Abstract

A design method is presented that enables the realization of a novel type of incoupling waveguide hologram (IWGH) that simultaneously focuses the incoupled light to any desired positions in the waveguide. IWGH’s, or grating couplers, are gratinglike structures etched into the waveguide surface. They couple the light incident from free space into the waveguide. The grating lines can be dislocated with respect to each other to provide phase modulation of the incoupled light. By use of this phase modulation, novel beam splitting and focusing functions can be built into the IWGH’s. The new design algorithm is based on a model that assumes a simple relation between the incident light wave and the locally excited guided wave. This model is used to obtain an efficient formulation of the optimization problem. Four different IWGH’s were designed and fabricated in InP for light at 1550-nm wavelength. Experiments confirm that these IWGH’s are capable of incoupling the incident wave and simultaneously splitting and focusing the guided wave into multiple positions in the waveguide at different distances from the IWGH.

© 1999 Optical Society of America

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References

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  1. S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988).
    [CrossRef]
  2. R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33, 623–624 (1997).
    [CrossRef]
  3. M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
    [CrossRef]
  4. M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
    [CrossRef]
  5. J. Bengtsson, “Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method,” Appl. Opt. 36, 8435–8444 (1997).
    [CrossRef]
  6. C. F. Carlström, G. Landgren, S. Anand, “Low energy ion beam etching of InP using methane chemistry,” J. Vac. Sci. Technol. B 16, 1018–1023 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. D. Pascal, R. Orobtchouk, A. Layadi, A. Koster, S. Laval, “Optimized coupling of a Gaussian beam into an optical waveguide with a grating coupler: comparison of experimental and theoretical results,” Appl. Opt. 36, 2443–2447 (1997).
    [CrossRef] [PubMed]
  10. T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
    [CrossRef]

1998 (2)

C. F. Carlström, G. Landgren, S. Anand, “Low energy ion beam etching of InP using methane chemistry,” J. Vac. Sci. Technol. B 16, 1018–1023 (1998).
[CrossRef]

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

1997 (4)

J. Bengtsson, “Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method,” Appl. Opt. 36, 8435–8444 (1997).
[CrossRef]

D. Pascal, R. Orobtchouk, A. Layadi, A. Koster, S. Laval, “Optimized coupling of a Gaussian beam into an optical waveguide with a grating coupler: comparison of experimental and theoretical results,” Appl. Opt. 36, 2443–2447 (1997).
[CrossRef] [PubMed]

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33, 623–624 (1997).
[CrossRef]

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

1996 (1)

M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
[CrossRef]

1993 (1)

1988 (1)

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988).
[CrossRef]

1977 (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Anand, S.

C. F. Carlström, G. Landgren, S. Anand, “Low energy ion beam etching of InP using methane chemistry,” J. Vac. Sci. Technol. B 16, 1018–1023 (1998).
[CrossRef]

Bengtsson, J.

J. Bengtsson, “Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method,” Appl. Opt. 36, 8435–8444 (1997).
[CrossRef]

M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
[CrossRef]

Bräuer, A.

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33, 623–624 (1997).
[CrossRef]

Carlström, C. F.

C. F. Carlström, G. Landgren, S. Anand, “Low energy ion beam etching of InP using methane chemistry,” J. Vac. Sci. Technol. B 16, 1018–1023 (1998).
[CrossRef]

Gallagher, N. C.

Gremaux, D. A.

Hagberg, M.

M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
[CrossRef]

Kley, E.-B.

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33, 623–624 (1997).
[CrossRef]

Koster, A.

Kristjansson, S.

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

Landgren, G.

C. F. Carlström, G. Landgren, S. Anand, “Low energy ion beam etching of InP using methane chemistry,” J. Vac. Sci. Technol. B 16, 1018–1023 (1998).
[CrossRef]

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

Larsson, A.

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
[CrossRef]

Laval, S.

Layadi, A.

Li, M.

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
[CrossRef]

Liang, T.

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

Modh, P.

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

Nishihara, H.

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988).
[CrossRef]

Orobtchouk, R.

Pascal, D.

Peng, S. T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Schnabel, B.

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33, 623–624 (1997).
[CrossRef]

Silfvenius, C.

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

Suhara, T.

M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988).
[CrossRef]

Sunagawa, H.

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988).
[CrossRef]

Tamir, T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Ura, S.

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988).
[CrossRef]

Waldhäusl, R.

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33, 623–624 (1997).
[CrossRef]

Ziolkowski, R. W.

