Abstract

Off-axis grating lenses and astigmatic grating lenses, designed for semiconductor laser wavelengths, have been fabricated by an electron-beam (EB) exposure system. High N.A. off-axis grating lenses with near-diffraction-limited operation were obtained. Grating lenses with a complex function, such as astigmatic lenses, are also available by EB lithography.

© 1985 Optical Society of America

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References

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  1. H. Nishihara, S. Inohara, T. Suhara, J. Koyama, “Holocoupler: A Novel Coupler for Optical Circuits,” IEEE J. Quantum Electron. QE-14, 794 (1975).
    [CrossRef]
  2. O. D. D. Soares, “Holographic Coupler for Fiber Optics,” Opt. Eng. 20, 740 (1981).
    [CrossRef]
  3. C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).
  4. D. C. Shaver, D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16, 1626 (1981).
    [CrossRef]
  5. J. R. Fienup, C. D. Leonard, “Holographic Optics for a Matched-Filter Optical Processor,” Appl. Opt. 18, 631 (1979).
    [CrossRef] [PubMed]
  6. D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
    [CrossRef]
  7. G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (JSAP, Kobe, 1983), paper F5.
  8. G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” Appl. Opt. 23, 1749 (1984).
    [CrossRef] [PubMed]
  9. T. Fujita, H. Nishihara, J. Koyama, “Fabrication of Micro Lenses Using Electron-Beam Lithography,” Opt. Lett. 6, 613 (1981).
    [CrossRef] [PubMed]
  10. T. Fujita, H. Nishihara, J. Koyama, “Blazed Gratings and Fresnel Lenses Fabricated by Electron-Beam Lithography,” Opt. Lett. 7, 578 (1982).
    [CrossRef] [PubMed]
  11. G. Hatakoshi, M. Yoshimi, K. Goto, “Off-Axis Grating Lenses Fabricated by EB Lithography,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.
  12. G. Hatakoshi, K. Goto, “Grating Lenses for Optical Components,” in Technical Digest, Fifth Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, D.C., 1984), paper ThE-E1.
  13. R. Magnusson, T. K. Gaylord, “Diffraction Regimes of Transmission Gratings,” J. Opt. Soc. Am. 68, 806 (1978).
    [CrossRef]
  14. K. Knop, “Rigorous Diffraction Theory for Transmission Phase Gratings with Deep Rectangular Grooves,” J. Opt. Soc. Am. 68, 1206 (1978).
    [CrossRef]
  15. M. G. Maharam, T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811 (1981).
    [CrossRef]

1984 (1)

1982 (1)

1981 (6)

O. D. D. Soares, “Holographic Coupler for Fiber Optics,” Opt. Eng. 20, 740 (1981).
[CrossRef]

C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).

D. C. Shaver, D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16, 1626 (1981).
[CrossRef]

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

T. Fujita, H. Nishihara, J. Koyama, “Fabrication of Micro Lenses Using Electron-Beam Lithography,” Opt. Lett. 6, 613 (1981).
[CrossRef] [PubMed]

M. G. Maharam, T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811 (1981).
[CrossRef]

1979 (1)

1978 (2)

1975 (1)

H. Nishihara, S. Inohara, T. Suhara, J. Koyama, “Holocoupler: A Novel Coupler for Optical Circuits,” IEEE J. Quantum Electron. QE-14, 794 (1975).
[CrossRef]

Fienup, J. R.

Flanders, D. C.

D. C. Shaver, D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16, 1626 (1981).
[CrossRef]

Fujima, H.

G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” Appl. Opt. 23, 1749 (1984).
[CrossRef] [PubMed]

G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (JSAP, Kobe, 1983), paper F5.

Fujita, T.

Gaylord, T. K.

Goto, K.

G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” Appl. Opt. 23, 1749 (1984).
[CrossRef] [PubMed]

G. Hatakoshi, K. Goto, “Grating Lenses for Optical Components,” in Technical Digest, Fifth Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, D.C., 1984), paper ThE-E1.

G. Hatakoshi, M. Yoshimi, K. Goto, “Off-Axis Grating Lenses Fabricated by EB Lithography,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (JSAP, Kobe, 1983), paper F5.

Hasegawa, K.

C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).

Hatakoshi, G.

G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” Appl. Opt. 23, 1749 (1984).
[CrossRef] [PubMed]

G. Hatakoshi, K. Goto, “Grating Lenses for Optical Components,” in Technical Digest, Fifth Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, D.C., 1984), paper ThE-E1.

G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (JSAP, Kobe, 1983), paper F5.

G. Hatakoshi, M. Yoshimi, K. Goto, “Off-Axis Grating Lenses Fabricated by EB Lithography,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

Heitmann, D.

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

Inohara, S.

H. Nishihara, S. Inohara, T. Suhara, J. Koyama, “Holocoupler: A Novel Coupler for Optical Circuits,” IEEE J. Quantum Electron. QE-14, 794 (1975).
[CrossRef]

Knop, K.

