Abstract

We present a transverse 1-D periodic nanostructure which exhibits lateral internal field localization for normally incident ultrashort pulses, and which may be applied to the enhancement of nonlinear optical phenomena. The peak intensity of an optical pulse propagating in the nanostructure is approximately 12 times that of an identical incident pulse propagating in a bulk material of the same refractive index. For second harmonic generation, an overall enhancement factor of approximately 10.8 is predicted. Modeling of pulse propagation is performed using Fourier spectrum decomposition and Rigorous Coupled-Wave Analysis (RCWA).

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. P. Lalanne and J.-P. Hugonin, "High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms," J. Opt. Soc. Am. A 15, 1843-1851 (1998).
    [CrossRef]
  2. J. N. Mait, D. W. Prather, and M. S. Mirotznik, "Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory," J. Opt. Soc. Am. A 16, 1157-1167 (1999).
    [CrossRef]
  3. F. Xu, R.-C. Tyan, P.-C. Sun, Y. Fainman, C.-C. Cheng, and A. Scherer, "Form-birefringent computer-generated holograms," Opt. Lett. 21, 1513-1515 (1996).
    [CrossRef] [PubMed]
  4. R.-C. Tyan, A. A. Salvekar, H.-P. Chou, C.-C. Cheng, A. Scherer, P.-C. Sun, F. Xu, and Y. Fainman, "Design, fabrication and characterization of form-birefringent multilayer polarizing beam splitter," J. Opt. Soc. Am. A 14, 1627-1636 (1997).
    [CrossRef]
  5. J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
    [CrossRef] [PubMed]
  6. R. W. Boyd and J. E. Sipe, "Nonlinear optical susceptibilities of layered composite materials," J. Opt. Soc. Am. B 11, 297-303 (1994).
    [CrossRef]
  7. G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A Weller-Brophy, "Enhanced nonlinear optical response of composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
    [CrossRef] [PubMed]
  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, 1416-1418 (1999).
    [CrossRef]
  9. K. P. Yuen, M. F. Law, K. W. Yu, and P. Sheng, "Enhancement of optical nonlinearity through anisotropic microstructures," Opt. Comm. 148, 197-207 (1998).
    [CrossRef]
  10. H. Ma, R. Xiao, and P. Sheng, "Third-order optical nonlinearity enhancement through composite microstructures," J. Opt. Soc. Am. B 15, 1022-1029 (1998).
    [CrossRef]
  11. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982).
    [CrossRef]
  12. N. Chateau and J.-P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," J. Opt. Soc. Am. A 11, 1321-1331 (1994).
    [CrossRef]
  13. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled- wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077- 1086 (1995).
    [CrossRef]
  14. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
    [CrossRef]
  15. M. Schmitz, R. Brauer, O. Bryngdahl, "Comment on numerical stability of rigorous differential methods of diffraction," Opt. Comm. 124, 1-8 (1996).
    [CrossRef]
  16. R. Tyan, "Design, modeling and characterization of multifunctional diffractive optical elements," Ph.D. Thesis, University of California, San Diego (1998).
  17. W. Nakagawa, R.-C. Tyan, P.-C. Sun, F. Xu, and Y. Fainman, "Ultrashort pulse propagation in near-Field periodic diffractive structures using Rigorous Coupled-Wave Analysis," submitted to J. Opt. Soc. Am. A (2000).

Other (17)

P. Lalanne and J.-P. Hugonin, "High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms," J. Opt. Soc. Am. A 15, 1843-1851 (1998).
[CrossRef]

J. N. Mait, D. W. Prather, and M. S. Mirotznik, "Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory," J. Opt. Soc. Am. A 16, 1157-1167 (1999).
[CrossRef]

F. Xu, R.-C. Tyan, P.-C. Sun, Y. Fainman, C.-C. Cheng, and A. Scherer, "Form-birefringent computer-generated holograms," Opt. Lett. 21, 1513-1515 (1996).
[CrossRef] [PubMed]

