Abstract

Scattering properties of a homogeneous anisotropic slab are investigated at fixed crystal anisotropy axis orientation. The penetration phenomenon for an incident wave propagating tangentially to the crystal surface is discussed. Slab-based nonreciprocal optical devices are proposed. Their operating principles are based on the slab scattering properties, but not on the Faraday effect. Numerical data for an optical isolator and frequency detector are presented.

© 2012 Optical Society of America

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References

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  1. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley Classics Library, 2003).
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  3. B. Lax and K. J. ButtonMicrowave Ferrites and Ferrimagnetics (McGraw-Hill, 1962).
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  12. R. G. HunspergerIntegrated Optics. Theory and Technology (University of Delaware, 2009).
  13. C. R. PollockFundamentals of Optoelectronics (Donnelley, 1995).
  14. T. F. Krauss, “Planar photonic crystal waveguide devices for integrated optics,” Phys. Status Solidi A 197, 688–702(2003).
    [CrossRef]
  15. K. R. SturleyRadio receiver design. Part 1: Radio Frequency Amplification and Detection (Wiley, 1943).
  16. K. A. Vytovtov, S. A. Volkova, and Y. S. Tarasenko, “Investigation of tangential wave propagation under a stratified anisotropic structure,” in Proceedings of International Conference on Mathematical Methods in Electromagnetic Theory (Kyiv, Ukraine, 2010).
  17. F. Lindell, “Olyslager: TE/TM decomposition of the Green dyadic in uniaxial anisotropic media,” Electromagnetics 18, 383–3941998.
    [CrossRef]
  18. R A. Silin, “Electromagnetic waves in artificial periodic structures,” Phys. Usp. 49, 542–545 (2006).
    [CrossRef]

2006

2005

2003

L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, “Magnetic photonic crystals,” J. Phys. D 36R277–R287 (2003).
[CrossRef]

T. F. Krauss, “Planar photonic crystal waveguide devices for integrated optics,” Phys. Status Solidi A 197, 688–702(2003).
[CrossRef]

1998

F. Lindell, “Olyslager: TE/TM decomposition of the Green dyadic in uniaxial anisotropic media,” Electromagnetics 18, 383–3941998.
[CrossRef]

1985

1972

1970

Berreman, D. W.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Button, K. J.

B. Lax and K. J. ButtonMicrowave Ferrites and Ferrimagnetics (McGraw-Hill, 1962).

Chang, W. S. C.

W. S. C. ChangFundamentals of Guided-Wave Optoelectronic Devices (Cambridge University2010).

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, 1985), pp. 215–216.

Dadoenkova, N. N.

L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, “Magnetic photonic crystals,” J. Phys. D 36R277–R287 (2003).
[CrossRef]

Escuti, M. J.

Henvis, B. W.

Hunsperger, R. G.

R. G. HunspergerIntegrated Optics. Theory and Technology (University of Delaware, 2009).

Krauss, T. F.

T. F. Krauss, “Planar photonic crystal waveguide devices for integrated optics,” Phys. Status Solidi A 197, 688–702(2003).
[CrossRef]

Lax, B.

B. Lax and K. J. ButtonMicrowave Ferrites and Ferrimagnetics (McGraw-Hill, 1962).

Lekner, J.

Lindell, F.

F. Lindell, “Olyslager: TE/TM decomposition of the Green dyadic in uniaxial anisotropic media,” Electromagnetics 18, 383–3941998.
[CrossRef]

Lyubchanskii, L. I.

L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, “Magnetic photonic crystals,” J. Phys. D 36R277–R287 (2003).
[CrossRef]

Lyubchanskii, M. I.

L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, “Magnetic photonic crystals,” J. Phys. D 36R277–R287 (2003).
[CrossRef]

Mayerhöfer, T. G.

Oh, C.

Pollock, C. R.

C. R. PollockFundamentals of Optoelectronics (Donnelley, 1995).

Popp, J.

Rasing, T.

L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, “Magnetic photonic crystals,” J. Phys. D 36R277–R287 (2003).
[CrossRef]

Shapovalov, E. A.

L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, “Magnetic photonic crystals,” J. Phys. D 36R277–R287 (2003).
[CrossRef]

Silin, R A.

R A. Silin, “Electromagnetic waves in artificial periodic structures,” Phys. Usp. 49, 542–545 (2006).
[CrossRef]

Sturley, K. R.

K. R. SturleyRadio receiver design. Part 1: Radio Frequency Amplification and Detection (Wiley, 1943).

Tarasenko, Y. S.

K. A. Vytovtov, S. A. Volkova, and Y. S. Tarasenko, “Investigation of tangential wave propagation under a stratified anisotropic structure,” in Proceedings of International Conference on Mathematical Methods in Electromagnetic Theory (Kyiv, Ukraine, 2010).

Teitler, S.

Volkova, S. A.

K. A. Vytovtov, S. A. Volkova, and Y. S. Tarasenko, “Investigation of tangential wave propagation under a stratified anisotropic structure,” in Proceedings of International Conference on Mathematical Methods in Electromagnetic Theory (Kyiv, Ukraine, 2010).

Vytovtov, K. A.

