Abstract

A dielectric-film waveguide with a grating etched on its film–cover interface can be used as a polarization converter. The e wave can be converted into the h wave and vice versa if the guided wave is incident obliquely to the grating vector. The polarization converter is analyzed by use of a quasi-optic technique. A high degree of polarization-conversion efficiency is achieved by a suitable choice of the grating length. The Bragg angles of incidence and observation, the maximum polarization-conversion efficiency, and the frequency and the angular selectivity are all found to increase with an increase in the grating period. An illustrative numerical example is presented.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  8. E. Popov, L. Mashev, “Analysis of mode coupling in planar optical waveguides,” Opt. Acta 32, 265–280 (1985).
    [CrossRef]
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    [CrossRef]
  10. L. A. Weller-Brophy, D. G. Hall, “Measured TM–TM coupling in waveguide gratings,” Opt. Lett. 12, 756–758 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  18. S. R. Seshadri, “Coupling of guided modes in thin films with surface corrugation,” J. Appl. Phys. 63, R115–R146 (1988).
    [CrossRef]
  19. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 95–111, 116–126.
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    [CrossRef]

1999 (1)

1998 (2)

1994 (1)

S. R. Seshadri, “Guided-mode interactions in thin films with surface corrugation,” J. Appl. Phys. 76, 7583–7600 (1994).
[CrossRef]

1993 (1)

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

1990 (1)

1989 (1)

1988 (2)

S. R. Seshadri, “Coupling of guided modes in thin films with surface corrugation,” J. Appl. Phys. 63, R115–R146 (1988).
[CrossRef]

L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” J. Lightwave Technol. LT-6, 1069–1082 (1988).
[CrossRef]

1987 (1)

1985 (2)

E. Popov, L. Mashev, “Analysis of mode coupling in planar optical waveguides,” Opt. Acta 32, 265–280 (1985).
[CrossRef]

E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

1981 (2)

1980 (1)

1979 (1)

K. Wagatsuma, H. Sakaki, S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979).
[CrossRef]

1978 (1)

1974 (1)

1973 (1)

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

Burke, J. J.

Hall, D. G.

Hardy, A.

Izhaky, N.

Kogelnik, H.

H. Kogelnik, H. P. Weber, “Rays, stored energy, and power flow in dielectric waveguides,” J. Opt. Soc. Am. 64, 174–185 (1974).
[CrossRef]

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

Lagasse, P. E.

Li, L.

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 95–111, 116–126.

Mashev, L.

E. Popov, L. Mashev, “Analysis of mode coupling in planar optical waveguides,” Opt. Acta 32, 265–280 (1985).
[CrossRef]

E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

Peng, S. T.

Popov, E.

E. Popov, L. Mashev, “Analysis of mode coupling in planar optical waveguides,” Opt. Acta 32, 265–280 (1985).
[CrossRef]

E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

Saito, S.

K. Wagatsuma, H. Sakaki, S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979).
[CrossRef]

Sakaki, H.

K. Wagatsuma, H. Sakaki, S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979).
[CrossRef]

Sarid, D.

Seshadri, S. R.

S. R. Seshadri, “Guided-mode interactions in thin films with surface corrugation,” J. Appl. Phys. 76, 7583–7600 (1994).
[CrossRef]

S. R. Seshadri, “Coupling of guided modes in thin films with surface corrugation,” J. Appl. Phys. 63, R115–R146 (1988).
[CrossRef]

Sosnowski, T. P.

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

Stegeman, G. I.

Stoll, H. M.

Van Roey, J.

Wagatsuma, K.

K. Wagatsuma, H. Sakaki, S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979).
[CrossRef]

Weber, H. P.

H. Kogelnik, H. P. Weber, “Rays, stored energy, and power flow in dielectric waveguides,” J. Opt. Soc. Am. 64, 174–185 (1974).
[CrossRef]

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

Weller-Brophy, L. A.

