Abstract

In this study the applicability of an interface procedure for combined ray-tracing and finite difference time domain (FDTD) simulations of optical systems which contain two diffractive gratings is discussed. The simulation of suchlike systems requires multiple FDTD↔RT steps. In order to minimize the error due to the loss of the phase information in an FDTD→RT step, we derive an equation for a maximal coherence correlation function (MCCF) which describes the maximum degree of impact of phase effects between these two different diffraction gratings and which depends on: the spatial distance between the gratings, the degree of spatial coherence of the light source and the diffraction angle of the first grating for the wavelength of light used. This MCCF builds an envelope of the oscillations caused by the distance dependent coupling effects between the two diffractive optical elements. Furthermore, by comparing the far field projections of pure FDTD simulations with the results of an RT→FDTD→RT→FDTD→RT interface procedure simulation we show that this function strongly correlates with the error caused by the interface procedure.

© 2014 Optical Society of America

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2014

2013

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

2012

2011

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt.58(5-6), 449–466 (2011).
[CrossRef]

A. Rohani, S. K. Chaudhuri, and S. Safavi-Naeini, “Gaussian Beam-Based Hybrid Method for Quasi-Optical Systems,” IEEE Trans. Antenn. Propag.59(12), 4679–4690 (2011).
[CrossRef]

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, “Metallic Bragg-gratings for light management in organic light-emitting devices,” Appl. Phys. Lett.99(10), 103303 (2011).
[CrossRef]

2010

C.-H. Lin, C.-Y. Chen, D.-M. Yeh, and C.-C. Yang, “Light extraction enhancement of a GaN-based light-emitting diode through grating-patterned photoelectrochemical surface etching with phase mask interferometry,” IEEE Photon. Technol. Lett.22(9), 640–642 (2010).
[CrossRef]

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Y. M. Song, J. S. Yu, and Y. T. Lee, “Antireflective submicrometer gratings on thin-film silicon solar cells for light-absorption enhancement,” Opt. Lett.35(3), 276–278 (2010).
[CrossRef] [PubMed]

S. Feng, X. Zhang, H. Wang, M. Xin, and Z. Lu, “Fiber coupled waveguide grating structures,” Appl. Phys. Lett.96(13), 133101 (2010).
[CrossRef]

P. Struk and T. Pustelny, “Design and numerical analyses of the planar grating coupler,” Bull. Polish Acad. Sci. Tech. Sci.58, 509–512 (2010).

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron.46(10), 1456–1463 (2010).
[CrossRef]

I. J. Buss, G. R. Nash, J. G. Rarity, and M. J. Cryan, “Finite-difference time-domain modeling of periodic and disordered surface gratings in AlInSb light emitting diodes with metallic back-reflectors,” J. Lightwave Technol.28(8), 1190–1200 (2010).
[CrossRef]

2009

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys.106(7), 074901 (2009).
[CrossRef]

2007

G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett.32(11), 1495–1497 (2007).
[CrossRef] [PubMed]

M. Lang and T. D. Milster, “Investigation of optics in the 10 – 200 µm size regime,” Opt. Rev.14(4), 189–193 (2007).
[CrossRef]

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys.46(1), 31–34 (2007).
[CrossRef]

2006

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency Silicon-on-Insulator grating coupler based on a poly-Silicon overlay,” Opt. Express14(24), 11622–11630 (2006).
[CrossRef] [PubMed]

2005

A. Taflove and S. C. Hagness, “Computational Electrodynamics,” The Finite-Difference Time-Domain Method2010, 1006 (2005).

2003

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

2002

Y. Wang, S. K. Chaudhuri, and S. Safavi-Naeini, “An FDTD/ray-tracing analysis method for wave penetration through inhomogeneous walls,” IEEE Trans. Antenn. Propag.50(11), 1598–1604 (2002).
[CrossRef]

2000

Y. Wang, S. Safavi-Naeini, and S. K. Chaudhuri, “A hybrid technique based on combining ray tracing and FDTD methods for site-specific modeling of indoor radio wave propagation,” IEEE Trans. Antenn. Propag.48(5), 743–754 (2000).
[CrossRef]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

Asche-Tauscher, J.