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Electron. Lett. (1)

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33, 623–624 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Li, J. Bengtsson, M. Hagberg, A. Larsson, T. Suhara, “Off-plane computer-generated waveguide hologram,” IEEE J. Sel. Top. Quantum Electron. 2, 226–235 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. Li, P. Modh, S. Kristjansson, A. Larsson, C. Silfvenius, G. Landgren, “Experimental and theoretical study on the wavelength response of a computer-generated waveguide hologram,” IEEE Photon. Technol. Lett. 9, 1376–1378 (1997).
[CrossRef]

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

J. Lightwave Technol. (1)

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988).
[CrossRef]

J. Vac. Sci. Technol. B (1)

C. F. Carlström, G. Landgren, S. Anand, “Low energy ion beam etching of InP using methane chemistry,” J. Vac. Sci. Technol. B 16, 1018–1023 (1998).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

IWGH focusing into three positions at the same distance from the IWGH. The geometry and indicated E-field polarization are those we used in the experiments.

Fig. 2
Fig. 2

Portion of the IWGH structure.

Fig. 3
Fig. 3

Excitation of waveguide emitters.

Fig. 4
Fig. 4

Obtained phase of the emitted wave in a cell with (a) zero dislocation and (b) dislocation Δ.

Fig. 5
Fig. 5

Top view of the geometry that was used to obtain the field from cell k in focus position m.

Fig. 6
Fig. 6

Complex number plane construction for determination of the optimal dislocation change of the grating lines in cell k.

Fig. 7
Fig. 7

Flow chart of the design algorithm.

Fig. 8
Fig. 8

Intensity in the focus positions and uniformity error as functions of the number of iterations in the design algorithm.

Fig. 9
Fig. 9

Numerical simulation of the intensity distribution in the waveguide, including an intensity profile at 4 mm from the IWGH.

Fig. 10
Fig. 10

CCD camera image of illuminated IWGH and cleaved edge (seen from an oblique angle to display both). The inset shows an enlarged and attenuated image of the edge.

Fig. 11
Fig. 11

Intensity profile along the cleaved edge, measured (solid curve) and simulated (dashed curve), that we obtained by convolving the calculated intensity profile in Fig. 9 with an aperture function for the pinhole.

Fig. 12
Fig. 12

Intensity scan along the cleaved edge for the IWGH in Subsection 3.B. The inset shows a CCD camera image of the edge.

Fig. 13
Fig. 13

Intensity scan along the cleaved edge for the IWGH in Subsection 3.C.

Fig. 14
Fig. 14

Numerical simulation of the intensity distribution in the waveguide in Subsection 3.D, showing the calculated intensity profiles at 2 and 4 mm from the IWGH.

Fig. 15
Fig. 15

Intensity profiles along the cleaved edge, measured (solid curve) and simulated (dashed curve), that we obtained by convolving the calculated intensity profiles in Fig. 14 with the pinhole aperture function at (a) 2 mm and (b) 4 mm from the IWGH.

Equations (18)

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φξ, η=φincξ, η-2πΛ ξ,
φξ, η=φincξ, η-2πΛξ-Δ.
Eu, v=Aincξ, ηrexp-αrg2expikeffr+φξ, η.
Ek,mtot=AincRexp-αRg2 cell kexpikeffr+φdξdη,
r=u-xc+ξ2+v-yc+η21/2R+xc-uξ+yc-vηR,
φincξ, η=kxξ+kyη+φC,
Ek,mtot=Ek,m expi2πΛ Δk,
Ek,m=AincRexp-αRg2expikeffR+φC×2k1sink1s22k2sink2t2,
k1=keffxc-uR+kx-2πΛ, k2=keffyc-vR+ky,
δAm=Ak,m cosβm-θk,m+δθk-Ak,m cosβm-θk,m,
m δAm=m Ak,m cosβm-θk,m+δθk-m Ak,m cosβm-θk,m=C1 cos δθk+C2 sin δθk-C1,
C1=m Ak,m cosβm-θk,m, C2=m Ak,m sinβm-θk,m.
m δAm=C3 cosδθk-γ-C1,
C3=sgnC1C12+C22,  γ=arctanC2/C1.
δθkopt=2πΛ δΔkopt=arctanC2/C1; C1>0π+arctanC2/C1; C1<0.
Em=k Ek,mtot=k Ek,m expi2πΛ Δk
C1=m WmAk,m cosβm-θk,m, C2=m WmAk,m sinβm-θk,m.
Wmnew=WmoldImdesiredImcalculatedq,

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