Abstract

The scattering of a surface plasmon polariton in a semiconductor slab by rapid plasma creation in the slab is explored. As a result of the scattering, the initial surface wave breaks up into two frequency-upshifted surface waves propagating in opposite directions along the slab and generates a static magnetic field and a dc inside the slab and transient radiation that escapes the slab. A part of the initial energy can also be trapped inside the slab owing to total internal reflection and forms frequency-upshifted guided modes of the slab. The scattering of a surface wave by a rapidly created plasma allows the analysis of basic processes that occur in nonstationary media in the presence of boundaries. The practical applications include the control of propagation of guided radiation in integrated optics devices, coupling the radiation out of waveguides, and ultrafast transient spectroscopy of an electron–hole plasma in semiconductors.

© 1999 Optical Society of America

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References

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  1. S. Nakamura and K. Tajima, “Ultrafast all-optical gate switch based on frequency shift accompanied by semiconductor band-filling effect,” Appl. Phys. Lett. 70, 3498–3500 (1997).
    [CrossRef]
  2. P. K. Benicewicz, J. P. Roberts, and A. J. Taylor, “Scaling of terahertz radiation from large-aperture biased photoconductors,” J. Opt. Soc. Am. B 11, 2533–2546 (1994).
    [CrossRef]
  3. F. R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microwave Theory Tech. 6, 167–172 (1958).
    [CrossRef]
  4. V. I. Semenova, “Reflection of electromagnetic waves from an ionization front,” Radiophys. Quantum Electron. 10, 599–604 (1967).
    [CrossRef]
  5. N. S. Stepanov, “Dielectric constant of unsteady plasma,” Radiophys. Quantum Electron. 19, 683–689 (1976).
    [CrossRef]
  6. D. K. Kalluri, “Conversion of a whistler wave into a controllable helical wiggler magnetic field,” J. Appl. Phys. 79, 6770–6774 (1996).
    [CrossRef]
  7. R. L. Fante, “Transmission of electromagnetic waves into time-varying media,” IEEE Trans. Antennas Propag. 19, 417–424 (1971).
    [CrossRef]
  8. V. V. Borisov, “Electromagnetic field transformation upon change in properties of the medium with time within a limited region,” Radiophys. Quantum Electron. 25, 759–764 (1982).
    [CrossRef]
  9. D. K. Kalluri, “On reflection from a suddenly created plasma half-space: transient solution,” IEEE Trans. Plasma Sci. 16, 11–16 (1988).
    [CrossRef]
  10. D. K. Kalluri and V. R. Goteti, “Frequency shifting of electromagnetic radiation by sudden creation of a plasma slab,” J. Appl. Phys. 72, 4575–4580 (1992).
    [CrossRef]
  11. H. L. Rappaport and C. D. Striffler, “Frequency up-conversion and time-dependent tunneling of electromagnetic radiation in step-ionized plasmas,” Phys. Plasmas 1, 780–784 (1994).
    [CrossRef]
  12. V. M. Agranovich and D. L. Mills, eds., Surface Polaritons (North-Holland, New York, 1982).
  13. F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett. 36, 216–219 (1976).
    [CrossRef]
  14. For a review, see e.g., E. A. Vinogradov, “Vibrational polaritons in semiconductor films on metal surfaces,” Phys. Rep. 217, 159–223 (1992) and references therein.
    [CrossRef]
  15. M. I. Bakunov and A. V. Maslov, “Trapping of an electromagnetic wave by the boundary of a nonstationary plasma,” Phys. Rev. E 57, 5978–5987 (1998); “Nonstationary input of an electromagnetic wave in a plasma waveguide structure,” J. Commun. Technol. Electron. 43, 924–929 (1998).
    [CrossRef]
  16. M. I. Bakunov and A. V. Maslov, “Trapping of electromagnetic wave by nonstationary plasma layer,” Phys. Rev. Lett. 79, 4585–4588 (1997).
    [CrossRef]
  17. M. I. Bakunov and S. N. Zhukov, “Trapping of an electromagnetic wave by the boundary of created plasma,” JETP 86, 696–702 (1998).
    [CrossRef]
  18. M. I. Bakunov and S. N. Zhukov, “Conversion of a surface electromagnetic wave at the boundary of a time-varying plasma,” Plasma Phys. Rep. 22, 649–658 (1996).
  19. T. Obunai and T. Takeda, “Propagation characteristics in 70 GHz solid-plasma waveguide containing n-InSb slab with light irradiation,” Jpn. J. Appl. Phys., Part 1 34, 4232–4233 (1995).
    [CrossRef]
  20. See, e.g., A. D. Boardman, “Hydrodynamic theory of plasmon-polaritons on plane surfaces,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 1–76.
  21. M. I. Bakunov and Yu. M. Sorokin, “Resonant conversion of TM wave in a moving plasma-production slab,” Sov. J. Plasma Phys. 13, 858–861 (1987); M. I. Bakunov and A. V. Maslov, “Transient input of an electromagnetic wave into an open waveguide coated with nonstationary plasma film,” J. Appl. Phys. 83, 3885–3891 (1998).
    [CrossRef]

