Abstract

Modern photolithography with its sub-hundred-nanometer-scale resolution and cm-scale spatial coherence provides for the creation of powerful waveguide diffractive structures useful as integrated spectral filters, multiplexers, spatial signal routers, interconnects, etc. Application of such structures is facilitated by a lithographically friendly means of amplitude apodization, which allows for programming of general spectral and spatial transfer functions. We describe here an approach to implementing flexible binary-etch-compatible diffractive amplitude control based on the decomposition of diffractive structures into subregions each of whose diffractive contours are spatially positioned so as to interferometrically control the net diffractive amplitude and phase of the subregion. The present approach is uniquely powerful because it allows for substantial decoupling of amplitude and phase apodization.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

B. Malo, S. Theriault, D. C. Johnson, F. Bilodeau, J. Albert, K. O. Hill, �??Apodisation of the spectral response of fibre Bragg gratings using a phase mask with variable diffraction efficiency,�?? Electron. Lett. 31, 223 �?? 225 (1995).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

D. Wiesmann, C. David, R. Germann, D. Erni, and G. L. Bona, �??Apodized surface-corrugated gratings with varying duty cycles,�?? IEEE Photonics Technol. Lett. 12, 639-641 (2000).
[CrossRef]

T. Komukai, K. Tamura, and M. Nakazawa, �??An efficient 0.04-nm apodized fiber Bragg grating and its application to narrow-band spectral filtering,�?? IEEE Photonics Technol. Lett. 9, 934-936 (1997).
[CrossRef]

J. Lightwave Technol. (3)

T. Erdogan, �??Fiber grating spectra,�?? J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

C. Greiner, D. Iazikov, and T. W. Mossberg, �??Lithographically-fabricated planar holographic Bragg reflectors,�?? J. Lightwave Technol. 22, 136-145 (2004).
[CrossRef]

J. L. Rebola and A. V. T. Cartaxo, �??Performance optimization of Gaussian apodized fiber Bragg grating filters in WDM systems,�?? J. Lightwave Technol. 8, 1537-1544 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Photonics Technology Lett. (1)

M. Ibsen, M. K. Durkin, M. J. Cole, R. I. Laming, �??Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,�?? Photonics Technology Lett. 10, 842 - 844 (1998).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a)–(b) Top and side views of channel waveguide grating, respectively. (c) Top-view of slab-waveguide holographic Bragg reflector with channel waveguide access. (d) Photograph of grating contours for channel waveguide grating prior to fill.

Fig, 2.
Fig, 2.

Basic concept of correlated-contour amplitude and phase control. (a) Uniform grating. (b) Blow-up of two adjacent grating contours with common and differential position shifts. (c) Five-contour subgroups with center contour deletion to provide room for centerwise displacement of outer contours. (d) Common mode and differential displacements of contour set elements (N=5) used to adjust phase and amplitude, respectively.

Fig. 3.
Fig. 3.

Reflection spectra of two channel waveguides (left and right) each containing four separate gratings. Top and bottom rows show different input polarizations. Each individual grating is written with identical contour sets adjusted to specific field reflectivity and grating lengths are adjusted to provide nearly uniform net reflectivity (see text).

Fig. 4.
Fig. 4.

Plot of measured amplitude reflection coefficient versus design reflection coefficient for the gratings of Table 1.

Fig. 5.
Fig. 5.

(a) Measured effective refractive index as a function of amplitude reflection coefficient for correlated-line-set gratings (solid circles) and a reference grating set (open triangles) whose reflectivity is controlled via the partial scribe method of Ref. 8. (b) Effective refractive index of the two grating sets after extracting intrinsic wavelength dependence.

Fig. 6.
Fig. 6.

Reflection spectra of HBRs apodized with 3-line (N=3) correlated-contour amplitude and phase control. In (a), the lower trace depicts the calculated reflective spectrum of a linearly chirped grating with no amplitude apodization, the middle (solid) trace is a measured reflection spectrum of an apodized HBR, the top trace (dashed) is the simulated HBR response, which is displaced upward by 5 dB for clarity. (b) is a blow-up of the measured reflection spectrum of part (a) with traces (TE top) for both polarizations and scalar simulated spectrum (flattest). The amplitude and phase apodization functions employed in the HBR of (a–b) are shown in (c) and (d), respectively.

Tables (1)

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Table 1. Channel Waveguide Grating Properties

Equations (2)

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E i ( δ i , ε i ) = E o exp ( 2 i k o ε i ) cos ( 2 k o δ i ) ,
ρ ( δ i ) = E i ( δ i ) E o = cos ( 2 k o δ i )

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