Abstract

The design of a bigrating for use as a beam splitter is presented. It is based on a rigorous formulation of plane-wave scattering by a bigrating that is composed of two individual gratings oriented in different directions. Numerical results are carried out to optimize the design of a bigrating to perform 1 × 4 beam splitting in two dimensions and to examine its fabrication and operation tolerances. It is found that a bigrating can be designed to perform two functions: beam splitting and polarization purification.

© 1997 Optical Society of America

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References

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  1. R. K. Kostuk, J. W. Goodman, L. Hesselink, “Optical imaging applied to microelectronic chip-to-chip interconnections,” Appl. Opt. 24, 2851–2858 (1985).
    [CrossRef] [PubMed]
  2. S. Esener, S. H. Lee, “Free space optical interconnects for microelectronics and parallel computing,” in Optical Interconnects in the Computer Environment, J. Pazaris, G. R. Willenbring, eds., Proc. SPIE1178, 84–92 (1990).
    [CrossRef]
  3. S. W. Walker, J. Jahns, L. Li, W. M. Mansfield, P. Mulgrew, D. M. Tennant, C. W. Roberts, L. C. West, N. K. Ailawadi, “Design and fabrication of high-efficiency beam splitters and beam deflectors for integrated planar micro-optic systems,” Appl. Opt. 32, 2494–2501 (1993).
    [CrossRef] [PubMed]
  4. E. Noponen, J. Turunen, “Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles,” J. Opt. Soc. Am. A 11, 2494–2502 (1994).
    [CrossRef]
  5. E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. 4, 2061–2080 (1987).
    [CrossRef]
  6. R. C. Hall, R. Mittra, K. M. Mitzner, “Analysis of multilayered periodic structures using generalized scattering matrix theory,” IEEE Trans. Antennas Propag. 36, 511–517 (1988).
    [CrossRef]
  7. S. T. Peng, “Rigorous analysis of guided waves in doubly periodic structures,” J. Opt. Soc. Am. 7, 1448–1456 (1990).
    [CrossRef]
  8. S. T. Peng, “Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence,” J. Opt. Soc. Am. 6, 1869–1883 (1989).
    [CrossRef]
  9. A. A. Oliner, S. T. Peng, “New physical effects on periodically grooved open dielectric waveguides,” Radio Sci. 19, 1251–1255 (1984).
    [CrossRef]
  10. S. T. Peng, M. J. Shiau, “Scattering of plane waves by corrugated dielectric layers,” presented at the International Union of Radio Science Symposium on Electromagnetic Waves, Santiago de Compostela, Spain (1983).
  11. T. Tamir, H. C. Wang, A. A. Oliner, “Wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microwave Theory Tech. MTT-12, 323–330 (1964).
    [CrossRef]

1994 (1)

1993 (1)

1990 (1)

S. T. Peng, “Rigorous analysis of guided waves in doubly periodic structures,” J. Opt. Soc. Am. 7, 1448–1456 (1990).
[CrossRef]

1989 (1)

S. T. Peng, “Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence,” J. Opt. Soc. Am. 6, 1869–1883 (1989).
[CrossRef]

1988 (1)

R. C. Hall, R. Mittra, K. M. Mitzner, “Analysis of multilayered periodic structures using generalized scattering matrix theory,” IEEE Trans. Antennas Propag. 36, 511–517 (1988).
[CrossRef]

1987 (1)

E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. 4, 2061–2080 (1987).
[CrossRef]

1985 (1)

1984 (1)

A. A. Oliner, S. T. Peng, “New physical effects on periodically grooved open dielectric waveguides,” Radio Sci. 19, 1251–1255 (1984).
[CrossRef]

1964 (1)

T. Tamir, H. C. Wang, A. A. Oliner, “Wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microwave Theory Tech. MTT-12, 323–330 (1964).
[CrossRef]

Ailawadi, N. K.

Esener, S.

S. Esener, S. H. Lee, “Free space optical interconnects for microelectronics and parallel computing,” in Optical Interconnects in the Computer Environment, J. Pazaris, G. R. Willenbring, eds., Proc. SPIE1178, 84–92 (1990).
[CrossRef]

Gaylord, T. K.

E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. 4, 2061–2080 (1987).
[CrossRef]

Glytsis, E. N.

E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. 4, 2061–2080 (1987).
[CrossRef]

Goodman, J. W.

Hall, R. C.

R. C. Hall, R. Mittra, K. M. Mitzner, “Analysis of multilayered periodic structures using generalized scattering matrix theory,” IEEE Trans. Antennas Propag. 36, 511–517 (1988).
[CrossRef]

Hesselink, L.

Jahns, J.

Kostuk, R. K.

Lee, S. H.

S. Esener, S. H. Lee, “Free space optical interconnects for microelectronics and parallel computing,” in Optical Interconnects in the Computer Environment, J. Pazaris, G. R. Willenbring, eds., Proc. SPIE1178, 84–92 (1990).
[CrossRef]

Li, L.

Mansfield, W. M.

Mittra, R.

R. C. Hall, R. Mittra, K. M. Mitzner, “Analysis of multilayered periodic structures using generalized scattering matrix theory,” IEEE Trans. Antennas Propag. 36, 511–517 (1988).
[CrossRef]

Mitzner, K. M.

R. C. Hall, R. Mittra, K. M. Mitzner, “Analysis of multilayered periodic structures using generalized scattering matrix theory,” IEEE Trans. Antennas Propag. 36, 511–517 (1988).
[CrossRef]

Mulgrew, P.

Noponen, E.

Oliner, A. A.