1998 (1)

M. I. Bakunov and S. N. Zhukov, “Trapping of an electromagnetic wave by the boundary of created plasma,” JETP 86, 696–702 (1998).
[CrossRef]

1997 (2)

S. Nakamura and K. Tajima, “Ultrafast all-optical gate switch based on frequency shift accompanied by semiconductor band-filling effect,” Appl. Phys. Lett. 70, 3498–3500 (1997).
[CrossRef]

M. I. Bakunov and A. V. Maslov, “Trapping of electromagnetic wave by nonstationary plasma layer,” Phys. Rev. Lett. 79, 4585–4588 (1997).
[CrossRef]

1996 (2)

M. I. Bakunov and S. N. Zhukov, “Conversion of a surface electromagnetic wave at the boundary of a time-varying plasma,” Plasma Phys. Rep. 22, 649–658 (1996).

D. K. Kalluri, “Conversion of a whistler wave into a controllable helical wiggler magnetic field,” J. Appl. Phys. 79, 6770–6774 (1996).
[CrossRef]

1995 (1)

T. Obunai and T. Takeda, “Propagation characteristics in 70 GHz solid-plasma waveguide containing n-InSb slab with light irradiation,” Jpn. J. Appl. Phys., Part 1 34, 4232–4233 (1995).
[CrossRef]

1994 (2)

P. K. Benicewicz, J. P. Roberts, and A. J. Taylor, “Scaling of terahertz radiation from large-aperture biased photoconductors,” J. Opt. Soc. Am. B 11, 2533–2546 (1994).
[CrossRef]

H. L. Rappaport and C. D. Striffler, “Frequency up-conversion and time-dependent tunneling of electromagnetic radiation in step-ionized plasmas,” Phys. Plasmas 1, 780–784 (1994).
[CrossRef]

1992 (2)

For a review, see e.g., E. A. Vinogradov, “Vibrational polaritons in semiconductor films on metal surfaces,” Phys. Rep. 217, 159–223 (1992) and references therein.
[CrossRef]

D. K. Kalluri and V. R. Goteti, “Frequency shifting of electromagnetic radiation by sudden creation of a plasma slab,” J. Appl. Phys. 72, 4575–4580 (1992).
[CrossRef]

1988 (1)

D. K. Kalluri, “On reflection from a suddenly created plasma half-space: transient solution,” IEEE Trans. Plasma Sci. 16, 11–16 (1988).
[CrossRef]

1982 (1)

V. V. Borisov, “Electromagnetic field transformation upon change in properties of the medium with time within a limited region,” Radiophys. Quantum Electron. 25, 759–764 (1982).
[CrossRef]

1976 (2)

N. S. Stepanov, “Dielectric constant of unsteady plasma,” Radiophys. Quantum Electron. 19, 683–689 (1976).
[CrossRef]

F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett. 36, 216–219 (1976).
[CrossRef]

1971 (1)

R. L. Fante, “Transmission of electromagnetic waves into time-varying media,” IEEE Trans. Antennas Propag. 19, 417–424 (1971).
[CrossRef]

1967 (1)

V. I. Semenova, “Reflection of electromagnetic waves from an ionization front,” Radiophys. Quantum Electron. 10, 599–604 (1967).
[CrossRef]

1958 (1)

F. R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microwave Theory Tech. 6, 167–172 (1958).
[CrossRef]

Bakunov, M. I.

