Abstract

We review recent investigations of nonlinear carrier transport and related optical nonlinearities in GaAs and InP crystals for the case in which photoexcited carriers are nonuniformly heated by a strong external electric field and are redistributed in a spatially nonuniform internal electric field. We simulated the nonequilibrium carrier and internal field spatial evolution in picosecond and nanosecond time domains and estimated criteria for bipolar high-field Gunn-domain grating formation in dc and ac fields. The coexisting refractive-index modulation mechanisms for free-carrier and electro-optic nonlinearities are analyzed for various external field strengths, grating periods, and excitation levels, thus providing conditions for an efficient and fast electro-optic refractive-index modulation by the transient Gunn-domain grating. Comparison of the experimentally observed enhancement of light’s self-diffraction efficiency with numerical calculations has confirmed that the nonresonant electro-optic Gunn-domain-based nonlinearity may exceed the free-carrier nonlinearity.

[Optical Society of America ]

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  1. A. Miller , D. A. Miller , and S. D. Smith , Dynamic nonlinear optical processes in semiconductors , Adv. Phys. ADPHAH 30 , 797 ( 1981
    [CrossRef]
  2. M. A. Glass and E. F. Shubert , eds., special issue on charge transport nonlinearities , Opt. Quantum Electron. OQELDI 22 , S1 S16 ( 1990
    [CrossRef]
  3. A. L. Smirl , G. C. Valley , K. M. Bohnert , and T. F. Bogges , Picosecond photorefractive and free-carrier transient energy transfer in GaAs at 1 m , IEEE J. Quantum Electron. IEJQA7 24 , 289 ( 1988
    [CrossRef]
  4. L. Disdier and G. Roosen , Nanosecond four-wave mixing in semi-insulating GaAs , Opt. Commun. OPCOB8 88 , 559 ( 1992
    [CrossRef]
  5. G. Montemezzani , P. Rogin , M. Zgonik , and P. Gunter , Interband photorefractive effects: theory and experiments in KNbO 3 , Phys. Rev. B PRBMDO 49 , 2484 ( 1994
    [CrossRef]
  6. W. A. Schroeder , T. S. Stark , M. D. Dawson , T. F. Boggess , A. L. Smirl , and G. C. Valley , Picosecond separation and measurements of coexisting photorefractive bound electrons, and free-carrier grating dynamics in GaAs , Opt. Lett. OPLEDP 16 , 159 ( 1991
    [PubMed]
  7. K. Jaras iu nas , P. Delaye , and G. Roosen , Optical nonlinearities and carrier transport in GaAs:EL2 at high excitation levels , Phys. Status Solidi B PSSBBD 175 , 445 ( 1993
    [CrossRef]
  8. A. Partovi and E. M. Garmire , Band-edge photorefractivity in semiconductors: theory and experiment , J. Appl. Phys. JAPIAU 69 , 6885 ( 1991
    [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 JOBPDE 9 , 1626 ( 1992
    [CrossRef]
  10. L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Enhancement of light diffraction efficiency in semiconductors by mw electric field: experiment and calculations , in International Conference on Optical Diagnostics of Materials and Devices for Opto-, Micro-, and Quantum Electronics , S. V. Svechnikov and M. Ya. Valakh, eds. , Proc. SPIE PSISDG 2648 , 207 ( 1995
    [CrossRef]
  11. K. Jaras iu nas , V. Gruz inskis , P. Shiktorov , E. Starikov , L. Subac ius , and G. Valus is , Hot carrier dynamics and light diffraction in non-uniform electric field: experiment and modeling , Lith. Phys. J. LPJOED 35 , 426 ( 1995
  12. L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Light diffraction on Gunn-domain gratings , Phys. Rev. B PRBMDO 55 , 12844 ( 1997
    [CrossRef]
  13. Q. Wang , R. M. Brubaker , and D. D. Nolte , Photorefractive phase shift induced by hot electron transport: multiple-quantum-well structures , J. Opt. Soc. Am. B JOBPDE 11 , 1773 ( 1994
    [CrossRef]
  14. R. M. Brubaker , Q. N. Wang , D. D. Nolte , and M. R. Melloch , Nonlocal photorefractive screening from hot electron velocity saturation in semiconductors , Phys. Rev. Lett. PRLTAO 77 , 4249 ( 1996
    [CrossRef] [PubMed]
  15. M. Segev , B. Collings , and D. Abraham , Photorefractive Gunn effect , Phys. Rev. Lett. PRLTAO 76 , 3798 ( 1996
    [CrossRef] [PubMed]
  16. V. Gruz inskis , E. Starikov , and P. Shiktorov , Conservation equations for hot carriers. I. Transport models , Solid-State Electron. SSELA5 36 , 1055 ( 1993
    [CrossRef]
  17. G. C. Valley , T. F. Boggess , J. Dubard , and A. L. Smirl , Picosecond pump-probe technique to measure deep-level, free carrier, and two-photon cross sections in GaAs , J. Appl. Phys. JAPIAU 66 , 2407 ( 1989
    [CrossRef]
  18. J. Vaitkus , K. Jaras iu nas , E. Gaubas , L. Jonikas , R. Pranaitis , and L. Subac ius , The diffraction of light by transient gratings in crystalline, ion-implanted, and amorphous silicon , IEEE J. Quantum Electron. IEJQA7 QE-22 , 1298 ( 1986
    [CrossRef]
  19. J. Vaitkus , E. Starikovas , L. Subac ius , and K. Jaras iu nas , Field dependencies of the efficiency of light self-diffraction and of diffusion coefficients in GaAs and Si , Litov. Fiz. Sb. LFRMA7 30 , 336 ( 1990
  20. J. C. Fabre , J. M. C. Jonathan , and G. Roosen , 4 3 m photorefractive materials in energy transfer experiments , Opt. Commun. OPCOB8 65 , 257 ( 1988
    [CrossRef]
  21. R. Orlowski , L. A. Boatner , and E. Kratzig , Photorefractive effects in the cubic phase of potassium tantalate-niobate , Opt. Commun. OPCOB8 35 , 45 ( 1980
    [CrossRef]
  22. K. Jaras iu nas and H. J. Gerritsen , Ambipolar diffusion measurements in semiconductors using nonlinear transient gratings , Appl. Phys. Lett. APPLAB 33 , 190 ( 1978
    [CrossRef]
  23. V. Gruzhinskis , E. Starikov , P. Shiktorov , L. Reggiani , and L. Varani , Linear and nonlinear analysis of microwave power generation in submicrometer n + nn + InP diodes , J. Appl. Phys. JAPIAU 76 , 5260 ( 1994
    [CrossRef]
  24. P. Shiktorov , V. Gruz inskis , E. Starikov , L. Reggiani , and L. Varani , Noise temperature of n + nn + GaAs structures , Phys. Rev. B PRBMDO 54 , 8821 ( 1996
    [CrossRef]

