Abstract

A two-dimensional model to describe the photorefractive behavior of a semiconductor multiple-quantum-well structure operating in the longitudinal geometry has been formulated. It takes into account longitudinal and transverse transport as well as both components of the space-charge field. The rate equations have been solved in the short-time regime, and the role of the various geometrical and physical parameters has been investigated. Special attention has been paid to clarifying the effects of transverse transport.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  2. F. Agulló-López, ed., feature on photorefractive materials, Mater. Res. Bull. 19(3) (1994).
  3. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
    [CrossRef]
  4. D. D. Nolte and M. R. Melloch, “Photorefractive quantum wells and thin films,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 373–451.
    [CrossRef]
  5. Y. Owechko and A. R. Tanguay, “Theoretical resolution limitation of electrooptic spatial light modulators. I. Fundamental considerations,” J. Opt. Soc. Am. A 1, 635–643 (1984).
    [CrossRef]
  6. A. Partovi, “Photorefractive multiple quantum well materials and applications to signal processing,” Opt. Mater. 4, 330–338 (1995).
    [CrossRef]
  7. W. S. Rabinovich, S. R. Bowman, D. S. Katzer, and C. S. Kyono, “Intrinsic multiple quantum well spatial light modulators,” Appl. Phys. Lett. 66, 1044–1046 (1995).
    [CrossRef]
  8. L. F. Magaña, F. Agulló-López, and M. Carrascosa, “Role of physical parameters on the photorefractive performance of semiconductor multiple quantum wells,” J. Opt. Soc. Am. B 11, 1651–1654 (1994).
    [CrossRef]
  9. Q. Wang, R. M. Brubaker, D. D. Nolte, and M. R. Melloch, “Photorefractive quantum wells: transverse Franz–Keldysh geometry,” J. Opt. Soc. Am. B 9, 1626–1641 (1992).
    [CrossRef]
  10. M. Aguilar, M. Carrascosa, F. Agulló-López, and L. F. Magaña, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840–4844 (1995).
    [CrossRef]
  11. D. D. Nolte, “Resolution of electro-optic spatial light modulators: the role of lateral transport,” Opt. Commun. 92, 199–204 (1992).
    [CrossRef]
  12. S. L. Smith and L. Hesselink, “Analytical model for grating dynamics in surface-charge dominated Pockels readout optical modulator devices,” J. Opt. Soc. Am. B 6, 1878–1885 (1994).
    [CrossRef]
  13. D. D. Nolte, I. Lahiri, and M. Aguilar, “Photorefractive Stark-geometry quantum wells: diffraction nonlinearities and displacement currents,” Opt. Commun. (to be published).
  14. F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics Phenomena, Materials and Applications (Academic, London, 1994).
  15. I. Lahiri, M. Aguilar, D. D. Nolte, and M. R. Melloch, “High-efficiency Stark-geometry photorefractive quantum wells with intrinsic cladding layers,” Appl. Phys. Lett. 68, 517–519 (1996).
    [CrossRef]

1996 (1)

I. Lahiri, M. Aguilar, D. D. Nolte, and M. R. Melloch, “High-efficiency Stark-geometry photorefractive quantum wells with intrinsic cladding layers,” Appl. Phys. Lett. 68, 517–519 (1996).
[CrossRef]

1995 (3)

A. Partovi, “Photorefractive multiple quantum well materials and applications to signal processing,” Opt. Mater. 4, 330–338 (1995).
[CrossRef]

W. S. Rabinovich, S. R. Bowman, D. S. Katzer, and C. S. Kyono, “Intrinsic multiple quantum well spatial light modulators,” Appl. Phys. Lett. 66, 1044–1046 (1995).
[CrossRef]

M. Aguilar, M. Carrascosa, F. Agulló-López, and L. F. Magaña, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840–4844 (1995).
[CrossRef]

1994 (3)

F. Agulló-López, ed., feature on photorefractive materials, Mater. Res. Bull. 19(3) (1994).

L. F. Magaña, F. Agulló-López, and M. Carrascosa, “Role of physical parameters on the photorefractive performance of semiconductor multiple quantum wells,” J. Opt. Soc. Am. B 11, 1651–1654 (1994).
[CrossRef]