L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” J. Lightwave Technol. LT-6, 1069–1082 (1988).
[CrossRef]

L. A. Weller-Brophy, D. G. Hall, “Measured TM–TM coupling in waveguide gratings,” Opt. Lett. 12, 756–758 (1987).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE J. Quantum Electron. (2)

K. Wagatsuma, H. Sakaki, S. Saito, “Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters,” IEEE J. Quantum Electron. QE-15, 632–637 (1979).
[CrossRef]

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

J. Appl. Phys. (2)

S. R. Seshadri, “Coupling of guided modes in thin films with surface corrugation,” J. Appl. Phys. 63, R115–R146 (1988).
[CrossRef]

S. R. Seshadri, “Guided-mode interactions in thin films with surface corrugation,” J. Appl. Phys. 76, 7583–7600 (1994).
[CrossRef]

J. Lightwave Technol. (1)

L. A. Weller-Brophy, D. G. Hall, “Local normal mode analysis of guided mode interactions with waveguide gratings,” J. Lightwave Technol. LT-6, 1069–1082 (1988).
[CrossRef]

J. Mod. Opt. (1)

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Acta (2)

E. Popov, L. Mashev, “Analysis of mode coupling in planar optical waveguides,” Opt. Acta 32, 265–280 (1985).
[CrossRef]

E. Popov, L. Mashev, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

Opt. Lett. (3)

Other (1)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), pp. 95–111, 116–126.

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Figures (6)

Fig. 1
Fig. 1

Geometry of a dielectric-film waveguide with a surface corrugation on the film–cover interface. The grating vector is in the z direction.

Fig. 2
Fig. 2

Directions of the incident (zepin) and the reflected (zhprf) guided modes with respect to the grating vector z.

Fig. 3
Fig. 3

Zigzag-ray model employed in the analysis of the coupling of the guided modes in a dielectric-film waveguide. For the incident e wave the parameters are m=e, t=p, and ir=in. For the reflected h wave the parameters are m=h, t=q, and ir=rf.

Fig. 4
Fig. 4

Maximum polarization-conversion coefficient (Reh)max plotted as a function of the Bragg angle of incidence ϕepinc=1.0, f=12.96, s=9.61, 2a=0.275 μm, λ0=0.8 μm, p=1, q=1, ω=ω0=2π/λ(μ00)1/2, and ω1=νeh=0.

Fig. 5
Fig. 5

Polarization-conversion coefficient Reh plotted as a function of ω1/ω0 for the Bragg angle of incidence ϕepin=67.5°, where ω0 is the Bragg frequency and ω1 is the deviation of the frequency from ω0. The waveguide, the grating, and the incident- and the reflected-wave parameters are the same as for Fig. 4.

Fig. 6
Fig. 6

Polarization-conversion coefficient Reh plotted as a function of the angle of incidence θepin for the Bragg angle of incidence ϕepin=67.5°, with ω1=0, νeh0; the other physical parameters are the same as for Fig. 4.

Equations (164)

