Abstract

We modified the theory of the holographic current, describing both the steady-state and the transient contributions and accounting for the parameters of the measurement circuit. In the model of the transient photocurrent we connected the observables of the steplike modulation experiment with the carrier transport parameters such as carrier diffusion and screening length, carrier effective lifetime, and Maxwell relaxation time. Experimentally, we have shown that theoretically predicted dependences of the photocurrent amplitude and relaxation time on the grating period, the light intensity, and the depth of the modulation were observed not only in the photorefractive Sr1-xBaxNb2O6 and Bi12TiO20 crystals but in Er-doped YSGG laser crystals as well.

© 1996 Optical Society of America

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References

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  1. P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, New York, 1989), Vols. I and II.
  2. N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
    [CrossRef]
  3. V. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic grating in nonmetallic crystals,” Sov. Phys. Solid State 16, 2414 (1975).
  4. G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1558 (1986).
  5. I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Holographic currents and the nonsteady-state photoelectromotive force in cubic photorefractive crystals,” J. Opt. Soc. Am. B 9, 173 (1992).
    [CrossRef]
  6. I. Sokolov and S. Stepanov, “Intensity-dependent non-steady-state photoelectromotive force in crystals with long photoelectron lifetimes,” Optik 93, 175 (1993).
  7. A. I. Kozyrev and G. S. Trofimov, “Dynamic interference grating—new technique for the study of non-crystalline films,” Int. J. Electron. 76, 1023 (1994).
    [CrossRef]
  8. A. Krumins and P. Gunter, “Holographic currents in reduced KNbO3 crystals,” Phys. Status Solidi 63, 111 (1981).
    [CrossRef]
  9. D. Ritter, E. Zeldov, and K. Weiser, “Ambipolar transport in amorphous semiconductors in the lifetime and relaxation-time regimes investigated by the steady-state photocarrier grating technique,” Phys. Rev. B 38, 8296 (1988).
    [CrossRef]
  10. F. Wang and R. Schwartz, “Characterization of optoelectronic properties of a Si1-xCx:H film,” J. Non-Cryst. Solids 164–166, 1039 (1993).
    [CrossRef]
  11. F. M. Davidson, C. C. Wang, C. T. Field, and S. Trivedi, “Photocurrents in photoconductive semiconductors generated by a moving space-charge field,” Opt. Lett. 19, 478 (1994).
    [CrossRef] [PubMed]
  12. F. Davidson, C. Wang, and S. Trivedi, “Transient photocurrents in photoconductive semiconductors generated by step-phase modulation,” Opt. Lett. 20, 175 (1995).
    [CrossRef] [PubMed]
  13. V. A. Smirnov and I. A. Scherbakov, “Rare-earth scandium chromium garnets as active media for solid-state lasers,” IEEE J. Quantum Electron. 24, 949 (1986).
    [CrossRef]
  14. M. V. Eremin, A. A. Kaminskii, and A. A. Kornienko, “Indirect interaction of 4f electrons with ligands through empty d shells,” Sov. Phys. Solid State 24, 1049 (1982).
  15. A. A. Kaminskii, A. A. Kornienko, and M. I. Chertanov, “Effective probability operator for spontaneous electric dipole transition in fN systems, considered allowing for electron correlation effects,” Sov. Phys. Solid State 27, 279 (1985).
  16. M. V. Eremin, A. A. Kaminskii, and O. A. Anikeenok, “Indirect interaction of 4f electrons with ligands via filled 5p shells,” Sov. Phys. Solid State 27, 339 (1985).
  17. M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

1995 (1)

1994 (2)

F. M. Davidson, C. C. Wang, C. T. Field, and S. Trivedi, “Photocurrents in photoconductive semiconductors generated by a moving space-charge field,” Opt. Lett. 19, 478 (1994).
[CrossRef] [PubMed]

A. I. Kozyrev and G. S. Trofimov, “Dynamic interference grating—new technique for the study of non-crystalline films,” Int. J. Electron. 76, 1023 (1994).
[CrossRef]

1993 (2)

I. Sokolov and S. Stepanov, “Intensity-dependent non-steady-state photoelectromotive force in crystals with long photoelectron lifetimes,” Optik 93, 175 (1993).