S. L. Smith and L. Hesselink, “Analytical model for grating dynamics in surface-charge dominated Pockels readout optical modulator devices,” J. Opt. Soc. Am. B 6, 1878–1885 (1994).
[CrossRef]

1992 (2)

Q. Wang, R. M. Brubaker, D. D. Nolte, and M. R. Melloch, “Photorefractive quantum wells: transverse Franz–Keldysh geometry,” J. Opt. Soc. Am. B 9, 1626–1641 (1992).
[CrossRef]

D. D. Nolte, “Resolution of electro-optic spatial light modulators: the role of lateral transport,” Opt. Commun. 92, 199–204 (1992).
[CrossRef]

1984 (1)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Aguilar, M.

I. Lahiri, M. Aguilar, D. D. Nolte, and M. R. Melloch, “High-efficiency Stark-geometry photorefractive quantum wells with intrinsic cladding layers,” Appl. Phys. Lett. 68, 517–519 (1996).
[CrossRef]

M. Aguilar, M. Carrascosa, F. Agulló-López, and L. F. Magaña, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840–4844 (1995).
[CrossRef]

D. D. Nolte, I. Lahiri, and M. Aguilar, “Photorefractive Stark-geometry quantum wells: diffraction nonlinearities and displacement currents,” Opt. Commun. (to be published).

Agulló-López, F.

M. Aguilar, M. Carrascosa, F. Agulló-López, and L. F. Magaña, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840–4844 (1995).
[CrossRef]

L. F. Magaña, F. Agulló-López, and M. Carrascosa, “Role of physical parameters on the photorefractive performance of semiconductor multiple quantum wells,” J. Opt. Soc. Am. B 11, 1651–1654 (1994).
[CrossRef]

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics Phenomena, Materials and Applications (Academic, London, 1994).

Agulló-Rueda, F.

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics Phenomena, Materials and Applications (Academic, London, 1994).

Bowman, S. R.

W. S. Rabinovich, S. R. Bowman, D. S. Katzer, and C. S. Kyono, “Intrinsic multiple quantum well spatial light modulators,” Appl. Phys. Lett. 66, 1044–1046 (1995).
[CrossRef]

Brubaker, R. M.

Cabrera, J. M.

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics Phenomena, Materials and Applications (Academic, London, 1994).

Carrascosa, M.

M. Aguilar, M. Carrascosa, F. Agulló-López, and L. F. Magaña, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840–4844 (1995).
[CrossRef]

L. F. Magaña, F. Agulló-López, and M. Carrascosa, “Role of physical parameters on the photorefractive performance of semiconductor multiple quantum wells,” J. Opt. Soc. Am. B 11, 1651–1654 (1994).
[CrossRef]

Hesselink, L.

S. L. Smith and L. Hesselink, “Analytical model for grating dynamics in surface-charge dominated Pockels readout optical modulator devices,” J. Opt. Soc. Am. B 6, 1878–1885 (1994).
[CrossRef]

Katzer, D. S.

W. S. Rabinovich, S. R. Bowman, D. S. Katzer, and C. S. Kyono, “Intrinsic multiple quantum well spatial light modulators,” Appl. Phys. Lett. 66, 1044–1046 (1995).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Kyono, C. S.

W. S. Rabinovich, S. R. Bowman, D. S. Katzer, and C. S. Kyono, “Intrinsic multiple quantum well spatial light modulators,” Appl. Phys. Lett. 66, 1044–1046 (1995).
[CrossRef]

Lahiri, I.

I. Lahiri, M. Aguilar, D. D. Nolte, and M. R. Melloch, “High-efficiency Stark-geometry photorefractive quantum wells with intrinsic cladding layers,” Appl. Phys. Lett. 68, 517–519 (1996).
[CrossRef]

D. D. Nolte, I. Lahiri, and M. Aguilar, “Photorefractive Stark-geometry quantum wells: diffraction nonlinearities and displacement currents,” Opt. Commun. (to be published).