Ayre, M.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Baets, R.

Bao, K.

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

Belegratis, M.

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Bienstman, P.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Bocksrocker, T.

Bogaerts, W.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Bower, C. A.

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

Branz, H. M.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Businaro, L.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Buss, I. J.

Cabrini, S.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Candeloro, P.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Chaudhuri, S. K.

A. Rohani, S. K. Chaudhuri, and S. Safavi-Naeini, “Gaussian Beam-Based Hybrid Method for Quasi-Optical Systems,” IEEE Trans. Antenn. Propag.59(12), 4679–4690 (2011).
[CrossRef]

Y. Wang, S. K. Chaudhuri, and S. Safavi-Naeini, “An FDTD/ray-tracing analysis method for wave penetration through inhomogeneous walls,” IEEE Trans. Antenn. Propag.50(11), 1598–1604 (2002).
[CrossRef]

Y. Wang, S. Safavi-Naeini, and S. K. Chaudhuri, “A hybrid technique based on combining ray tracing and FDTD methods for site-specific modeling of indoor radio wave propagation,” IEEE Trans. Antenn. Propag.48(5), 743–754 (2000).
[CrossRef]

Chen, C.-Y.

C.-H. Lin, C.-Y. Chen, D.-M. Yeh, and C.-C. Yang, “Light extraction enhancement of a GaN-based light-emitting diode through grating-patterned photoelectrochemical surface etching with phase mask interferometry,” IEEE Photon. Technol. Lett.22(9), 640–642 (2010).
[CrossRef]

Cingolani, R.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Cojoc, D.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Cryan, M. J.

Dai, T.

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

Degiorgio, V.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Dewan, R.

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys.106(7), 074901 (2009).
[CrossRef]

Di Fabrizio, E.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Eschenbaum, C.

Fan, S.

Feng, S.

S. Feng, X. Zhang, H. Wang, M. Xin, and Z. Lu, “Fiber coupled waveguide grating structures,” Appl. Phys. Lett.96(13), 133101 (2010).
[CrossRef]

Gerardino, A.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Gerken, M.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, “Metallic Bragg-gratings for light management in organic light-emitting devices,” Appl. Phys. Lett.99(10), 103303 (2011).
[CrossRef]

Geyer, U.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, “Metallic Bragg-gratings for light management in organic light-emitting devices,” Appl. Phys. Lett.99(10), 103303 (2011).
[CrossRef]

Gigli, G.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Grego, S.

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

Grenville, A.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Hagness, S. C.

A. Taflove and S. C. Hagness, “Computational Electrodynamics,” The Finite-Difference Time-Domain Method2010, 1006 (2005).

Hartmann, P.

C. Leiner, S. Schweitzer, F. P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “A simulation procedure interfacing ray-tracing and finite-difference time-domain methods for a combined simulation of diffractive and refractive optical elements,” J. Lightwave Technol.32(6), 1054–1062 (2014).
[CrossRef]

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Hauss, J.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, “Metallic Bragg-gratings for light management in organic light-emitting devices,” Appl. Phys. Lett.99(10), 103303 (2011).
[CrossRef]

Hohenester, U.

C. Leiner, S. Schweitzer, F. P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “A simulation procedure interfacing ray-tracing and finite-difference time-domain methods for a combined simulation of diffractive and refractive optical elements,” J. Lightwave Technol.32(6), 1054–1062 (2014).
[CrossRef]

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Huffman, A.

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

Jin, X.

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron.46(10), 1456–1463 (2010).
[CrossRef]

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

Jin, Y.

Kang, X.-N.

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

Katsuda, H.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys.46(1), 31–34 (2007).
[CrossRef]

Kawaguchi, Y.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys.46(1), 31–34 (2007).
[CrossRef]

Keszler, D. A.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Knipp, D.

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys.106(7), 074901 (2009).
[CrossRef]

Kuhn, M.

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt.58(5-6), 449–466 (2011).
[CrossRef]

Kumar, R.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Lang, M.