F. Wang and R. Schwartz, “Characterization of optoelectronic properties of a Si1-xCx:H film,” J. Non-Cryst. Solids 164–166, 1039 (1993).
[CrossRef]

1992 (1)

1988 (1)

D. Ritter, E. Zeldov, and K. Weiser, “Ambipolar transport in amorphous semiconductors in the lifetime and relaxation-time regimes investigated by the steady-state photocarrier grating technique,” Phys. Rev. B 38, 8296 (1988).
[CrossRef]

1986 (2)

G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1558 (1986).

V. A. Smirnov and I. A. Scherbakov, “Rare-earth scandium chromium garnets as active media for solid-state lasers,” IEEE J. Quantum Electron. 24, 949 (1986).
[CrossRef]

1985 (2)

A. A. Kaminskii, A. A. Kornienko, and M. I. Chertanov, “Effective probability operator for spontaneous electric dipole transition in fN systems, considered allowing for electron correlation effects,” Sov. Phys. Solid State 27, 279 (1985).

M. V. Eremin, A. A. Kaminskii, and O. A. Anikeenok, “Indirect interaction of 4f electrons with ligands via filled 5p shells,” Sov. Phys. Solid State 27, 339 (1985).

1982 (1)

M. V. Eremin, A. A. Kaminskii, and A. A. Kornienko, “Indirect interaction of 4f electrons with ligands through empty d shells,” Sov. Phys. Solid State 24, 1049 (1982).

1981 (1)

A. Krumins and P. Gunter, “Holographic currents in reduced KNbO3 crystals,” Phys. Status Solidi 63, 111 (1981).
[CrossRef]

1979 (1)

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

1975 (1)

V. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic grating in nonmetallic crystals,” Sov. Phys. Solid State 16, 2414 (1975).

Anikeenok, O. A.

M. V. Eremin, A. A. Kaminskii, and O. A. Anikeenok, “Indirect interaction of 4f electrons with ligands via filled 5p shells,” Sov. Phys. Solid State 27, 339 (1985).

Caulfield, H. J.

M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

Chertanov, M. I.

A. A. Kaminskii, A. A. Kornienko, and M. I. Chertanov, “Effective probability operator for spontaneous electric dipole transition in fN systems, considered allowing for electron correlation effects,” Sov. Phys. Solid State 27, 279 (1985).

Davidson, F.

Davidson, F. M.

Eremin, M. V.

M. V. Eremin, A. A. Kaminskii, and O. A. Anikeenok, “Indirect interaction of 4f electrons with ligands via filled 5p shells,” Sov. Phys. Solid State 27, 339 (1985).

M. V. Eremin, A. A. Kaminskii, and A. A. Kornienko, “Indirect interaction of 4f electrons with ligands through empty d shells,” Sov. Phys. Solid State 24, 1049 (1982).

Field, C. T.

Gunter, P.

A. Krumins and P. Gunter, “Holographic currents in reduced KNbO3 crystals,” Phys. Status Solidi 63, 111 (1981).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, A. A. Kornienko, and M. I. Chertanov, “Effective probability operator for spontaneous electric dipole transition in fN systems, considered allowing for electron correlation effects,” Sov. Phys. Solid State 27, 279 (1985).

M. V. Eremin, A. A. Kaminskii, and O. A. Anikeenok, “Indirect interaction of 4f electrons with ligands via filled 5p shells,” Sov. Phys. Solid State 27, 339 (1985).

M. V. Eremin, A. A. Kaminskii, and A. A. Kornienko, “Indirect interaction of 4f electrons with ligands through empty d shells,” Sov. Phys. Solid State 24, 1049 (1982).

Kornienko, A. A.