Abraham, D

M. Segev , B. Collings , and D. Abraham , Photorefractive Gunn effect , Phys. Rev. Lett. PRLTAO 76 , 3798 ( 1996
[CrossRef] [PubMed]

Bogges, T. F

A. L. Smirl , G. C. Valley , K. M. Bohnert , and T. F. Bogges , Picosecond photorefractive and free-carrier transient energy transfer in GaAs at 1 m , IEEE J. Quantum Electron. IEJQA7 24 , 289 ( 1988
[CrossRef]

Collings, B

M. Segev , B. Collings , and D. Abraham , Photorefractive Gunn effect , Phys. Rev. Lett. PRLTAO 76 , 3798 ( 1996
[CrossRef] [PubMed]

Dawson, M. D

Disdier, L

L. Disdier and G. Roosen , Nanosecond four-wave mixing in semi-insulating GaAs , Opt. Commun. OPCOB8 88 , 559 ( 1992
[CrossRef]

Gaubas, E

J. Vaitkus , K. Jaras iu nas , E. Gaubas , L. Jonikas , R. Pranaitis , and L. Subac ius , The diffraction of light by transient gratings in crystalline, ion-implanted, and amorphous silicon , IEEE J. Quantum Electron. IEJQA7 QE-22 , 1298 ( 1986
[CrossRef]

