Abstract

We present a new method for modeling and design of photonic crystal nano-beam resonators (PCNBRs) based on cascaded transmission lines. The proposed model provides an accurate estimate of the PCNBRs properties such as resonance wavelength and quality factor $(Q)$ with much smaller computation cost as compared to the brute-force numerical methods. Furthermore, we have developed a straightforward technique for the design of high-$Q$ PCNBRs based on resonance modes with Gaussian electromagnetic field profiles. The results obtained by using the proposed transmission line model are compared against numerical and experimental results and the accuracy of the model is verified. The proposed model provides an insight to silicon cavity design and significantly reduces computational burden.

© 2013 IEEE

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  1. M. Belotti, M. Galli, D. Gerace, L. Andreani, G. Guizzetti, A. MdZain, N. Johnson, M. Sorel, R. De La Rue, "All-optical switching in silicon-on-insulator photonic wire nano-cavities," Opt. Exp. 18, 1450-1461 (2010).
  2. B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, M. Lipson, " Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes ," Opt. Exp. 15, 3140-3148 (2007).
  3. R. Ohta, Y. Ota, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, Y. Arakawa, "Strong coupling between a photonic crystal nanobeam cavity and a single quantum dot ," Appl. Phys. Lett. 98, 173104-1-173104-3 (2011).
  4. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, O. Painter, "A picogram- and nanometre-scale photonic-crystal optomechanical cavity," Nature 459, 550-555 (2009).
  5. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, M. Loncar, " High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106-1-121106-3 (2009).
  6. E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. Roh, M. Notomi, "Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings," Opt. Exp. 18, 15859-15869 (2010).
  7. J. D. Ryckman, S. M. Weiss, "Low mode volume slotted photonic crystal single nanobeam cavity," Appl. Phys. Lett. 101, 071104-1- 071104-3 (2012).
  8. M. Notomi, E. Kuramochi, H. Taniyama, "Ultrahigh-Q nanocavity with 1D photonic gap," Opt. Exp. 16, 11095-11102 (2008).
  9. M. McCutcheon, M. Loncar, " Design of a silicon nitride photonic crystal nanocavity with a quality factor of one million for coupling to a diamond nanocrystal," Opt. Exp. 16, 19136-19145 (2008).
  10. Q. Quan, P. B. Deotare, M. Loncar, "Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide," Appl. Phys. Lett. 96 , 203102-203104 (2010).
  11. Y. Gong, B. Ellis, G. Shambat, T. Sarmiento, J. Harris, J. Vuckovic, "Nanobeam photonic crystal cavity quantum dot laser," Opt. Exp. 18, 8781-8789 (2010).
  12. Y. Zhang, M. Khan, Y. Huang, J. Ryou, P. Deotare, R. Dupuis, M. Loncar, "Photonic crystal nanobeam lasers," Appl. Phys. Lett. 97, 051104-051106 (2010).
  13. B. Ahn, J. Kang, M. Kim, J. Song, B. Min, K. Kim, Y. Lee, "One-dimensional parabolic-beam photonic crystal laser," Opt. Exp. 18, 5654-5660 (2010).
  14. P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, E. Hadji, " Ultra-high-reflectivity photonic-bandgap mirrors in a ridge SOI waveguide," New J. Phys. 8, 204 (2006).
  15. Q. Quan, M. Loncar, " Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities," Opt. Exp. 19, 18529-18542 (2011).
  16. P. Velha, E. Picard, T. Charvolin, E. Hadji, J. Rodier, P. Lalanne, D. Peyrade, "Ultra-high Q/V Fabry–Perot microcavity on SOI substrate ," Opt. Exp. 15, 16090-16096 (2007).
  17. A. Md Zain, N. Johnson, M. Sorel, R. De La Rue, "Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI)," Opt. Exp. 16 , 12084-12089 (2008).
  18. M. Miri, A. Khavasi, K. Mehrany, B. Rashidian, "Transmission-line model to design matching stage for light coupling into two-dimensional photonic crystals," Opt. Lett. 35, 115-117 (2010).
  19. M. A. Miri, A. Khavasi, M. Miri, K. Mehrany, "A transmission line resonator model for fast extraction of electromagnetic properties of cavities in two-dimensional photonic crystals," IEEE Photon. J. 2, 677-685 (2010).
  20. R. E. Collin, Foundation for Microwave Engineering (McGraw-Hill, 1992).
  21. Y. Akahane, T. Asano1, B. S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
  22. K. Srinivasan, O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Exp. 10, 670-684 (2002).

