Abstract

The performance limitations of linear chirped grating lenses on single-mode planar optical waveguides due to positional error and to the variation of line-to-space width ratios of the grating grooves are discussed.

© 1985 Optical Society of America

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References

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  1. S.K. Yao, D. E. Thompson, “Chirp Grating Lenses for Guided Wave Optics” Appl. Phys. Lett. 33, 635 (1978).
    [CrossRef]
  2. S. Forouhar, R.-X. Lu, W. S. C. Chang, R. L. Davis, S.-K. Yao, “Chirped Grating Lenses on Nb2O5 Transition Waveguides,” Appl. Opt. 22, 3128 (1983).
    [CrossRef] [PubMed]
  3. C. Warren, S. Forouhar, W. S. C. Chang, S. K. Yao, “Double Ion Exchanged Chirped Grating Lens in Lithium Niobate Waveguide,” Appl. Phys. Lett. 43, 424 (1983).
    [CrossRef]
  4. S. Forouhar, W. S. C. Chang, “Performances and Limitations on Grating Lenses on Ti-indiffused LiNBO3 Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-2, 503 (1984).
    [CrossRef]
  5. Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).
  6. J-M. P. Delavaux, W. S. C. Chang, “Fundamental Limitations in the Performance of Chirped Grating Lenses on Planar Optical Waveguides,” to be published.
  7. G. Dahlquist, A. Bjorck, Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J.1974).
  8. J. Melngailis, H. I. Smith, N. Efremow, “Instrumentation of Conformable Photomask Lithography,” IEEE Trans. Electron Devices ED-22, 496 (1975).
    [CrossRef]
  9. B. Zhang, J-M. P. Delavaux, W. S. C. Chang, “Ion Beam Etching of BaO Glass and SiO2 Thin Films and Their Application to Optical Waveguides,” Appl. Opt. 25, 777 (1984).
    [CrossRef]
  10. W. Streifer, D. R. Safers, R. D. Burnham, “Analysis of Grating-Coupled Radiation in GaAs:GaAlAs Lasers and Waveguides, IEEE,” J. Quantum Electron. QE-12, N7 (1976).
  11. J-M. P. Delavaux, W. S. C. Chang, “Design and Fabrication of Efficient Diffraction Transmission Gratings on Step-Index Optical Waveguides,” to be published.

1984 (2)

S. Forouhar, W. S. C. Chang, “Performances and Limitations on Grating Lenses on Ti-indiffused LiNBO3 Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-2, 503 (1984).
[CrossRef]

B. Zhang, J-M. P. Delavaux, W. S. C. Chang, “Ion Beam Etching of BaO Glass and SiO2 Thin Films and Their Application to Optical Waveguides,” Appl. Opt. 25, 777 (1984).
[CrossRef]

1983 (2)

S. Forouhar, R.-X. Lu, W. S. C. Chang, R. L. Davis, S.-K. Yao, “Chirped Grating Lenses on Nb2O5 Transition Waveguides,” Appl. Opt. 22, 3128 (1983).
[CrossRef] [PubMed]

C. Warren, S. Forouhar, W. S. C. Chang, S. K. Yao, “Double Ion Exchanged Chirped Grating Lens in Lithium Niobate Waveguide,” Appl. Phys. Lett. 43, 424 (1983).
[CrossRef]

1981 (1)

Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).

1978 (1)

S.K. Yao, D. E. Thompson, “Chirp Grating Lenses for Guided Wave Optics” Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

1976 (1)

W. Streifer, D. R. Safers, R. D. Burnham, “Analysis of Grating-Coupled Radiation in GaAs:GaAlAs Lasers and Waveguides, IEEE,” J. Quantum Electron. QE-12, N7 (1976).

1975 (1)

J. Melngailis, H. I. Smith, N. Efremow, “Instrumentation of Conformable Photomask Lithography,” IEEE Trans. Electron Devices ED-22, 496 (1975).
[CrossRef]

Bjorck, A.

G. Dahlquist, A. Bjorck, Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J.1974).

Burnham, R. D.

W. Streifer, D. R. Safers, R. D. Burnham, “Analysis of Grating-Coupled Radiation in GaAs:GaAlAs Lasers and Waveguides, IEEE,” J. Quantum Electron. QE-12, N7 (1976).

Chang, W. S. C.