Gerritsen, H. J

K. Jaras iu nas and H. J. Gerritsen , Ambipolar diffusion measurements in semiconductors using nonlinear transient gratings , Appl. Phys. Lett. APPLAB 33 , 190 ( 1978
[CrossRef]

Glass, M. A

M. A. Glass and E. F. Shubert , eds., special issue on charge transport nonlinearities , Opt. Quantum Electron. OQELDI 22 , S1 S16 ( 1990
[CrossRef]

Gruzhinskis, V

V. Gruzhinskis , E. Starikov , P. Shiktorov , L. Reggiani , and L. Varani , Linear and nonlinear analysis of microwave power generation in submicrometer n + nn + InP diodes , J. Appl. Phys. JAPIAU 76 , 5260 ( 1994
[CrossRef]

Gruzinskis, V

L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Enhancement of light diffraction efficiency in semiconductors by mw electric field: experiment and calculations , in International Conference on Optical Diagnostics of Materials and Devices for Opto-, Micro-, and Quantum Electronics , S. V. Svechnikov and M. Ya. Valakh, eds. , Proc. SPIE PSISDG 2648 , 207 ( 1995
[CrossRef]

Jonikas, L

J. Vaitkus , K. Jaras iu nas , E. Gaubas , L. Jonikas , R. Pranaitis , and L. Subac ius , The diffraction of light by transient gratings in crystalline, ion-implanted, and amorphous silicon , IEEE J. Quantum Electron. IEJQA7 QE-22 , 1298 ( 1986
[CrossRef]

Pranaitis, R

J. Vaitkus , K. Jaras iu nas , E. Gaubas , L. Jonikas , R. Pranaitis , and L. Subac ius , The diffraction of light by transient gratings in crystalline, ion-implanted, and amorphous silicon , IEEE J. Quantum Electron. IEJQA7 QE-22 , 1298 ( 1986
[CrossRef]

Reggiani, L

V. Gruzhinskis , E. Starikov , P. Shiktorov , L. Reggiani , and L. Varani , Linear and nonlinear analysis of microwave power generation in submicrometer n + nn + InP diodes , J. Appl. Phys. JAPIAU 76 , 5260 ( 1994
[CrossRef]

Shiktorov, P

L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Enhancement of light diffraction efficiency in semiconductors by mw electric field: experiment and calculations , in International Conference on Optical Diagnostics of Materials and Devices for Opto-, Micro-, and Quantum Electronics , S. V. Svechnikov and M. Ya. Valakh, eds. , Proc. SPIE PSISDG 2648 , 207 ( 1995
[CrossRef]

Shubert, E. F

M. A. Glass and E. F. Shubert , eds., special issue on charge transport nonlinearities , Opt. Quantum Electron. OQELDI 22 , S1 S16 ( 1990
[CrossRef]

Starikov, E

L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Enhancement of light diffraction efficiency in semiconductors by mw electric field: experiment and calculations , in International Conference on Optical Diagnostics of Materials and Devices for Opto-, Micro-, and Quantum Electronics , S. V. Svechnikov and M. Ya. Valakh, eds. , Proc. SPIE PSISDG 2648 , 207 ( 1995
[CrossRef]

Starikovas, E

J. Vaitkus , E. Starikovas , L. Subac ius , and K. Jaras iu nas , Field dependencies of the efficiency of light self-diffraction and of diffusion coefficients in GaAs and Si , Litov. Fiz. Sb. LFRMA7 30 , 336 ( 1990

Stark, T. S

Subacius, L

L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Enhancement of light diffraction efficiency in semiconductors by mw electric field: experiment and calculations , in International Conference on Optical Diagnostics of Materials and Devices for Opto-, Micro-, and Quantum Electronics , S. V. Svechnikov and M. Ya. Valakh, eds. , Proc. SPIE PSISDG 2648 , 207 ( 1995
[CrossRef]