2012

J. D. Ryckman, S. M. Weiss, "Low mode volume slotted photonic crystal single nanobeam cavity," Appl. Phys. Lett. 101, 071104-1- 071104-3 (2012).

2011

Q. Quan, M. Loncar, " Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities," Opt. Exp. 19, 18529-18542 (2011).

R. Ohta, Y. Ota, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, Y. Arakawa, "Strong coupling between a photonic crystal nanobeam cavity and a single quantum dot ," Appl. Phys. Lett. 98, 173104-1-173104-3 (2011).

2010

M. Belotti, M. Galli, D. Gerace, L. Andreani, G. Guizzetti, A. MdZain, N. Johnson, M. Sorel, R. De La Rue, "All-optical switching in silicon-on-insulator photonic wire nano-cavities," Opt. Exp. 18, 1450-1461 (2010).

Q. Quan, P. B. Deotare, M. Loncar, "Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide," Appl. Phys. Lett. 96 , 203102-203104 (2010).

Y. Gong, B. Ellis, G. Shambat, T. Sarmiento, J. Harris, J. Vuckovic, "Nanobeam photonic crystal cavity quantum dot laser," Opt. Exp. 18, 8781-8789 (2010).

Y. Zhang, M. Khan, Y. Huang, J. Ryou, P. Deotare, R. Dupuis, M. Loncar, "Photonic crystal nanobeam lasers," Appl. Phys. Lett. 97, 051104-051106 (2010).

B. Ahn, J. Kang, M. Kim, J. Song, B. Min, K. Kim, Y. Lee, "One-dimensional parabolic-beam photonic crystal laser," Opt. Exp. 18, 5654-5660 (2010).

M. Miri, A. Khavasi, K. Mehrany, B. Rashidian, "Transmission-line model to design matching stage for light coupling into two-dimensional photonic crystals," Opt. Lett. 35, 115-117 (2010).

M. A. Miri, A. Khavasi, M. Miri, K. Mehrany, "A transmission line resonator model for fast extraction of electromagnetic properties of cavities in two-dimensional photonic crystals," IEEE Photon. J. 2, 677-685 (2010).

E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. Roh, M. Notomi, "Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings," Opt. Exp. 18, 15859-15869 (2010).

2009

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, O. Painter, "A picogram- and nanometre-scale photonic-crystal optomechanical cavity," Nature 459, 550-555 (2009).

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, M. Loncar, " High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106-1-121106-3 (2009).

2008

M. Notomi, E. Kuramochi, H. Taniyama, "Ultrahigh-Q nanocavity with 1D photonic gap," Opt. Exp. 16, 11095-11102 (2008).

M. McCutcheon, M. Loncar, " Design of a silicon nitride photonic crystal nanocavity with a quality factor of one million for coupling to a diamond nanocrystal," Opt. Exp. 16, 19136-19145 (2008).

A. Md Zain, N. Johnson, M. Sorel, R. De La Rue, "Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI)," Opt. Exp. 16 , 12084-12089 (2008).

2007

P. Velha, E. Picard, T. Charvolin, E. Hadji, J. Rodier, P. Lalanne, D. Peyrade, "Ultra-high Q/V Fabry–Perot microcavity on SOI substrate ," Opt. Exp. 15, 16090-16096 (2007).

B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, M. Lipson, " Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes ," Opt. Exp. 15, 3140-3148 (2007).