M. Lang and T. D. Milster, “Investigation of optics in the 10 – 200 µm size regime,” Opt. Rev.14(4), 189–193 (2007).
[CrossRef]

Lee, B. G.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Lee, J.-S.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys.46(1), 31–34 (2007).
[CrossRef]

Lee, Y. T.

Leiner, C.

C. Leiner, S. Schweitzer, F. P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “A simulation procedure interfacing ray-tracing and finite-difference time-domain methods for a combined simulation of diffractive and refractive optical elements,” J. Lightwave Technol.32(6), 1054–1062 (2014).
[CrossRef]

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Lemmer, U.

Li, Q.

Liberale, C.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Lin, C.-H.

C.-H. Lin, C.-Y. Chen, D.-M. Yeh, and C.-C. Yang, “Light extraction enhancement of a GaN-based light-emitting diode through grating-patterned photoelectrochemical surface etching with phase mask interferometry,” IEEE Photon. Technol. Lett.22(9), 640–642 (2010).
[CrossRef]

Lu, Z.

S. Feng, X. Zhang, H. Wang, M. Xin, and Z. Lu, “Fiber coupled waveguide grating structures,” Appl. Phys. Lett.96(13), 133101 (2010).
[CrossRef]

Maier-Flaig, F.

Meyers, S. T.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Milster, T. D.

M. Lang and T. D. Milster, “Investigation of optics in the 10 – 200 µm size regime,” Opt. Rev.14(4), 189–193 (2007).
[CrossRef]

Nash, G. R.

Naskar, S.

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

Nishizono, K.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys.46(1), 31–34 (2007).
[CrossRef]

Pargner, A.

Patel, A. M.

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

Pisignano, D.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Prasciolu, M.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Preinfalk, J. B.

Pustelny, T.

P. Struk and T. Pustelny, “Design and numerical analyses of the planar grating coupler,” Bull. Polish Acad. Sci. Tech. Sci.58, 509–512 (2010).

Rarity, J. G.

Riedel, B.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, “Metallic Bragg-gratings for light management in organic light-emitting devices,” Appl. Phys. Lett.99(10), 103303 (2011).
[CrossRef]

Roelkens, G.

Rohani, A.

A. Rohani, S. K. Chaudhuri, and S. Safavi-Naeini, “Gaussian Beam-Based Hybrid Method for Quasi-Optical Systems,” IEEE Trans. Antenn. Propag.59(12), 4679–4690 (2011).
[CrossRef]

Safavi-Naeini, S.

A. Rohani, S. K. Chaudhuri, and S. Safavi-Naeini, “Gaussian Beam-Based Hybrid Method for Quasi-Optical Systems,” IEEE Trans. Antenn. Propag.59(12), 4679–4690 (2011).
[CrossRef]

Y. Wang, S. K. Chaudhuri, and S. Safavi-Naeini, “An FDTD/ray-tracing analysis method for wave penetration through inhomogeneous walls,” IEEE Trans. Antenn. Propag.50(11), 1598–1604 (2002).
[CrossRef]

Y. Wang, S. Safavi-Naeini, and S. K. Chaudhuri, “A hybrid technique based on combining ray tracing and FDTD methods for site-specific modeling of indoor radio wave propagation,” IEEE Trans. Antenn. Propag.48(5), 743–754 (2000).
[CrossRef]

Schmidt, V.

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Schweitzer, S.

C. Leiner, S. Schweitzer, F. P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “A simulation procedure interfacing ray-tracing and finite-difference time-domain methods for a combined simulation of diffractive and refractive optical elements,” J. Lightwave Technol.32(6), 1054–1062 (2014).
[CrossRef]

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Sommer, C.

C. Leiner, S. Schweitzer, F. P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “A simulation procedure interfacing ray-tracing and finite-difference time-domain methods for a combined simulation of diffractive and refractive optical elements,” J. Lightwave Technol.32(6), 1054–1062 (2014).
[CrossRef]

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Song, Y. M.

Stoner, B. R.

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

Struk, P.

