Abstract

Infrared beam-splitting transmission gratings that utilize anisotropically etched v-grooves on silicon wafers are proposed. With scalar diffraction theory to find the amplitudes of the different diffraction orders, a numerical search is used to find optimum designs for 1:3, 1:5, and 1:7 splitters with efficiencies greater than 70% with a standard deviation in intensity of no more than 7%.

© 1995 Optical Society of America

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References

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  1. H. Dammann, E. Klotz, “Coherent-optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
    [CrossRef]
  2. J. Jahns, M. M. Downs, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
  3. S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.
  4. K. E. Bean, “Anisotropic etching of silicon,” IEEE Trans. Electron Devices ED-25, 1185–1193 (1978).
    [CrossRef]
  5. U. U. Graf, D. T. Joffe, E. J. Kim, J. H. Lacy, H. Ling, J. T. Moore, G. Rebeiz, “Fabrication and evaluation of an etched infrared diffraction grating,” Appl. Opt. 33, 96–102 (1994).
    [CrossRef] [PubMed]
  6. R. Narendra, J. N. McMullin, “Single-mode, phosphorous-doped silica waveguides in silicon V-grooves,” IEEE Photon. Technol. Lett. 5, 43–46 (1993).
    [CrossRef]
  7. W. Tsang, S. Wang, “Thin-film beam splitter and reflector for optical guided waves,” Appl. Phys. Lett. 27, 588–590 (1975).
    [CrossRef]
  8. S. Sriram, G. B. Brandt, E. P. Supertzi, “Heterodyne receiver on silicon: an exercise in integration,” in Integrated Optics II, D. G. Hall, ed., Proc. Soc. Photo-Opt. Instrum. Eng.321, 15–22 (1982).
  9. S. Sriram, E. P. Supertzi, “Novel V-groove structures on silicon,” Appl. Opt. 24, 1784–1787 (1985).
    [CrossRef] [PubMed]
  10. J. A. Cox, F. P. Shvartsman, “Image quality assessment of diffractive elements replicated in SURPHEX™,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DThB4, pp. 346–349.

1994 (1)

1993 (1)

R. Narendra, J. N. McMullin, “Single-mode, phosphorous-doped silica waveguides in silicon V-grooves,” IEEE Photon. Technol. Lett. 5, 43–46 (1993).
[CrossRef]

1989 (1)

J. Jahns, M. M. Downs, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).

1985 (1)

1978 (1)

K. E. Bean, “Anisotropic etching of silicon,” IEEE Trans. Electron Devices ED-25, 1185–1193 (1978).
[CrossRef]

1977 (1)

H. Dammann, E. Klotz, “Coherent-optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1975 (1)

W. Tsang, S. Wang, “Thin-film beam splitter and reflector for optical guided waves,” Appl. Phys. Lett. 27, 588–590 (1975).
[CrossRef]

Bean, K. E.

K. E. Bean, “Anisotropic etching of silicon,” IEEE Trans. Electron Devices ED-25, 1185–1193 (1978).
[CrossRef]

Brandt, G. B.

S. Sriram, G. B. Brandt, E. P. Supertzi, “Heterodyne receiver on silicon: an exercise in integration,” in Integrated Optics II, D. G. Hall, ed., Proc. Soc. Photo-Opt. Instrum. Eng.321, 15–22 (1982).

Bussjager, R.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Chen, F. T.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Cook, P.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Cox, J. A.

J. A. Cox, F. P. Shvartsman, “Image quality assessment of diffractive elements replicated in SURPHEX™,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DThB4, pp. 346–349.

Craighead, H. G.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Dammann, H.

H. Dammann, E. Klotz, “Coherent-optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Downs, M. M.

J. Jahns, M. M. Downs, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).

Graf, U. U.

Haas, F.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Honey, D. A.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Jahns, J.

J. Jahns, M. M. Downs, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).

Joffe, D. T.

Kim, E. J.

Klotz, E.

H. Dammann, E. Klotz, “Coherent-optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Lacy, J. H.

Ling, H.

McMullin, J. N.

R. Narendra, J. N. McMullin, “Single-mode, phosphorous-doped silica waveguides in silicon V-grooves,” IEEE Photon. Technol. Lett. 5, 43–46 (1993).
[CrossRef]

Moore, J. T.

Narendra, R.

R. Narendra, J. N. McMullin, “Single-mode, phosphorous-doped silica waveguides in silicon V-grooves,” IEEE Photon. Technol. Lett. 5, 43–46 (1993).
[CrossRef]

Rebeiz, G.

Shank, S. M.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Shvartsman, F. P.

J. A. Cox, F. P. Shvartsman, “Image quality assessment of diffractive elements replicated in SURPHEX™,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DThB4, pp. 346–349.

Skvarla, M.

