## Plasmonic grating as a nonlinear converter-coupler |

Optics Express, Vol. 20, Issue 2, pp. 1392-1405 (2012)

http://dx.doi.org/10.1364/OE.20.001392

Acrobat PDF (1647 KB)

### Abstract

The paper introduces a wavelength converter composed of a metallic finite 2-dimensional particle grating on top of an optical waveguide. The particles sustain plasmonic resonances which will result in the near-field enhancement and therefore, high conversion efficiency. Due to near-field interaction of the grating field with the propagating modes of the waveguide, the generated third harmonic wave is phase-matched to a propagating mode of the waveguide, while the fundamental frequency component is not coupled into the output waveguide of the structure. The performance of this structure is numerically investigated using a full-wave transmission line method for the linear analysis and a three-dimensional finite-difference time-domain method for the nonlinear analysis.

© 2012 OSA

## 1. Introduction

1. B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B **68**(3), 419–423 (1999). [CrossRef]

2. T. Zentgraf, A. Christ, J. Kuhl, and H. Giessen, “Tailoring the ultrafast dephasing of quasiparticles in metallic photonic crystals,” Phys. Rev. Lett. **93**(24), 243901 (2004). [CrossRef] [PubMed]

3. Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B **82**(15), 155107 (2010). [CrossRef]

4. M. D. Wissert, K. S. Ilin, M. Siegel, U. Lemmer, and H. J. Eisler, “Coupled nanoantenna plasmon resonance spectra from two-photon laser excitation,” Nano Lett. **10**(10), 4161–4165 (2010). [CrossRef] [PubMed]

5. T. Uthayakumar, C. P. Jisha, K. Porsezian, and V. C. Kuriakose, “Switching dynamics of a two- dimensional nonlinear directional coupler in a photopolymer,” J. Opt. **12**(1), 015204 (2010). [CrossRef]

6. S. Kim, J. H. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature **453**(7196), 757–760 (2008). [CrossRef] [PubMed]

7. K. Dolgaleva and R. W. Boyd, “Laser gain media based on nanocomposite materials,” J. Opt. Soc. Am. B **24**(10), A19–A25 (2007). [CrossRef]

8. R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, “Accessing the optical nonlinearity of metals with metal- dielectric photonic bandgap structures,” Opt. Lett. **24**(20), 1416–1418 (1999). [CrossRef] [PubMed]

9. D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. **33**(11), 2038–2059 (1997). [CrossRef]

12. S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A **13**(5), 993–1005 (1996). [CrossRef]

13. R. W. Day, S. S. Wang, and R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. **14**(8), 1815–1824 (1996). [CrossRef]

14. D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Design considerations for narrow-band dielectric resonant grating reflection filters of finite length,” J. Opt. Soc. Am. A **17**(7), 1241–1249 (2000). [CrossRef] [PubMed]

15. A. Selle, C. Kappel, M. A. Bader, G. Marowsky, K. Winkler, and U. Alexiev, “Picosecond-pulse-induced two-photon fluorescence enhancement in biological material by application of grating waveguide structures,” Opt. Lett. **30**(13), 1683–1685 (2005). [CrossRef] [PubMed]

16. S. Soria, T. Katchalski, E. Teitelbaum, A. A. Friesem, and G. Marowsky, “Enhanced two-photon fluorescence excitation by resonant grating waveguide structures,” Opt. Lett. **29**(17), 1989–1991 (2004). [CrossRef] [PubMed]

17. C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structures as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B **21**(6), 1127–1136 (2004). [CrossRef]

18. A. M. Ferrie, Q. Wu, and Y. Fang, “Resonant waveguide grating imager for live cell sensing,” Appl. Phys. Lett. **97**(22), 223704 (2010). [CrossRef] [PubMed]

19. H. N. Daghestani and B. W. Day, “Theory and applications of surface plasmon resonance, resonant mirror, resonant waveguide grating, and dual polarization interferometry biosensors,” Sensors (Basel Switzerland) **10**(11), 9630–9646 (2010). [CrossRef]