P. Struk and T. Pustelny, “Design and numerical analyses of the planar grating coupler,” Bull. Polish Acad. Sci. Tech. Sci.58, 509–512 (2010).

Taflove, A.

A. Taflove and S. C. Hagness, “Computational Electrodynamics,” The Finite-Difference Time-Domain Method2010, 1006 (2005).

Taillaert, D.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Tormen, M.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Trieu, S. S.

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron.46(10), 1456–1463 (2010).
[CrossRef]

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

Van Laere, F.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Van Thourhout, D.

Wang, H.

S. Feng, X. Zhang, H. Wang, M. Xin, and Z. Lu, “Fiber coupled waveguide grating structures,” Appl. Phys. Lett.96(13), 133101 (2010).
[CrossRef]

Wang, Y.

Y. Wang, S. K. Chaudhuri, and S. Safavi-Naeini, “An FDTD/ray-tracing analysis method for wave penetration through inhomogeneous walls,” IEEE Trans. Antenn. Propag.50(11), 1598–1604 (2002).
[CrossRef]

Y. Wang, S. Safavi-Naeini, and S. K. Chaudhuri, “A hybrid technique based on combining ray tracing and FDTD methods for site-specific modeling of indoor radio wave propagation,” IEEE Trans. Antenn. Propag.48(5), 743–754 (2000).
[CrossRef]

Weiss, D. N.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Wenzel, F. P.

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

Wenzl, F. P.

Wyrowski, F.

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt.58(5-6), 449–466 (2011).
[CrossRef]

Xin, M.

S. Feng, X. Zhang, H. Wang, M. Xin, and Z. Lu, “Fiber coupled waveguide grating structures,” Appl. Phys. Lett.96(13), 133101 (2010).
[CrossRef]

Yang, C.-C.

C.-H. Lin, C.-Y. Chen, D.-M. Yeh, and C.-C. Yang, “Light extraction enhancement of a GaN-based light-emitting diode through grating-patterned photoelectrochemical surface etching with phase mask interferometry,” IEEE Photon. Technol. Lett.22(9), 640–642 (2010).
[CrossRef]

Yang, F.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

Yeh, D.-M.

C.-H. Lin, C.-Y. Chen, D.-M. Yeh, and C.-C. Yang, “Light extraction enhancement of a GaN-based light-emitting diode through grating-patterned photoelectrochemical surface etching with phase mask interferometry,” IEEE Photon. Technol. Lett.22(9), 640–642 (2010).
[CrossRef]

Yu, J. S.

Yuan, H.-C.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Zhang, B.

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

Zhang, G.-Y.

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

Zhang, X.

S. Feng, X. Zhang, H. Wang, M. Xin, and Z. Lu, “Fiber coupled waveguide grating structures,” Appl. Phys. Lett.96(13), 133101 (2010).
[CrossRef]

Zhu, J.

Zhu, Z.

Appl. Phys. Lett.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, “Metallic Bragg-gratings for light management in organic light-emitting devices,” Appl. Phys. Lett.99(10), 103303 (2011).
[CrossRef]

S. Feng, X. Zhang, H. Wang, M. Xin, and Z. Lu, “Fiber coupled waveguide grating structures,” Appl. Phys. Lett.96(13), 133101 (2010).
[CrossRef]

Bull. Polish Acad. Sci. Tech. Sci.

P. Struk and T. Pustelny, “Design and numerical analyses of the planar grating coupler,” Bull. Polish Acad. Sci. Tech. Sci.58, 509–512 (2010).

IEEE J. Quantum Electron.

S. S. Trieu and X. Jin, “Study of top and bottom photonic gratings on GaN LED with error grating models,” IEEE J. Quantum Electron.46(10), 1456–1463 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

C.-H. Lin, C.-Y. Chen, D.-M. Yeh, and C.-C. Yang, “Light extraction enhancement of a GaN-based light-emitting diode through grating-patterned photoelectrochemical surface etching with phase mask interferometry,” IEEE Photon. Technol. Lett.22(9), 640–642 (2010).
[CrossRef]

IEEE Trans. Antenn. Propag.