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a(z)=a(1+δη cos Kz),
βepsin ϕepin-βhqsin ϕhqrf=0.
βepcos ϕepin+βhqcos ϕhqrf=K,
βepsin θepin-βhqsin θhqrf=0.
βepcos θepin+βhqcos θhqrf=K+δνeh,
2x2+2y2+2z2+ω2μ00ν(Aν, Fν)=0
E=(μ00ν)-1×(×xˆAν)+iω×xˆFν,
H=-iω(μ0)-1×xˆAν+(μ0)-1×(×xˆFν),
Aν=Aνin=Aνin(x)exp(iβepzepin),
Fν=Fνin=0.
Eypνin=Hxνin=Hzpνin=0,
Exνin=βep2(μ00ν)-1Aνin,
Ezpνin=i βepμ00νx Aνin,
Hypνin=ωβep(μ0)-1Aνin.
Afin(x)=Asin(x),forx=-a,
1fx Afin(x)=1sx Asin(x),forx=-a.
Aν=Aνrf=0,
Fν=Fνrf=Fνrf(x)exp(iβhqzhqrf).
Exνrf=Ezqνrf=Hyqνrf=0,
Eyqνrf=-ωβhqFνrf,
Hxνrf=βhq2(μ0)-1Fνrf,
Hzqνrf=i βhqμ0x Fνrf.
Ffrf(x)=Fsrf(x),forx=-a,
x Ffrf(x)=x Fsrf(x),forx=-a.
Hyf=Hyc,forx=a(z), 
Hzf+da(z)dz Hxf=Hzc+da(z)dz Hxc,forx=a(z),
Eyf=Eyc,forx=a(z),
Ezf+da(z)dz Exf=Ezc+da(z)dz Exc,forx=a(z).
Hyf+δa η cos Kz x Hyf0
=Hyc+δa η cos Kz x Hyc0,forx=a,
Hzf+δa η cos Kz x Hzf0-δa ηK sin KzHxf0
=Hzc+δa η cos Kz x Hzc0-δa ηK sin KzHxc0,
forx=a,
Eyf+δa η cos Kz x Eyf0
=Eyc+δa η cos Kz x Eyc0,forx=a,
Ezf+δa η cos Kz x Ezf0-δa ηK sin KzExf0
=Ezc+δa η cos Kz x Ezc0-δa ηK sin KzExc0,
forx=a.
Hypν=Hyνcos θepin-Hzνsin θepin
Hypf+δa η cos Kz x Hypf0+δa ηK sin Kz sin θepinHxf0
=Hypc+δa η cos Kz x Hypc0+δa ηK sin Kz sin θepinHxc0.
Hypν0rf=i βhqμ0sin(θepin+θhqrf) x Fν0rf.
Afin(x)=Acin(x) +δ a η2ω i βhqβepsin(θepin+θhqrf) 2x2× [Fc0rf(x)-Ff0rf(x)]exp(-iδνeh z),
forx=a.
Ezpν=Eyνsin θepin+Ezνcos θepin
Ezpf+δa η cos Kz x Ezpf 0-δa ηK sin Kz cos θepinEx f 0
=Ezpc+δa η cos KzxEzpc0-δa ηK sin Kz cos θepinExc0,forx=a.
Ezpν0rf=ωβhqsin(θepin+θhqrf)Fν0rf.
1fx Afin(x)=1cx Acin(x),forx=a.
Eyqν=-Eyνcos θhqrf-Ezνsin θhqrf
Eyqf+δa η cos Kz x Eyqf0+δa ηK sin Kz sin θhqrfExf0
=Eyqc+δa η cos Kz x Eyqc0+δa ηK sin Kz sin θhqrfExc0,forx=a.
Eyqν0in=-iβepsin(θepin+θhqrf) 1μ00νx Aν0in.
Ffrf(x)=Fcrf(x) +δ iaη2ωβepβhqsin(θepin+θhqrf) 1μ00×1c2x2 Ac0in(x)-1f2x2 Af0in(x)×exp(iδνeh z)-δ iaη2ω K sin θhqrfβep2βhqμ00×1c Ac0in(x)-1f Af0in(x)exp(iδνeh z),
forx=a.
Hzqν=Hyνsin θhqrf-Hzνcos θhqrf
Hzqf+δa η cos Kz x Hzqf0+δa ηK sin Kz cos θhqrfHxf0
=Hzqc+δa η cos Kz x Hzqc0+δa ηK sin Kz cos θhqrfHxc0,forx=a.
Hzqν0in=ωβep(μ0)-1sin(θepin+θhqrf)Aν0in.