20. J. Y. Andersson, L. Lundqvist, and Z. F. Paska, “Quantum efficiency enhancement of AlGaAs/GaAs quantum-Well Infrared detectors using a wave-guide with a grating coupler,” Appl. Phys. Lett. **58**(20), 2264–2266 (1991). [CrossRef]

21. S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A **13**(5), 993–1005 (1996). [CrossRef]

_{WG}(Output detector), while both the fundamental and converted beams are present at the location of D

_{T}. This detector is placed just below the substrate, enabling the detection of near-field intensities of the electromagnetic field. In [22

22. N. Talebi and M. Shahabadi, “All-optical wavelength converter based on a heterogeneously integrated GaP on a silicon-on-insulator waveguide,” J. Opt. Soc. Am. B **27**(11), 2273–2278 (2010). [CrossRef]

23. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B **80**(19), 195415 (2009). [CrossRef]

24. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. **106**(13), 133901 (2011). [CrossRef] [PubMed]

23. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B **80**(19), 195415 (2009). [CrossRef]

24. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. **106**(13), 133901 (2011). [CrossRef] [PubMed]

25. Y. Dumeige, F. Raineri, A. Levenson, and X. Letartre, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **68**(6), 066617 (2003). [CrossRef] [PubMed]

26. B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B **22**(7), 1378–1383 (2005). [CrossRef]

27. B. Maes, P. Bienstman, R. Baets, B. B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. **40**(1), 13–22 (2008). [CrossRef]

22. N. Talebi and M. Shahabadi, “All-optical wavelength converter based on a heterogeneously integrated GaP on a silicon-on-insulator waveguide,” J. Opt. Soc. Am. B **27**(11), 2273–2278 (2010). [CrossRef]

28. C. M. Reinke, A. Jafarpour, B. Momeni, M. Soltani, S. Khorasani, A. Adibi, Y. Xu, and R. K. Lee, “Nonlinear finite-difference time-domain method for the simulation of anisotropic,**24**(1), 624–634 (2006). [CrossRef]

29. R. M. Joseph and A. Taflove, “FDTD Maxwell's equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. **45**(3), 364–374 (1997). [CrossRef]

## 2. Structure and linear analysis

_{x}<<λ

_{0}and L

_{y}<<λ

_{0}. In order to couple the THS to the propagating modes of the waveguide, the following phase matching condition must be satisfied:Here,

_{x}is the periodicity of the structure in the

_{y}or TM

_{y}modes of the waveguide at the third harmonic frequency. We assume that the fundamental beam is at a wavelength of

_{2}layer used here has a thickness of 180nm. The analytical relation for the dispersion diagram of the bare slab waveguide (far away from the converter-coupler area) shows the values of

_{y}and TE

_{y}modes of the waveguide, respectively. The fundamental wavelength is λ

_{0}= 800nm, and the height of the HfO

_{2}slab waveguide is 180nm. Using Eq. (1), and considering

_{y}and TE

_{y}modes of the waveguide, respectively. The negative angle means that the second-order mode is in the opposite direction of propagation compared with the incident beam. This is because of the influence of the periodic grating which folds the band-diagram of the structures at the boundary of the Brillouin zone (X-point).

30. J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. **9**(6), 2372–2377 (2009). [CrossRef] [PubMed]

32. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. **125**(16), 164705 (2006). [CrossRef] [PubMed]

33. J. B. Schneider, “Understanding the finite-difference time-domain method” (2010), retrieved December 5th, 2011, www.eecs.wsu.edu/~schneidj/ufdtd.