A. Rohani, S. K. Chaudhuri, and S. Safavi-Naeini, “Gaussian Beam-Based Hybrid Method for Quasi-Optical Systems,” IEEE Trans. Antenn. Propag.59(12), 4679–4690 (2011).
[CrossRef]

Y. Wang, S. Safavi-Naeini, and S. K. Chaudhuri, “A hybrid technique based on combining ray tracing and FDTD methods for site-specific modeling of indoor radio wave propagation,” IEEE Trans. Antenn. Propag.48(5), 743–754 (2000).
[CrossRef]

Y. Wang, S. K. Chaudhuri, and S. Safavi-Naeini, “An FDTD/ray-tracing analysis method for wave penetration through inhomogeneous walls,” IEEE Trans. Antenn. Propag.50(11), 1598–1604 (2002).
[CrossRef]

K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

J. Appl. Phys.

R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys.106(7), 074901 (2009).
[CrossRef]

J. Lightwave Technol.

J. Mod. Opt.

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt.58(5-6), 449–466 (2011).
[CrossRef]

J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.

D. N. Weiss, H.-C. Yuan, B. G. Lee, H. M. Branz, S. T. Meyers, A. Grenville, and D. A. Keszler, “Nanoimprinting for diffractive light trapping in solar cells,” J. Vac. Sci. Technol. B-Microelectron. and Nanom. Struct.28, C6M98 (2010).

Jpn. J. Appl. Phys.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys.46(1), 31–34 (2007).
[CrossRef]

Microelectron. Eng.

M. Prasciolu, D. Cojoc, S. Cabrini, L. Businaro, P. Candeloro, M. Tormen, R. Kumar, C. Liberale, V. Degiorgio, A. Gerardino, G. Gigli, D. Pisignano, E. Di Fabrizio, and R. Cingolani, “Design and fabrication of on-fiber diffractive elements for fiber-waveguide coupling by means of e-beam lithography,” Microelectron. Eng.68, 169–174 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

M. Lang and T. D. Milster, “Investigation of optics in the 10 – 200 µm size regime,” Opt. Rev.14(4), 189–193 (2007).
[CrossRef]

Proc. SPIE

S. Grego, S. Naskar, A. M. Patel, A. Huffman, C. A. Bower, and B. R. Stoner, “Novel optical-waveguide sensing platform based on input grating coupler,” Proc. SPIE6123, 61230D (2006).
[CrossRef]

S. S. Trieu, X. Jin, B. Zhang, T. Dai, K. Bao, X.-N. Kang, and G.-Y. Zhang, “Light Extraction Improvement of GaN-based Light Emitting Diodes using Patterned Undoped GaN Bottom Reflection Gratings,” Proc. SPIE7216, 72162Q (2009).
[CrossRef]

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F. P. Wenzel, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE8781, 87810Z (2013).
[CrossRef]

The Finite-Difference Time-Domain Method

A. Taflove and S. C. Hagness, “Computational Electrodynamics,” The Finite-Difference Time-Domain Method2010, 1006 (2005).

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

M. Born and E. Wolf, Principles of Optics (1999), Vol. 1.

L.-W. Cheng, Y. Sheng, C.-S. Xia, W. Lu, M. Lestrade, and Z.-M. Li, “Simulation for light power distribution of 3D InGaN/GaN MQW LED with textured surface,” Numer Simul Optoelectron Devices 1-2 (2010).

Y. Sheng, C. S. Xia, Z. M. Simon Li, and L. W. Cheng, “Simulation of InGaN/GaN light-emitting diodes with patterned sapphire substrate,” 2012 12th Int. Conf. Numer. Simul. Optoelectron. Devices 23–24 (2012).
[CrossRef]

LightTrans,” http://www.lighttrans.com/ .

Breault Research Organization, ASAP - Getting started guide,” http://www.breault.com/resources/kbasePDF/broman0108_getstart.pdf .

Lumerical Solutions, FDTD Solutions Knowledge Base,” http://docs.lumerical.com/en/fdtd/knowledge_base.html .

