Abstract

The diffraction regime of a thin grating inserted in a Fabry–Perot cavity is investigated. Our calculations show that, at Bragg incidence, a single diffraction order can be selectively enhanced, giving rise to a very efficient Bragg-like diffraction regime. The optimization of the device is studied as a function of the resonator thickness and finesse and the grating position inside the Fabry–Perot cavity. The angular and wavelength selectivities are also investigated. The device could be easily integrated and would be very useful for optical signal-processing applications.

© 2005 Optical Society of America

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  1. L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE  92, 1231–1280 (2004).
    [CrossRef]
  2. J. Zhao, X. Shen, and Y. Xia, “Beam splitting, combining and cross coupling through multiple superimposed volume index gratings,” Opt. Laser Technol.  33, 23–28 (2001).
    [CrossRef]
  3. Y. Ding, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Time domain image processing using dynamic holography,” IEEE J. Sel. Top. Quantum Electron.  4, 332–340 (1998).
    [CrossRef]
  4. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun.  32, 14–18 (1980).
    [CrossRef]
  5. L. Menez, I. Zaquine, A. Maruani, and R. Frey, “Intracavity Bragg grating,” J. Opt. Soc. Am. B  16, 1849–1855 (1999).
    [CrossRef]
  6. L. Menez, I. Zaquine, A. Maruani, and R. Frey, “Bragg thickness criterion for intracavity diffraction grating,” J. Opt. Soc. Am. B  19, 965–972 (2002).
    [CrossRef]
  7. D. D. Nolte, K. M. Kwolek, C. Lenox, and B. Streetman, “Dynamic holography in a broad-area optically pumped vertical GaAs microcavity,” J. Opt. Soc. Am. B  18, 257–263 (2001).
    [CrossRef]
  8. A. Sinha and G. Barbastathis, “Resonant holography,” Opt. Lett.  27, 385–387 (2002).
    [CrossRef]
  9. L. Escoubas, F. Flory, F. Lemarchand, A. During, and L. Roux, “Enhanced diffraction efficiency of gratings in multilayers,” Opt. Lett.  25, 194–196 (2000).
    [CrossRef]
  10. C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
    [CrossRef]
  11. R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
    [CrossRef]
  12. K. Tian and G. Barbastathis, “Cross talk in resonant holographic memories,” J. Opt. Soc. Am. A  21, 751–756 (2004).
    [CrossRef]
  13. D. D. Nolte and K. M. Kwolek, “Diffraction from a short-cavity Fabry–Pérot: application to photorefractive quantum wells,” Opt. Commun.  115, 606–616 (1995)
    [CrossRef]
  14. M. Born and E. Wolf, Principle of Optics (Pergamon, 1970), p. 55.

2004

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE  92, 1231–1280 (2004).
[CrossRef]

K. Tian and G. Barbastathis, “Cross talk in resonant holographic memories,” J. Opt. Soc. Am. A  21, 751–756 (2004).
[CrossRef]

2002

2001

D. D. Nolte, K. M. Kwolek, C. Lenox, and B. Streetman, “Dynamic holography in a broad-area optically pumped vertical GaAs microcavity,” J. Opt. Soc. Am. B  18, 257–263 (2001).
[CrossRef]

J. Zhao, X. Shen, and Y. Xia, “Beam splitting, combining and cross coupling through multiple superimposed volume index gratings,” Opt. Laser Technol.  33, 23–28 (2001).
[CrossRef]

2000

1999

L. Menez, I. Zaquine, A. Maruani, and R. Frey, “Intracavity Bragg grating,” J. Opt. Soc. Am. B  16, 1849–1855 (1999).
[CrossRef]

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

1998

Y. Ding, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Time domain image processing using dynamic holography,” IEEE J. Sel. Top. Quantum Electron.  4, 332–340 (1998).
[CrossRef]

1997

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

1995

D. D. Nolte and K. M. Kwolek, “Diffraction from a short-cavity Fabry–Pérot: application to photorefractive quantum wells,” Opt. Commun.  115, 606–616 (1995)
[CrossRef]

1980

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun.  32, 14–18 (1980).
[CrossRef]

Barbastathis, G.

Bashaw, M. C.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE  92, 1231–1280 (2004).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principle of Optics (Pergamon, 1970), p. 55.

Collet, J. H.

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

De Matos, C.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Ding, Y.

Y. Ding, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Time domain image processing using dynamic holography,” IEEE J. Sel. Top. Quantum Electron.  4, 332–340 (1998).
[CrossRef]

During, A.

Escoubas, L.

Flory, F.

Frey, R.

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun.  32, 14–18 (1980).
[CrossRef]

Grac, R.

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Hesselink, L.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE  92, 1231–1280 (2004).
[CrossRef]

Kéromnès, J. C.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

Kwolek, K. M.

D. D. Nolte, K. M. Kwolek, C. Lenox, and B. Streetman, “Dynamic holography in a broad-area optically pumped vertical GaAs microcavity,” J. Opt. Soc. Am. B  18, 257–263 (2001).
[CrossRef]

D. D. Nolte and K. M. Kwolek, “Diffraction from a short-cavity Fabry–Pérot: application to photorefractive quantum wells,” Opt. Commun.  115, 606–616 (1995)
[CrossRef]

L’Haridon, H.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Lambert, B.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Le Corre, A.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Lemarchand, F.

Lenox, C.

Lever, R.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

Magnusson, R.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun.  32, 14–18 (1980).
[CrossRef]

Maruani, A.

Melloch, M. R.

Y. Ding, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Time domain image processing using dynamic holography,” IEEE J. Sel. Top. Quantum Electron.  4, 332–340 (1998).
[CrossRef]

Menez, L.