34. M. Shahabadi, S. Atakaramians, and N. Hojjat, “Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals,” IEEE P Sci.Meas. Tech. **151**(5), 327–334 (2004). [CrossRef]

2. T. Zentgraf, A. Christ, J. Kuhl, and H. Giessen, “Tailoring the ultrafast dephasing of quasiparticles in metallic photonic crystals,” Phys. Rev. Lett. **93**(24), 243901 (2004). [CrossRef] [PubMed]

23. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B **80**(19), 195415 (2009). [CrossRef]

24. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. **106**(13), 133901 (2011). [CrossRef] [PubMed]

_{y}mode. Figure 4(b) shows the magnitude of the E

_{y}field component at λ = 267nm when the structure is exposed to a

## 3. Nonlinear analysis using FDTD method

_{2}waveguide with a quartz substrate. The particles are arranged in two rows along the

_{y}optical pulse of 50 fs duration and a carrier wavelength of 800nm.

_{max}= 61kW, which is smaller than the one reported in [6

6. S. Kim, J. H. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature **453**(7196), 757–760 (2008). [CrossRef] [PubMed]

_{y}and TE

_{y}modes of the waveguide. Due to the angular extent of the Gaussian excitation beam used here, TM

_{y}and TE

_{y}modes are excited simultaneously (see also Fig. 4). Curiously, though, they propagate away from the coupling region in opposite directions, as can be clearly seen from Fig. 6(b) and Fig. 6(c). A sharp dip is observed in the logarithmic power spectrum

_{y}mode of the waveguide. Figure 8 shows the guided power versus the angle of incidence for the input optical pulse. The optical pulse introduced here has a large broadening angle of

6. S. Kim, J. H. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature **453**(7196), 757–760 (2008). [CrossRef] [PubMed]

**453**(7196), 757–760 (2008). [CrossRef] [PubMed]

^{11}W cm

^{−2}. Moreover, a hybrid photonic-plasmonic waveguide has been proposed in Ref [3

3. Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B **82**(15), 155107 (2010). [CrossRef]

_{3}. Since the fundamental and produced second-harmonics are both propagating through a lossy silver waveguide, the efficiency very much depends on the length of the structure. Using a waveguide length of only 3μm and an incident intensity of 10

^{7}W cm

^{−2}, the reported conversion efficiency for the second-harmonic generation is about −33dB.

## 4. Conclusion

## Acknowledgments

## References and links

1. | B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B |

2. | T. Zentgraf, A. Christ, J. Kuhl, and H. Giessen, “Tailoring the ultrafast dephasing of quasiparticles in metallic photonic crystals,” Phys. Rev. Lett. |

3. | Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B |

4. | M. D. Wissert, K. S. Ilin, M. Siegel, U. Lemmer, and H. J. Eisler, “Coupled nanoantenna plasmon resonance spectra from two-photon laser excitation,” Nano Lett. |

5. | T. Uthayakumar, C. P. Jisha, K. Porsezian, and V. C. Kuriakose, “Switching dynamics of a two- dimensional nonlinear directional coupler in a photopolymer,” J. Opt. |

6. | S. Kim, J. H. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature |

7. | K. Dolgaleva and R. W. Boyd, “Laser gain media based on nanocomposite materials,” J. Opt. Soc. Am. B |

8. | R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, “Accessing the optical nonlinearity of metals with metal- dielectric photonic bandgap structures,” Opt. Lett. |

9. | D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. |

10. | R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. |

11. | D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett. |

12. | S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A |

13. | R. W. Day, S. S. Wang, and R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. |

14. | D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Design considerations for narrow-band dielectric resonant grating reflection filters of finite length,” J. Opt. Soc. Am. A |

15. | A. Selle, C. Kappel, M. A. Bader, G. Marowsky, K. Winkler, and U. Alexiev, “Picosecond-pulse-induced two-photon fluorescence enhancement in biological material by application of grating waveguide structures,” Opt. Lett. |

16. | S. Soria, T. Katchalski, E. Teitelbaum, A. A. Friesem, and G. Marowsky, “Enhanced two-photon fluorescence excitation by resonant grating waveguide structures,” Opt. Lett. |

17. | C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structures as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B |

18. | A. M. Ferrie, Q. Wu, and Y. Fang, “Resonant waveguide grating imager for live cell sensing,” Appl. Phys. Lett. |