B. Zhang, J-M. P. Delavaux, W. S. C. Chang, “Ion Beam Etching of BaO Glass and SiO2 Thin Films and Their Application to Optical Waveguides,” Appl. Opt. 25, 777 (1984).
[CrossRef]

S. Forouhar, W. S. C. Chang, “Performances and Limitations on Grating Lenses on Ti-indiffused LiNBO3 Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-2, 503 (1984).
[CrossRef]

C. Warren, S. Forouhar, W. S. C. Chang, S. K. Yao, “Double Ion Exchanged Chirped Grating Lens in Lithium Niobate Waveguide,” Appl. Phys. Lett. 43, 424 (1983).
[CrossRef]

S. Forouhar, R.-X. Lu, W. S. C. Chang, R. L. Davis, S.-K. Yao, “Chirped Grating Lenses on Nb2O5 Transition Waveguides,” Appl. Opt. 22, 3128 (1983).
[CrossRef] [PubMed]

Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).

J-M. P. Delavaux, W. S. C. Chang, “Design and Fabrication of Efficient Diffraction Transmission Gratings on Step-Index Optical Waveguides,” to be published.

J-M. P. Delavaux, W. S. C. Chang, “Fundamental Limitations in the Performance of Chirped Grating Lenses on Planar Optical Waveguides,” to be published.

Dahlquist, G.

G. Dahlquist, A. Bjorck, Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J.1974).

Davis, R. L.

Delavaux, J-M. P.

B. Zhang, J-M. P. Delavaux, W. S. C. Chang, “Ion Beam Etching of BaO Glass and SiO2 Thin Films and Their Application to Optical Waveguides,” Appl. Opt. 25, 777 (1984).
[CrossRef]

Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).

J-M. P. Delavaux, W. S. C. Chang, “Fundamental Limitations in the Performance of Chirped Grating Lenses on Planar Optical Waveguides,” to be published.

J-M. P. Delavaux, W. S. C. Chang, “Design and Fabrication of Efficient Diffraction Transmission Gratings on Step-Index Optical Waveguides,” to be published.

Efremow, N.

J. Melngailis, H. I. Smith, N. Efremow, “Instrumentation of Conformable Photomask Lithography,” IEEE Trans. Electron Devices ED-22, 496 (1975).
[CrossRef]

Forouhar, S.

S. Forouhar, W. S. C. Chang, “Performances and Limitations on Grating Lenses on Ti-indiffused LiNBO3 Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-2, 503 (1984).
[CrossRef]

C. Warren, S. Forouhar, W. S. C. Chang, S. K. Yao, “Double Ion Exchanged Chirped Grating Lens in Lithium Niobate Waveguide,” Appl. Phys. Lett. 43, 424 (1983).
[CrossRef]

S. Forouhar, R.-X. Lu, W. S. C. Chang, R. L. Davis, S.-K. Yao, “Chirped Grating Lenses on Nb2O5 Transition Waveguides,” Appl. Opt. 22, 3128 (1983).
[CrossRef] [PubMed]

Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).

Lin, Z.-Q.

Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).

Lu, R.-X.

Melngailis, J.

J. Melngailis, H. I. Smith, N. Efremow, “Instrumentation of Conformable Photomask Lithography,” IEEE Trans. Electron Devices ED-22, 496 (1975).
[CrossRef]

Safers, D. R.

W. Streifer, D. R. Safers, R. D. Burnham, “Analysis of Grating-Coupled Radiation in GaAs:GaAlAs Lasers and Waveguides, IEEE,” J. Quantum Electron. QE-12, N7 (1976).

Smith, H. I.

J. Melngailis, H. I. Smith, N. Efremow, “Instrumentation of Conformable Photomask Lithography,” IEEE Trans. Electron Devices ED-22, 496 (1975).
[CrossRef]

Streifer, W.

W. Streifer, D. R. Safers, R. D. Burnham, “Analysis of Grating-Coupled Radiation in GaAs:GaAlAs Lasers and Waveguides, IEEE,” J. Quantum Electron. QE-12, N7 (1976).

Thompson, D. E.

S.K. Yao, D. E. Thompson, “Chirp Grating Lenses for Guided Wave Optics” Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

Warren, C.

C. Warren, S. Forouhar, W. S. C. Chang, S. K. Yao, “Double Ion Exchanged Chirped Grating Lens in Lithium Niobate Waveguide,” Appl. Phys. Lett. 43, 424 (1983).
[CrossRef]

Yao, S. K.

C. Warren, S. Forouhar, W. S. C. Chang, S. K. Yao, “Double Ion Exchanged Chirped Grating Lens in Lithium Niobate Waveguide,” Appl. Phys. Lett. 43, 424 (1983).
[CrossRef]

Yao, S.K.