M. I. Bakunov and S. N. Zhukov, “Trapping of an electromagnetic wave by the boundary of created plasma,” JETP 86, 696–702 (1998).
[CrossRef]

M. I. Bakunov and A. V. Maslov, “Trapping of electromagnetic wave by nonstationary plasma layer,” Phys. Rev. Lett. 79, 4585–4588 (1997).
[CrossRef]

M. I. Bakunov and S. N. Zhukov, “Conversion of a surface electromagnetic wave at the boundary of a time-varying plasma,” Plasma Phys. Rep. 22, 649–658 (1996).

Benicewicz, P. K.

Borisov, V. V.

V. V. Borisov, “Electromagnetic field transformation upon change in properties of the medium with time within a limited region,” Radiophys. Quantum Electron. 25, 759–764 (1982).
[CrossRef]

De Martini, F.

F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett. 36, 216–219 (1976).
[CrossRef]

Fante, R. L.

R. L. Fante, “Transmission of electromagnetic waves into time-varying media,” IEEE Trans. Antennas Propag. 19, 417–424 (1971).
[CrossRef]

Goteti, V. R.

D. K. Kalluri and V. R. Goteti, “Frequency shifting of electromagnetic radiation by sudden creation of a plasma slab,” J. Appl. Phys. 72, 4575–4580 (1992).
[CrossRef]

Kalluri, D. K.

D. K. Kalluri, “Conversion of a whistler wave into a controllable helical wiggler magnetic field,” J. Appl. Phys. 79, 6770–6774 (1996).
[CrossRef]

D. K. Kalluri and V. R. Goteti, “Frequency shifting of electromagnetic radiation by sudden creation of a plasma slab,” J. Appl. Phys. 72, 4575–4580 (1992).
[CrossRef]

D. K. Kalluri, “On reflection from a suddenly created plasma half-space: transient solution,” IEEE Trans. Plasma Sci. 16, 11–16 (1988).
[CrossRef]

Maslov, A. V.

M. I. Bakunov and A. V. Maslov, “Trapping of electromagnetic wave by nonstationary plasma layer,” Phys. Rev. Lett. 79, 4585–4588 (1997).
[CrossRef]

Morgenthaler, F. R.

F. R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microwave Theory Tech. 6, 167–172 (1958).
[CrossRef]

Nakamura, S.

S. Nakamura and K. Tajima, “Ultrafast all-optical gate switch based on frequency shift accompanied by semiconductor band-filling effect,” Appl. Phys. Lett. 70, 3498–3500 (1997).
[CrossRef]

Obunai, T.

T. Obunai and T. Takeda, “Propagation characteristics in 70 GHz solid-plasma waveguide containing n-InSb slab with light irradiation,” Jpn. J. Appl. Phys., Part 1 34, 4232–4233 (1995).
[CrossRef]

Rappaport, H. L.

H. L. Rappaport and C. D. Striffler, “Frequency up-conversion and time-dependent tunneling of electromagnetic radiation in step-ionized plasmas,” Phys. Plasmas 1, 780–784 (1994).
[CrossRef]

Roberts, J. P.

Semenova, V. I.

V. I. Semenova, “Reflection of electromagnetic waves from an ionization front,” Radiophys. Quantum Electron. 10, 599–604 (1967).
[CrossRef]

Shen, Y. R.

F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett. 36, 216–219 (1976).
[CrossRef]

Stepanov, N. S.

N. S. Stepanov, “Dielectric constant of unsteady plasma,” Radiophys. Quantum Electron. 19, 683–689 (1976).
[CrossRef]

Striffler, C. D.

H. L. Rappaport and C. D. Striffler, “Frequency up-conversion and time-dependent tunneling of electromagnetic radiation in step-ionized plasmas,” Phys. Plasmas 1, 780–784 (1994).
[CrossRef]

Tajima, K.