19. | H. N. Daghestani and B. W. Day, “Theory and applications of surface plasmon resonance, resonant mirror, resonant waveguide grating, and dual polarization interferometry biosensors,” Sensors (Basel Switzerland) |

20. | J. Y. Andersson, L. Lundqvist, and Z. F. Paska, “Quantum efficiency enhancement of AlGaAs/GaAs quantum-Well Infrared detectors using a wave-guide with a grating coupler,” Appl. Phys. Lett. |

21. | S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A |

22. | N. Talebi and M. Shahabadi, “All-optical wavelength converter based on a heterogeneously integrated GaP on a silicon-on-insulator waveguide,” J. Opt. Soc. Am. B |

23. | T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B |

24. | T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. |

25. | Y. Dumeige, F. Raineri, A. Levenson, and X. Letartre, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

26. | B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B |

27. | B. Maes, P. Bienstman, R. Baets, B. B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. |

28. | C. M. Reinke, A. Jafarpour, B. Momeni, M. Soltani, S. Khorasani, A. Adibi, Y. Xu, and R. K. Lee, “Nonlinear finite-difference time-domain method for the simulation of anisotropic, |

29. | R. M. Joseph and A. Taflove, “FDTD Maxwell's equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. |

30. | J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. |

31. | T. Verbiest, K. Clays, and V. Rodriguez, |

32. | P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. |

33. | J. B. Schneider, “Understanding the finite-difference time-domain method” (2010), retrieved December 5th, 2011, www.eecs.wsu.edu/~schneidj/ufdtd. |

34. | M. Shahabadi, S. Atakaramians, and N. Hojjat, “Transmission line formulation for the full-wave analysis of two-dimensional dielectric photonic crystals,” IEEE P Sci.Meas. Tech. |

35. | P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B |

36. | L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. Mu, X. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B |

37. | R. W. Boyd, |

38. | F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles - surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(190.2620) Nonlinear optics : Harmonic generation and mixing

(240.6680) Optics at surfaces : Surface plasmons

(230.7405) Optical devices : Wavelength conversion devices

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: October 12, 2011

Revised Manuscript: December 9, 2011

Manuscript Accepted: December 9, 2011

Published: January 9, 2012

**Citation**

Nahid Talebi, Mahmoud Shahabadi, Worawut Khunsin, and Ralf Vogelgesang, "Plasmonic grating as a nonlinear converter-coupler," Opt. Express **20**, 1392-1405 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1392

