Abstract

We report on several new types of sub-wavelength grating (SWG) gradient index structures for efficient mode coupling in high index contrast slab waveguides. Using a SWG, an adiabatic transition is achieved at the interface between silicon-on-insulator waveguides of different geometries. The SWG transition region minimizes both fundamental mode mismatch loss and coupling to higher order modes. By creating the gradient effective index region in the direction of propagation, we demonstrate that efficient vertical mode transformation can be achieved between slab waveguides of different core thickness. The structures which we propose can be fabricated by a single etch step. Using 3D finite-difference time-domain simulations we study the loss, polarization dependence and the higher order mode excitation for two types (triangular and triangular-transverse) of SWG transition regions between silicon-on-insulator slab waveguides of different core thicknesses. We demonstrate two solutions to reduce the polarization dependent loss of these structures. Finally, we propose an implementation of SWG structures to reduce loss and higher order mode excitation between a slab waveguide and a phase array of an array waveguide grating (AWG). Compared to a conventional AWG, the loss is reduced from −1.4 dB to < −0.2 dB at the slab-array interface.

© 2009 OSA

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References

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  1. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  2. P. Lalanne and J.-P. Hugonin, “High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms,” J. Opt. Soc. Am. A 15(7), 1843–1851 (1998).
    [CrossRef]
  3. H. Kikuta, H. Toyota, and W. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Rev. 10(2), 63–73 (2003).
    [CrossRef]
  4. C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
    [CrossRef]
  5. P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
    [CrossRef] [PubMed]
  6. P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, and S. Tanev, “Highly efficient broad-band waveguide grating coupler with a sub-wavelength grating mirror,”, in Frontiers in planar lightwave circuit technology, S. Janz et al., eds. (Springer, 2006), 235–243.
  7. R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
    [CrossRef] [PubMed]
  8. J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D.-X. Xu, “Gradient-index antireflective subwavelength structures for planar waveguide facets,” Opt. Lett. 32(13), 1794–1796 (2007).
    [CrossRef] [PubMed]
  9. J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Delâge, A. Densmore, B. Lamontagne, P. Waldron and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Advances in Optical Technologies: Special Issue on Silicon Photonics, 2008, Article ID 685489, doi:10.1155/2008/685489 (invited), (2008).
  10. 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. Lakshminarayanan, eds. (CRC Press, 2007), 173–230.
  11. P. Cheben, A. Delâge, S. Janz, and D.-X. Xu, “Echelle gratings and arrayed waveguide gratings for WDM and spectral analysis,” in Advances in information optics and photonics, A.T. Friberg and R. Dändliker, eds. (SPIE Press, 2008), 599–632.
  12. C. R. Doerr and K. Okamoto, “Advances in silica planar lightwave circuits,” J. Lightwave Technol. 24(12), 4763–4789 (2006).
    [CrossRef]
  13. X. J. M. Leijtens, B. Kuhlow, and M. K. Smit, “Arrayed waveguide gratings,” in Wavelength filters in fiber optics, H. Venghaus, (Springer Verlag, 2006), 125–187.
  14. P. Cheben, A. Delâge, A. Densmore, M. Florjanczyk, S. Janz, B. Lamontagne, J. Lapointe, E. Post, J. Schmid and D.-X. Xu, “Silicon photonic waveguide structures and devices: From fundamentals to implementations in spectroscopy and biological sensing,” NATO Advanced Study Institute, (Springer 2009).
  15. 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(5), 2299–2306 (2007).
    [CrossRef] [PubMed]
  16. Y. Komai, H. Nagano, K. Okamoto, and K. Kodate, “Spectroscopic sensing using a visible arrayed-waveguide grating,” Proc. SPIE 5867, 91–102 (2005).
  17. J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
    [CrossRef]
  18. 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).
    [CrossRef]
  19. P. J. Bock, P. Cheben, A. Delâge, J. H. Schmid, D.-X. Xu, S. Janz, and T. J. Hall, “Demultiplexer with blazed waveguide sidewall grating and sub-wavelength grating structure,” Opt. Express 16(22), 17616–17625 (2008).
    [CrossRef] [PubMed]
  20. S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nanometer resolution,” Science 272(5258), 85–87 (1996).
    [CrossRef]
  21. P. Cheben, J. H. Schmid, P. J. Bock, D.-X. Xu, S. Janz, A. Delâge, J. Lapointe, B. Lamontagne, A. Densmore, and T. Hall, “Sub-wavelength nanostructures for engineering the effective index of silicon-on-insulator waveguides,” presented at the 11th International Conference on Transparent Optical Networks, Azores, Portugal, June 28 - July 2, 2009.
  22. J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
    [CrossRef]
  23. Y. P. Li, “Optical device having low insertion loss,” Patent 5745618 (1998).