A. A. Oliner, S. T. Peng, “New physical effects on periodically grooved open dielectric waveguides,” Radio Sci. 19, 1251–1255 (1984).
[CrossRef]

T. Tamir, H. C. Wang, A. A. Oliner, “Wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microwave Theory Tech. MTT-12, 323–330 (1964).
[CrossRef]

Peng, S. T.

S. T. Peng, “Rigorous analysis of guided waves in doubly periodic structures,” J. Opt. Soc. Am. 7, 1448–1456 (1990).
[CrossRef]

S. T. Peng, “Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence,” J. Opt. Soc. Am. 6, 1869–1883 (1989).
[CrossRef]

A. A. Oliner, S. T. Peng, “New physical effects on periodically grooved open dielectric waveguides,” Radio Sci. 19, 1251–1255 (1984).
[CrossRef]

S. T. Peng, M. J. Shiau, “Scattering of plane waves by corrugated dielectric layers,” presented at the International Union of Radio Science Symposium on Electromagnetic Waves, Santiago de Compostela, Spain (1983).

Roberts, C. W.

Shiau, M. J.

S. T. Peng, M. J. Shiau, “Scattering of plane waves by corrugated dielectric layers,” presented at the International Union of Radio Science Symposium on Electromagnetic Waves, Santiago de Compostela, Spain (1983).

Tamir, T.

T. Tamir, H. C. Wang, A. A. Oliner, “Wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microwave Theory Tech. MTT-12, 323–330 (1964).
[CrossRef]

Tennant, D. M.

Turunen, J.

Walker, S. W.

Wang, H. C.

T. Tamir, H. C. Wang, A. A. Oliner, “Wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microwave Theory Tech. MTT-12, 323–330 (1964).
[CrossRef]

West, L. C.

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

R. C. Hall, R. Mittra, K. M. Mitzner, “Analysis of multilayered periodic structures using generalized scattering matrix theory,” IEEE Trans. Antennas Propag. 36, 511–517 (1988).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

T. Tamir, H. C. Wang, A. A. Oliner, “Wave propagation in sinusoidally stratified dielectric media,” IEEE Trans. Microwave Theory Tech. MTT-12, 323–330 (1964).
[CrossRef]

J. Opt. Soc. Am. (3)

E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. 4, 2061–2080 (1987).
[CrossRef]

S. T. Peng, “Rigorous analysis of guided waves in doubly periodic structures,” J. Opt. Soc. Am. 7, 1448–1456 (1990).
[CrossRef]

S. T. Peng, “Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence,” J. Opt. Soc. Am. 6, 1869–1883 (1989).
[CrossRef]

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

Radio Sci. (1)

A. A. Oliner, S. T. Peng, “New physical effects on periodically grooved open dielectric waveguides,” Radio Sci. 19, 1251–1255 (1984).
[CrossRef]

Other (2)

S. T. Peng, M. J. Shiau, “Scattering of plane waves by corrugated dielectric layers,” presented at the International Union of Radio Science Symposium on Electromagnetic Waves, Santiago de Compostela, Spain (1983).

S. Esener, S. H. Lee, “Free space optical interconnects for microelectronics and parallel computing,” in Optical Interconnects in the Computer Environment, J. Pazaris, G. R. Willenbring, eds., Proc. SPIE1178, 84–92 (1990).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Structure configuration of a bigrating.

Fig. 2
Fig. 2

Propagation vector in spherical and rectangular coordinate systems.

Fig. 3
Fig. 3

Effect of grating thickness on the diffraction efficiency.

Fig. 4
Fig. 4

Effect of crossing angle on the diffraction efficiency.

Fig. 5
Fig. 5

Effect of the wavelength on the diffraction efficiency.

Fig. 6
Fig. 6

1 × 4 beam splitting in two dimensions.

Equations (28)

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

εis=εi1+δi cos2πΛis+pi for i=1 and 2,
kx=ka sin θinc cos ϕinc,
ky=ka sin θinc sin ϕinc,
kz=ka cos θinc.
kxmn=kx+m2πa+n2πbcos φ,
kyn=ky+n2πbsin φ,
kumn=ku+m2πacos φ+n2πb,
kvm=kv-m2πasin φ,
kukv=cos φsin φ-sin φcos φkxky.
z0×Etmnρ, z=amnVmn z+amnVmnz×exp-jkρmn·ρ,
Htmnρ, z=amnImnz+amnImnz×exp-jkρmn·ρ,
amn=kρmn/kρmn,
amn=z0×amn=z0×kρmn/kρmn.
Vmnz=Vmn exp-jkzmnz+V¯mn expjkzmnz,
Imnz=YmnVmn exp-jkzmnz-V¯mn expjkzmnz,
kxmn2+kyn2+kzmn2=k02ε,
Ymn=Ymn=kzmnωμ0for TE polarization,Ymn=ωε0εkzmnfor TM polarization,
V¯mn=p=- Gmnp1,1Vmp+p=- Gmnp1,2Vmp,
V¯mn=p=- Gmnp2,1Vmp+p=- Gmnp2,2Vmp,
Bmn=Γmn1,1A00+Γmn1,2A00,
Bmn=Γmn2,1A00+Γmn2,2A00,
Cmn=Tmn1,1A00+Tmn1,2A00,
Cmn=Tmn2,1A00+Tmn2,2A00,
ku=kx cos φ+ky sin φ=ka sin θinc cosφ-φinc,
kv=-kx sin φ+ky cos φ=ka sin θinc sinφ-φinc,
sin θinc cos ϕinc=Mλ/2a.
sin θinc cosφ-ϕinc=Nλ/2b.
cos ϕinccosφ-ϕinc=MbNa

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