Abstract

The complex coupling constant of a photorefractive polymer was measured as a function of an applied electric field by use of a modified ac phase modulation technique. We determined that both a photorefractive index grating and a nonphotorefractive absorption grating were present. The electric field dependencies of the amplitude and the phase of the photorefractive gain coefficient were accurately described by standard photorefractive theory. The accuracy of the photorefractive phase shift as measured by this phase-modulation technique was ±1° near phase shifts of 90° and ±3° near phase shifts of 45°.

[Optical Society of America ]

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  1. R. B. Bylsma , D. H. Olson , and A. M. Glass , Photochromic gratings in photorefractive materials , Opt. Lett. OPLEDP 13 , 853 ( 1988
    [CrossRef] [PubMed]
  2. R. S. Cudney , R. M. Pierce , G. D. Bacher , and J. Feinberg , Absorption gratings in photorefractive crystals with multiple levels , J. Opt. Soc. Am. B JOBPDE 8 , 1326 ( 1991
    [CrossRef]
  3. M. Z. Zha , P. Amrhein , and P. Gu nter , Measurement of phase shift of photorefractive gratings by a novel method , IEEE J. Quantum Electron. IEJQA7 26 , 788 ( 1990
    [CrossRef]
  4. P. A. M. D. Santos , L. Cescato , and J. Frejlich , Interference-term real-time measurement for self-stabilized two-wave mixing in photorefractive crystals , Opt. Lett. OPLEDP 13 , 1014 ( 1988
    [CrossRef] [PubMed]
  5. P. M. Garcia , L. Cescato , and J. Frejlich , Phase-shift measurement in photorefractive holographic recording , J. Appl. Phys. JAPIAU 66 , 47 ( 1989
    [CrossRef]
  6. P. N. Ilinykh , O. P. Nestiorkin , and B. Ya. Zel dovich , Phase shift in nondegenerate coupling of waves in the photorefractive crystal , Opt. Commun. OPCOB8 80 , 249 ( 1991
    [CrossRef]
  7. R. Hofmeister , A. Yariv , A. Kewitsch , and S. Yagi , Simple methods of measuring the net photorefractive phase shift and coupling constant , Opt. Lett. OPLEDP 18 , 488 ( 1993
    [CrossRef]
  8. R. K. Ing and J.-P. Monchalin , Measurement of the photorefractive phase shift by polarization interferometry , Opt. Lett. OPLEDP 18 , 852 ( 1993
    [CrossRef] [PubMed]
  9. J. Frejlich , Real-time photorefractive hologram phase-shift measurement and self-diffraction effects , Opt. Commun. OPCOB8 107 , 260 ( 1994
    [CrossRef]
  10. M. Gehrtz , J. Pinsl , and C. Bra uchle , Sensitive detection of phase and absorption gratings: phase-modulated, homodyne detected holography , Appl. Phys. B APPCDL 43 , 61 ( 1987
    [CrossRef]
  11. R. S. Cudney , G. D. Bacher , R. M. Pierce , and J. Feinberg , Measurement of the photorefractive phase shift , Opt. Lett. OPLEDP 17 , 67 ( 1992
    [CrossRef] [PubMed]
  12. R. M. Montgomery and M. R. Lange , Amplitude and phase measurement technique for photorefractive gratings , J. Appl. Phys. JAPIAU 68 , 4782 ( 1990
    [CrossRef]
  13. W. B. Lawler , C. J. Sherman , and M. G. Moharam , Direct measurement of the amplitude and the phase of photorefractive fields in KNbO 3 :Ta and BaTiO 3 , J. Opt. Soc. Am. B JOBPDE 8 , 2190 ( 1991
    [CrossRef]
  14. P. N. Ilinykh , O. P. Nestiorkin , and B. Ya. Zel dovich , Recording a static hologram with laser beams of different frequencies in photorefractive crystals , J. Opt. Soc. Am. B JOBPDE 8 , 1042 ( 1991
    [CrossRef]
  15. D. G. Gray , M. G. Moharam , and T. M. Ayres , Heterodyne technique for the direct measurement of the amplitude and phase of photorefractive space-charge fields , J. Opt. Soc. Am. B JOBPDE 11 , 470 ( 1994
    [CrossRef]
  16. V. Kondilenko , V. Markov , S. G. Odulov , and M. Soskin , Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern , Opt. Acta OPACAT 26 , 239 ( 1979
    [CrossRef]
  17. R. Kapoor , M. Moghbel , and P. Venkateswarlu , Energy-transfer measurement and determination of the phase shift between the holographic grating and the fringe pattern in photorefractive materials , Opt. Lett. OPLEDP 18 , 696 ( 1993