x Ffrf(x)=x Fcrf(x) -δ i2 a ηω βepβhqsin(θepin+θhqrf)×x Ac0in(x)-x Af0in(x)exp(iδνeh z),
forx=a.
Aν=Aνin(x)exp[iβep(y sin θepin+z cos θepin)]
=Aνin(x)exp(iβep zepin)
Acin(x)=Mepexp[-αc,ep(x-a)],fora<x<,
Afin(x)=Pepexp[-ikep(x-a)]+Qepexp[ikep(x-a)],
for-a<x<a,
Asin(x)=Sepexp[αs,ep(x+a)],for-<x<-a,
αν,mt=(βmt2-ω2μ00ν)1/2,
for ν=c,s,mt=ep,hq,
kmt=(ω2μ00f-βmt2)1/2,formt=ep,hq.
Pepexp(i2kepa)=exp(iϕeps)(2 cos ϕeps)-1Sep,
Qepexp(-i2kepa)=exp(-iϕeps)(2 cos ϕeps)-1Sep,
tan ϕepν=fαν,ep/kepν,for ν=c, s.
Qepexp(-i2kepa)Pepexp(i2kepa)=reps,
SepPepexp(i2kepa)=teps,
rmtν=exp(-i2ϕmtν),
tmtν=1+rmtν,
Fν=Fνrf(x)exp[iβhq(y sin θhqrf-z cos θhqrf)]=Fνrf(x)exp(iβhq zhqrf)
Fcrf(x)=Mhqexp[-αc,hq(x-a)],fora<x<,
Ffrf(x)=Phqexp[-ikhq(x-a)]+Qhqexp[ikhq(x-a)],
for-a<x<a,
Fsrf(x)=Shqexp[αs,hq(x+a)],for-<x<-a.
tan ϕhqν=αν,hq/khq,for ν=c, s.
Phq+Qhq=Mhq.
Afin(x)=Acin(x)+δ 12a ηω i βhqβepsin(θepin+θhqrf)×ω2μ00(f-c)Mhqexp(-iδνeh z),
forx=a.
Pep+Qep=Mep,
Pep-Qep=-i f αc,epkepc Mep.
Ffrf(x)=Fcrf(x),forx=a.
x Ffrf(x)=x Fcrf(x)-δ i2 a ηω βepβhqsin(θepin+θhqrf)×(f-c) αc,epc Mepexp(iδνeh z),
forx=a.
Pep=exp(-i2ϕepc)Qep+δi sin ϕepcexp(-iϕepc)×12a ηω i βhqβepsin(θepin+θhqrf)×ω2μ00(f-c)Mhqexp(-iδνeh z),
Mep=2 cos ϕepcexp(iϕepc)Pep+O(δ).
Phq=exp(-i2ϕhqc)Qhq+δ cos ϕhqcexp(-iϕhqc) 1khq×12 a ηω βepβhqsin(θepin+θhqrf)(f-c) αν,epc Mep×exp(iδνeh z),
Mhq=2 cos ϕhqcexp(iϕhqc)Phq+O(δ).
νg,mt=xˆνgx,mt+z^mtirνgz,mt=(xˆkt+z^mtirβmt)/ωμ00f,
for(mt, ir)=(ep, in), (hq, rf).
zν,mt=2 βmt ϕmtν,ν=c, s,
(mt, ir)=(ep, in), (hq, rf),
tν,mt=-2 ω ϕmtν,ν=c, s,mt=ep, hq.
sin Θmt=βmt/ω(μ00f)1/2,formt=ep, hq.
ZB,mt=zc,mt+zs,mt+4a tan Θmt,mt=ep, hq.
tB,mt=tc,mt+ts,mt+4a tan Θmt/νgz,mt,
mt=ep, hq.
Pep(a; 0; zepin-ZB,ep)=Pep(-a; 0; zepin-ZB,ep+zc,ep+ 2a tan Θep).
Qep(a; 0; zepin)
=Qep(-a; 0; zepin-ZB,ep+zc,ep+2a tan Θep).
Pep(a; 0; zepin)=exp[iDep(ω, βep)]Pep(a; 0; zepin-ZB,ep)+δi sin ϕepcexp(-iϕepc) 12a ηω i βhqβepsin(θepin+θhqrf)ω2μ00(f-c)Mhqexp(-iδνeh z),
Dmt(ω, βmt)=4kmta-2ϕmtc-2ϕmts,
formt=ep, hq.
Phq(a; 0; zhqrf)=exp[iDhq(ω, βhq)]×Phq(a; 0; zhqrf-ZB,hq)+δ cos ϕhqcexp(-iϕhqc) 1khq12 a ηω βepβhq×sin(θepin+θhqrf)(f-c) αc,epc Mep×exp(iδνeh z).
ZB,mt=-βmt Dmt(ω, βmt),