R.-C. Tyan, A. A. Salvekar, H.-P. Chou, C.-C. Cheng, A. Scherer, P.-C. Sun, F. Xu, and Y. Fainman, "Design, fabrication and characterization of form-birefringent multilayer polarizing beam splitter," J. Opt. Soc. Am. A 14, 1627-1636 (1997).
[CrossRef]

J. E. Sipe and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

R. W. Boyd and J. E. Sipe, "Nonlinear optical susceptibilities of layered composite materials," J. Opt. Soc. Am. B 11, 297-303 (1994).
[CrossRef]

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A Weller-Brophy, "Enhanced nonlinear optical response of composite materials," Phys. Rev. Lett. 74, 1871-1874 (1995).
[CrossRef] [PubMed]

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, 1416-1418 (1999).
[CrossRef]

K. P. Yuen, M. F. Law, K. W. Yu, and P. Sheng, "Enhancement of optical nonlinearity through anisotropic microstructures," Opt. Comm. 148, 197-207 (1998).
[CrossRef]

H. Ma, R. Xiao, and P. Sheng, "Third-order optical nonlinearity enhancement through composite microstructures," J. Opt. Soc. Am. B 15, 1022-1029 (1998).
[CrossRef]

M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982).
[CrossRef]

N. Chateau and J.-P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," J. Opt. Soc. Am. A 11, 1321-1331 (1994).
[CrossRef]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled- wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077- 1086 (1995).
[CrossRef]

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
[CrossRef]

M. Schmitz, R. Brauer, O. Bryngdahl, "Comment on numerical stability of rigorous differential methods of diffraction," Opt. Comm. 124, 1-8 (1996).
[CrossRef]

R. Tyan, "Design, modeling and characterization of multifunctional diffractive optical elements," Ph.D. Thesis, University of California, San Diego (1998).

W. Nakagawa, R.-C. Tyan, P.-C. Sun, F. Xu, and Y. Fainman, "Ultrashort pulse propagation in near-Field periodic diffractive structures using Rigorous Coupled-Wave Analysis," submitted to J. Opt. Soc. Am. A (2000).

Supplementary Material (2)

» Media 1: MOV (2564 KB)     
» Media 2: MOV (2138 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the transverse field localization nanostructure: an infinitely periodic square subwavelength grating with period Λ, fill factor F, and depth d.

Fig. 2.
Fig. 2.

Normalized squared magnitude of the electric field of an ultrashort optical pulse (center wavelength 1.0 µm, 167 fs FWHM) propagating inside the structure shown in Fig. 1. Each movie shows one period of an infinitely periodic structure for: (a) (2.5 MB) TE polarized incident pulse and (b) (2.0 MB) TM polarized incident pulse.

Fig. 3.
Fig. 3.

Transverse profiles of the squared field magnitude at the pulse peak in one period of an infinitely periodic nanostructure for several fill factors. The grating period is 0.65 µm, and the normally incident pulse has a FWHM of 167 fs. The colored vertical lines indicate the respective boundaries of the high index region of the structure for the five fractional fill factors.

Fig. 4.
Fig. 4.

Group velocity and peak field magnitude squared as a function of fill factor for a 167 fs FWHM pulse propagating in the structure of Fig. 1.

Fig. 5.
Fig. 5.

SHG enhancement factor for the nanostructure of Fig. 1, with fill factor varying from 1% to 12%. The enhancement factor is computed by integrating |E|4 over the part of the grating period corresponding to the high refractive index material, and normalizing to the bulk case.

Equations (2)

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

E ̚ ( r ̚ , t ) = { a ̂ 0 exp [ ( t ( k ̂ 0 · r ̚ ) v g t 0 ) 2 2 τ 2 ] exp [ j ( k ̚ 0 · r ̚ ω 0 t ) ] } n = δ ( t n Δ T )
E ˜ ( r ̚ , ω ) = a ̂ 0 2 π τ exp [ j k ̚ 0 · r ̚ j Ω ( k ̚ 0 · r ̚ v g + t 0 ) τ 2 Ω 2 2 ] · n = M M δ ( Ω n δ ω ) ,

Metrics