Kojima, C.

C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).

Koyama, J.

Leonard, C. D.

Magnusson, R.

Maharam, M. G.

Miyahara, K.

C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).

Nishihara, H.

Ooki, H.

C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).

Ortiz, C.

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

Otobe, T.

C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).

Shaver, D. C.

D. C. Shaver, D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16, 1626 (1981).
[CrossRef]

Soares, O. D. D.

O. D. D. Soares, “Holographic Coupler for Fiber Optics,” Opt. Eng. 20, 740 (1981).
[CrossRef]

Suhara, T.

H. Nishihara, S. Inohara, T. Suhara, J. Koyama, “Holocoupler: A Novel Coupler for Optical Circuits,” IEEE J. Quantum Electron. QE-14, 794 (1975).
[CrossRef]

Yoshimi, M.

G. Hatakoshi, M. Yoshimi, K. Goto, “Off-Axis Grating Lenses Fabricated by EB Lithography,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

H. Nishihara, S. Inohara, T. Suhara, J. Koyama, “Holocoupler: A Novel Coupler for Optical Circuits,” IEEE J. Quantum Electron. QE-14, 794 (1975).
[CrossRef]

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Vac. Sci. Technol. (1)

D. C. Shaver, D. C. Flanders, “X-Ray Zone Plates Fabricated Using Electron-Beam and X-Ray Lithography,” J. Vac. Sci. Technol. 16, 1626 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (1)

C. Kojima, K. Miyahara, K. Hasegawa, T. Otobe, H. Ooki, “In-Line Holographic Lenses of High Numerical Aperture,” Jpn. J. Appl. Phys. 20, Suppl. 20-1, 199 (1981).

Opt. Eng. (1)

O. D. D. Soares, “Holographic Coupler for Fiber Optics,” Opt. Eng. 20, 740 (1981).
[CrossRef]

Opt. Lett. (2)

Other (3)

G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (JSAP, Kobe, 1983), paper F5.

G. Hatakoshi, M. Yoshimi, K. Goto, “Off-Axis Grating Lenses Fabricated by EB Lithography,” in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

G. Hatakoshi, K. Goto, “Grating Lenses for Optical Components,” in Technical Digest, Fifth Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, D.C., 1984), paper ThE-E1.

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Figures (10)

Fig. 1
Fig. 1

Light-wave diffraction in an (a) in-line grating lens and (b) off-axis grating lens.

Fig. 2
Fig. 2

Off-axis grating lens configuration.

Fig. 3
Fig. 3

(a) Microscopic and (b) SEM photographs of the off-axis grating lens fabricated by EB lithography.

Fig. 4
Fig. 4

Intensity profiles for the diffracted light wave near the focal plane.

Fig. 5
Fig. 5

Comparison between measured intensity profiles and theoretical curves.

Fig. 6
Fig. 6

Measured spot diameter compared with theoretical value.

Fig. 7
Fig. 7

Astigmatic grating lens configuration.

Fig. 8
Fig. 8

Microscopic photograph of astigmatic grating lens.

Fig. 9
Fig. 9

Variation in beam pattern for diffracted light observed at the ξη j plane.

Fig. 10
Fig. 10

Quadrant optical sensor output as a function of light source displacement.

Equations (15)

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Ω = 2 π λ ( l + x sin θ ) ,
l = i = 0 2 n i 2 d i n i 2 sin 2 ψ ,
x 2 + y 2 = sin ψ i = 0 2 d i n i 2 sin 2 ψ .
Ω ( X , Y ) = 2 π λ { X 2 + f X 2 + Y 2 + f Y 2 } + Ω 1 ( X , Y ) ,
h = λ / [ 2 ( n 1 ) ] ,
l = sec ψ [ d 0 + n 1 2 d 1 / ( n 1 2 1 ) sec 2 ψ + 1 ] ,
x 2 + y 2 = tan ψ [ d 0 + d 1 / ( n 1 2 1 ) tan 2 ψ + n 1 2 ] .
sec ψ = 1 2 l d 0 + a + A 2 b a + A / 2 + 2 a A 2 ,
A = β + β 2 α 3 3 + β β 2 α 3 3 ,
α = α 1 2 ,
β = a 1 3 + b 1 2 ,
a 1 = 1 6 [ ( l d 0 ) 2 + 1 n 1 4 ( d 1 / d 0 ) 2 n 1 2 1 ] ,
b 1 = 1 2 · l d 0 · d 1 d 0 · n 1 2 n 1 2 1 ,
a = 1 6 [ 1 2 ( l d 0 ) 2 1 n 1 4 ( d 1 / d 0 2 ) n 1 2 1 ] ,
b = 1 4 l d 0 · 1 + n 1 4 ( d 1 / d 0 ) 2 n 1 2 1 .

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