Fresnel diffraction effects in Fourier-transform arrayed waveguide grating spectrometer
Optics Express, Vol. 15, Issue 25, pp. 16431-16441 (2007)
http://dx.doi.org/10.1364/OE.15.016431
Acrobat PDF (967 KB)
Abstract
We present an analysis of Fourier-transform arrayed waveguide gratings in the Fresnel diffraction regime. We report a distinct spatial modulation of the interference pattern referred to as the Moiré-Talbot effect. The effect and its influence in a FT AWG device is explained by deriving an original analytical expression for the modulated field, and is also confirmed by numerical simulations using the angular spectrum method to solve the Fresnel diffraction integral. We illustrate the retrieval of spectral information in a waveguide Fourier-transform spectrometer in the presence of the Moiré-Talbot effect. The simulated device comprises two interleaved waveguide arrays each with 180 waveguides and the interference order of 40. It is designed with a Rayleigh spectral resolution of 0.1 nm and 8 nm bandwidth at wavelength λ~1.5 µm. We also demonstrate by numerical simulations that the spectrometer crosstalk is reduced from -20 dB to -40 dB by Gaussian apodization.
© 2007 Optical Society of America
1. Introduction
2. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15, 2299–2306 (2007). [CrossRef] [PubMed]
3. P. Jacquinot, “The luminosity of spectrometers with prisms, gratings, or Fabry Perot etalons,” J. Opt. Soc. Am. 44, 761 (1954). [CrossRef]
5. P. Cheben, I. Powell, S. Janz, and D.-X. Xu, “Wavelength-dispersive device based on a Fourier-transform Michelson-type arrayed waveguide grating,” Opt. Lett. 30, 1824–1826 (2005). [CrossRef] [PubMed]
6. J. M. Harlander, F. L. Roesler, Ch. R. Englert, J. G. Cardon, R. R. Conway, Ch. M. Brown, and J. Wimperis, “Robust monolithic ultraviolet interferometer for the SHIMMER instrument on STPSat-1,” Appl. Opt. 42, 2829–2834 (2003). [CrossRef] [PubMed]
2. Moiré-Talbot effect in Fourier-transform AWG devices
10. M. K. Smit and C. van Dam, “Phasar-based WDM-devices: principles, design, and applications,” IEEE J. Sel. Top. Quantum Electron. , 2, 236 (1996). [CrossRef]
5. P. Cheben, I. Powell, S. Janz, and D.-X. Xu, “Wavelength-dispersive device based on a Fourier-transform Michelson-type arrayed waveguide grating,” Opt. Lett. 30, 1824–1826 (2005). [CrossRef] [PubMed]
5. P. Cheben, I. Powell, S. Janz, and D.-X. Xu, “Wavelength-dispersive device based on a Fourier-transform Michelson-type arrayed waveguide grating,” Opt. Lett. 30, 1824–1826 (2005). [CrossRef] [PubMed]
11. D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407 (1997). [CrossRef]
12. H. Hamam and J. L. De Bougrenet de la Tocnaye, “Programmable joint fractional Talbot computer-generated holograms,” J. Opt. Soc. Am. A 12, 314 (1995). [CrossRef]
13. H. Hamam and J. L. de Bougrenet de la Tocnaye, “Efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920 (1995). [CrossRef]
2. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15, 2299–2306 (2007). [CrossRef] [PubMed]
3. Conclusions
Acknowledgements
References and links
1. | P. Cheben, “Wavelength dispersive planar waveguide devices: Echelle gratings and arrayed waveguide gratings,” in Optical Waveguides: From Theory to Applied Technologies, Eds. M. L. Calvo and V. Laksminarayanan, Chapter 5, CRC Press, London, (2007). |
2. | P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15, 2299–2306 (2007). [CrossRef] [PubMed] |
3. | P. Jacquinot, “The luminosity of spectrometers with prisms, gratings, or Fabry Perot etalons,” J. Opt. Soc. Am. 44, 761 (1954). [CrossRef] |
4. | P.B. Fellgett, PhD Thesis, University of Cambridge, (1951). |
5. | P. Cheben, I. Powell, S. Janz, and D.-X. Xu, “Wavelength-dispersive device based on a Fourier-transform Michelson-type arrayed waveguide grating,” Opt. Lett. 30, 1824–1826 (2005). [CrossRef] [PubMed] |
6. | J. M. Harlander, F. L. Roesler, Ch. R. Englert, J. G. Cardon, R. R. Conway, Ch. M. Brown, and J. Wimperis, “Robust monolithic ultraviolet interferometer for the SHIMMER instrument on STPSat-1,” Appl. Opt. 42, 2829–2834 (2003). [CrossRef] [PubMed] |
7. | M. Florjańczyk, P. Cheben, S. Janz, A. Scott, B. Solheim, and D.-X. Xu, Planar waveguide spatial heterodyne spectrometer, Proc. Photonics North Conference, 4–7 June, 2007, Ottawa, Canada. |