S.K. Yao, D. E. Thompson, “Chirp Grating Lenses for Guided Wave Optics” Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

Yao, S.-K.

Zhang, B.

B. Zhang, J-M. P. Delavaux, W. S. C. Chang, “Ion Beam Etching of BaO Glass and SiO2 Thin Films and Their Application to Optical Waveguides,” Appl. Opt. 25, 777 (1984).
[CrossRef]

Zhou, S.-T.

Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).

Appl. Opt. (2)

S. Forouhar, R.-X. Lu, W. S. C. Chang, R. L. Davis, S.-K. Yao, “Chirped Grating Lenses on Nb2O5 Transition Waveguides,” Appl. Opt. 22, 3128 (1983).
[CrossRef] [PubMed]

B. Zhang, J-M. P. Delavaux, W. S. C. Chang, “Ion Beam Etching of BaO Glass and SiO2 Thin Films and Their Application to Optical Waveguides,” Appl. Opt. 25, 777 (1984).
[CrossRef]

Appl. Phys. Lett. (2)

S.K. Yao, D. E. Thompson, “Chirp Grating Lenses for Guided Wave Optics” Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

C. Warren, S. Forouhar, W. S. C. Chang, S. K. Yao, “Double Ion Exchanged Chirped Grating Lens in Lithium Niobate Waveguide,” Appl. Phys. Lett. 43, 424 (1983).
[CrossRef]

IEEE Trans. Electron Devices (1)

J. Melngailis, H. I. Smith, N. Efremow, “Instrumentation of Conformable Photomask Lithography,” IEEE Trans. Electron Devices ED-22, 496 (1975).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

Z.-Q. Lin, S.-T. Zhou, W. S. C. Chang, S. Forouhar, J-M. P. Delavaux, “A Generalized Two-Dimensional Coupled Mode Analysis in Open Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 881 (1981).

IEEE/OSA J. Lightwave Technol. (1)

S. Forouhar, W. S. C. Chang, “Performances and Limitations on Grating Lenses on Ti-indiffused LiNBO3 Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-2, 503 (1984).
[CrossRef]

J. Quantum Electron. (1)

W. Streifer, D. R. Safers, R. D. Burnham, “Analysis of Grating-Coupled Radiation in GaAs:GaAlAs Lasers and Waveguides, IEEE,” J. Quantum Electron. QE-12, N7 (1976).

Other (3)

J-M. P. Delavaux, W. S. C. Chang, “Design and Fabrication of Efficient Diffraction Transmission Gratings on Step-Index Optical Waveguides,” to be published.

J-M. P. Delavaux, W. S. C. Chang, “Fundamental Limitations in the Performance of Chirped Grating Lenses on Planar Optical Waveguides,” to be published.

G. Dahlquist, A. Bjorck, Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J.1974).

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Figures (4)

Fig. 1
Fig. 1

Linear chirped grating waveguide lens.

Fig. 2
Fig. 2

Microphotographs of high-resolution flexible masks of a f/20 linear chirped grating lens (f/20, f = 20 mm, d = 100 μm, Λmax = 7.76 μm, and Λmin = 4 μm): (a) generated in a 1-mm field of view (i.e., positional error ±625 Å); (b) generated in a 4-mm field of view (i.e., positional error ±2500 Å).

Fig. 3
Fig. 3

Photomicrographs of (a) high resolution flexible chromium masks of a f/20 linear chirped grating lens (W/Λ = ⅝) and (b) its etched replication in BaO glass waveguide.

Fig. 4
Fig. 4

Diffraction efficiency η as a function of the linewidth change of a f/20 linear chirped grating lens for the (a) TE mode and (b) TM mode. Dash, dot, and solid lines are the theoretical prediction obtained from the GCMT when Kc is given by Eq. (7).

Tables (2)

Tables Icon

Table I Polynomial Expression of the Phase Γ of a F/20 Linear Chirped Grating Lens

Tables Icon

Table II Measured Performance of a F/20 Linear Chirped Grating Lenses

Equations (9)

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Γ k 0 n eff = ϕ i ϕ d .
Γ ( x , y ) = α y + β y 2 ,
α = 4 λ 0 n eff sin θ B ,
β = α C ,
Γ ( x , y ) = α y + β y 2 = m ( m = 1 , 2 , 3 , ) .
Γ ( x , y ) = m ,
Γ = p = 1 n a p y P .
j = 1 m [ ( a 1 y j + a 2 y j 2 + a 3 y j 3 + + a n y j n ) Γ ( y j ) ] 2 .
K c = Δ n eff λ 0 / 2 sin ( W Λ ) ,

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