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]
  2. 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]
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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)

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]

S. R. Seshadri, “Coupling of guided modes in thin films with surface corrugation,” J. Appl. Phys. 63, R115–R146 (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, “The determination of mode coupling coefficients,” Opt. Acta 32, 635–637 (1985).
[CrossRef]

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

Peng, S. T.

Popov, E.

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

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