A. W. Greynolds, “Vector Formulation Of The Ray-Equivalent Method For General Gaussian Beam Propagation,” Proc. of SPIE 0679 (1986).

Breault Research Organization, Wave Optics in ASAP,” http://www.breault.com/resources/kbasePDF/brotg0919_wave.pdf .

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T. Pustelny, I. Zielonka, P. Karasinski, and J. Jurusik, “Bragg ’ s grating coupler in planar optical sol-gel waveguides,” Opt. Appl. XXXIV, Vol. 4 (2004).

K. Schmitt and C. Hoffmann, High-Refractive-Index Waveguide Platforms for Chemical and Biosensing, Optical Gu, Springer Series on Chemical Sensors and Biosensors (Springer Berlin Heidelberg, 2009), Vol. 7, pp. 21–55.

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Figures (5)

Fig. 1
Fig. 1

(a) Sketch to illustrate the notation for the far-zone form of the van Cittert-Zernike theorem, adopted from [36], (b) Illustration of the parameters needed for the derivation of the MCCF, (c) Plot of the MCCF for a diffraction angle of the first grating β = 43.43°.

Fig. 2
Fig. 2

(a) Scheme of the orientation of the FDTD simulation area between the two periodic gratings. (b) Illustration of the FDTD simulation area and its components: The orange lines define the boundary conditions of the simulation area; the green line shows the position of the injected plane wave; the yellow line indicates the position of the standard Fourier transformation (SFT) monitor. The simulation area contains unit cells of grating B and grating C which are separated by the distance dBC. They are replicated in x-direction by the Bloch boundary conditions to simulate two gratings with an orientation as given in Fig. 2(a).

Fig. 3
Fig. 3

(a), (b) Simulation results for the simulation model of Fig. 2, recorded with the SFT-monitor for different distances dBC using two identical diffraction gratings with β = 43.43° and (a) for an angle of incident 0°, (b) for a superposition of different angles of incidence from −1.5° up to + 1.5° in 0.1° steps. (c) Modulation of |<S>|2 extracted from the data of (b) compared with the MCCF j(α = 1.5°, β = 43.43°, dBC).

Fig. 4
Fig. 4

(a),(c),(e) Far field transformations of the SFT-monitor data of Fig. 3(b) (colored lines) compared with the simulation results using the interface procedure (thick black line). (a) SFT data for 0 µm < dBC < 5 µm, (c) SFT data for 5 µm < dBC < 10 µm, (e) SFT data for 20 µm < dBC < 25 µm, (b) (d) (f) show zooms of the zeroth order of the far field distributions and the deviations of the FDTD far field results from the interface result.

Fig. 5
Fig. 5

(a) Modulation of |<(S)>|2 compared with the MCCF and an average of the different possible combinations of coherence correlations between the orders (b),(c) Far field transformations of the SFT-monitor data for two rectangular gratings with a grating constant of 1400 nm (colored lines) compared with the simulation results using the interface procedure (thick black line). (b) SFT data for 0 µm < dBC < 15 µm, (c) SFT data for 20 µm < dBC < 25 µm.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

j ( r 1 , r 2 ) = e i k ¯ ( r 2 r 1 ) σ I ( r ' ) e i k ¯ ( s 2 s 1 ) r ' d 2 r ' σ I ( r ' ) d 2 r ' ,
j( r 1 , r 2 )= 1 π a 2 0 a 0 2π e i k ¯ ρwcos(θψ) ρdρdθ .
j( r 1 , r 2 )= 2 J 1 (ν) ν with ν= k ¯ a| s 2 s 1 |
| s 2 s 1 |= d 12 d AB
α= a d AB
j(α, d 12 )= 2 J 1 (ν) ν ,with ν= k ¯ d 12 α.
j(α,β, d BC )= 2 J 1 (ν) ν ,with ν= k ¯ α d BC tanβ
j( r 1 , r 2 )= 1 2a a a e i k ¯ ( s 2 s 1 )x dx
j(α,β, d BC )= sin(ν) ν ,with ν= k ¯ α d BC tanβ.

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