A. A. Kaminskii, A. A. Kornienko, and M. I. Chertanov, “Effective probability operator for spontaneous electric dipole transition in fN systems, considered allowing for electron correlation effects,” Sov. Phys. Solid State 27, 279 (1985).

M. V. Eremin, A. A. Kaminskii, and A. A. Kornienko, “Indirect interaction of 4f electrons with ligands through empty d shells,” Sov. Phys. Solid State 24, 1049 (1982).

Kozyrev, A. I.

A. I. Kozyrev and G. S. Trofimov, “Dynamic interference grating—new technique for the study of non-crystalline films,” Int. J. Electron. 76, 1023 (1994).
[CrossRef]

Krumins, A.

A. Krumins and P. Gunter, “Holographic currents in reduced KNbO3 crystals,” Phys. Status Solidi 63, 111 (1981).
[CrossRef]

Kukhtarev, N.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

V. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic grating in nonmetallic crystals,” Sov. Phys. Solid State 16, 2414 (1975).

M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

Mahdi, M.

M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

Markov, V.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Noginov, M. A.

M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

Noginova, N.

M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

Odoulov, S.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Ritter, D.

D. Ritter, E. Zeldov, and K. Weiser, “Ambipolar transport in amorphous semiconductors in the lifetime and relaxation-time regimes investigated by the steady-state photocarrier grating technique,” Phys. Rev. B 38, 8296 (1988).
[CrossRef]

Scherbakov, I. A.

V. A. Smirnov and I. A. Scherbakov, “Rare-earth scandium chromium garnets as active media for solid-state lasers,” IEEE J. Quantum Electron. 24, 949 (1986).
[CrossRef]

Schwartz, R.

F. Wang and R. Schwartz, “Characterization of optoelectronic properties of a Si1-xCx:H film,” J. Non-Cryst. Solids 164–166, 1039 (1993).
[CrossRef]

Smirnov, V. A.

V. A. Smirnov and I. A. Scherbakov, “Rare-earth scandium chromium garnets as active media for solid-state lasers,” IEEE J. Quantum Electron. 24, 949 (1986).
[CrossRef]

Sokolov, I.

I. Sokolov and S. Stepanov, “Intensity-dependent non-steady-state photoelectromotive force in crystals with long photoelectron lifetimes,” Optik 93, 175 (1993).

Sokolov, I. A.

Soskin, M.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Stepanov, S.

I. Sokolov and S. Stepanov, “Intensity-dependent non-steady-state photoelectromotive force in crystals with long photoelectron lifetimes,” Optik 93, 175 (1993).

Stepanov, S. I.

I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Holographic currents and the nonsteady-state photoelectromotive force in cubic photorefractive crystals,” J. Opt. Soc. Am. B 9, 173 (1992).
[CrossRef]

G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1558 (1986).

Trivedi, S.

Trofimov, G. S.

A. I. Kozyrev and G. S. Trofimov, “Dynamic interference grating—new technique for the study of non-crystalline films,” Int. J. Electron. 76, 1023 (1994).
[CrossRef]

I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Holographic currents and the nonsteady-state photoelectromotive force in cubic photorefractive crystals,” J. Opt. Soc. Am. B 9, 173 (1992).
[CrossRef]

G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1558 (1986).

Venkateswarlu, P.

M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

Vinetskii, V.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

V. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic grating in nonmetallic crystals,” Sov. Phys. Solid State 16, 2414 (1975).

Wang, C.

Wang, C. C.

Wang, F.

F. Wang and R. Schwartz, “Characterization of optoelectronic properties of a Si1-xCx:H film,” J. Non-Cryst. Solids 164–166, 1039 (1993).
[CrossRef]

Weiser, K.

D. Ritter, E. Zeldov, and K. Weiser, “Ambipolar transport in amorphous semiconductors in the lifetime and relaxation-time regimes investigated by the steady-state photocarrier grating technique,” Phys. Rev. B 38, 8296 (1988).
[CrossRef]

Zeldov, E.

