A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for
electromagnetic simulations by the FDTD method," Comput. Phys. Commun. 181, 687-702 (2010).

J. Wierer, A. David, M. Megens, "III-nitride photonic-crystal light-emitting diodes
with high extraction efficiency," Nat. Photon. 7, (2009).

I. J. Buss, "Three-dimensional numerical modeling of emission from
InSb light-emitting diodes with patterned surfaces," J. Opt. Soc. Amer. B 25, 810-817 (2008).

M. K. Haigh, G. R. Nash, S. J. Smith, L. Buckle, M. T. Emeny, T. Ashley, "Mid-infrared AlxIn1-xSb light-emitting diodes," Appl. Phys. Lett. 90, 231116- (2007).

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, S. P. DenBaars, C. Weisbuch, H. Benisty, "GaN light-emitting diodes with archimedean lattice
photonic crystals," Appl. Phys. Lett. 88, 073510- (2006).

N. G. Skinner, D. M. Byrne, "Finite-difference time-domain analysis of
frequency-selective surfaces in the midinfrared," Appl. Opt. 45, 1943-1950 (2006).

C. A. Flory, "Analysis of directional grating-coupled radiation in
waveguide structures," IEEE J. Quantum Electron. 40, 949-957 (2004).

D. S. Wuu, S. C. Hsu, S. H. Huang, C. C. Wu, C. E. Lee, R. H. Horng, "GaN/mirror/Si light-emitting diodes for vertical
current injection by laser lift-off and wafer bonding techniques," Jpn. J. Appl. Phys. 43, 5239-5242 (2004).

A. M. Green, D. G. Gevaux, C. Roberts, C. C. Phillips, "Resonant-cavity-enhanced photodetectors and LEDs in
the midinfrared," Physica E 20, 531-535 (2004).

D. G. Gevaux, A. Green, C. Palmer, P. Stavrinou, C. Roberts, C. Phillips, "Resonant-cavity light-emitting diodes (RC-LEDs) and
detectors for midIR gas-sensing applications," Proc. IEE Optoelectron. 150, 360-364 (2003).

D. Delbeke, P. Bienstman, R. Bockstaele, R. Baets, "Rigorous electromagnetic analysis of dipole emission
in periodically corrugated layers: The grating-assisted
resonant-cavity light-emitting diode," J. Opt. Soc. Am. A 19, 871-880 (2002).

J. G. Crowder, H. R. Hardaway, C. T. Elliott, "Mid-infrared gas detection using optically immersed,
room-temperature, semiconductor devices," Meas. Sci. Technol. 13, 882-884 (2002).

G. R. Nash, T. Ashley, N. T. Gordon, C. Jones, C. Maxey, "Micromachined optical concentrators for IR negative
luminescent devices," J. Mod. Opt. 811-820 (2002).

W. Schmid, M. Scherer, C. Karnutsch, A. Plossl, W. Wegleiter, S. S. Schad, B. Neubert, K. Streubel, "High-efficiency red and infrared light-emitting diodes
using radial outcoupling taper," IEEE J. Sel. Top. Quantum Electron. 8, 256-263 (2002).

R. Windisch, B. Dutta, M. Kuijk, A. Knobloch, S. Meinlschmidt, S. Schoberth, P. Kiesel, G. Borghs, G. Dohler, P. Heremans, "40% efficient thin-film surface-textured
light-emitting diodes by optimization of natural lithography," IEEE Trans. Electron. Dev. 47, 1492-1498 (2000).

M. R. Krames, M. Ochiai-Holcomb, G. E. Hofler, C. Carter-Coman, E. I. Chen, I. H. Tan, P. Grillot, N. F. Gardner, H. C. Chui, J. W. Wang, S. A. Stockman, F. A. Kish, M. G. Craford, T. S. Tan, C. P. Kocot, M. Hueschen, J. Posselt, B. Loh, G. Sasser, D. Collins, "High-power truncated-inverted-pyramid
(AlxGa1-x)(0.5)In0.5P/GaP light-emitting diodes exhibiting $> 50\hbox{\%}$ external quantum efficiency," Appl. Phys. Lett. 5, 2365-2367 (1999).

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, "Light extraction from optically pumped light-emitting
diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).

R. Windisch, P. Heremans, B. Dutta, M. Kuijk, S. Schoberth, P. Kiesel, G. H. Dohler, G. Borghs, "High-efficiency non-resonant cavity light-emitting
diodes," Electron. Lett. 34, 1153-1155 (1998).

H. Benisty, H. De Neve, C. Weisbuch, "Impact of planar microcavity effects on light
extraction-Part I: Basic concepts and analytical trends," IEEE J. Quantum Electron. 34, 1612-1631 (1998).

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, A. Scherer, "30% external quantum efficiency from surface textured,
thin-film light-emitting diodes," Appl. Phys. Lett. 63, 2174-2176 (1993).

Y. Yamamoto, T. Kamiya, H. Yanai, "Improved coupled mode analysis of corrugated
waveguides and lasers," IEEE J. Quantum Electron. QE-14, 245-258 (1978).

S. T. Peng, T. Tamir, H. L. Bertoni, "Theory of periodic dielect waveguides," IEEE Trans. Microw. Theory Techniques 23, 123-133 (1975).

W. N. Carr, "Photometric figures of merit for semiconductor
luminescent sources operating in spontaneous mode," Infrared Phys. 1-19 (1966).

