The effect of interfacial roughness on the normal incidence bandgap of one-dimensional photonic crystals
Optics Express, Vol. 13, Issue 21, pp. 8380-8389 (2005)
http://dx.doi.org/10.1364/OPEX.13.008380
Acrobat PDF (379 KB)
Abstract
As discussed previously, interfacial roughness in one-dimensional photonic crystals (1DPCs) can have a significant effect on their normal reflectivity at the quarter-wave tuned wavelength. We report additional finite-difference time-domain (FDTD) simulations that reveal the effect of interfacial roughness on the normal-incidence reflectivity at several other wavelengths within the photonic bandgaps of various 1DPC quarter-wave stacks. The results predict that both a narrowing and red-shifting of the bandgaps will occur due to the roughness features. These FDTD results are compared to results obtained when the homogenization approximation is applied to the same structures. The homogenization approximation reproduces the FDTD results, revealing that this approximation is applicable to roughened 1DPCs within the parameter range tested (rms roughnesses < 20% and rms wavelengths < 50% of the photonic crystal periodicity) across the entire normal incidence bandgap.
© 2005 Optical Society of America
1. Introduction
1 . K. R. Maskaly , G. R. Maskaly , W. C. Carter , and J. L. Maxwell , “ Diminished normal reflectivity of one-dimensional photonic crystals due to dielectric interfacial roughness ,” Opt. Lett. 29 , 2791 – 2793 ( 2004 ). [CrossRef] [PubMed]
2 . G. S. He , T.-C. Lin , V. K. S. Hsiao , A. N. Cartwright , P. N. Prasad , L. V. Natarajan , V. P. Tondiglia , R. Jakubiak , R. A. Vaia , and T. J. Bunning , “ Tunable two-photon pumped lasing using a holographic polymer-dispersed liquid-crystal crating as a distributed feedback element ,” Appl. Phys. Lett. 83 , 2733 – 2735 ( 2003 ). [CrossRef]
3 . V. K. S. Hsiao , T.-C. Lin , G. S. He , A. N. Cartwright , P. N. Prasad , L. V. Natarajan , V. P. Tondiglia , and T. J. Bunning , “ Optical microfabrication of highly reflective volume Bragg gratings ,” Appl. Phys. Lett. 86 , 131113 ( 2005 ). [CrossRef]
4 . V. Agarwal and J. A. del Rio , “ Tailoring the photonic bandgap of a porous silicon dielectric mirror ”, Appl. Phys. Lett. 82 , 1512 – 1514 ( 2003 ). [CrossRef]
5 . S. M. Weiss , H. Ouyang , J. Zhang , and P. M. Fauchet , “ Electrical and thermal modulation of silicon photonic bandgap microcavities containing liquid crystals ,” Opt. Express 13 , 1090 – 1097 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1090 . [CrossRef] [PubMed]
6 . K. R. Maskaly , W. C. Carter , R. D. Averitt , and J. L. Maxwell , “ Application of the homogenization approximation to roughened one-dimensional photonic crystals ,” Opt. Lett. (to be published). [PubMed]
2. FDTD reflectivity results
1 . K. R. Maskaly , G. R. Maskaly , W. C. Carter , and J. L. Maxwell , “ Diminished normal reflectivity of one-dimensional photonic crystals due to dielectric interfacial roughness ,” Opt. Lett. 29 , 2791 – 2793 ( 2004 ). [CrossRef] [PubMed]
10 . K. S. Yee , “ Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media ,” IEEE Trans. Antennas Propag. 14 , 302 – 307 ( 1966 ). [CrossRef]
11 . D. M. Sullivan , Electromagnetic Simulation Using the FDTD Method ( Institute of Electrical and Electronics Engineers, Piscataway, N.J. , 2000 ). [CrossRef]
14 . Previously, we have referred to the quantity reported in Eq. (2) as the “percent” change in reflectivity. Here, we have changed the wording to “relative” as it is a more accurate description of the quantity in Eq. (2). Please note this change when comparing this manuscript to our previous ones.