    [CrossRef] [PubMed]
  18. V. Markov , S. Odulov , and M. Soskin , Properties of the three-dimensional phase holograms in activated and reduced LiNbO 3 crystals , Bull. Acad. Sci. USSR Phys. Ser. BUPSAA 41 , 144 ( 1977
  19. K. Sutter and P. Gu nter , Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane , J. Opt. Soc. Am. B JOBPDE 7 , 2274 ( 1990
    [CrossRef]
  20. C. A. Walsh and W. E. Moerner , Two-beam coupling measurements of grating phase in a photorefractive polymer , J. Opt. Soc. Am. B JOBPDE 9 , 1642 ( 1992
    [CrossRef]
  21. A. Grunnet-Jepsen , C. I. Thompson , and W. E. Moerner , Measurement of the spatial phase shift in high-gain photorefractive materials , Opt. Lett. OPLEDP 22 , 874 ( 1997
    [CrossRef] [PubMed]
  22. B. E. Jones , S. Ducharme , A. Goonesekera , M. Liphardt , R. V. Athalye , L. Zhang , and J. M. Takacs , Photoconductivity and grating response time of a photorefractive polymer , J. Opt. Soc. Am. B JOBPDE 11 , 1064 ( 1994
    [CrossRef]
  23. H. Kogelnik , Coupled wave theory for thick hologram gratings , Bell Syst. Tech. J. BSTJAN 48 , 2909 ( 1969
    [CrossRef]
  24. M. Liphardt , A. Goonesekera , S. Ducharme , J. M. Takacs , and L. Zhang , Effect of beam attenuation on photorefractive grating erasure , J. Opt. Soc. Am. B JOBPDE 13 , 2252 ( 1996
    [CrossRef]
  25. N. V. Kukhtarev , Kinetics of hologram recording and erasure in electro-optic crystals , Sov. Tech. Phys. Lett. STPLD2 2 , 438 ( 1976
  26. P. Gu nter and F. Micheron , Photorefractive effects and photocurrents in KNbO 3 :Fe , Ferroelectrics FEROA8 18 , 27 ( 1978
    [CrossRef]
  27. W. E. Moerner , S. M. Silence , F. Hache , and G. C. Bjorklund , Orientationally enhanced photorefractive effect in polymers , J. Opt. Soc. Am. B JOBPDE 11 , 320 ( 1994
    [CrossRef]
  28. A. Goonesekera , M. Liphardt , S. Ducharme , J. M. Takacs , and L. Zhang , The role of photoconductivity in molecularly doped photorefractive polymers , in Xerographic Photoreceptors and Photorefractive Polymers , S. Ducharme and P. M. Borsenberger, eds. , Proc. SPIE PSISDG 2526 , 109 ( 1995
    [CrossRef]
  29. N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. I. Steady state , Ferroelectrics FEROA8 22 , 949 ( 1979
    [CrossRef]
  30. A. Twarowski , Geminate recombination in photorefractive crystals , J. Appl. Phys. JAPIAU 65 , 2833 ( 1989
    [CrossRef]
  31. J. S. Schildkraut and A. V. Buettner , Theory and simulation of the formation and erasure of space-charge gratings in photoconductive polymers , J. Appl. Phys. JAPIAU 72 , 1888 ( 1992
    [CrossRef]
  32. J. S. Schildkraut and Y. Cui , Zero-order and first-order theory of the formation of space-charge gratings in photoconductive polymers , J. Appl. Phys. JAPIAU 72 , 5055 ( 1992
    [CrossRef]
  33. L. B. Schein , Comparison of charge transport models in molecularly doped polymers , Philos. Mag. B PMABDJ 65 , 795 ( 1992
    [CrossRef]
  34. J. C. Scott , L. T. Pautmeier , and W. E. Moerner , Photoconductivity studies of photorefractive polymers , J. Opt. Soc. Am. B JOBPDE 9 , 2059 ( 1992
    [CrossRef]
  35. S. Ducharme , R. W. Twieg , J. C. Scott , and W. E. Moerner , Observation of the photorefractive effect in a polymer , Phys. Rev. Lett. PRLTAO 66 , 1846 ( 1991
    [CrossRef] [PubMed]
  36. M. Liphardt , A. Goonesekera , B. E. Jones , S. Ducharme , J. M. Takacs , and L. Zhang , High performance photorefractive polymers , Science SCIEAS 263 , 367 ( 1994
    [CrossRef] [PubMed]
  37. W. E. Moerner and S. Silence , Polymeric photorefractive materials , Chem. Rev. CHREAY 94 , 127 ( 1994
    [CrossRef]
  38. N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. II. Beam coupling-light amplification , Ferroelectrics FEROA8 22 , 961 ( 1979
    [CrossRef]
  39. K. Meerholz , B. L. Volodin , Sandalphon , B. Kippelen , and N. Peyghambarian , A photorefractive polymer with high optical gain and diffraction efficiency near 100 , Nature NATUAS 371 , 497 ( 1994
    [CrossRef]