Vaitkus, J

J. Vaitkus , K. Jaras iu nas , E. Gaubas , L. Jonikas , R. Pranaitis , and L. Subac ius , The diffraction of light by transient gratings in crystalline, ion-implanted, and amorphous silicon , IEEE J. Quantum Electron. IEJQA7 QE-22 , 1298 ( 1986
[CrossRef]

Valusis, G

K. Jaras iu nas , V. Gruz inskis , P. Shiktorov , E. Starikov , L. Subac ius , and G. Valus is , Hot carrier dynamics and light diffraction in non-uniform electric field: experiment and modeling , Lith. Phys. J. LPJOED 35 , 426 ( 1995

Varani, L

V. Gruzhinskis , E. Starikov , P. Shiktorov , L. Reggiani , and L. Varani , Linear and nonlinear analysis of microwave power generation in submicrometer n + nn + InP diodes , J. Appl. Phys. JAPIAU 76 , 5260 ( 1994
[CrossRef]

Other (24)

A. Miller , D. A. Miller , and S. D. Smith , Dynamic nonlinear optical processes in semiconductors , Adv. Phys. ADPHAH 30 , 797 ( 1981
[CrossRef]

M. A. Glass and E. F. Shubert , eds., special issue on charge transport nonlinearities , Opt. Quantum Electron. OQELDI 22 , S1 S16 ( 1990
[CrossRef]

A. L. Smirl , G. C. Valley , K. M. Bohnert , and T. F. Bogges , Picosecond photorefractive and free-carrier transient energy transfer in GaAs at 1 m , IEEE J. Quantum Electron. IEJQA7 24 , 289 ( 1988
[CrossRef]

L. Disdier and G. Roosen , Nanosecond four-wave mixing in semi-insulating GaAs , Opt. Commun. OPCOB8 88 , 559 ( 1992
[CrossRef]

G. Montemezzani , P. Rogin , M. Zgonik , and P. Gunter , Interband photorefractive effects: theory and experiments in KNbO 3 , Phys. Rev. B PRBMDO 49 , 2484 ( 1994
[CrossRef]

W. A. Schroeder , T. S. Stark , M. D. Dawson , T. F. Boggess , A. L. Smirl , and G. C. Valley , Picosecond separation and measurements of coexisting photorefractive bound electrons, and free-carrier grating dynamics in GaAs , Opt. Lett. OPLEDP 16 , 159 ( 1991
[PubMed]

K. Jaras iu nas , P. Delaye , and G. Roosen , Optical nonlinearities and carrier transport in GaAs:EL2 at high excitation levels , Phys. Status Solidi B PSSBBD 175 , 445 ( 1993
[CrossRef]

A. Partovi and E. M. Garmire , Band-edge photorefractivity in semiconductors: theory and experiment , J. Appl. Phys. JAPIAU 69 , 6885 ( 1991
[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 JOBPDE 9 , 1626 ( 1992
[CrossRef]

L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Enhancement of light diffraction efficiency in semiconductors by mw electric field: experiment and calculations , in International Conference on Optical Diagnostics of Materials and Devices for Opto-, Micro-, and Quantum Electronics , S. V. Svechnikov and M. Ya. Valakh, eds. , Proc. SPIE PSISDG 2648 , 207 ( 1995
[CrossRef]

K. Jaras iu nas , V. Gruz inskis , P. Shiktorov , E. Starikov , L. Subac ius , and G. Valus is , Hot carrier dynamics and light diffraction in non-uniform electric field: experiment and modeling , Lith. Phys. J. LPJOED 35 , 426 ( 1995

L. Subac ius , V. Gruz inskis , E. Starikov , P. Shiktorov , and K. Jaras iu nas , Light diffraction on Gunn-domain gratings , Phys. Rev. B PRBMDO 55 , 12844 ( 1997
[CrossRef]

Q. Wang , R. M. Brubaker , and D. D. Nolte , Photorefractive phase shift induced by hot electron transport: multiple-quantum-well structures , J. Opt. Soc. Am. B JOBPDE 11 , 1773 ( 1994
[CrossRef]