D. Ritter, E. Zeldov, and K. Weiser, “Ambipolar transport in amorphous semiconductors in the lifetime and relaxation-time regimes investigated by the steady-state photocarrier grating technique,” Phys. Rev. B 38, 8296 (1988).
[CrossRef]

Ferroelectrics (1)

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

V. A. Smirnov and I. A. Scherbakov, “Rare-earth scandium chromium garnets as active media for solid-state lasers,” IEEE J. Quantum Electron. 24, 949 (1986).
[CrossRef]

Int. J. Electron. (1)

A. I. Kozyrev and G. S. Trofimov, “Dynamic interference grating—new technique for the study of non-crystalline films,” Int. J. Electron. 76, 1023 (1994).
[CrossRef]

J. Non-Cryst. Solids (1)

F. Wang and R. Schwartz, “Characterization of optoelectronic properties of a Si1-xCx:H film,” J. Non-Cryst. Solids 164–166, 1039 (1993).
[CrossRef]

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

Opt. Lett. (2)

Optik (1)

I. Sokolov and S. Stepanov, “Intensity-dependent non-steady-state photoelectromotive force in crystals with long photoelectron lifetimes,” Optik 93, 175 (1993).

Phys. Rev. B (1)

D. Ritter, E. Zeldov, and K. Weiser, “Ambipolar transport in amorphous semiconductors in the lifetime and relaxation-time regimes investigated by the steady-state photocarrier grating technique,” Phys. Rev. B 38, 8296 (1988).
[CrossRef]

Phys. Status Solidi (1)

A. Krumins and P. Gunter, “Holographic currents in reduced KNbO3 crystals,” Phys. Status Solidi 63, 111 (1981).
[CrossRef]

Sov. Phys. Solid State (5)

V. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic grating in nonmetallic crystals,” Sov. Phys. Solid State 16, 2414 (1975).

G. S. Trofimov and S. I. Stepanov, “Time-dependent holographic currents in photorefractive crystals,” Sov. Phys. Solid State 28, 1558 (1986).

M. V. Eremin, A. A. Kaminskii, and A. A. Kornienko, “Indirect interaction of 4f electrons with ligands through empty d shells,” Sov. Phys. Solid State 24, 1049 (1982).

A. A. Kaminskii, A. A. Kornienko, and M. I. Chertanov, “Effective probability operator for spontaneous electric dipole transition in fN systems, considered allowing for electron correlation effects,” Sov. Phys. Solid State 27, 279 (1985).

M. V. Eremin, A. A. Kaminskii, and O. A. Anikeenok, “Indirect interaction of 4f electrons with ligands via filled 5p shells,” Sov. Phys. Solid State 27, 339 (1985).

Other (2)

M. A. Noginov, N. Kukhtarev, N. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, “Photoconductivity and electro-motive force study of rare earth doped YSGG laser crystals,” in OSA Trends in Optics and Photonics on Advanced Solid State Lasers, S. A. Payne and C. R. Pollock, eds. (Optical Society of America, Washington, D.C., 1996), Vol. 1, p. 595.

P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, New York, 1989), Vols. I and II.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for registration of photocurrent: BS, beam splitter; M1, M2, mirrors. Mirror M2 is attached to the speaker.

Fig. 2
Fig. 2

Typical photocurrent response to the steplike modulation of the mirror position; the dependence is taken in an Er(2×1020 cm-3):YSGG crystal at a light intensity of 25 W/cm2.

Fig. 3
Fig. 3

Photocurrent amplitude (squares) and relaxation time (circles) versus light intensity for an SBN crystal. Solid curve, theory (Id=0.03 W/cm2).

Fig. 4
Fig. 4

a, Photocurrent and b, relaxation time as functions of the grating period in SBN. Squares, experiment; solid curves, theory. 2πLD0.3 µm, 2πLS0.9 µm, τM120 ms, I01.5 W/cm2.

Fig. 5
Fig. 5

a, Photocurrent amplitude and b, relaxation time versus the grating period in a BTO crystal. Squares, experiment; solid curves, theory. 2πLD1.3 µm, 2πLS0.8 µm, τM=43 ms, I00.8 W/cm2.