K. A. Vytovtov, S. A. Volkova, and Y. S. Tarasenko, “Investigation of tangential wave propagation under a stratified anisotropic structure,” in Proceedings of International Conference on Mathematical Methods in Electromagnetic Theory (Kyiv, Ukraine, 2010).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley Classics Library, 2003).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley Classics Library, 2003).

Electromagnetics

F. Lindell, “Olyslager: TE/TM decomposition of the Green dyadic in uniaxial anisotropic media,” Electromagnetics 18, 383–3941998.
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D

L. I. Lyubchanskii, N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and T. Rasing, “Magnetic photonic crystals,” J. Phys. D 36R277–R287 (2003).
[CrossRef]

Opt. Express

Phys. Status Solidi A

T. F. Krauss, “Planar photonic crystal waveguide devices for integrated optics,” Phys. Status Solidi A 197, 688–702(2003).
[CrossRef]

Phys. Usp.

R A. Silin, “Electromagnetic waves in artificial periodic structures,” Phys. Usp. 49, 542–545 (2006).
[CrossRef]

Other

K. R. SturleyRadio receiver design. Part 1: Radio Frequency Amplification and Detection (Wiley, 1943).

K. A. Vytovtov, S. A. Volkova, and Y. S. Tarasenko, “Investigation of tangential wave propagation under a stratified anisotropic structure,” in Proceedings of International Conference on Mathematical Methods in Electromagnetic Theory (Kyiv, Ukraine, 2010).

W. S. C. ChangFundamentals of Guided-Wave Optoelectronic Devices (Cambridge University2010).

R. G. HunspergerIntegrated Optics. Theory and Technology (University of Delaware, 2009).

C. R. PollockFundamentals of Optoelectronics (Donnelley, 1995).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley Classics Library, 2003).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

B. Lax and K. J. ButtonMicrowave Ferrites and Ferrimagnetics (McGraw-Hill, 1962).

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-Free Approach (McGraw-Hill, 1985), pp. 215–216.

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Figures (8)

Fig. 1.
Fig. 1.

Geometry of the problem.

Fig. 2.
Fig. 2.

Dependence of permeability of dyadic elements on a frequency.

Fig. 3.
Fig. 3.

(a) Schematic view of penetration phenomenon; kpi is wavevector of the wave within a media, and kinc is wavevector of incident wave, kinc=kτ. (b) Schematic view for the Poynting vector; possible directions of wave transmission.

Fig. 4.
Fig. 4.

Dependence of the intensity reflection coefficient on a frequency and a slab thickness for (a) αinc=90° and (b) αinc=90° (d=2μm)

Fig. 5.
Fig. 5.

Structure of the frequency detector of the optical range based on penetration effect.

Fig. 6.
Fig. 6.

Dependence of the intensity reflection coefficient on a frequency for an optical isolator.

Fig. 7.
Fig. 7.

(a) Dependence of the intensity reflection coefficient on a frequency for forward (solid line) and backward (dot line) waves. (b) Schematic view of the operation principle for analog frequency detector; d=2μm, ε=1.

Fig. 8.
Fig. 8.

Stages of signal transformation: (a) initial linear signal, (b) frequency-modulated signal, (c) output signal at the output of frequency detector.

Equations (6)

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μ¯¯norm=|μxx0jμxy0μzz0jμxy0μxx|.
kz4+c2kz2+c0=0,
c2=ω4ε02μzzμzz(μzz2+μzzμxxμxy2μ0μxxμ0μzz),c0=ω4ε02μzzμxx[μxy2(μxxμ0)2].
Ex=Aωμ0kyexp[j(kxx+kyy+kzz)],Ey=jAky(ω2ε0μxxky2kz2)ωμxy(ω2μ0μzzkz2)exp[j(kxx+kyy+kzz)],Ez=jAky2(ω2ε0μzzkz2)+kz2[ω2ε0(μxxμzz)kz2]ω4ε02μxxμzzkyωμxy(ω2ε0μzzkz2)exp[j(kxx+kyy+kzz)],Hx=jAμxx(ω2ε0μxxky2kz2)ωμxy(ω2ε0μzzkz2)exp[j(kxx+kyy+kzz)],Hy=Akzkyexp[j(kxx+kyy+kzz)],Hz=Aexp[j(kxx+kyy+kzz)],
Pz=12(ExHy*EyHx*)=A22[ωε0kzky2kyμxx(ω2ε0μxxky2kz2)2ω2μxy2(ω2ε0μxxky2kz2)2],Py=12(EzHx*ExHz*)=A22{ky2(ω2ε0μzzky2)+kz2[ω2ε0(μxx+μzz)kz2]ω4ε02μxxμzzky2ωμxy(ω2ε0μzzkz2)×μzz(ω2ε0μxxky2kz2)ωμxy(ω2ε0μzzkz2)ωμ0ky},Px=12(EyHz*EzHy2)=jA22{ky(ω2ε0μxxky2kz2)ωμxy(ω2ε0μzzkz2)ky2(ω2ε0μzzkz2)+kz2[ω2ε0(μxxμzz)kz2]ω4ε02μxxμzzky2ωμxy(ω2ε0μzzkz2)kz}.
αp=arctan(Py/Pz)

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