R. M. Brubaker , Q. N. Wang , D. D. Nolte , and M. R. Melloch , Nonlocal photorefractive screening from hot electron velocity saturation in semiconductors , Phys. Rev. Lett. PRLTAO 77 , 4249 ( 1996
[CrossRef] [PubMed]

M. Segev , B. Collings , and D. Abraham , Photorefractive Gunn effect , Phys. Rev. Lett. PRLTAO 76 , 3798 ( 1996
[CrossRef] [PubMed]

V. Gruz inskis , E. Starikov , and P. Shiktorov , Conservation equations for hot carriers. I. Transport models , Solid-State Electron. SSELA5 36 , 1055 ( 1993
[CrossRef]

G. C. Valley , T. F. Boggess , J. Dubard , and A. L. Smirl , Picosecond pump-probe technique to measure deep-level, free carrier, and two-photon cross sections in GaAs , J. Appl. Phys. JAPIAU 66 , 2407 ( 1989
[CrossRef]

J. Vaitkus , K. Jaras iu nas , E. Gaubas , L. Jonikas , R. Pranaitis , and L. Subac ius , The diffraction of light by transient gratings in crystalline, ion-implanted, and amorphous silicon , IEEE J. Quantum Electron. IEJQA7 QE-22 , 1298 ( 1986
[CrossRef]

J. Vaitkus , E. Starikovas , L. Subac ius , and K. Jaras iu nas , Field dependencies of the efficiency of light self-diffraction and of diffusion coefficients in GaAs and Si , Litov. Fiz. Sb. LFRMA7 30 , 336 ( 1990

J. C. Fabre , J. M. C. Jonathan , and G. Roosen , 4 3 m photorefractive materials in energy transfer experiments , Opt. Commun. OPCOB8 65 , 257 ( 1988
[CrossRef]

R. Orlowski , L. A. Boatner , and E. Kratzig , Photorefractive effects in the cubic phase of potassium tantalate-niobate , Opt. Commun. OPCOB8 35 , 45 ( 1980
[CrossRef]

K. Jaras iu nas and H. J. Gerritsen , Ambipolar diffusion measurements in semiconductors using nonlinear transient gratings , Appl. Phys. Lett. APPLAB 33 , 190 ( 1978
[CrossRef]

V. Gruzhinskis , E. Starikov , P. Shiktorov , L. Reggiani , and L. Varani , Linear and nonlinear analysis of microwave power generation in submicrometer n + nn + InP diodes , J. Appl. Phys. JAPIAU 76 , 5260 ( 1994
[CrossRef]

P. Shiktorov , V. Gruz inskis , E. Starikov , L. Reggiani , and L. Varani , Noise temperature of n + nn + GaAs structures , Phys. Rev. B PRBMDO 54 , 8821 ( 1996
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Mechanisms of EO refractive-index modulation ΔnEO and the corresponding experimental data of light phase modulation ΔΦ in GaAs: A, by quantum-confined excitons12; B, by the Gunn-effect14; C, by the Franz–Keldysh effect11; and D, by the Pockels effect.5

Fig. 2
Fig. 2

Field dependencies of drift velocity (left-hand scale) and hot-electron transport coefficients (right-hand scale), calculated by the Monte Carlo method for 1, n-GaAs; 2, n-InP; and 3, p-GaAs crystals.

Fig. 3
Fig. 3

Spatial distributions of light intensity I(x), internal electric field Eint, and electron concentration N in GaAs at external dc field Eext=8 kV/cm. Monte Carlo simulation results are given at t=1, 30; 2, 100; 3, 200; and 4, 400 ps.

Fig. 4
Fig. 4

Spatial distributions of light intensity I(x), internal electric field Eint, and electron concentration N, calculated in GaAs by the MCP (dotted curves) and EDD (solid curves) methods at t=650 ps and at t=700 ps coinciding with peaks of the mw field during the negative and the positive half-periods. Applied field amplitude, Em=8 kV/cm.

Fig. 5
Fig. 5

Spatial profiles of electron concentration N (left-hand scale) and internal electric field Eint (right-hand scale) in GaAs for (mw-field amplitudes) Em=1 kV/cm and Em=4 kV/cm. Carrier and field profiles are calculated at t=1, 100; 2, 300; and 3, 500 ps.

