. Wang, "Experimental study of the free spectral range (FSR) in FPI with a small plate gap," Opt. Express 11, 3147-3152 (2004).
    [CrossRef]
  4. E. Garmire, "Theory of quarter-wave stack dielectric mirrors used in a thin Fabry-Perot filter," Appl. Opt. 42, 5442-5449 (2003).
    [CrossRef] [PubMed]
  5. W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
    [CrossRef]
  6. A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
    [CrossRef]
  7. C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
    [CrossRef]
  8. X. Chen, F. Shen, Z. Wang, Z. Huang, and A. Wang, "Micro-air-gap-based intrinsic Fabry-Perot interferometric fiber-optic sensor," Appl. Opt. 45, 7760-7766 (2006).
    [CrossRef] [PubMed]
  9. B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
    [CrossRef]
  10. M. M. Sánchez-López, J. A. Davis, and K. Crabtree, "Coaxial cable analogs of multilayer dielectric optical coatings," Am. J. Phys. 71, 1314-1319 (2003).
    [CrossRef]
  11. M. M. Sánchez-López, J. Cos, J. A. Davis, D. A. Miller, and I. Moreno, "Fourier analysis of harmonic frequency transmission dielectric structures," Appl. Opt. 44, 3774-3783 (2005).
    [CrossRef]
  12. A. Haché and L. Poirier, "Long-range superluminal pulse propagation in a coaxial photonic crystal," Appl. Phys. Lett. 80, 518-520 (2002).
    [CrossRef]
  13. J. N. Munday and W. M. Robertson, "Negative group velocity pulse tunneling through a coaxial photonic crystal," Appl. Phys. Lett. 81, 2127-2129 (2002).
    [CrossRef]
  14. R. D. Pradhan and G. H. Watson, "Impurity effects in coaxial connector photonic crystals: A quasi-one-dimensional periodic system," Phys. Rev. B 60, 2410-2415 (1999).
    [CrossRef]
  15. G. J. Schneider, S. Hanna, J. L. Davis, and G. H. Watson, "Defect modes in coaxial photonic crystals," J. Appl. Phys. 90, 2642-2649 (2001).
    [CrossRef]
  16. L. Poirier and A. Haché, "Nonlinear coaxial photonic crystal," Appl. Phys. Lett. 78, 2626-2628 (2001).
    [CrossRef]
  17. H. A. Macleod, Thin-Film Optical Filters (Institute of Physics, 2001), Chap. 5.
    [CrossRef]

2006 (1)

2005 (1)

2004 (2)

M. Xiang, Y. M. Cai, Y. M. Yu, J. Y. Yang, and Y. L. Wang, "Experimental study of the free spectral range (FSR) in FPI with a small plate gap," Opt. Express 11, 3147-3152 (2004).
[CrossRef]

W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
[CrossRef]

2003 (2)

M. M. Sánchez-López, J. A. Davis, and K. Crabtree, "Coaxial cable analogs of multilayer dielectric optical coatings," Am. J. Phys. 71, 1314-1319 (2003).
[CrossRef]

E. Garmire, "Theory of quarter-wave stack dielectric mirrors used in a thin Fabry-Perot filter," Appl. Opt. 42, 5442-5449 (2003).
[CrossRef] [PubMed]

2002 (2)

A. Haché and L. Poirier, "Long-range superluminal pulse propagation in a coaxial photonic crystal," Appl. Phys. Lett. 80, 518-520 (2002).
[CrossRef]

J. N. Munday and W. M. Robertson, "Negative group velocity pulse tunneling through a coaxial photonic crystal," Appl. Phys. Lett. 81, 2127-2129 (2002).
[CrossRef]

2001 (2)

G. J. Schneider, S. Hanna, J. L. Davis, and G. H. Watson, "Defect modes in coaxial photonic crystals," J. Appl. Phys. 90, 2642-2649 (2001).
[CrossRef]

L. Poirier and A. Haché, "Nonlinear coaxial photonic crystal," Appl. Phys. Lett. 78, 2626-2628 (2001).
[CrossRef]

2000 (1)

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

1999 (2)

R. D. Pradhan and G. H. Watson, "Impurity effects in coaxial connector photonic crystals: A quasi-one-dimensional periodic system," Phys. Rev. B 60, 2410-2415 (1999).
[CrossRef]

B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
[CrossRef]

1997 (1)

1996 (2)

J. T. Knudtson, D. S. Levy, and K. C. Herr, "Electronically tunable, first-order Fabry-Perot infrared filter," Opt. Eng. 35, 2313-2320 (1996).
[CrossRef]

A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
[CrossRef]

Berthelot, L.

B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
[CrossRef]

Cai, Y. M.

