Abstract

Bragg diffraction of a read beam is studied theoretically when the refractive-index grating is placed inside a Fabry–Perot cavity. Diffraction efficiency, angular selectivity, and signal-to-noise ratio are largely enhanced compared with those for the bare Bragg grating, which may permit the use of low-efficiency or short-length materials as well. The results are much better for an asymmetric cavity operated in reflection than for a symmetric cavity in transmission.

© 1999 Optical Society of America

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References

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  1. 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]
  2. K. M. Kwolek, M. R. Melloch, and D. D. Nolte, “Photorefractive asymmetric Fabry–Pérot quantum wells: transverse-field geometry,” Appl. Phys. Lett. 67, 736–738 (1995).
    [CrossRef]
  3. C. De Matos, H. L’Haridon, A. Le Corre, R. Lever, J. C. Keromnes, G. Ropars, C. Vaudry, B. Lambert, and M. Pugnet, “Epitaxial lift-off microcavities for 1.55 μm quantum well spatial light modulators,” IEEE Photonics Technol. Lett. 11, 57–59 (1999).
    [CrossRef]
  4. Q. Byron He, P. Yeh, and C. Gu, “Analysis of photorefractive Fabry–Perot etalons: a novel device,” Opt. Lett. 17, 664–666 (1992).
    [CrossRef]
  5. Q. B. He, H. K. Liu, and P. Yeh, “Asymmetric photorefractive Fabry–Perot etalons,” Appl. Phys. B: Lasers Opt. 59, 467–470 (1994).
    [CrossRef]
  6. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  7. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  8. J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
    [CrossRef]
  9. H.-Y. S. Li and D. Psaltis, “Three-dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
    [CrossRef] [PubMed]
  10. K. Rastani, “Storage capacity and cross talk in angularly multiplexed holograms: two case studies,” Appl. Opt. 32, 3772–3778 (1993).
    [CrossRef] [PubMed]
  11. F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. (Bellingham) 36, 1691–1699 (1997).
    [CrossRef]
  12. Ph. Delaye, J. M. C. Jonathan, G. Pauliat, and G. Roosen, “Photorefractive materials: specifications relevant to applications,” Pure Appl. Opt. 5, 541–559 (1996).
    [CrossRef]

1999 (1)

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

1997 (2)

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. (Bellingham) 36, 1691–1699 (1997).
[CrossRef]

1996 (1)

Ph. Delaye, J. M. C. Jonathan, G. Pauliat, and G. Roosen, “Photorefractive materials: specifications relevant to applications,” Pure Appl. Opt. 5, 541–559 (1996).
[CrossRef]

1995 (2)

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]

K. M. Kwolek, M. R. Melloch, and D. D. Nolte, “Photorefractive asymmetric Fabry–Pérot quantum wells: transverse-field geometry,” Appl. Phys. Lett. 67, 736–738 (1995).
[CrossRef]

1994 (2)

H.-Y. S. Li and D. Psaltis, “Three-dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
[CrossRef] [PubMed]

Q. B. He, H. K. Liu, and P. Yeh, “Asymmetric photorefractive Fabry–Perot etalons,” Appl. Phys. B: Lasers Opt. 59, 467–470 (1994).
[CrossRef]

1993 (1)

1992 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Byron He, Q.

Caulfield, H. J.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Dai, F.

F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. (Bellingham) 36, 1691–1699 (1997).
[CrossRef]

De Matos, C.

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

Delaye, Ph.

Ph. Delaye, J. M. C. Jonathan, G. Pauliat, and G. Roosen, “Photorefractive materials: specifications relevant to applications,” Pure Appl. Opt. 5, 541–559 (1996).
[CrossRef]

Fournier, J. F.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Gu, C.

F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. (Bellingham) 36, 1691–1699 (1997).
[CrossRef]

Q. Byron He, P. Yeh, and C. Gu, “Analysis of photorefractive Fabry–Perot etalons: a novel device,” Opt. Lett. 17, 664–666 (1992).
[CrossRef]

He, Q. B.

Q. B. He, H. K. Liu, and P. Yeh, “Asymmetric photorefractive Fabry–Perot etalons,” Appl. Phys. B: Lasers Opt. 59, 467–470 (1994).
[CrossRef]

Hemmer, P.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Jonathan, J. M. C.

Ph. Delaye, J. M. C. Jonathan, G. Pauliat, and G. Roosen, “Photorefractive materials: specifications relevant to applications,” Pure Appl. Opt. 5, 541–559 (1996).
[CrossRef]

Keromnes, J. C.

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

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Korzinin, Y. L.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Kwolek, K. M.