Fig. 6
Fig. 6

Experimental data (points) and calculations of normalized self-diffraction efficiency versus mw-field amplitude in GaAs (1–4) and InP (5–7) for grating spacing Λ=25 μm. Calculated lines 3 and 6, for EO gratings; 4 and 7, FC gratings. 1, 2, Measurement results for two different GaAs samples.

Fig. 7
Fig. 7

Spatial distributions of internal electric field Eint and electron concentration N in GaAs for applied field amplitude Em=8 kV/cm and grating spacing Λ=25 μm. Calculated results are (in nanoseconds): 1, 6; 2, 12; 3, 18; 4, 30; and 5, 36 after the laser pulse is switched on with τL=10 ns.

Fig. 8
Fig. 8

Temporal evolution of normalized refractive-index modulation by FC’s ΔnFC and by the quadratic EO effect ΔnFCE2 calculated for 1h, the first and 2h, the second spatial Fourier harmonics of Eint averaged over a mw period. Results are given for 1, GaAs and 2, InP. I(t) is the temporal shape of the laser pulse.

Fig. 9
Fig. 9

Experimental data (points) and calculations of normalized self-diffraction efficiency versus mw-field amplitude in InP for three grating periods Λ μm: 1, 2, 20; 3, 4, 30; and 5, 6, 35. Simulated lines (2, 4, 6), the quadratic EO effect.

Fig. 10
Fig. 10

Dependencies of light self-diffraction efficiency on grating period in GaAs for FC grating η1FC and for EO grating η1EOE4, calculated without (right-hand scale) and with (left-hand scale) an external mw field. Applied field amplitude Em, in kilovolts per centimeter: 1, 0; 2, 2; 3, 4; and 4, 8.

Fig. 11
Fig. 11

Same as Fig. 10, but for InP.

Tables (1)

Tables Icon

Table 1 Parameters for Monte Carlo Simulation

Equations (26)

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

N/t=SnIN0(hν)-1+βI2(2hν)-1-γnNNi-γnpNP-(Nvn)/x,
P/t=SpINi(hν)-1+βI2(2hν)-1-γpPN0-γnpNP-(Pvp)/x,
Ni/t=SnIN0(hν)-1-SpINi(hν)-1-γnNNi-γpPN0,
E/x=(e/κ0κ)(P+Ni-N-NA-),
vn(x, t)=μn(E)E(x, t)-Dn(E)N(x, t)/x-Nτv(E)φ(E)/x,
vp(x, t)=μp(E)E(x, t)-Dp(E)P(x, t)/x,
ΔnFC(x)=-(e/2nκ0κω2)[ΔN(x)/m*(x)+ΔP(x)/mp].
ΔnEO=-n3gEO(κ-1)2κ02Eint2/2,
I1*=const.×02t[IA(t)Δn21h+IB(t)Δn22h]dt,
t+ve,h(p) x+qE(x, t) pxfe,h(p, x, t)
=Ge,h(p)-Re,h(p)+S^e,h[fe,h],
Sˆ[f]=-ν(p)f(p, x, t)+W(p, p)f(p, x, t)dp,
ν(p)=W(p, p)dp
E(x, t)x=eκκ0 [P(x, t)-N(x, t)+Ni(x, t)-NA-(x, t)],
N(x, t)=fe(p, x, t)dp,
P(x, t)=fh(p, x, t)dp
E(x, t)=E(0, t)+Eρ(x, t),
Eρ(x, t)=eκκ0 0x[P(x, t)-N(x, t)+Ni(x, t)-NA-(x, t)]dx
E(0, t)=1L U(t)-0LEρ(x, t)dx.
Nt=G-R-x (vN).
vt=eEm-1-vνv-v vx-1N x (nQv),
t=eEv-(-th)ν-v x-1N x (nQ).
v=μ(E)E-D(E) 1N Nx-τv(E) φ(E)x,
μ=em-1(E)τv(E)
D(E)=τv(E)δv20
φ(E)=δv20+½v2

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