S. Nakamura and K. Tajima, “Ultrafast all-optical gate switch based on frequency shift accompanied by semiconductor band-filling effect,” Appl. Phys. Lett. 70, 3498–3500 (1997).
[CrossRef]

Takeda, T.

T. Obunai and T. Takeda, “Propagation characteristics in 70 GHz solid-plasma waveguide containing n-InSb slab with light irradiation,” Jpn. J. Appl. Phys., Part 1 34, 4232–4233 (1995).
[CrossRef]

Taylor, A. J.

Vinogradov, E. A.

For a review, see e.g., E. A. Vinogradov, “Vibrational polaritons in semiconductor films on metal surfaces,” Phys. Rep. 217, 159–223 (1992) and references therein.
[CrossRef]

Zhukov, S. N.

M. I. Bakunov and S. N. Zhukov, “Trapping of an electromagnetic wave by the boundary of created plasma,” JETP 86, 696–702 (1998).
[CrossRef]

M. I. Bakunov and S. N. Zhukov, “Conversion of a surface electromagnetic wave at the boundary of a time-varying plasma,” Plasma Phys. Rep. 22, 649–658 (1996).

Appl. Phys. Lett. (1)

S. Nakamura and K. Tajima, “Ultrafast all-optical gate switch based on frequency shift accompanied by semiconductor band-filling effect,” Appl. Phys. Lett. 70, 3498–3500 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. L. Fante, “Transmission of electromagnetic waves into time-varying media,” IEEE Trans. Antennas Propag. 19, 417–424 (1971).
[CrossRef]

IEEE Trans. Plasma Sci. (1)

D. K. Kalluri, “On reflection from a suddenly created plasma half-space: transient solution,” IEEE Trans. Plasma Sci. 16, 11–16 (1988).
[CrossRef]

IRE Trans. Microwave Theory Tech. (1)

F. R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microwave Theory Tech. 6, 167–172 (1958).
[CrossRef]

J. Appl. Phys. (2)

D. K. Kalluri and V. R. Goteti, “Frequency shifting of electromagnetic radiation by sudden creation of a plasma slab,” J. Appl. Phys. 72, 4575–4580 (1992).
[CrossRef]

D. K. Kalluri, “Conversion of a whistler wave into a controllable helical wiggler magnetic field,” J. Appl. Phys. 79, 6770–6774 (1996).
[CrossRef]

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

JETP (1)

M. I. Bakunov and S. N. Zhukov, “Trapping of an electromagnetic wave by the boundary of created plasma,” JETP 86, 696–702 (1998).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (1)

T. Obunai and T. Takeda, “Propagation characteristics in 70 GHz solid-plasma waveguide containing n-InSb slab with light irradiation,” Jpn. J. Appl. Phys., Part 1 34, 4232–4233 (1995).
[CrossRef]

Phys. Plasmas (1)

H. L. Rappaport and C. D. Striffler, “Frequency up-conversion and time-dependent tunneling of electromagnetic radiation in step-ionized plasmas,” Phys. Plasmas 1, 780–784 (1994).
[CrossRef]

Phys. Rep. (1)

For a review, see e.g., E. A. Vinogradov, “Vibrational polaritons in semiconductor films on metal surfaces,” Phys. Rep. 217, 159–223 (1992) and references therein.
[CrossRef]

Phys. Rev. Lett. (2)

F. De Martini and Y. R. Shen, “Nonlinear excitation of surface polaritons,” Phys. Rev. Lett. 36, 216–219 (1976).
[CrossRef]

M. I. Bakunov and A. V. Maslov, “Trapping of electromagnetic wave by nonstationary plasma layer,” Phys. Rev. Lett. 79, 4585–4588 (1997).
[CrossRef]

Plasma Phys. Rep. (1)

M. I. Bakunov and S. N. Zhukov, “Conversion of a surface electromagnetic wave at the boundary of a time-varying plasma,” Plasma Phys. Rep. 22, 649–658 (1996).