Magaña, L. F.

M. Aguilar, M. Carrascosa, F. Agulló-López, and L. F. Magaña, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840–4844 (1995).
[CrossRef]

L. F. Magaña, F. Agulló-López, and M. Carrascosa, “Role of physical parameters on the photorefractive performance of semiconductor multiple quantum wells,” J. Opt. Soc. Am. B 11, 1651–1654 (1994).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Melloch, M. R.

I. Lahiri, M. Aguilar, D. D. Nolte, and M. R. Melloch, “High-efficiency Stark-geometry photorefractive quantum wells with intrinsic cladding layers,” Appl. Phys. Lett. 68, 517–519 (1996).
[CrossRef]

Q. Wang, R. M. Brubaker, D. D. Nolte, and M. R. Melloch, “Photorefractive quantum wells: transverse Franz–Keldysh geometry,” J. Opt. Soc. Am. B 9, 1626–1641 (1992).
[CrossRef]

D. D. Nolte and M. R. Melloch, “Photorefractive quantum wells and thin films,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 373–451.
[CrossRef]

Nolte, D. D.

I. Lahiri, M. Aguilar, D. D. Nolte, and M. R. Melloch, “High-efficiency Stark-geometry photorefractive quantum wells with intrinsic cladding layers,” Appl. Phys. Lett. 68, 517–519 (1996).
[CrossRef]

Q. Wang, R. M. Brubaker, D. D. Nolte, and M. R. Melloch, “Photorefractive quantum wells: transverse Franz–Keldysh geometry,” J. Opt. Soc. Am. B 9, 1626–1641 (1992).
[CrossRef]

D. D. Nolte, “Resolution of electro-optic spatial light modulators: the role of lateral transport,” Opt. Commun. 92, 199–204 (1992).
[CrossRef]

D. D. Nolte and M. R. Melloch, “Photorefractive quantum wells and thin films,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 373–451.
[CrossRef]

D. D. Nolte, I. Lahiri, and M. Aguilar, “Photorefractive Stark-geometry quantum wells: diffraction nonlinearities and displacement currents,” Opt. Commun. (to be published).

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Owechko, Y.

Partovi, A.

A. Partovi, “Photorefractive multiple quantum well materials and applications to signal processing,” Opt. Mater. 4, 330–338 (1995).
[CrossRef]

Rabinovich, W. S.

W. S. Rabinovich, S. R. Bowman, D. S. Katzer, and C. S. Kyono, “Intrinsic multiple quantum well spatial light modulators,” Appl. Phys. Lett. 66, 1044–1046 (1995).
[CrossRef]

Smith, S. L.

S. L. Smith and L. Hesselink, “Analytical model for grating dynamics in surface-charge dominated Pockels readout optical modulator devices,” J. Opt. Soc. Am. B 6, 1878–1885 (1994).
[CrossRef]

Soskin, M.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Tanguay, A. R.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Wang, Q.

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Appl. Phys. Lett. (2)

W. S. Rabinovich, S. R. Bowman, D. S. Katzer, and C. S. Kyono, “Intrinsic multiple quantum well spatial light modulators,” Appl. Phys. Lett. 66, 1044–1046 (1995).
[CrossRef]

I. Lahiri, M. Aguilar, D. D. Nolte, and M. R. Melloch, “High-efficiency Stark-geometry photorefractive quantum wells with intrinsic cladding layers,” Appl. Phys. Lett. 68, 517–519 (1996).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

J. Appl. Phys. (1)

M. Aguilar, M. Carrascosa, F. Agulló-López, and L. F. Magaña, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840–4844 (1995).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

Mater. Res. Bull. (1)

F. Agulló-López, ed., feature on photorefractive materials, Mater. Res. Bull. 19(3) (1994).

Opt. Commun. (1)

D. D. Nolte, “Resolution of electro-optic spatial light modulators: the role of lateral transport,” Opt. Commun. 92, 199–204 (1992).
[CrossRef]

Opt. Mater. (1)

A. Partovi, “Photorefractive multiple quantum well materials and applications to signal processing,” Opt. Mater. 4, 330–338 (1995).
[CrossRef]

Other (4)

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

D. D. Nolte and M. R. Melloch, “Photorefractive quantum wells and thin films,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 373–451.
[CrossRef]

D. D. Nolte, I. Lahiri, and M. Aguilar, “Photorefractive Stark-geometry quantum wells: diffraction nonlinearities and displacement currents,” Opt. Commun. (to be published).