2009 (1)

2008 (1)

2007 (2)

2006 (2)

2005 (1)

Y. Komai, H. Nagano, K. Okamoto, and K. Kodate, “Spectroscopic sensing using a visible arrayed-waveguide grating,” Proc. SPIE 5867, 91–102 (2005).

2004 (1)

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

2003 (2)

H. Kikuta, H. Toyota, and W. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Rev. 10(2), 63–73 (2003).
[CrossRef]

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).
[CrossRef]

2002 (1)

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

1999 (1)

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
[CrossRef]

1998 (1)

1996 (1)

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nanometer resolution,” Science 272(5258), 85–87 (1996).
[CrossRef]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Bock, P. J.

Chang-Hasnain, C. J.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Cheben, P.

Chen, L.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Chou, S. Y.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nanometer resolution,” Science 272(5258), 85–87 (1996).
[CrossRef]

Dalacu, D.

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).
[CrossRef]

Davies, M.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
[CrossRef]

Delâge, A.

P. J. Bock, P. Cheben, A. Delâge, J. H. Schmid, D.-X. Xu, S. Janz, and T. J. Hall, “Demultiplexer with blazed waveguide sidewall grating and sub-wavelength grating structure,” Opt. Express 16(22), 17616–17625 (2008).
[CrossRef] [PubMed]

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(5), 2299–2306 (2007).
[CrossRef] [PubMed]

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).
[CrossRef]

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
[CrossRef]

den Besten, J. H.

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

Densmore, A.

Dessens, M. P.

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

Doerr, C. R.

Erickson, L.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
[CrossRef]

Groen, F. H.

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

Halir, R.

Hall, T. J.

He, J.-J.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
[CrossRef]

Herben, C. G. P.

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Hugonin, J.-P.

Janz, S.

Kikuta, H.

H. Kikuta, H. Toyota, and W. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Rev. 10(2), 63–73 (2003).
[CrossRef]

Kodate, K.

Y. Komai, H. Nagano, K. Okamoto, and K. Kodate, “Spectroscopic sensing using a visible arrayed-waveguide grating,” Proc. SPIE 5867, 91–102 (2005).

Komai, Y.

Y. Komai, H. Nagano, K. Okamoto, and K. Kodate, “Spectroscopic sensing using a visible arrayed-waveguide grating,” Proc. SPIE 5867, 91–102 (2005).

Koteles, E. S.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
[CrossRef]

Krauss, P. R.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nanometer resolution,” Science 272(5258), 85–87 (1996).
[CrossRef]

Lalanne, P.

Lamontagne, B.

Lapointe, J.

Leijtens, X. J. M.

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

Leys, M. R.

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Molina-Fernández, I.

Nagano, H.

Y. Komai, H. Nagano, K. Okamoto, and K. Kodate, “Spectroscopic sensing using a visible arrayed-waveguide grating,” Proc. SPIE 5867, 91–102 (2005).

Okamoto, K.