Amrhein, P

M. Z. Zha , P. Amrhein , and P. Gu nter , Measurement of phase shift of photorefractive gratings by a novel method , IEEE J. Quantum Electron. IEJQA7 26 , 788 ( 1990
[CrossRef]

Athalye, R. V

Ayres, T. M

Bylsma, R. B

Goonesekera, A

Gray, D. G

Ilinykh, P. N

P. N. Ilinykh , O. P. Nestiorkin , and B. Ya. Zel dovich , Phase shift in nondegenerate coupling of waves in the photorefractive crystal , Opt. Commun. OPCOB8 80 , 249 ( 1991
[CrossRef]

Jones, B. E

Kapoor, R

Kondilenko, V

V. Kondilenko , V. Markov , S. G. Odulov , and M. Soskin , Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern , Opt. Acta OPACAT 26 , 239 ( 1979
[CrossRef]

Lange, M. R

R. M. Montgomery and M. R. Lange , Amplitude and phase measurement technique for photorefractive gratings , J. Appl. Phys. JAPIAU 68 , 4782 ( 1990
[CrossRef]

Lawler, W. B

Liphardt, M

Moghbel, M

Montgomery, R. M

R. M. Montgomery and M. R. Lange , Amplitude and phase measurement technique for photorefractive gratings , J. Appl. Phys. JAPIAU 68 , 4782 ( 1990
[CrossRef]

Pautmeier, L. T

Pinsl, J

M. Gehrtz , J. Pinsl , and C. Bra uchle , Sensitive detection of phase and absorption gratings: phase-modulated, homodyne detected holography , Appl. Phys. B APPCDL 43 , 61 ( 1987
[CrossRef]

Sandalphon,

K. Meerholz , B. L. Volodin , Sandalphon , B. Kippelen , and N. Peyghambarian , A photorefractive polymer with high optical gain and diffraction efficiency near 100 , Nature NATUAS 371 , 497 ( 1994
[CrossRef]