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun.  32, 14–18 (1980).
[CrossRef]

Nolte, D. D.

D. D. Nolte, K. M. Kwolek, C. Lenox, and B. Streetman, “Dynamic holography in a broad-area optically pumped vertical GaAs microcavity,” J. Opt. Soc. Am. B  18, 257–263 (2001).
[CrossRef]

Y. Ding, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Time domain image processing using dynamic holography,” IEEE J. Sel. Top. Quantum Electron.  4, 332–340 (1998).
[CrossRef]

D. D. Nolte and K. M. Kwolek, “Diffraction from a short-cavity Fabry–Pérot: application to photorefractive quantum wells,” Opt. Commun.  115, 606–616 (1995)
[CrossRef]

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE  92, 1231–1280 (2004).
[CrossRef]

Pugnet, M.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Ropars, G.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

Roux, L.

Shen, X.

J. Zhao, X. Shen, and Y. Xia, “Beam splitting, combining and cross coupling through multiple superimposed volume index gratings,” Opt. Laser Technol.  33, 23–28 (2001).
[CrossRef]

Sinha, A.

Streetman, B.

Tian, K.

Vaudry, C.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

Weiner, A. M.

Y. Ding, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Time domain image processing using dynamic holography,” IEEE J. Sel. Top. Quantum Electron.  4, 332–340 (1998).
[CrossRef]

White, J. O.

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principle of Optics (Pergamon, 1970), p. 55.

Xia, Y.

J. Zhao, X. Shen, and Y. Xia, “Beam splitting, combining and cross coupling through multiple superimposed volume index gratings,” Opt. Laser Technol.  33, 23–28 (2001).
[CrossRef]

Zaquine, I.

Zhao, J.

J. Zhao, X. Shen, and Y. Xia, “Beam splitting, combining and cross coupling through multiple superimposed volume index gratings,” Opt. Laser Technol.  33, 23–28 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

Y. Ding, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Time domain image processing using dynamic holography,” IEEE J. Sel. Top. Quantum Electron.  4, 332–340 (1998).
[CrossRef]

IEEE Photonics Technol. Lett.

C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Kéromnès, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial liftoff microcavities for 1.55 μm quantum-well spatial light modulators,” IEEE Photonics Technol. Lett.  11, 57–59 (1999).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

D. D. Nolte and K. M. Kwolek, “Diffraction from a short-cavity Fabry–Pérot: application to photorefractive quantum wells,” Opt. Commun.  115, 606–616 (1995)
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun.  32, 14–18 (1980).
[CrossRef]

Opt. Laser Technol.

J. Zhao, X. Shen, and Y. Xia, “Beam splitting, combining and cross coupling through multiple superimposed volume index gratings,” Opt. Laser Technol.  33, 23–28 (2001).
[CrossRef]

Opt. Lett.

Proc. IEEE

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE  92, 1231–1280 (2004).
[CrossRef]

Superlattices Microstruct.

R. Grac, M. Pugnet, J. H. Collet, B. Lambert, C. De Matos, H. L’Haridon, A. Le Corre, and J. O. White, “Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity,” Superlattices Microstruct.  22, 505–509 (1997).
[CrossRef]

Other

M. Born and E. Wolf, Principle of Optics (Pergamon, 1970), p. 55.

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Figures (7)

Fig. 1
Fig. 1

(a) Setup of the thin grating inside the Fabry–Perot resonator and (b) the wave vectors of all considered diffraction orders.

Fig. 2
Fig. 2

Logarithmic plot of diffraction efficiencies as a function of resonator length with ρ g = 10 4 and R 1 = 0.8 .

Fig. 3
Fig. 3

(a) Diffraction efficiency of order 1 and (b) Bragg ratios as a function of the reflection coefficient of the first mirror, with ρ g = 10 4 and L = 3.55 μ m .

Fig. 4
Fig. 4

(a) Order 1 diffraction efficiency and (b) Bragg ratios as a function of the one-pass efficiency of the grating with L = 3.55 μ m and R 1 = 0.8 .

Fig. 5
Fig. 5

Logarithmic plot of diffraction efficiencies as a function of the position of the grating inside the cavity with ρ g = 10 4 , L = 3.55 μ m , and R 1 = 0.8 .

Fig. 6
Fig. 6

Logarithmic plot of diffraction efficiencies as a function of incidence angle (inside the cavity) with ρ g = 10 4 , L = 3.55 μ m , and R 1 = 0.8 .

Fig. 7
Fig. 7

(a) Order 1 diffraction efficiency and (b) Diffraction efficiencies plotted as a function of wavelength with ρ g = 10 4 , L = 3.55 μ m , and R 1 = 0.8 .

Equations (6)

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

F ( resp B ) = ( S 2 S 1 S 0 S + 1 ) F ( resp B ) .
( F bd B bd ) = M 1 P 1 D P 2 M 2 ( F ad B ad ) ,
M i = 1 t i ( I 4 r i I 4 r i I 4 I 4 ) for i = ( 1 , 2 ) ,
P i = ( P i 4 * 0 4 0 4 P i 4 ) for i = ( 1 , 2 ) ,
P i 4 = ( exp ( j k 2 z l i ) 0 0 0 0 exp ( j k 1 z l i ) 0 0 0 0 exp ( j k 0 z l i ) 0 0 0 0 exp ( j k + 1 z l i ) ) .
D = ( D 4 1 0 4 0 4 D 4 ) , with D 4 = ( t g d g 0 0 d g t g d g 0 0 d g t g d g 0 0 d g t g ) .

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