3. Homogenization approximation reflectivity results
6 . K. R. Maskaly , W. C. Carter , R. D. Averitt , and J. L. Maxwell , “ Application of the homogenization approximation to roughened one-dimensional photonic crystals ,” Opt. Lett. (to be published). [PubMed]
6 . K. R. Maskaly , W. C. Carter , R. D. Averitt , and J. L. Maxwell , “ Application of the homogenization approximation to roughened one-dimensional photonic crystals ,” Opt. Lett. (to be published). [PubMed]
6 . K. R. Maskaly , W. C. Carter , R. D. Averitt , and J. L. Maxwell , “ Application of the homogenization approximation to roughened one-dimensional photonic crystals ,” Opt. Lett. (to be published). [PubMed]
4. Conclusions
6 . K. R. Maskaly , W. C. Carter , R. D. Averitt , and J. L. Maxwell , “ Application of the homogenization approximation to roughened one-dimensional photonic crystals ,” Opt. Lett. (to be published). [PubMed]
Acknowledgments
References and links
1 . | K. R. Maskaly , G. R. Maskaly , W. C. Carter , and J. L. Maxwell , “ Diminished normal reflectivity of one-dimensional photonic crystals due to dielectric interfacial roughness ,” Opt. Lett. 29 , 2791 – 2793 ( 2004 ). [CrossRef] [PubMed] |
2 . | G. S. He , T.-C. Lin , V. K. S. Hsiao , A. N. Cartwright , P. N. Prasad , L. V. Natarajan , V. P. Tondiglia , R. Jakubiak , R. A. Vaia , and T. J. Bunning , “ Tunable two-photon pumped lasing using a holographic polymer-dispersed liquid-crystal crating as a distributed feedback element ,” Appl. Phys. Lett. 83 , 2733 – 2735 ( 2003 ). [CrossRef] |
3 . | V. K. S. Hsiao , T.-C. Lin , G. S. He , A. N. Cartwright , P. N. Prasad , L. V. Natarajan , V. P. Tondiglia , and T. J. Bunning , “ Optical microfabrication of highly reflective volume Bragg gratings ,” Appl. Phys. Lett. 86 , 131113 ( 2005 ). [CrossRef] |
4 . | V. Agarwal and J. A. del Rio , “ Tailoring the photonic bandgap of a porous silicon dielectric mirror ”, Appl. Phys. Lett. 82 , 1512 – 1514 ( 2003 ). [CrossRef] |
5 . | S. M. Weiss , H. Ouyang , J. Zhang , and P. M. Fauchet , “ Electrical and thermal modulation of silicon photonic bandgap microcavities containing liquid crystals ,” Opt. Express 13 , 1090 – 1097 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1090 . [CrossRef] [PubMed] |
6 . | K. R. Maskaly , W. C. Carter , R. D. Averitt , and J. L. Maxwell , “ Application of the homogenization approximation to roughened one-dimensional photonic crystals ,” Opt. Lett. (to be published). [PubMed] |
7 . | A. Sentenac , G. Toso , and M. Saillard , “ Study of coherent scattering from one-dimensional rough surfaces with a mean-field theory ,” J. Opt. Soc. Am. A 15 , 924 – 931 ( 1998 ). [CrossRef] |
8 . | T. K. Gaylord , W. E. Baird , and M. G. Moharam , “ Zero-reflectivity high spatial frequency rectangular groove dielectric surface relief gratings ,” Appl. Opt. 25 , 4562 – 4567 ( 1986 ). [CrossRef] [PubMed] |
9 . | G. Voronovich , Wave Scattering from Rough Surfaces ( Springer-Verlag, Berlin , 1994 ). |
10 . | K. S. Yee , “ Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media ,” IEEE Trans. Antennas Propag. 14 , 302 – 307 ( 1966 ). [CrossRef] |
11 . | D. M. Sullivan , Electromagnetic Simulation Using the FDTD Method ( Institute of Electrical and Electronics Engineers, Piscataway, N.J. , 2000 ). [CrossRef] |
12 . | A. Taflove and S. C. Hagness , Computational Electrodynamics, 2nd ed. ( Artech House, Norwood, Mass. , 2000 ). |
13 . | J. P. Berenger , “ A perfectly matched layer for the absorption of electromagnetic waves ,” J. Comput. Phys. 114 , 185 – 200 ( 1994 ). [CrossRef] |