Santos, P. A. M. D

Sherman, C. J

Silence, S

W. E. Moerner and S. Silence , Polymeric photorefractive materials , Chem. Rev. CHREAY 94 , 127 ( 1994
[CrossRef]

Takacs, J. M

Thompson, C. I

Twarowski, A

A. Twarowski , Geminate recombination in photorefractive crystals , J. Appl. Phys. JAPIAU 65 , 2833 ( 1989
[CrossRef]

Twieg, R. W

S. Ducharme , R. W. Twieg , J. C. Scott , and W. E. Moerner , Observation of the photorefractive effect in a polymer , Phys. Rev. Lett. PRLTAO 66 , 1846 ( 1991
[CrossRef] [PubMed]

Other (39)

M. Z. Zha , P. Amrhein , and P. Gu nter , Measurement of phase shift of photorefractive gratings by a novel method , IEEE J. Quantum Electron. IEJQA7 26 , 788 ( 1990
[CrossRef]

P. M. Garcia , L. Cescato , and J. Frejlich , Phase-shift measurement in photorefractive holographic recording , J. Appl. Phys. JAPIAU 66 , 47 ( 1989
[CrossRef]

P. N. Ilinykh , O. P. Nestiorkin , and B. Ya. Zel dovich , Phase shift in nondegenerate coupling of waves in the photorefractive crystal , Opt. Commun. OPCOB8 80 , 249 ( 1991
[CrossRef]

J. Frejlich , Real-time photorefractive hologram phase-shift measurement and self-diffraction effects , Opt. Commun. OPCOB8 107 , 260 ( 1994
[CrossRef]

M. Gehrtz , J. Pinsl , and C. Bra uchle , Sensitive detection of phase and absorption gratings: phase-modulated, homodyne detected holography , Appl. Phys. B APPCDL 43 , 61 ( 1987
[CrossRef]

R. M. Montgomery and M. R. Lange , Amplitude and phase measurement technique for photorefractive gratings , J. Appl. Phys. JAPIAU 68 , 4782 ( 1990
[CrossRef]

V. Kondilenko , V. Markov , S. G. Odulov , and M. Soskin , Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern , Opt. Acta OPACAT 26 , 239 ( 1979
[CrossRef]

V. Markov , S. Odulov , and M. Soskin , Properties of the three-dimensional phase holograms in activated and reduced LiNbO 3 crystals , Bull. Acad. Sci. USSR Phys. Ser. BUPSAA 41 , 144 ( 1977

H. Kogelnik , Coupled wave theory for thick hologram gratings , Bell Syst. Tech. J. BSTJAN 48 , 2909 ( 1969
[CrossRef]

N. V. Kukhtarev , Kinetics of hologram recording and erasure in electro-optic crystals , Sov. Tech. Phys. Lett. STPLD2 2 , 438 ( 1976

P. Gu nter and F. Micheron , Photorefractive effects and photocurrents in KNbO 3 :Fe , Ferroelectrics FEROA8 18 , 27 ( 1978
[CrossRef]

A. Goonesekera , M. Liphardt , S. Ducharme , J. M. Takacs , and L. Zhang , The role of photoconductivity in molecularly doped photorefractive polymers , in Xerographic Photoreceptors and Photorefractive Polymers , S. Ducharme and P. M. Borsenberger, eds. , Proc. SPIE PSISDG 2526 , 109 ( 1995
[CrossRef]

N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. I. Steady state , Ferroelectrics FEROA8 22 , 949 ( 1979
[CrossRef]

A. Twarowski , Geminate recombination in photorefractive crystals , J. Appl. Phys. JAPIAU 65 , 2833 ( 1989
[CrossRef]

J. S. Schildkraut and A. V. Buettner , Theory and simulation of the formation and erasure of space-charge gratings in photoconductive polymers , J. Appl. Phys. JAPIAU 72 , 1888 ( 1992
[CrossRef]