Chen, X.

Cos, J.

Crabtree, K.

M. M. Sánchez-López, J. A. Davis, and K. Crabtree, "Coaxial cable analogs of multilayer dielectric optical coatings," Am. J. Phys. 71, 1314-1319 (2003).
[CrossRef]

Davis, J. A.

M. M. Sánchez-López, J. Cos, J. A. Davis, D. A. Miller, and I. Moreno, "Fourier analysis of harmonic frequency transmission dielectric structures," Appl. Opt. 44, 3774-3783 (2005).
[CrossRef]

M. M. Sánchez-López, J. A. Davis, and K. Crabtree, "Coaxial cable analogs of multilayer dielectric optical coatings," Am. J. Phys. 71, 1314-1319 (2003).
[CrossRef]

Davis, J. L.

G. J. Schneider, S. Hanna, J. L. Davis, and G. H. Watson, "Defect modes in coaxial photonic crystals," J. Appl. Phys. 90, 2642-2649 (2001).
[CrossRef]

Ford, J. E.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

Gagnaire, A.

B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
[CrossRef]

Garmire, E.

Goossen, K. W.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

Gu, P.

W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
[CrossRef]

Haché, A.

A. Haché and L. Poirier, "Long-range superluminal pulse propagation in a coaxial photonic crystal," Appl. Phys. Lett. 80, 518-520 (2002).
[CrossRef]

L. Poirier and A. Haché, "Nonlinear coaxial photonic crystal," Appl. Phys. Lett. 78, 2626-2628 (2001).
[CrossRef]

Hanna, S.

G. J. Schneider, S. Hanna, J. L. Davis, and G. H. Watson, "Defect modes in coaxial photonic crystals," J. Appl. Phys. 90, 2642-2649 (2001).
[CrossRef]

Haronian, D.

A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
[CrossRef]

Herr, K. C.

J. T. Knudtson, D. S. Levy, and K. C. Herr, "Electronically tunable, first-order Fabry-Perot infrared filter," Opt. Eng. 35, 2313-2320 (1996).
[CrossRef]

Hilgeman, T.

Huang, B.

W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
[CrossRef]

Huang, Z.

Joseph, J.

B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
[CrossRef]

Knudtson, J. T.

J. T. Knudtson, D. S. Levy, and K. C. Herr, "Electronically tunable, first-order Fabry-Perot infrared filter," Opt. Eng. 35, 2313-2320 (1996).
[CrossRef]

Lenz, G.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

Lesyna, L.

Levy, D. S.

J. T. Knudtson, D. S. Levy, and K. C. Herr, "Electronically tunable, first-order Fabry-Perot infrared filter," Opt. Eng. 35, 2313-2320 (1996).
[CrossRef]

Liu, X.

W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
[CrossRef]

Lo, Y. H.

A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Institute of Physics, 2001), Chap. 5.
[CrossRef]

Madonna, R. G.

Madsen, C. K.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

Masenelli, B.

B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
[CrossRef]

Mielke, S. L.

Miller, D. A.

Moreno, I.

Mozdy, E.

A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
[CrossRef]

Munday, J. N.

J. N. Munday and W. M. Robertson, "Negative group velocity pulse tunneling through a coaxial photonic crystal," Appl. Phys. Lett. 81, 2127-2129 (2002).
[CrossRef]

Nielsen, T. N.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

Poirier, L.

A. Haché and L. Poirier, "Long-range superluminal pulse propagation in a coaxial photonic crystal," Appl. Phys. Lett. 80, 518-520 (2002).
[CrossRef]

L. Poirier and A. Haché, "Nonlinear coaxial photonic crystal," Appl. Phys. Lett. 78, 2626-2628 (2001).
[CrossRef]

Pradhan, R. D.

R. D. Pradhan and G. H. Watson, "Impurity effects in coaxial connector photonic crystals: A quasi-one-dimensional periodic system," Phys. Rev. B 60, 2410-2415 (1999).
[CrossRef]

Robertson, W. M.

J. N. Munday and W. M. Robertson, "Negative group velocity pulse tunneling through a coaxial photonic crystal," Appl. Phys. Lett. 81, 2127-2129 (2002).
[CrossRef]

Ryan, R. E.

Sánchez-López, M. M.

M. M. Sánchez-López, J. Cos, J. A. Davis, D. A. Miller, and I. Moreno, "Fourier analysis of harmonic frequency transmission dielectric structures," Appl. Opt. 44, 3774-3783 (2005).
[CrossRef]

M. M. Sánchez-López, J. A. Davis, and K. Crabtree, "Coaxial cable analogs of multilayer dielectric optical coatings," Am. J. Phys. 71, 1314-1319 (2003).
[CrossRef]

Schneider, G. J.

