Abstract

The problem of divergent electromagnetic dipole waves propagating through parallel dielectric interfaces is solved. The solution is obtained in an analytic form that can be readily evaluated numerically. The result is obtained as a solution to a boundary-value problem. Applications of the solution are described.

© 2000 Optical Society of America

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References

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  1. J. J. Stamnes and V. Dhayalan, Pure Appl. Opt. 5, 195 (1996).
    [CrossRef]
  2. V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 317 (1997).
    [CrossRef]
  3. V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 347 (1997).
    [CrossRef]
  4. C. J. R. Sheppard and T. Wilson, Proc. R. Soc. London Ser. A 379, 145 (1982).
    [CrossRef]
  5. P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 12 (1998).
    [CrossRef]
  6. P. D. Higdon, P. Török, and T. Wilson, J. Microsc. (Oxford) 193, 127 (1999).
    [CrossRef]
  7. P. Selényi, Phys. Rev. 56, 477 (1936).
    [CrossRef]
  8. P. Török, P. Varga, Z. Laczik, and G. R. Booker, J. Opt. Soc. Am. A 12, 325 (1995).
    [CrossRef]
  9. P. Török, J. Opt. Soc. Am. A 15, 3009 (1998).
    [CrossRef]
  10. D. G. Flagello, T. Milster, and A. E. Rosenbluth, J. Opt. Soc. Am. A 13, 53 (1996).
    [CrossRef]
  11. P. Török and P. Varga, Appl. Opt. 36, 2305 (1997).
    [CrossRef]
  12. J. J. Stamnes, Waves in Focal Regions (Hilger, London, 1986), Sec. 16.1.
  13. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  14. P. Varga, “The use of confocal microscopes in conoscopy and ellipsometry: 1. Electromagnetic theory,” Appl. Opt. (to be published).

1999

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. (Oxford) 193, 127 (1999).
[CrossRef]

1998

P. Török, J. Opt. Soc. Am. A 15, 3009 (1998).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 12 (1998).
[CrossRef]

1997

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 317 (1997).
[CrossRef]

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 347 (1997).
[CrossRef]

P. Török and P. Varga, Appl. Opt. 36, 2305 (1997).
[CrossRef]

1996

1995

1982

C. J. R. Sheppard and T. Wilson, Proc. R. Soc. London Ser. A 379, 145 (1982).
[CrossRef]

1959

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

1936

P. Selényi, Phys. Rev. 56, 477 (1936).
[CrossRef]

Booker, G. R.

Dhayalan, V.

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 317 (1997).
[CrossRef]

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 347 (1997).
[CrossRef]

J. J. Stamnes and V. Dhayalan, Pure Appl. Opt. 5, 195 (1996).
[CrossRef]

Flagello, D. G.

Higdon, P. D.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. (Oxford) 193, 127 (1999).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 12 (1998).
[CrossRef]

Laczik, Z.

Milster, T.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Rosenbluth, A. E.

Selényi, P.

P. Selényi, Phys. Rev. 56, 477 (1936).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and T. Wilson, Proc. R. Soc. London Ser. A 379, 145 (1982).
[CrossRef]

Stamnes, J. J.

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 347 (1997).
[CrossRef]

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 317 (1997).
[CrossRef]

J. J. Stamnes and V. Dhayalan, Pure Appl. Opt. 5, 195 (1996).
[CrossRef]

J. J. Stamnes, Waves in Focal Regions (Hilger, London, 1986), Sec. 16.1.

Török, P.

Varga, P.

P. Török and P. Varga, Appl. Opt. 36, 2305 (1997).
[CrossRef]

P. Török, P. Varga, Z. Laczik, and G. R. Booker, J. Opt. Soc. Am. A 12, 325 (1995).
[CrossRef]

P. Varga, “The use of confocal microscopes in conoscopy and ellipsometry: 1. Electromagnetic theory,” Appl. Opt. (to be published).

Wilson, T.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. (Oxford) 193, 127 (1999).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 12 (1998).
[CrossRef]

C. J. R. Sheppard and T. Wilson, Proc. R. Soc. London Ser. A 379, 145 (1982).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Appl. Opt.

J. Microsc. (Oxford)

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. (Oxford) 193, 127 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 12 (1998).
[CrossRef]

Phys. Rev.

P. Selényi, Phys. Rev. 56, 477 (1936).
[CrossRef]

Proc. R. Soc. London Ser. A

C. J. R. Sheppard and T. Wilson, Proc. R. Soc. London Ser. A 379, 145 (1982).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Pure Appl. Opt.

J. J. Stamnes and V. Dhayalan, Pure Appl. Opt. 5, 195 (1996).
[CrossRef]

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 317 (1997).
[CrossRef]

V. Dhayalan and J. J. Stamnes, Pure Appl. Opt. 6, 347 (1997).
[CrossRef]

Other

P. Varga, “The use of confocal microscopes in conoscopy and ellipsometry: 1. Electromagnetic theory,” Appl. Opt. (to be published).