J. S. Schildkraut and Y. Cui , Zero-order and first-order theory of the formation of space-charge gratings in photoconductive polymers , J. Appl. Phys. JAPIAU 72 , 5055 ( 1992
[CrossRef]

L. B. Schein , Comparison of charge transport models in molecularly doped polymers , Philos. Mag. B PMABDJ 65 , 795 ( 1992
[CrossRef]

S. Ducharme , R. W. Twieg , J. C. Scott , and W. E. Moerner , Observation of the photorefractive effect in a polymer , Phys. Rev. Lett. PRLTAO 66 , 1846 ( 1991
[CrossRef] [PubMed]

M. Liphardt , A. Goonesekera , B. E. Jones , S. Ducharme , J. M. Takacs , and L. Zhang , High performance photorefractive polymers , Science SCIEAS 263 , 367 ( 1994
[CrossRef] [PubMed]

W. E. Moerner and S. Silence , Polymeric photorefractive materials , Chem. Rev. CHREAY 94 , 127 ( 1994
[CrossRef]

N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. II. Beam coupling-light amplification , Ferroelectrics FEROA8 22 , 961 ( 1979
[CrossRef]

K. Meerholz , B. L. Volodin , Sandalphon , B. Kippelen , and N. Peyghambarian , A photorefractive polymer with high optical gain and diffraction efficiency near 100 , Nature NATUAS 371 , 497 ( 1994
[CrossRef]

P. N. Ilinykh , O. P. Nestiorkin , and B. Ya. Zel dovich , Recording a static hologram with laser beams of different frequencies in photorefractive crystals , J. Opt. Soc. Am. B JOBPDE 8 , 1042 ( 1991
[CrossRef]

R. S. Cudney , R. M. Pierce , G. D. Bacher , and J. Feinberg , Absorption gratings in photorefractive crystals with multiple levels , J. Opt. Soc. Am. B JOBPDE 8 , 1326 ( 1991
[CrossRef]

W. B. Lawler , C. J. Sherman , and M. G. Moharam , Direct measurement of the amplitude and the phase of photorefractive fields in KNbO 3 :Ta and BaTiO 3 , J. Opt. Soc. Am. B JOBPDE 8 , 2190 ( 1991
[CrossRef]

C. A. Walsh and W. E. Moerner , Two-beam coupling measurements of grating phase in a photorefractive polymer , J. Opt. Soc. Am. B JOBPDE 9 , 1642 ( 1992
[CrossRef]

J. C. Scott , L. T. Pautmeier , and W. E. Moerner , Photoconductivity studies of photorefractive polymers , J. Opt. Soc. Am. B JOBPDE 9 , 2059 ( 1992
[CrossRef]

W. E. Moerner , S. M. Silence , F. Hache , and G. C. Bjorklund , Orientationally enhanced photorefractive effect in polymers , J. Opt. Soc. Am. B JOBPDE 11 , 320 ( 1994
[CrossRef]

D. G. Gray , M. G. Moharam , and T. M. Ayres , Heterodyne technique for the direct measurement of the amplitude and phase of photorefractive space-charge fields , J. Opt. Soc. Am. B JOBPDE 11 , 470 ( 1994
[CrossRef]

B. E. Jones , S. Ducharme , A. Goonesekera , M. Liphardt , R. V. Athalye , L. Zhang , and J. M. Takacs , Photoconductivity and grating response time of a photorefractive polymer , J. Opt. Soc. Am. B JOBPDE 11 , 1064 ( 1994
[CrossRef]

R. B. Bylsma , D. H. Olson , and A. M. Glass , Photochromic gratings in photorefractive materials , Opt. Lett. OPLEDP 13 , 853 ( 1988
[CrossRef] [PubMed]

P. A. M. D. Santos , L. Cescato , and J. Frejlich , Interference-term real-time measurement for self-stabilized two-wave mixing in photorefractive crystals , Opt. Lett. OPLEDP 13 , 1014 ( 1988
[CrossRef] [PubMed]