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]

K. M. Kwolek, M. R. Melloch, and D. D. Nolte, “Photorefractive asymmetric Fabry–Pérot quantum wells: transverse-field geometry,” Appl. Phys. Lett. 67, 736–738 (1995).
[CrossRef]

L’Haridon, H.

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

Lambert, B.

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

Le Corre, A.

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

Lever, R.

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

Li, H.-Y. S.

Liu, H. K.

Q. B. He, H. K. Liu, and P. Yeh, “Asymmetric photorefractive Fabry–Perot etalons,” Appl. Phys. B: Lasers Opt. 59, 467–470 (1994).
[CrossRef]

Ludman, J. E.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Melloch, M. R.

K. M. Kwolek, M. R. Melloch, and D. D. Nolte, “Photorefractive asymmetric Fabry–Pérot quantum wells: transverse-field geometry,” Appl. Phys. Lett. 67, 736–738 (1995).
[CrossRef]

Nolte, D. D.

K. M. Kwolek, M. R. Melloch, and D. D. Nolte, “Photorefractive asymmetric Fabry–Pérot quantum wells: transverse-field geometry,” Appl. Phys. Lett. 67, 736–738 (1995).
[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]

Pauliat, G.

Ph. Delaye, J. M. C. Jonathan, G. Pauliat, and G. Roosen, “Photorefractive materials: specifications relevant to applications,” Pure Appl. Opt. 5, 541–559 (1996).
[CrossRef]

Psaltis, D.

Pugnet, M.

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

Rastani, K.

Reinhand, N. O.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Riccobono, J. R.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Roosen, G.

Ph. Delaye, J. M. C. Jonathan, G. Pauliat, and G. Roosen, “Photorefractive materials: specifications relevant to applications,” Pure Appl. Opt. 5, 541–559 (1996).
[CrossRef]

Ropars, G.

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

Semenova, I. V.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Shahriar, S. M.

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

Vaudry, C.

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

Yeh, P.

Q. B. He, H. K. Liu, and P. Yeh, “Asymmetric photorefractive Fabry–Perot etalons,” Appl. Phys. B: Lasers Opt. 59, 467–470 (1994).
[CrossRef]

Q. Byron He, P. Yeh, and C. Gu, “Analysis of photorefractive Fabry–Perot etalons: a novel device,” Opt. Lett. 17, 664–666 (1992).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B: Lasers Opt. (1)

Q. B. He, H. K. Liu, and P. Yeh, “Asymmetric photorefractive Fabry–Perot etalons,” Appl. Phys. B: Lasers Opt. 59, 467–470 (1994).
[CrossRef]

Appl. Phys. Lett. (1)

K. M. Kwolek, M. R. Melloch, and D. D. Nolte, “Photorefractive asymmetric Fabry–Pérot quantum wells: transverse-field geometry,” Appl. Phys. Lett. 67, 736–738 (1995).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

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

Opt. Commun. (1)

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]

Opt. Eng. (Bellingham) (2)

J. E. Ludman, J. R. Riccobono, N. O. Reinhand, I. V. Semenova, Y. L. Korzinin, S. M. Shahriar, H. J. Caulfield, J. F. Fournier, and P. Hemmer, “Very thick holographic nonspatial filtering of laser beams,” Opt. Eng. (Bellingham) 36, 1700–1705 (1997).
[CrossRef]

F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. (Bellingham) 36, 1691–1699 (1997).
[CrossRef]

Opt. Lett. (1)

Pure Appl. Opt. (1)

Ph. Delaye, J. M. C. Jonathan, G. Pauliat, and G. Roosen, “Photorefractive materials: specifications relevant to applications,” Pure Appl. Opt. 5, 541–559 (1996).
[CrossRef]

Other (1)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the intracavity Bragg structure: EI,ER,ET, ERD, and ETD are, respectively, incident, reflected, transmitted, reflected, diffracted, and transmitted diffracted amplitudes in the intracavity Bragg diffractor; kF,kB,kF, and kB are the intracavity wave vectors; Λ is the grating period; and l is the thickness of the Fabry–Perot cavity.

Fig. 2
Fig. 2

(a) Transmitted and (b) reflected diffraction efficiency gains versus coupling strength β in symmetric [(a) R1=R2=R] and asymmetric [(b) R1=R,R2=1] Fabry–Perot cavities for four values of reflectivity R of the mirrors.

Fig. 3
Fig. 3

(a) Transmitted and (b) reflected diffraction efficiency gains versus mirror reflectivity R in symmetric [(a) R1=R2=R] and asymmetric [(b) R1=R,R2=1] Fabry–Perot cavities for four values of coupling strength β.

Fig. 4
Fig. 4

Normalized FWHM Δm1/2 versus coupling strength β in symmetric [(a) R1=R2=R] and asymmetric [(b) R1=R,R2=1] structures for four values of the reflection coefficient of the mirrors.