2006

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, E. Hadji, " Ultra-high-reflectivity photonic-bandgap mirrors in a ridge SOI waveguide," New J. Phys. 8, 204 (2006).

2003

Y. Akahane, T. Asano1, B. S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).

2002

K. Srinivasan, O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Exp. 10, 670-684 (2002).

Opt. Exp.

K. Srinivasan, O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Exp. 10, 670-684 (2002).

Appl. Phys. Lett.

J. D. Ryckman, S. M. Weiss, "Low mode volume slotted photonic crystal single nanobeam cavity," Appl. Phys. Lett. 101, 071104-1- 071104-3 (2012).

Appl. Phys. Lett.

Y. Zhang, M. Khan, Y. Huang, J. Ryou, P. Deotare, R. Dupuis, M. Loncar, "Photonic crystal nanobeam lasers," Appl. Phys. Lett. 97, 051104-051106 (2010).

Appl. Phys. Lett.

Q. Quan, P. B. Deotare, M. Loncar, "Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide," Appl. Phys. Lett. 96 , 203102-203104 (2010).

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, M. Loncar, " High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106-1-121106-3 (2009).

R. Ohta, Y. Ota, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, Y. Arakawa, "Strong coupling between a photonic crystal nanobeam cavity and a single quantum dot ," Appl. Phys. Lett. 98, 173104-1-173104-3 (2011).

IEEE Photon. J.

M. A. Miri, A. Khavasi, M. Miri, K. Mehrany, "A transmission line resonator model for fast extraction of electromagnetic properties of cavities in two-dimensional photonic crystals," IEEE Photon. J. 2, 677-685 (2010).

Nature

Y. Akahane, T. Asano1, B. S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, O. Painter, "A picogram- and nanometre-scale photonic-crystal optomechanical cavity," Nature 459, 550-555 (2009).

New J. Phys.

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, E. Hadji, " Ultra-high-reflectivity photonic-bandgap mirrors in a ridge SOI waveguide," New J. Phys. 8, 204 (2006).

Opt. Exp.

B. Ahn, J. Kang, M. Kim, J. Song, B. Min, K. Kim, Y. Lee, "One-dimensional parabolic-beam photonic crystal laser," Opt. Exp. 18, 5654-5660 (2010).

Opt. Exp.

Y. Gong, B. Ellis, G. Shambat, T. Sarmiento, J. Harris, J. Vuckovic, "Nanobeam photonic crystal cavity quantum dot laser," Opt. Exp. 18, 8781-8789 (2010).

Q. Quan, M. Loncar, " Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities," Opt. Exp. 19, 18529-18542 (2011).

P. Velha, E. Picard, T. Charvolin, E. Hadji, J. Rodier, P. Lalanne, D. Peyrade, "Ultra-high Q/V Fabry–Perot microcavity on SOI substrate ," Opt. Exp. 15, 16090-16096 (2007).

A. Md Zain, N. Johnson, M. Sorel, R. De La Rue, "Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI)," Opt. Exp. 16 , 12084-12089 (2008).

M. Belotti, M. Galli, D. Gerace, L. Andreani, G. Guizzetti, A. MdZain, N. Johnson, M. Sorel, R. De La Rue, "All-optical switching in silicon-on-insulator photonic wire nano-cavities," Opt. Exp. 18, 1450-1461 (2010).

B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, M. Lipson, " Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes ," Opt. Exp. 15, 3140-3148 (2007).

E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. Roh, M. Notomi, "Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings," Opt. Exp. 18, 15859-15869 (2010).

M. Notomi, E. Kuramochi, H. Taniyama, "Ultrahigh-Q nanocavity with 1D photonic gap," Opt. Exp. 16, 11095-11102 (2008).

M. McCutcheon, M. Loncar, " Design of a silicon nitride photonic crystal nanocavity with a quality factor of one million for coupling to a diamond nanocrystal," Opt. Exp. 16, 19136-19145 (2008).

Opt. Lett.

Other

R. E. Collin, Foundation for Microwave Engineering (McGraw-Hill, 1992).

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