C. R. Doerr and K. Okamoto, “Advances in silica planar lightwave circuits,” J. Lightwave Technol. 24(12), 4763–4789 (2006).
[CrossRef]

Y. Komai, H. Nagano, K. Okamoto, and K. Kodate, “Spectroscopic sensing using a visible arrayed-waveguide grating,” Proc. SPIE 5867, 91–102 (2005).

Post, E.

Renstrom, P. J.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nanometer resolution,” Science 272(5258), 85–87 (1996).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Schmid, J. H.

Smit, M. K.

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

Suzuki, Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Toyota, H.

H. Kikuta, H. Toyota, and W. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Rev. 10(2), 63–73 (2003).
[CrossRef]

Waldron, P.

Wangüemert-Pérez, J. G.

Xu, D.-X.

Yu, W.

H. Kikuta, H. Toyota, and W. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Rev. 10(2), 63–73 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delâge, and M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photon. Technol. Lett. 11(2), 224–226 (1999).
[CrossRef]

J. H. den Besten, M. P. Dessens, C. G. P. Herben, X. J. M. Leijtens, F. H. Groen, M. R. Leys, and M. K. Smit, “Low-loss, compact, and polarization independent phasar demultiplexer fabricated by using a double-etch process,” IEEE Photon. Technol. Lett. 14(1), 62–64 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (3)

Opt. Lett. (2)

Opt. Rev. (1)

H. Kikuta, H. Toyota, and W. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Rev. 10(2), 63–73 (2003).
[CrossRef]

Proc. SPIE (2)

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).
[CrossRef]

Y. Komai, H. Nagano, K. Okamoto, and K. Kodate, “Spectroscopic sensing using a visible arrayed-waveguide grating,” Proc. SPIE 5867, 91–102 (2005).

Science (1)

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint lithography with 25-nanometer resolution,” Science 272(5258), 85–87 (1996).
[CrossRef]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (8)

Y. P. Li, “Optical device having low insertion loss,” Patent 5745618 (1998).

P. Cheben, J. H. Schmid, P. J. Bock, D.-X. Xu, S. Janz, A. Delâge, J. Lapointe, B. Lamontagne, A. Densmore, and T. Hall, “Sub-wavelength nanostructures for engineering the effective index of silicon-on-insulator waveguides,” presented at the 11th International Conference on Transparent Optical Networks, Azores, Portugal, June 28 - July 2, 2009.

X. J. M. Leijtens, B. Kuhlow, and M. K. Smit, “Arrayed waveguide gratings,” in Wavelength filters in fiber optics, H. Venghaus, (Springer Verlag, 2006), 125–187.

P. Cheben, A. Delâge, A. Densmore, M. Florjanczyk, S. Janz, B. Lamontagne, J. Lapointe, E. Post, J. Schmid and D.-X. Xu, “Silicon photonic waveguide structures and devices: From fundamentals to implementations in spectroscopy and biological sensing,” NATO Advanced Study Institute, (Springer 2009).

P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, and S. Tanev, “Highly efficient broad-band waveguide grating coupler with a sub-wavelength grating mirror,”, in Frontiers in planar lightwave circuit technology, S. Janz et al., eds. (Springer, 2006), 235–243.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Delâge, A. Densmore, B. Lamontagne, P. Waldron and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Advances in Optical Technologies: Special Issue on Silicon Photonics, 2008, Article ID 685489, doi:10.1155/2008/685489 (invited), (2008).

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. Lakshminarayanan, eds. (CRC Press, 2007), 173–230.

P. Cheben, A. Delâge, S. Janz, and D.-X. Xu, “Echelle gratings and arrayed waveguide gratings for WDM and spectral analysis,” in Advances in information optics and photonics, A.T. Friberg and R. Dändliker, eds. (SPIE Press, 2008), 599–632.