14 . | Previously, we have referred to the quantity reported in Eq. (2) as the “percent” change in reflectivity. Here, we have changed the wording to “relative” as it is a more accurate description of the quantity in Eq. (2). Please note this change when comparing this manuscript to our previous ones. |
15 . | J. A. Kong , Electromagnetic Wave Theory ( EMW, Cambridge, Mass ., 2000 ). |
16 . | C. F. Bohren and D. R. Huffman , Absorption and Scattering of Light by Small Particles ( Wiley, New York , 1983 ). |
OCIS Codes
(230.1480) Optical devices : Bragg reflectors
(240.5770) Optics at surfaces : Roughness
ToC Category:
Research Papers
History
Original Manuscript: July 25, 2005
Revised Manuscript: September 26, 2005
Published: October 17, 2005
Citation
Karlene Maskaly, W. Carter, Richard Averitt, and James Maxwell, "The effect of interfacial roughness on the normal incidence bandgap of one-dimensional photonic crystals," Opt. Express 13, 8380-8389 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-21-8380
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References
- K. R. Maskaly, G. R. Maskaly, W. C. Carter, and J. L. Maxwell, �??Diminished normal reflectivity of one-dimensional photonic crystals due to dielectric interfacial roughness,�?? Opt. Lett. 29, 2791-2793 (2004). [CrossRef] [PubMed]
- G. S. He, T.-C. Lin, V. K. S. Hsiao, A. N. Cartwright, P. N. Prasad, L. V. Natarajan, V. P. Tondiglia, R. Jakubiak, R. A. Vaia, and T. J. Bunning, �??Tunable two-photon pumped lasing using a holographic polymer-dispersed liquid-crystal crating as a distributed feedback element,�?? Appl. Phys. Lett. 83, 2733-2735 (2003). [CrossRef]
- V. K. S. Hsiao, T.-C. Lin, G. S. He, A. N. Cartwright, P. N. Prasad, L. V. Natarajan, V. P. Tondiglia, and T. J. Bunning, �??Optical microfabrication of highly reflective volume Bragg gratings,�?? Appl. Phys. Lett. 86, 131113 (2005). [CrossRef]
- V. Agarwal and J. A. del Rio, �??Tailoring the photonic bandgap of a porous silicon dielectric mirror,�?? Appl. Phys. Lett. 82, 1512-1514 (2003). [CrossRef]
- S. M. Weiss, H. Ouyang, J. Zhang, and P. M. Fauchet, �??Electrical and thermal modulation of silicon photonic bandgap microcavities containing liquid crystals,�?? 13, 1090-1097 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1090">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1090</a>. [CrossRef] [PubMed]
- K. R. Maskaly, W. C. Carter, R. D. Averitt, and J. L. Maxwell, �??Application of the homogenization approximation to roughened one-dimensional photonic crystals,�?? Opt. Lett. (to be published). [PubMed]
- A. Sentenac, G. Toso, and M. Saillard, �??Study of coherent scattering from one-dimensional rough surfaces with a mean-field theory,�?? J. Opt. Soc. Am. A 15, 924-931 (1998). [CrossRef]
- T. K. Gaylord, W. E. Baird, and M. G. Moharam, �??Zero-reflectivity high spatial frequency rectangular groove dielectric surface relief gratings,�?? Appl. Opt. 25, 4562-4567 (1986). [CrossRef] [PubMed]
- G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).
- K. S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas Propag. 14, 302-307 (1966). [CrossRef]
- D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics, 2nd ed. (Artech House, Norwood, Mass., 2000).
- J. P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comput. Phys. 114, 185-200 (1994). [CrossRef]
- Previously, we have referred to the quantity reported in Eq. (2) as the �??percent�?? change in reflectivity. Here, we have changed the wording to �??relative�?? as it is a more accurate description of the quantity in Eq. (2). Please note this change when comparing this manuscript to our previous ones.
- J. A. Kong, Electromagnetic Wave Theory (EMW, Cambridge, Mass., 2000).
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
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