R. S. Cudney , G. D. Bacher , R. M. Pierce , and J. Feinberg , Measurement of the photorefractive phase shift , Opt. Lett. OPLEDP 17 , 67 ( 1992
[CrossRef] [PubMed]

R. Hofmeister , A. Yariv , A. Kewitsch , and S. Yagi , Simple methods of measuring the net photorefractive phase shift and coupling constant , Opt. Lett. OPLEDP 18 , 488 ( 1993
[CrossRef]

R. Kapoor , M. Moghbel , and P. Venkateswarlu , Energy-transfer measurement and determination of the phase shift between the holographic grating and the fringe pattern in photorefractive materials , Opt. Lett. OPLEDP 18 , 696 ( 1993
[CrossRef] [PubMed]

R. K. Ing and J.-P. Monchalin , Measurement of the photorefractive phase shift by polarization interferometry , Opt. Lett. OPLEDP 18 , 852 ( 1993
[CrossRef] [PubMed]

M. Liphardt , A. Goonesekera , S. Ducharme , J. M. Takacs , and L. Zhang , Effect of beam attenuation on photorefractive grating erasure , J. Opt. Soc. Am. B JOBPDE 13 , 2252 ( 1996
[CrossRef]

A. Grunnet-Jepsen , C. I. Thompson , and W. E. Moerner , Measurement of the spatial phase shift in high-gain photorefractive materials , Opt. Lett. OPLEDP 22 , 874 ( 1997
[CrossRef] [PubMed]

K. Sutter and P. Gu nter , Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane , J. Opt. Soc. Am. B JOBPDE 7 , 2274 ( 1990
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup to measure the photorefractive phase shift. The glass plates of the sample are omitted for clarity.  

Fig. 2
Fig. 2

Amplitude of the coupling strength ΓL coefficient from index (ΓR) and absorption (ΓI) gratings as a function of the applied electric field strength along the grating wave vector. The solid curve is a least-squares fit of the index grating gain to Eq. (8).

Fig. 3
Fig. 3

Real (squares) and imaginary (circles) parts of (a) the index grating and of (b) the absorption grating as a function of the applied electric field strength along the grating wave vector. The solid curves are least-squares fits of the index grating gain to Eqs. (8) and (9).

Fig. 4
Fig. 4

Phase shift of the index grating as a function of the applied electric field strength along the grating wave vector. The solid curve is a least-squares fit to Eq. (9).

Tables (2)

Tables Icon

Table 1 Contributions to the Complex Coupling Constant Γ when Both Probe and Pump Beams Are Monitored

Tables Icon

Table 2 Contributions to the Complex Coupling Constant Γ for Both Directions (+, -) of the Applied Electric Field

Equations (13)

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

n˜=n0+n1 cos(Kx+ϕn)+i[κ0+κ1 cos(Kx+ϕκ)],
cos θ1 dE1(z, t)dz=-Γ14 m*(z, t)tE2(z, t)-α2 E1(z, t),
cos θ2 dE2(z, t)dz=-Γ24 m(z, t)tE1(z, t)-α2 E2(z, t),
I2[0]=I20 exp(ΓRL),
I2[Ω]=2μI20 exp(ΓRL/2)sin(ΓIL/2),
I2[2Ω]=μ22 I20[exp(ΓRL/2)cos(ΓIL/2)-1],
tan ϕPR=ΓR/ΓI.
1/2(Γ+R-Γ-R)=nPR sin(ϕPR),
1/2(Γ+R+Γ-R)=κPOP cos(ϕPOP)+κPC,
1/2(Γ+I+Γ-I)=nPR cos(ϕPR),
1/2(Γ+I-Γ-I)=κPOP sin(ϕPOP).
Esc=mEqE02+Ed2E02+(Ed+Eq)21/2,
tan ϕPR=Im(Esc)Re(Esc)=Ed(Ed+Eq)+E02E0Eq.

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