Radiophys. Quantum Electron. (3)

V. I. Semenova, “Reflection of electromagnetic waves from an ionization front,” Radiophys. Quantum Electron. 10, 599–604 (1967).
[CrossRef]

N. S. Stepanov, “Dielectric constant of unsteady plasma,” Radiophys. Quantum Electron. 19, 683–689 (1976).
[CrossRef]

V. V. Borisov, “Electromagnetic field transformation upon change in properties of the medium with time within a limited region,” Radiophys. Quantum Electron. 25, 759–764 (1982).
[CrossRef]

Other (4)

V. M. Agranovich and D. L. Mills, eds., Surface Polaritons (North-Holland, New York, 1982).

See, e.g., A. D. Boardman, “Hydrodynamic theory of plasmon-polaritons on plane surfaces,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 1–76.

M. I. Bakunov and Yu. M. Sorokin, “Resonant conversion of TM wave in a moving plasma-production slab,” Sov. J. Plasma Phys. 13, 858–861 (1987); M. I. Bakunov and A. V. Maslov, “Transient input of an electromagnetic wave into an open waveguide coated with nonstationary plasma film,” J. Appl. Phys. 83, 3885–3891 (1998).
[CrossRef]

M. I. Bakunov and A. V. Maslov, “Trapping of an electromagnetic wave by the boundary of a nonstationary plasma,” Phys. Rev. E 57, 5978–5987 (1998); “Nonstationary input of an electromagnetic wave in a plasma waveguide structure,” J. Commun. Technol. Electron. 43, 924–929 (1998).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Geometry of the problem: Initial surface wave propagates along the plasma slab.

Fig. 2
Fig. 2

Dispersion curves for, 1, the surface wave and, 2, guided modes that can propagate along the plasma slab (with b=10 and ωp1d/c=1) deposited on a perfectly conducting substrate. Curve 1 is asymptotic to ϖ=ωp1/(1+b-1)1/2. The disper- sion curves 2 start on the light line h=ω/c at the cutoff frequencies ω=[ωp1/(1-b-1)1/2]{1+b-1[mπc/(ωp1d)]2}1/2, m=0, 1, 2, and asymptotically approach line h=(ω/c)b as ω. The region to the right of dashed curve 3, ch/ωp1=b[(ω/ωp1)2-1]1/2, corresponds to the waves propagating in the slab; the region to the right of the light line corresponds to the waves propagating in vacuum. The guided modes are located in the region between curve 3 and the light line h=ω/c.

Fig. 3
Fig. 3

Frequencies of curves 1–3, the excited surface waves ωs/ω0, and curve 4, the guided mode ωg(0)/ω0 of zero order (m=0) as a function of the plasma density shift in the plasma slabs of different thicknesses. Curve 1, ωp1d/c=1, b=1; 2, ωp1d/c=0.1, b=1; 3, ωp1d/c=0.1, b=10. For curves 1–4 n0=4. Curve 5 corresponds to the case n0.

Fig. 4
Fig. 4

Amplitude of the copropagating (B+>0) and counterpropagating (B-<0) surface wave for (curve 1) b=1, (curve 2) b=10 and (curve 3) guided wave for b=10. For all cases ωp1d/c=0.1, n0=4.

Fig. 5
Fig. 5

Static magnetic field and current lines of the free-streaming mode.

Fig. 6
Fig. 6

Angular density of the outgoing radiation Wv(θ) for ΔN/N1=10, n0=4 and (a) b=1, and (b) b=10 for different plasma slab thicknesses: ωp1d/c=1 (dashed curves) and ωp1d/c=0.1 (solid curves); (a) shows the unit length, which corresponds to normalization to cB02/(16π2ω0).

Fig. 7
Fig. 7

Energy transformation into curve 1, copropagating surface wave W+/W0; 2, counterpropagating surface wave W-/W0; 3, outgoing radiation Wv/W0; and, 4, free-streaming mode Wf/W0 as a function of the density shift ΔN/N1 for b=1, ωp1d/c=0.1, and n0=4.