G. J. Schneider, S. Hanna, J. L. Davis, and G. H. Watson, "Defect modes in coaxial photonic crystals," J. Appl. Phys. 90, 2642-2649 (2001).
[CrossRef]

Shen, F.

Shen, W.

W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
[CrossRef]

Tardy, J.

B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
[CrossRef]

Tran, A. T. T. D.

A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
[CrossRef]

Van Nostrand, W. C.

Walker, J. A.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

Wang, A.

Wang, Y. L.

Wang, Z.

Watson, G. H.

G. J. Schneider, S. Hanna, J. L. Davis, and G. H. Watson, "Defect modes in coaxial photonic crystals," J. Appl. Phys. 90, 2642-2649 (2001).
[CrossRef]

R. D. Pradhan and G. H. Watson, "Impurity effects in coaxial connector photonic crystals: A quasi-one-dimensional periodic system," Phys. Rev. B 60, 2410-2415 (1999).
[CrossRef]

Xiang, M.

Yang, J. Y.

Yu, Y. M.

Zhu, Y.

W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
[CrossRef]

Zhu, Z. H.

A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
[CrossRef]

Am. J. Phys. (1)

M. M. Sánchez-López, J. A. Davis, and K. Crabtree, "Coaxial cable analogs of multilayer dielectric optical coatings," Am. J. Phys. 71, 1314-1319 (2003).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (3)

L. Poirier and A. Haché, "Nonlinear coaxial photonic crystal," Appl. Phys. Lett. 78, 2626-2628 (2001).
[CrossRef]

A. Haché and L. Poirier, "Long-range superluminal pulse propagation in a coaxial photonic crystal," Appl. Phys. Lett. 80, 518-520 (2002).
[CrossRef]

J. N. Munday and W. M. Robertson, "Negative group velocity pulse tunneling through a coaxial photonic crystal," Appl. Phys. Lett. 81, 2127-2129 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. T. T. D. Tran, Y. H. Lo, Z. H. Zhu, D. Haronian, and E. Mozdy, "Surface micromachined Fabry-Perot tunable filter," IEEE Photon. Technol. Lett. 8, 393-395 (1996).
[CrossRef]

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, "A tunable dispersion compensating MEMS all-pass filter," IEEE Photon. Technol. Lett. 12, 651-653 (2000).
[CrossRef]

J. Appl. Phys. (2)

B. Masenelli, A. Gagnaire, L. Berthelot, J. Tardy, and J. Joseph, "Controlled spontaneous emission of a tri(8-hydroxyquinoline) aluminium layer in a microcavity," J. Appl. Phys. 85, 3032-3037 (1999).
[CrossRef]

G. J. Schneider, S. Hanna, J. L. Davis, and G. H. Watson, "Defect modes in coaxial photonic crystals," J. Appl. Phys. 90, 2642-2649 (2001).
[CrossRef]

J. Opt. A (1)

W. Shen, X. Liu, B. Huang, Y. Zhu, and P. Gu, "The effects of reflection phase shift on the optical properties of a micro-opto-electromechanical system Fabry-Perot tunable filter," J. Opt. A 6, 853-858 (2004).
[CrossRef]

Opt. Eng. (1)

J. T. Knudtson, D. S. Levy, and K. C. Herr, "Electronically tunable, first-order Fabry-Perot infrared filter," Opt. Eng. 35, 2313-2320 (1996).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

R. D. Pradhan and G. H. Watson, "Impurity effects in coaxial connector photonic crystals: A quasi-one-dimensional periodic system," Phys. Rev. B 60, 2410-2415 (1999).
[CrossRef]

Other (1)

H. A. Macleod, Thin-Film Optical Filters (Institute of Physics, 2001), Chap. 5.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Experimental transmission coefficient magnitude and (b) reflection coefficient phase for ( HL ) N H coaxial cable mirrors with N = 2 , 4, and 6 unit cells.

Fig. 2
Fig. 2

Experimental transmission coefficient magnitude for ( HL ) N H - L - ( HL ) N H Fabry–Perot structures with (a) a fixed number of unit cells N = 4 and different mirror spacings d, (b) a fixed d = 24.3   cm and different N. Experimental (symbols) and theoretical (lines) peak frequency, (c) versus mirror spacing for various N, and (d) versus N for different mirror spacing d.

Equations (4)

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

2 π m = 2 π 2 n d ν c Φ M 1 ( ν ) Φ M 2 ( ν ) .
Φ M ( ν ) = ϕ D + ε ( ν ) .
Φ M ( ν ) = π + α ( ν ν D ) .
ν = π ( m + 1 ) α ν D ( 2 π n d / c ) α .

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