Abstract

We propose a method for miniaturization of filters based on curved waveguide Bragg gratings, so that long structures can be packed into a small area on a chip. This eliminates the stitching errors introduced in the fabrication process, which compromise the performance of long Bragg gratings. Our approach relies on cascading curved waveguide Bragg gratings with the same radius of curvature. An analytical model for the analysis of these devices was developed, and a filter based on this model was designed and fabricated in a silicon on insulator platform. The filter had a total length of 920μm, occupied an area of 190μm×114μm, and exhibited a stop band of 1.7nm at 1.55μm and an extinction ratio larger than 23dB.

© 2010 Optical Society of America

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References

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  1. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 3, pp. 65–111.
  2. A. Yariv, Optical Electronics, 3rd ed. (Holt McDougal, 1985), Chap. 13, pp. 402–421.
  3. H.-C. Kim, K. Ikeda, and Y. Fainman, J. Lightwave Technol. 25, 1147 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. D. T. H. Tan, K. Ikeda, and Y. Fainman, Opt. Lett. 34, 1357 (2009).
    [CrossRef] [PubMed]
  7. D. T. H. Tan, K. Ikeda, and Y. Fainman, Appl. Phys. Lett. 95, 141109 (2009).
    [CrossRef]
  8. V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972), Chap. 9, pp. 379–386.
  13. D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
    [CrossRef]

2009

D. T. H. Tan, K. Ikeda, and Y. Fainman, Opt. Lett. 34, 1357 (2009).
[CrossRef] [PubMed]

D. T. H. Tan, K. Ikeda, and Y. Fainman, Appl. Phys. Lett. 95, 141109 (2009).
[CrossRef]

2008

2007

2005

1995

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 3, pp. 65–111.

1987

1985

A. Yariv, Optical Electronics, 3rd ed. (Holt McDougal, 1985), Chap. 13, pp. 402–421.

1974

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

1972

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972), Chap. 9, pp. 379–386.

1961

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961), Chap. 8, p. 381–400.

Coldren, L. A.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 3, pp. 65–111.

Corzine, S. W.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 3, pp. 65–111.

Damask, J. N.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

Fainman, Y.

Ferrera, J.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

Flanders, D. C.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961), Chap. 8, p. 381–400.

Haus, H. A.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

Helmfrid, S.

Ikeda, K.

Kim, H. C.

Kim, H.-C.

Kogelnik, H.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972), Chap. 9, pp. 379–386.

Murphy, T. E.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

Petermann, I.

Sakuda, K.

Saperstein, R. E.

Schmidt, R. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Shank, C. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Slutsky, B.

Smith, H. I.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

Tan, D. T. H.

Wong, V. V.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

Yamada, M.

Yariv, A.

A. Yariv, Optical Electronics, 3rd ed. (Holt McDougal, 1985), Chap. 13, pp. 402–421.

Appl. Opt.

Appl. Phys. Lett.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

D. T. H. Tan, K. Ikeda, and Y. Fainman, Appl. Phys. Lett. 95, 141109 (2009).
[CrossRef]

J. Lightwave Technol.

J. Vac. Sci. Technol. B

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, J. Vac. Sci. Technol. B 13, 2859 (1995).
[CrossRef]

Opt. Lett.

Other

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995), Chap. 3, pp. 65–111.

A. Yariv, Optical Electronics, 3rd ed. (Holt McDougal, 1985), Chap. 13, pp. 402–421.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972), Chap. 9, pp. 379–386.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961), Chap. 8, p. 381–400.

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Figures (3)

Fig. 1
Fig. 1

(a) Dark-field micrograph of the fabricated structures: the marking shows the curved and the straight gratings of the same length. Insets (i) and (ii) show SEM micrographs of the straight and the curved gratings, respectively. (b) Array of curved waveguide Bragg gratings. (c) Schematic of the transmission matrix formalism.

Fig. 2
Fig. 2

Design of the filter. (a) Schematics of the waveguide Bragg grating. (b) Coupling coefficient (log scale) as a function of the gap between the cylinders and the waveguide, obtained from 3D FEM simulations, as shown in the upper inset. The point marked by the blue dot corresponds to the fabricated structure with G = 115 ± 15 nm and κ = 80 ± 15 cm 1 . (c) A resonator used to analyze the losses, based on two curved waveguides with a junction in the joint. (d) Normalized losses obtained from the Q factor of the resonator, as a function of the curvature radius of the waveguide: bending loss, α b / π R (dashed black curve) and loss at a junction, α j / π R (solid red curve).

Fig. 3
Fig. 3

Measured transmission spectra for straight (red crosses) and curved (black dots) gratings. The solid curves show the fitted transmission spectra of Bragg gratings with κ = 90 cm 1 , n g = 4.27 , L = 920 μm , and n e = 2.340 for the straight grating and n e = 2.336 for the curved grating, with a constant background 23 dB below the signal.

Equations (5)

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[ A i + 1 B i + 1 ] = T [ A i B i ] = [ ( 1 α ) t 1 r t - 1 r t 1 t 1 ] [ A i B i ] ,
T b = [ ( 1 α b ) t b 1 r b t b 1 r b t b 1 t b 1 ] ,
T j 1 t j [ ( 1 α j ) 0 0 1 ] ,
t 0 = ( T 0 ) 2 , 2 1 = ( η η 1 ) ( η N η N ) t b 1 t j 1 ( η N 1 η 1 N ) ,
( α b + α j ) N 1.

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