8. | P. Cheben, A. Delâge, L. Erickson, S. Janz, and D.-X. Xu, “Polarization compensation in silicon-on-insulator arrayed waveguide grating devices,” in Silicon-based and hybrid optoelectronics III, SPIE Proc. 4293, 15–22, (2001). |
9. | P. Cheben, D.-X. Xu, S. Janz, A. Delâge, and D. Dalacu, “Birefringence compensation in silicon-on-insulator planar waveguide demultiplexers using a buried oxide layer,” in Optoelectronic Integration on Silicon, SPIE Proc. 4997, 181–189, (2003). |
10. | M. K. Smit and C. van Dam, “Phasar-based WDM-devices: principles, design, and applications,” IEEE J. Sel. Top. Quantum Electron. , 2, 236 (1996). [CrossRef] |
11. | D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407 (1997). [CrossRef] |
12. | H. Hamam and J. L. De Bougrenet de la Tocnaye, “Programmable joint fractional Talbot computer-generated holograms,” J. Opt. Soc. Am. A 12, 314 (1995). [CrossRef] |
13. | H. Hamam and J. L. de Bougrenet de la Tocnaye, “Efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920 (1995). [CrossRef] |
OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(130.1750) Integrated optics : Components
(130.3120) Integrated optics : Integrated optics devices
(230.7380) Optical devices : Waveguides, channeled
(230.7390) Optical devices : Waveguides, planar
(250.5300) Optoelectronics : Photonic integrated circuits
ToC Category:
Diffraction and Gratings
History
Original Manuscript: September 25, 2007
Revised Manuscript: November 20, 2007
Manuscript Accepted: November 20, 2007
Published: November 27, 2007
Citation
J. A. Rodrigo, P. Cheben, T. Alieva, M. L. Calvo, M. Florjanczyk, S. Janz, A. Scott, B. Solheim, D. X. Xu, and A. Deláge, "Fresnel diffraction effects in Fourier-transform arrayed waveguide grating spectrometer," Opt. Express 15, 16431-16441 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16431
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References
- P. Cheben, Wavelength dispersive planar waveguide devices: Echelle gratings and arrayed waveguide gratings," in Optical Waveguides: From Theory to Applied Technologies, M. L. Calvo and V. Laksminarayanan, eds., (CRC Press, London, 2007) Chap. 5.
- P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, "A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with submicrometer aperture waveguides," Opt. Express 15, 2299-2306 (2007). [CrossRef] [PubMed]
- P. Jacquinot, "The luminosity of spectrometers with prisms, gratings, or Fabry Perot etalons," J. Opt. Soc. Am. 44, 761 (1954). [CrossRef]
- P. B. Fellgett, PhD Thesis, University of Cambridge, (1951).
- P. Cheben, I. Powell, S. Janz, and D.-X. Xu, "Wavelength-dispersive device based on a Fourier-transform Michelson-type arrayed waveguide grating," Opt. Lett. 30, 1824-1826 (2005). [CrossRef] [PubMed]
- J. M. Harlander, F. L. Roesler, Ch. R. Englert, J. G. Cardon, R. R. Conway, Ch. M. Brown, and J. Wimperis, "Robust monolithic ultraviolet interferometer for the SHIMMER instrument on STPSat-1," Appl. Opt. 42, 2829-2834 (2003). [CrossRef] [PubMed]
- M. Florjańczyk, P. Cheben, S. Janz, A. Scott, B. Solheim, and D.-X. Xu, Planar waveguide spatial heterodyne spectrometer, Proc. Photonics North Conference, 4-7 June, 2007, Ottawa, Canada.
- P. Cheben, A. Delâge, L. Erickson, S. Janz, and D.-X. Xu, "Polarization compensation in silicon-on-insulator arrayed waveguide grating devices," in Silicon-based and hybrid optoelectronics III, Proc SPIE 4293, 15-22 (2001).
- P. Cheben, D.-X. Xu, S. Janz, A. Delâge, and D. Dalacu, "Birefringence compensation in silicon-on-insulator planar waveguide demultiplexers using a buried oxide layer," Proc SPIE 4997, 181-189 (2003).
- M. K. Smit and C. van Dam, "Phasar-based WDM-devices: principles, design, and applications," IEEE J. Sel. Top. Quantum Electron. 2, 236 (1996). [CrossRef]
- D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt. 44, 407 (1997). [CrossRef]
- H. Hamam and J. L. De Bougrenet de la Tocnaye, "Programmable joint fractional Talbot computer-generated holograms," J. Opt. Soc. Am. A 12, 314 (1995). [CrossRef]
- H. Hamam and J. L. De Bougrenet de la Tocnaye, "Efficient Fresnel transform algorithm based on fractional Fresnel diffraction," J. Opt. Soc. Am. A 12, 1920 (1995). [CrossRef]
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