tB,mt=ω Dmt(ω, Bmt).
Dmt(ω, βmt)=2π(t-1),t=1, 2,,
mt=ep, hq
ω=ω0+δω1.
Dmt(ω, βmt)=2π(t-1)+δω1tB,mt.
ω1Mep+iVg,epzepin Mep
=-Vg,epZB,epcos ϕepcsin ϕepca ηω0 i βhqβepsin(ϕepin+ϕhqrf)×ω02μ00(f-c)Mhqexp(-iδνeh z),
ω1Mhq+iVg,hqzhqrf Mhq
=i Vg,hqZB,hqcos2 ϕepc1khq a ηω0βepβhqsin(ϕepin+ϕhqrf)×(f-c) αc,epc Mepexp(iδνeh z),
Vg,mt=(Vg,mt)n/(Vg,mt)d,
(Vg,ep)n=βep2a+fc(kep2+αc,ep2)αc,ep(c2kep2+f2αc,ep2) +fs(kep2+αs,ep2)αs,ep(s2kep2+f2αs,ep2),
(Vg,ep)d=ω0μ00f2a+c(ckep2+fαc,ep2)αc,ep(c2kep2+f2αc,ep2)+s(skep2+fαs,ep2)αs,ep(s2kep2+f2αs,ep2),
(Vg,hq)n=βhq[2a+1/αc,hq+1/αs,hq],
(Vg,hq)d=ω0μ00f2a+(ckhq2+fαc,hq2)fαc,hq(khq2+αc,hq2)+(skhq2+fαs,hq2)fαs,hq(khq2+αs,hq2).
ZB,mt=2(Vg,mt)n/kmt,formt=ep, hq.
Afin(x)=Mepcos[kep(x-a)+ϕepc]cos ϕepc,
Asin(x)=Mepcos ϕepscos ϕepc (-1)(p-1)exp[αs,ep(x+a)].
Ffrf(x)=Mhqcos[khq(x-a)+ϕhqc]cos ϕhqc,
Fsrf(x)=Mhqcos ϕhqscos ϕhqc (-1)(q-1)exp[αs,hq(x+a)].
Pzp=|Aep|2,
Nep=MepAep=8μ020fcos2 ϕepcwpω0βep2kepZB,ep1/2.
Pzq=|Bhq|2,
Nhq=MhqBhq=8μ0cos2 ϕhqcwqω0βhq2khqZB,hq1/2.
ω1Aep+iVg,epzepin Aep
=-iVg,epCep,hqBhqexp(-iδνeh z),
ω1Bhq+iVg,hqzhqrf Bhq
=iVg,hqCep,hqAepexp(iδνeh z),
Cep,hq=18 a ηNepNhqβepβhqsin(ϕepin+ϕhqrf)
×wμ0 ω02(f-c) αc,epc
zepin=sin ϕepiny+cos ϕepinz,
zhqrf=sin ϕhqrfy -cos ϕhqrfz.
y (|Aep|2sin ϕepin+|Bhq|2sin ϕhqrf)
+z (|Aep|2cos ϕepin-|Bhq|2cos ϕhqrf)=0
Bhq(z=zf)=0.
Tee+Reh=1,
Tee=|Aep(z=zf)|2/|Aep(z=zb)|2,
Reh=cos ϕhqrf|Bhq(z=zb)|2cos ϕepin|Aep(z=zb)|2.
Vgz,ep=Vg,epcos ϕepin,
Vgz,hq=Vg,hqcos ϕhqrf,
D=ω121Vgz,hq1Vgz,ep,
Aep(z)=(cos ϕepin)-1/2exp[-i(D-+0.5νeh)z]A˜ep(z),
Bhq(z)=(cos ϕhqrf)-1/2exp[-i(D--0.5νeh)z]B˜hq(z),
Kn=Cep,hq(cos ϕepincos ϕhqrf)-1/2.
z-iD++νeh2A˜ep(z)=-KnB˜hq(z),
z+iD++νeh2B˜hq(z)=-KnA˜ep(z).
A˜ep(z)=-B˜hq(z=zb)Knsinh GL {-G cosh[G(zf-z)]+i(D++0.5νeh)sinh[G(zf-z)]},
B˜hq(z)=B˜hq(z=zb) sinh[G(zf-z)]sinh GL,
G=[Kn2-(D++0.5νeh)2]1/2forKn2>(D++0.5νeh)2iH=i[(D++0.5νeh)2-Kn2]1/2forKn2<(D++0.5νeh)2.
Reh=|B˜hq(z=zb)|2|A˜ep(z=zb)|2=|Knsinh(GL)|2[|G cosh(GL)|2+|(D++0.5νeh)sinh(GL)|2].
Reh=(Reh)max=tanh2(|Kn|L),ω1=0,νeh=0.
ω1n=±Δωn2=±121Vgz,hq+1Vgz,ep-1Kn2-nπL21/2
cos θepincos ϕepin1+νehK.

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