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics Phenomena, Materials and Applications (Academic, London, 1994).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the experimental geometry.

Fig. 2
Fig. 2

Initial growth rates for the amplitudes of the Ex [(a) solid line, (b) solid curve] and Ez [(a) dashed curve, (b) dashed line] components of the space-charge field associated with (a) the surface-charge and (b) the volume-charge gratings.

Fig. 3
Fig. 3

Dependence of (a) Ez(0) and (b) Ex(0) on the ratio Λ/L.

Fig. 4
Fig. 4

Ratio Ex(0)/Ez(0) as a function of Λ/L.

Fig. 5
Fig. 5

Initial growth rates for (a) Ez(0) and (b) Ex(0) as a function of the trap density.

Fig. 6
Fig. 6

Ex(0)/Ez(0) as a function of the mobility ratio r=μx/μz.

Fig. 7
Fig. 7

Total diffraction efficiency from the 2K grating as a function of Λ/L. The diffraction efficiencies for the surface and the volume gratings are also included for comparison.

Tables (1)

Tables Icon

Table 1 Material Parameters of a GaAs/AlxGa1−xAs MQW Structure

Equations (40)

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

I=I0(1+m cos Kx)[α(z-L/2)],
net=αhνI-γneND++1e·je,
nht=αhνI-γnhND0-1e·jh,
ND+t=-ND0t=-γneND++γnhND0,
Exx+Ezz=ρ0,
Exz-Ezx=0.
ρ=e(ND+-NA-),
je=eμeneE+eDene,
jh=eμhnhE-eDhnh,
τe=1γND+=2×10-10 s,
τh=1γND0=2×10-10 s,
τtranse=1DexK2=2×10-10 s,
τtransh=1DhxK2=3.3×10-9 s,
τdie xe=0eμxen0e=4×10-6 s,
τdie xh=0eμxhn0h=7×10-5 s,
τdie ze=0eμzen0e=4×10-4 s,
τdie zh=0eμzhn0h=7×10-3 s,
ne(x,z)=ne0(z)+Re[ne1 exp(iKx)],
nh(x,z)=nh0(z)+Re[nh1 exp(iKx)].
ne0=αI0/hνγND+(0), ne1=αI0m/hνγND+(0)+DexK2,
nh0=αI0/hνγND0(0), nh1=αI0m/hνγND0(0)+DhxK2.
1ejxxdif=EDμxKn1,
1ejxxsurf=Ex surf μxKn0,
dρdt=-·j,
ρ1=-eDexK2ne1t+eDhxK2nh1t.
σ=jzt=σ0+Re[σ1 exp(iKx)],
σ0=e(μezne0+μhznh0)E0t,
σ1=e(μezne1+μhznh1)E0t.
ExI(±L/2)-ExII(±L/2)=0,
2EzII(±L/2)-1EzI(±L/2)=±σ1,
ExII[±(L+d)/2]=0,
Ex=Cv cosh Kz+Cs sinh Kz-ρ1K1×Re[i exp(iKx)],
Ez=(Cv sinh Kz+Cs cosh Kz)Re[exp(iKx)],
Cs=σ12tanh Kd/2sinh KL/2+12tanh Kd/2 cosh KL/2,
Cv=ρ1K1cosh KL/2+12tanh Kd/2 sinh KL/2,
Δ1n2ij=sijklEkEl,
Δn110=-12n0312(s11+s12)Ex2+s13Ez2+14s66Ex2
Δn11¯0=-12n0312(s11+s12)Ex2+s13Ez2-14s66Ex2
η±1=πΔlλ cos θ2,
Δl=-L/2L/2Δn(z)dz

Metrics