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

Sriram, S.

S. Sriram, E. P. Supertzi, “Novel V-groove structures on silicon,” Appl. Opt. 24, 1784–1787 (1985).
[CrossRef] [PubMed]

S. Sriram, G. B. Brandt, E. P. Supertzi, “Heterodyne receiver on silicon: an exercise in integration,” in Integrated Optics II, D. G. Hall, ed., Proc. Soc. Photo-Opt. Instrum. Eng.321, 15–22 (1982).

Streibl, N.

J. Jahns, M. M. Downs, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).

Supertzi, E. P.

S. Sriram, E. P. Supertzi, “Novel V-groove structures on silicon,” Appl. Opt. 24, 1784–1787 (1985).
[CrossRef] [PubMed]

S. Sriram, G. B. Brandt, E. P. Supertzi, “Heterodyne receiver on silicon: an exercise in integration,” in Integrated Optics II, D. G. Hall, ed., Proc. Soc. Photo-Opt. Instrum. Eng.321, 15–22 (1982).

Tsang, W.

W. Tsang, S. Wang, “Thin-film beam splitter and reflector for optical guided waves,” Appl. Phys. Lett. 27, 588–590 (1975).
[CrossRef]

Walker, S. J.

J. Jahns, M. M. Downs, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).

Wang, S.

W. Tsang, S. Wang, “Thin-film beam splitter and reflector for optical guided waves,” Appl. Phys. Lett. 27, 588–590 (1975).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

W. Tsang, S. Wang, “Thin-film beam splitter and reflector for optical guided waves,” Appl. Phys. Lett. 27, 588–590 (1975).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Narendra, J. N. McMullin, “Single-mode, phosphorous-doped silica waveguides in silicon V-grooves,” IEEE Photon. Technol. Lett. 5, 43–46 (1993).
[CrossRef]

IEEE Trans. Electron Devices (1)

K. E. Bean, “Anisotropic etching of silicon,” IEEE Trans. Electron Devices ED-25, 1185–1193 (1978).
[CrossRef]

Opt. Acta (1)

H. Dammann, E. Klotz, “Coherent-optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Eng. (1)

J. Jahns, M. M. Downs, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).

Other (3)

S. M. Shank, M. Skvarla, F. T. Chen, H. G. Craighead, P. Cook, R. Bussjager, F. Haas, D. A. Honey, “Fabrication of multi-level phase gratings using focused ion beam milling and electron beam lithography,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DWD3, pp. 302–305.

S. Sriram, G. B. Brandt, E. P. Supertzi, “Heterodyne receiver on silicon: an exercise in integration,” in Integrated Optics II, D. G. Hall, ed., Proc. Soc. Photo-Opt. Instrum. Eng.321, 15–22 (1982).

J. A. Cox, F. P. Shvartsman, “Image quality assessment of diffractive elements replicated in SURPHEX™,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper DThB4, pp. 346–349.

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Figures (6)

Fig. 1
Fig. 1

Structure of a grating with v-grooves etched in silicon, index n 0, and covered with a material of index n 1.

Fig. 2
Fig. 2

Standard deviation with respect to the mean of the m = −1, 0, and 1 diffraction orders as a function of grating half-width for five values of the grating period. Length units are micrometers.

Fig. 3
Fig. 3

Diffraction efficiencies for the same cases as Fig. 2.

Fig. 4
Fig. 4

Optimized grating efficiencies as functions of overlayer thickness for several values of overlayer index of refraction.

Fig. 5
Fig. 5

Grating profile for generation of (a) 1:3, (b) 1:5, (c) 1:7 beam splitters.

Fig. 6
Fig. 6

Effect of fabrication errors on the efficiency and the uniformity of replicated gratings.

Tables (1)

Tables Icon

Table 1 Optimum Design Parameters for 1:3, 1:5, and 1:7 Gratings Replicated from Silicon Masters

Equations (8)

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d 0 ( x ) = [ D s ( x 1 | x | ) x 1 | x | D | x | < x 1 ] ,
d 1 ( x ) = [ t x 1 | x | T / 2 t + s ( x 1 | x | ) x 2 | x | < x 1 t 3 0 | x | < x 2 ] ,
d 2 ( x ) = [ s ( x 2 | x | ) | x | < x 2 0 x 2 | x | < L / 2 ] ,
T ( x ) = exp { 2 π j λ [ n 0 d 0 ( x ) + n 1 d 1 ( x ) + n 2 d 2 ( x ) ] }
C m = 1 L L / 2 L / 2 T ( x ) exp ( 2 π j m x L ) d x .
| C m | 2 = 1 ( 2 M + 1 )
σ = 1 μ [ 1 2 M m = M M ( | C m | 2 μ ) 2 ] 1 / 2 ,
η = m = M M | C m | 2 ,

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