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### References

- B. Lamprecht, A. Leitner, and F. R. Aussenegg, “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B68(3), 419–423 (1999). [CrossRef]
- T. Zentgraf, A. Christ, J. Kuhl, and H. Giessen, “Tailoring the ultrafast dephasing of quasiparticles in metallic photonic crystals,” Phys. Rev. Lett.93(24), 243901 (2004). [CrossRef] [PubMed]
- Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B82(15), 155107 (2010). [CrossRef]
- M. D. Wissert, K. S. Ilin, M. Siegel, U. Lemmer, and H. J. Eisler, “Coupled nanoantenna plasmon resonance spectra from two-photon laser excitation,” Nano Lett.10(10), 4161–4165 (2010). [CrossRef] [PubMed]
- T. Uthayakumar, C. P. Jisha, K. Porsezian, and V. C. Kuriakose, “Switching dynamics of a two- dimensional nonlinear directional coupler in a photopolymer,” J. Opt.12(1), 015204 (2010). [CrossRef]
- S. Kim, J. H. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008). [CrossRef] [PubMed]
- K. Dolgaleva and R. W. Boyd, “Laser gain media based on nanocomposite materials,” J. Opt. Soc. Am. B24(10), A19–A25 (2007). [CrossRef]
- R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, “Accessing the optical nonlinearity of metals with metal- dielectric photonic bandgap structures,” Opt. Lett.24(20), 1416–1418 (1999). [CrossRef] [PubMed]
- D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron.33(11), 2038–2059 (1997). [CrossRef]
- R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett.61(9), 1022–1024 (1992). [CrossRef]
- D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett.23(9), 700–702 (1998). [CrossRef] [PubMed]
- S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A13(5), 993–1005 (1996). [CrossRef]
- R. W. Day, S. S. Wang, and R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol.14(8), 1815–1824 (1996). [CrossRef]
- D. K. Jacob, S. C. Dunn, and M. G. Moharam, “Design considerations for narrow-band dielectric resonant grating reflection filters of finite length,” J. Opt. Soc. Am. A17(7), 1241–1249 (2000). [CrossRef] [PubMed]
- A. Selle, C. Kappel, M. A. Bader, G. Marowsky, K. Winkler, and U. Alexiev, “Picosecond-pulse-induced two-photon fluorescence enhancement in biological material by application of grating waveguide structures,” Opt. Lett.30(13), 1683–1685 (2005). [CrossRef] [PubMed]
- S. Soria, T. Katchalski, E. Teitelbaum, A. A. Friesem, and G. Marowsky, “Enhanced two-photon fluorescence excitation by resonant grating waveguide structures,” Opt. Lett.29(17), 1989–1991 (2004). [CrossRef] [PubMed]
- C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structures as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B21(6), 1127–1136 (2004). [CrossRef]
- A. M. Ferrie, Q. Wu, and Y. Fang, “Resonant waveguide grating imager for live cell sensing,” Appl. Phys. Lett.97(22), 223704 (2010). [CrossRef] [PubMed]
- H. N. Daghestani and B. W. Day, “Theory and applications of surface plasmon resonance, resonant mirror, resonant waveguide grating, and dual polarization interferometry biosensors,” Sensors (Basel Switzerland)10(11), 9630–9646 (2010). [CrossRef]
- J. Y. Andersson, L. Lundqvist, and Z. F. Paska, “Quantum efficiency enhancement of AlGaAs/GaAs quantum-Well Infrared detectors using a wave-guide with a grating coupler,” Appl. Phys. Lett.58(20), 2264–2266 (1991). [CrossRef]
- S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A13(5), 993–1005 (1996). [CrossRef]
- N. Talebi and M. Shahabadi, “All-optical wavelength converter based on a heterogeneously integrated GaP on a silicon-on-insulator waveguide,” J. Opt. Soc. Am. B27(11), 2273–2278 (2010). [CrossRef]
- T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B80(19), 195415 (2009). [CrossRef]
- T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett.106(13), 133901 (2011). [CrossRef] [PubMed]
- Y. Dumeige, F. Raineri, A. Levenson, and X. Letartre, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.68(6), 066617 (2003). [CrossRef] [PubMed]
- B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B22(7), 1378–1383 (2005). [CrossRef]
- B. Maes, P. Bienstman, R. Baets, B. B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron.40(1), 13–22 (2008). [CrossRef]
- C. M. Reinke, A. Jafarpour, B. Momeni, M. Soltani, S. Khorasani, A. Adibi, Y. Xu, and R. K. Lee, “Nonlinear finite-difference time-domain method for the simulation of anisotropic,χ(2)χ(3) ” J. Lightwave Technol.24(1), 624–634 (2006). [CrossRef]
- R. M. Joseph and A. Taflove, “FDTD Maxwell's equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag.45(3), 364–374 (1997). [CrossRef]
- J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett.9(6), 2372–2377 (2009). [CrossRef] [PubMed]
- T. Verbiest, K. Clays, and V. Rodriguez, Second-Order Nonlinear Optical Characterization Technique (CRC Press, 2009) 96–97.
- P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys.125(16), 164705 (2006). [CrossRef] [PubMed]
- J. B. Schneider, “Understanding the finite-difference time-domain method” (2010), retrieved December 5th, 2011, www.eecs.wsu.edu/~schneidj/ufdtd .
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