Fig. 6
Fig. 6

a, Photocurrent amplitude and b, relaxation time versus the grating period for an Er(2×1020 cm3):YSSG laser crystal. Squares, experiment; solid curves, theory. 2πLD0.36 µm, 2πLS0.54 µm; τM215 ms; I025 W/cm2.

Fig. 7
Fig. 7

a, Photocurrent amplitude and b, relaxation time versus the grating period for an Er(4×1021 cm-3):YSGG laser crystal. Squares, experiment; solid curves, theory. 2πLD0.36 µm, 2πLS0.3 µm, τM145 ms; I025 W/cm2.

Equations (34)

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

nt=N+t-div je,
N+t=(β+sI)(N-N+)-rnN+.
j=eμnE-eDn,
div(0E)=e(NA+n-N+),
jΣ=j+0Et,
div jΣ=0,
jΣRS+E0d=V.
jΣ=eμE0n-1-1+0n-1-1Ent.
0E˙0+[eμn0+(d/RS)]E0=(V/RS)-eμδnδE.
E0=VRS0(τM-1+τC-1)×{1-A exp[-t(τM-1+τC-1)]},
I(x,t)=I01+m2exp(iKx)+c.c.,
n=n0+[n1 exp(iKx)+c.c.],
E=E0+[E1 exp(iKx)]+c.c.],
n0t=sI0(1+γ)(N-NA)-n0τr,
τrn1t=n0m2(1+γ)-iE1Em+iE1EK-n11+EDEm+iE0Em,
τME1t=(iED-E0)n1n0-E1,
jΣ=eμn0E01-mn2-02E1tmn*+mnE1*t,
m(t)=m0,t0,m(t)=m0 exp(iϕ),t>0,
j=-eμ(n1*E1+c.c.)=Dπen0m021-exp(-DK2t)exp-tτr(1+γ)2×L3 sin ϕ[L2+(2πLD)2][L2+(2πLS)2]exp-tτR.
τR=τML2+(2πLD)2L2+(2πLS)2,
jmaxI1I2I0+Id, τRτd1+I0/Id,
m(t)=m0 exp(iM cos ωt),
exp(iM cos ωt)=J0(M)+i2 cos ωtJ1(M)+=J0(M)+i[exp(iωt)+exp(-iωt)]J1(M)+,
n1=n10+n1ω2exp(iωt)+n1-ω2exp(-iωt),
E1=E10+E1ω2exp(iωt)+E1-ω2exp(-iωt).
n10=m0J0n0(1+γ)(1+δDK+iδ0K),
E10=-m0J0(E0-iED)(1+γ)(1+δDK+iδ0K),
n1ω=(n1-ω)*=in0m0J1(1+iδM)(1+γ)[1+iδM(1+δD+iδE)+i(δr+δ0K)+δDK],
E1ω=(E1-ω)*=-im0J1(E0-iED)(1+γ)[1+iδM(1+δD+iδE)+i(δr+δ0K)+δDK],
jst=eμn0E01-m02J02(M)(1+γ)2[(1+δDK)2+δ0K2]1/2.
jω=1/2eμ[(n10)*E1ω+n10(E1-ω)*+n1ω(E10)*+(n1-ω)*E10].
jω=im02J0J1eμn02(1+γ)2[(1+δDK)2+δ0K2]E0(2+δDK-iδ0K)+δ0KED+δM(ED+δDKED+δ0KE0+iE0)iδM(1+δD-iδE)+iδr(1+iδM)+1+δDK-iδ0K-E0(2+δDK+2iδ0K)-iδ0KED+iδM{E0+i[ED(1+δDK)+δ0KE0]}iδM(1+δD+iδE)+iδr(1+iδM)+1+δDK+iδ0K.
|jω|=eμn0m02J0J1δMED(1+γ)2[(1+δDK-δMδr)2+(δr+δM+δMδD)2]1/2,
tan ϕ=δM(1+δD)+δr1+δDK-δMδr.

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