Fig. 5
Fig. 5

Normalized FWHM Δm1/2 versus mirror reflectivity R in symmetric [(a) R1=R2=R] and asymmetric [(b) R1=R,R2=1] structures for four values of coupling strength β.

Fig. 6
Fig. 6

Normalized diffraction efficiency versus Δm=m-m0 for a bare sample (dotted curve) and a symmetric (dashed–dotted curve) and an asymmetric (solid curve) intracavity Bragg diffractor.

Fig. 7
Fig. 7

Intracavity SNR normalized to a simple Bragg SNR versus (a) β and (b) R for an asymmetric intracavity structure (R1=R,R2=1).

Equations (51)

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R=RF+RB={RF(z)exp[iϕRF(x)]exp(ikF·r)+RB(z)exp[iϕRB(x)]exp(ikB·r)}eˆ,
S=SF+SB={SF(z)exp[iϕSF(x)]exp(ikF·r)+SB(z)exp[iϕSB(x)]exp(ikB·r)}eˆ.
PNL(ω)=(n0/4π)[Δn exp(iK·r)+Δn* exp(-iK·r)](R+S),
kˆF·RF=iπΔn*λSF(z)exp[iϕSF(x)]exp(iΔk·r),
kˆB·RB=iπΔn*λSB(z)exp[iϕSB(x)]exp(iΔk·r),
kˆF·SF=iπΔnλRF(z)exp[iϕRF(x)]exp(-iΔk·r),
kˆB·SB=iπΔnλRB(z)exp[iϕRB(x)]exp(-iΔk·r).
RF(0)=t1EI(0)+r1RB(0),
SF(0)=r1SB(0),
ER(0)=-r1EI(0)+t1RB(0),
EDR(0)=t1SB(0),
RB(l)=r2RF(l),
SB(l)=r2SF(l),
ED(l)=t2SF(l),
ET(l)=t2RF(l).
ϕRF(x)=ϕRF(0)=ϕRF,
ϕRB(x)=ϕRB(0)=ϕRB.
ϕSF(x)=(K+2k sin θ)x+ϕSF(0),
ϕSB(x)=(K+2k sin θ)x+ϕSB(0).
dRF(z)d zcos θ=iπΔn*λSF(z)exp(iϕ1),
dSF(z)dzcos θ-i(K+2k sin θ)SF(z)sin θ
=iπΔnλRF(z)exp(-iϕ1),
dRB(z)d zcos θ=-iπΔn*λSB(z)exp(iϕ2), 
dSB(z)d zcos θ+i(K+2k sin θ)SB(z)sin θ
=-iπΔnλRB(z)exp(-iϕ2),
RF(z)exp(iϕRF)
=RF+ exp(irF+z)+RF- exp(irF-z),
SF(z)exp[iϕSF(x)]
=λ cos θ exp(-iϕ1)πΔn*
×[rF+RF+ exp(irF+z)+rF-RF- exp(irF-z)],
rF±=12 cos θ×(K+2k sin θ)sin θ±4π2|Δn|2λ2+sin2 θ(K+2k sin θ)21/2,
RF±=±t1EI rF/(rF--rF+)1-r1r2 exp[2i(rF±+k cos θ)l],
EI=EI(0),
RB(z)exp(iϕRB)
=RB+ exp(-irF-z)+RB- exp(-irF+z),
SB(z)exp[iϕSB(x)]
=λ cos θ exp(-iϕ1)πΔn*
×[rF-RB+ exp(-irF-z)+rF+RB- exp(-irF+z)],
RB±=±t1EI rF±(rF+-rF-)×r1r2 exp[2i(rF+k cos θ)l]1-r1r2 exp[2i(rF+k cos θ)l].
ρTD=T1T2 β2b2sin2(πb)|1+r1r2 exp(2iπa)|2|1+r12r22 exp(4iπa)-2r1r2 exp(2iπa)cos(2πb)|2,
ρRD=T12R2 β2b2sin2(2πb)|1+r12r22 exp(4iπa)-2r1r2 exp(2iπa)cos(2πb)|2,
ρBragg=β2b2sin2(πb),
a=2 lλcos θ+1Λ+2λsin θl tan θ,
b=lcos θ|Δn|2λ2+sin2 θ1Λ+2λsin θ21/2,
β=l|Δn|λ cos θ,
a=m+c,
b=β2+c2,
GT=T1T2 |1+r1r2|2|1+r12r22-2r1r2 cos(2πβ)|2,
GR=T12R2 4 cos2(πβ)|1+r12r22-2r1r2 cos(2πβ)|2.
Δmz±(q)q+q2m0(Λ2/l2).
SNR=ρRD(m0)max[ρRD(msec+), ρRD(msec-)].

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