K. S. Yee, "Numerical solution of initial boundary value problems
involving maxwells equations in isotropic media," IEEE Trans. Ant. Prop. AP-14, 302-307 (1966).

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, A. Scherer, "30% external quantum efficiency from surface textured,
thin-film light-emitting diodes," Appl. Phys. Lett. 63, 2174-2176 (1993).

M. K. Haigh, G. R. Nash, S. J. Smith, L. Buckle, M. T. Emeny, T. Ashley, "Mid-infrared AlxIn1-xSb light-emitting diodes," Appl. Phys. Lett. 90, 231116- (2007).

M. R. Krames, M. Ochiai-Holcomb, G. E. Hofler, C. Carter-Coman, E. I. Chen, I. H. Tan, P. Grillot, N. F. Gardner, H. C. Chui, J. W. Wang, S. A. Stockman, F. A. Kish, M. G. Craford, T. S. Tan, C. P. Kocot, M. Hueschen, J. Posselt, B. Loh, G. Sasser, D. Collins, "High-power truncated-inverted-pyramid
(AlxGa1-x)(0.5)In0.5P/GaP light-emitting diodes exhibiting $> 50\hbox{\%}$ external quantum efficiency," Appl. Phys. Lett. 5, 2365-2367 (1999).

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, E. Yablonovitch, "Light extraction from optically pumped light-emitting
diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, S. P. DenBaars, C. Weisbuch, H. Benisty, "GaN light-emitting diodes with archimedean lattice
photonic crystals," Appl. Phys. Lett. 88, 073510- (2006).

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for
electromagnetic simulations by the FDTD method," Comput. Phys. Commun. 181, 687-702 (2010).

R. Windisch, P. Heremans, B. Dutta, M. Kuijk, S. Schoberth, P. Kiesel, G. H. Dohler, G. Borghs, "High-efficiency non-resonant cavity light-emitting
diodes," Electron. Lett. 34, 1153-1155 (1998).

H. Benisty, H. De Neve, C. Weisbuch, "Impact of planar microcavity effects on light
extraction-Part I: Basic concepts and analytical trends," IEEE J. Quantum Electron. 34, 1612-1631 (1998).

Y. Yamamoto, T. Kamiya, H. Yanai, "Improved coupled mode analysis of corrugated
waveguides and lasers," IEEE J. Quantum Electron. QE-14, 245-258 (1978).

C. A. Flory, "Analysis of directional grating-coupled radiation in
waveguide structures," IEEE J. Quantum Electron. 40, 949-957 (2004).

W. Schmid, M. Scherer, C. Karnutsch, A. Plossl, W. Wegleiter, S. S. Schad, B. Neubert, K. Streubel, "High-efficiency red and infrared light-emitting diodes
using radial outcoupling taper," IEEE J. Sel. Top. Quantum Electron. 8, 256-263 (2002).

K. S. Yee, "Numerical solution of initial boundary value problems
involving maxwells equations in isotropic media," IEEE Trans. Ant. Prop. AP-14, 302-307 (1966).

R. Windisch, B. Dutta, M. Kuijk, A. Knobloch, S. Meinlschmidt, S. Schoberth, P. Kiesel, G. Borghs, G. Dohler, P. Heremans, "40% efficient thin-film surface-textured
light-emitting diodes by optimization of natural lithography," IEEE Trans. Electron. Dev. 47, 1492-1498 (2000).

S. T. Peng, T. Tamir, H. L. Bertoni, "Theory of periodic dielect waveguides," IEEE Trans. Microw. Theory Techniques 23, 123-133 (1975).

W. N. Carr, "Photometric figures of merit for semiconductor
luminescent sources operating in spontaneous mode," Infrared Phys. 1-19 (1966).

G. R. Nash, T. Ashley, N. T. Gordon, C. Jones, C. Maxey, "Micromachined optical concentrators for IR negative
luminescent devices," J. Mod. Opt. 811-820 (2002).

I. J. Buss, "Three-dimensional numerical modeling of emission from
InSb light-emitting diodes with patterned surfaces," J. Opt. Soc. Amer. B 25, 810-817 (2008).

D. S. Wuu, S. C. Hsu, S. H. Huang, C. C. Wu, C. E. Lee, R. H. Horng, "GaN/mirror/Si light-emitting diodes for vertical
current injection by laser lift-off and wafer bonding techniques," Jpn. J. Appl. Phys. 43, 5239-5242 (2004).

J. G. Crowder, H. R. Hardaway, C. T. Elliott, "Mid-infrared gas detection using optically immersed,
room-temperature, semiconductor devices," Meas. Sci. Technol. 13, 882-884 (2002).

J. Wierer, A. David, M. Megens, "III-nitride photonic-crystal light-emitting diodes
with high extraction efficiency," Nat. Photon. 7, (2009).

A. M. Green, D. G. Gevaux, C. Roberts, C. C. Phillips, "Resonant-cavity-enhanced photodetectors and LEDs in
the midinfrared," Physica E 20, 531-535 (2004).

D. G. Gevaux, A. Green, C. Palmer, P. Stavrinou, C. Roberts, C. Phillips, "Resonant-cavity light-emitting diodes (RC-LEDs) and
detectors for midIR gas-sensing applications," Proc. IEE Optoelectron. 150, 360-364 (2003).

T. S. Moss, G. J. Burrell, B. Ellis, Semiconductor Opto-Electronics (Butterworths, 1973).

A. Yariv, P. Yeh, Photonics .

http://ab-initio.mit.edu/wiki/index.php/Meep.

http://www.luxpop.com/.