J. J. Stamnes, Waves in Focal Regions (Hilger, London, 1986), Sec. 16.1.

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Equations (22)

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E=-ik2πΩE*sexp-ikr·sdp1dq1m1,
r=rt+zk=xi+yj+zk,s=st+mk=pi+qj+mk.
E1rt,z1=-ik12πΩE*s1exp-ik1rt·s1t×exp-ik1m1z1dp1dq1m1.
Enrt,zn-1=-ik12πΩΛE*s1exp-ik1rt·s1t×exp-ik1m1zn-1dp1dq1m1,
Enrt,z=-ikn2πΩF exp-iknrt·snt×exp-iknmnzdpndqn,
F=knk1ΛE*m1exp-izn-1k1m1-knmn=knk1ΛE*m1exp-iΦ.
Enr=-ikn22k1πΩΛE*s1exp-iΦ×exp-iknr·sndpndqnm1.
ml=1-pl2-ql21/2, l=1,2,,n.
Ee=-Aerdp×rdp×pe, and hence Ee*=-Ae*rdp×rdp×pe,
Em=-Amrdp×pm, and hence Em*=-Am*rdp×pm,
Λ=R-1·Pn-1·In-1·P1·R.
ΛEex*=Ae*2pxeTs+Tp cos θ1 cos θn-2pzeTp sin θ1 cos θn cos ϕn-Ts-Tp cos θ1 cos θn×pxe cos 2ϕn+pye sin 2ϕn,
ΛEey*=Ae*2pyeTs+Tp cos θ1 cos θn-2pzeTp sin θ1 cos θn sin ϕn-Ts-Tp cos θ1 cos θn×pxe sin 2ϕn-pye cos 2ϕn,
ΛEez*=Ae*pzeTp sin θ1 sin θn-Tp cos θ1 sin θn×pxe cos ϕn+pye sin ϕn,
ΛEmx*=Am*2pymTs cos θ1+Tp cos θn-2pzmTs sin θ1 sin ϕn-Ts cos θ1-Tp cos θn×pym cos 2ϕn-pxm sin 2ϕn,
ΛEmy*=Am*2-pxmTs cos θ1+Tp cos θn-2pzmTs sin θ1 cos ϕn-Ts cos θ1-Tp cos θn×pxm cos 2ϕn+pym sin 2ϕn,
ΛEmz*=Am*Tp sin θnpxm sin ϕn-pym cos ϕn.
Enxe=iAe*kn22k1pxeI0e,1-2ipzeI1e,1 cos ϕp+I2epxe cos 2ϕp+pye sin 2ϕp,Enye=iAe*kn22k1pyeI0e,1-2ipzeI1e,1 sin ϕp+I2epxe sin 2ϕp-pye cos 2ϕp,Enze=-2iAe*kn22k1pzeI0e,2-iI1e,2×pxe cos ϕp+pye sin ϕp,
Enxm=-iAm*kn22k1pymI0m-2ipzmI1m,1 sin ϕp+I2mpym cos 2ϕp-pxm sin 2ϕp,Enym=-iAm*kn22k1-pxmI0m-2ipzmI1m,1 cos ϕp+I2epxm cos 2ϕp+pym sin 2ϕp,Enzm=-2iAm*kn22k1iI1m,2pxm sin ϕp-pym cos ϕp,
I0e,1=0π/2Ts+Tp cos θ1 cos θnsin θncos θncos θ1×J0knρ sin θnexp-iΨdθn,I0e,2=0π/2Tp sin θ1 sin2 θncos θncos θ1×J0knρ sin θnexp-iΨdθn,I1e,1=0π/2Tp sin θ1 cos θn sin θncos θncos θ1×J1knρ sin θnexp-iΨdθn,I1e,2=0π/2Tp sin2 θn cos θnJ1knρ sin θn×exp-iΨdθn,I2e=0π/2Ts-Tp cos θ1 cos θn sin θncos θncos θ1×J2knρ sin θnexp-iΨdθn,
I0m=0π/2Ts cos θ1+Tp cos θnsin θncos θncos θ1×J0knρ sin θnexp-iΨdθn,I1m,1=0π/2Ts sin θ1 sin θncos θncos θ1×J1knρ sin θnexp-iΨdθn,I1m,2=0π/2Tp sin2 θncos θncos θ1×J1knρ sin θnexp-iΨdθn,I2m=0π/2Ts cos θ1-Tp cos θn×sin θncos θncos θ1J2knρ sin θnexp-iΨdθn,
exp-iΨ=exp-izn-1k1 cos θ1-kn cos θn×exp-ikn cos θnz.

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