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Figures (11)

Fig. 1
Fig. 1

3D schematics of junctions between two waveguides of different geometries, with: a) conventional single step interface, b) 1D grating, triangular SWG transition region, and c) 2D grating, triangular-transverse SWG transition region. d) SWG structure at the boundary between slab waveguide and a waveguide array.

Fig. 2
Fig. 2

Top view of mode transformer. a) Triangular SWG structure; b) Triangular-transverse SWG structure. 3D FDTD simulations were performed for both structures for three different thicknesses of slab waveguide A: d A = 0.5 μm, 1.0 μm and 1.5 μm, with variable etch depth (d A-d B).

Fig. 3
Fig. 3

First order effective medium theory approximation of effective index of SWG upper cladding transition region as a function of position (z in Fig. 1) for TE and TM polarization.

Fig. 4
Fig. 4

Loss dependence for triangular SWGs of different lengths. TE and TM polarization, d A = 1.0 µm, and d e = 0.4 µm (40% etch). Loss is calculated as power transfer from the fundamental mode of slab waveguide A to the fundamental mode of slab waveguide B (Fig. 1(b)).

Fig. 5
Fig. 5

Vertical mode transformer loss comparison for conventional single-step, triangular SWG and triangular-transverse SWG for TE polarization. a) Initial slab thickness d A = 1.5 µm, etch depth range d e = 0.2 µm – 0.8 µm (10% – 50% etch) ; b) d A = 1.0 µm, d e = 0.2 µm – 0.6 µm (20% – 60% etch); c) d A = 0.5 µm, d e = 0.05 µm – 0.15 µm (10% – 30% etch). Loss is calculated as power transfer from the fundamental mode of slab waveguide A to the fundamental mode of slab waveguide B (see Figs. 1(b) and 1(c)).

Fig. 6
Fig. 6

Vertical mode transformer loss comparison for conventional single-step, triangular SWG and triangular-transverse, SWG for TM polarization. a) Initial slab thickness d A = 1.5 µm, etch depth range d e = 0.2 µm – 0.8 µm (10% – 50% etch); b) d A = 1.0 µm, d e = 0.2 µm – 0.6 µm (20% – 60% etch); c) d A = 0.5 µm, d e = 0.05 µm – 0.15 µm (10% – 30% etch). Loss calculated as power transfer from the fundamental mode of slab waveguide A to the fundamental mode of slab waveguide B (see Figs. 1(b) and 1(c)).

Fig. 7
Fig. 7

TE and TM mode profiles for d A = 1.0 μm and d e = 0.4 μm. TE polarization: a) Conventional single-step, indicates higher order mode excitation, b) Triangular SWG showing higher mode mismatch than, c) Triangular-transverse SWG. TM polarization: d) Conventional etch indicates significant mode mismatch, e) Triangular SWG showing lower mode mismatch than, f) Triangular-transverse SWG.

Fig. 8
Fig. 8

3D mode transformers with reduced PDL. a) Partial transverse SWG with length L T; b) Transverse SWG in the region between the triangular teeth.

Fig. 9
Fig. 9

Power coupled to the fundamental mode for a structure shown in Fig. 8(a). Negligible PDL is predicted for triangular-transverse length L T ~18 μm. Dotted lines indicate the loss for a conventional step for TE and TM polarization, respectively.

Fig. 10
Fig. 10

AWG with close-up of the slab-array boundary using conventional tapers and SWG tapers to reduce loss and higher order mode excitation at the slab-array boundary.

Fig. 11
Fig. 11

Layout, mode evolution and field profiles for an AWG slab-array boundary. a) Conventional taper simulation layout. b) SWG taper simulation layout. c) Field evolution in conventional tapers, higher order mode excitation is noticeable. d) Field evolution in SWG taper with suppressed higher order mode excitation. e) Conventional taper field amplitude profile at the output plane of the waveguide array indicating the presence of higher order modes. f) SWG taper field amplitude profile at the output plane of the waveguide array indicating suppressed higher order mode excitation.

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