Fig. 8
Fig. 8

Energy transformation into curve 1, copropagating surface wave W+/W0; 2, counterpropagating surface wave W-/W0; 3, outgoing radiation Wv/W0; 4, free-streaming mode Wf/W0; 5, copropagating guided mode Wg+(0)/W0; and, 6, counterpropagating guided mode Wg-(0)/W0 as a function of the density shift ΔN/N1 for b=10, ωp1d/c=0.1, and n0=4.

Fig. 9
Fig. 9

Energy transformation into the outgoing radiation Wv/W0 as a function of the density shift ΔN/N1 for b=10, n0=4 and, curve 1, ωp1d/c=1; 2, ωp1d/c=0.1. Curve 2 is the same as curve 3 in Fig. 8.

Fig. 10
Fig. 10

Kinematic diagram that illustrates the transformation of a backward surface wave (point ω0, h0 on curve 1) into a copropagating forward surface wave (point ω, h0 on curve 2) in a thin plasma slab with growing plasma density. Curve 3 is the light line h=ω/c.

Equations (29)

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

Bz(x, y, t)=B0 exp(iω0t-ih0x)exp[-κv1(y-d)]ify>dB0 exp(iω0t-ih0x) cosh(κp1y)cosh(κp1d)if0<y<d,
κp1 tanh(κp1d)+1κv1=0.
Ex(x, y, t)
=(cBz/iω0)(-κv1)ify>d(cBz/iω0)κp11-1 tanh(κp1y)if0<y<d,
Ey(x, y, t)
=(ch0Bz/ω0)ify>d(ch0Bz/ω0)1-1if0<y<d.
Exy+ih0Ey
=1cBzt,
Bzy=bcExt-4πec[N1V1x+η(t)ΔNV2x],
ih0Bz=bcEyt-4πec[N1V1y+η(t)ΔNV2y],
Vt=-emE.
b(x, y, s)=Bz(x, y, 0)s-iω0+Av(s)exp[-ih0x-κv(y-d)]
b(x, y, s)=s2+iω0s+Δωp2s(s2+ω02+Δωp2)Bz(x, y, 0)+Ap(s) cosh(κpy)cosh(κpd)exp(-ih0x)
Av(s)=B0 iΔωp2[s22κv1-ω02κp tanh(κpd)]ω0s(s-iω0)(s2+ω02+Δωp2)D(s),
Ap(s)=B0 iΔωp22(ω02κv+s2κv1)ω0s(s-iω0)(s2+ω02+Δωp2)D(s),
D(s)=κp tanh(κpd)+2κv,
Bz(x, y, t)=Bz(x, y, 0)Δωp2ω02+Δωp2+± ω02ω0±(ω02+Δωp2)1/2ω02+Δωp2×exp[±it(ω02+Δωp2)1/2].
B±=B0 Δωp2(ω2-ωp22)(c2h02-ω2)1/2ω0(ω0ω)(ω02-ω2+Δωp2)V(ω)×[ω02(c2h02-ω2)1/2-ω2(c2h02-ω02)1/2],
V(ω)=ω2(ω2+ωp22)-2ωp22c2h02-ω42(κv/κp)2+ω4κvd/cosh2(κpd),
Bf(x, y)=B0 exp(-ih0x) Δωp2ω02+Δωp2×cosh(κp1y)cosh(κp1d)-cosh(κfy)cosh(κfd),
Wv=-π/2π/2Wv(θ)dθ,
Wv(θ)=c2h016π2|Av(s=iω)|2 cot2 θ,
W0=B0216πc2h02ω2κv1+bd1 cosh2(κp1d)+1-b+(c2h02/ω02)(2b-1)/11κp1 coth(κp1d).
2 y12by-s2c22+h2b=F(x, y, s),
F(x, y, s)=-s2+iω0γc2Bz(x, y, 0)-Ex(x, y, 0) 2cyγ2,
2(y, s)=1ify>db(1+ωp22/s2)if0<y<d,
γ(y, s)=1ify>db[1-ωp12/(iω0s)]if0<y<d,
{b}=0,12by+γc2Ex(x, y, 0)=0aty=d,
by=0aty=0

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