Abstract

We present a method for near-field analysis of ultrashort optical pulse propagation in periodic structures—including subwavelength and resonant grating structures—based on the integration of Fourier spectrum decomposition and rigorous coupled-wave analysis (RCWA). We discuss the spectral decomposition, including considerations for computational efficiency, the application of the RCWA method to compute the internal and external fields of the structure, and the synthesis of the resulting fields to obtain the time-domain solution. We apply this tool to the analysis of two photonic structures: (1) a nanostructured polarization-selective mirror that exhibits the desired broadband performance characteristics when operated at the design wavelength but yields strongly diminished polarization selectivity and modulation of the pulse envelope at an offset wavelength and (2) a two-mode coupled waveguide structure that produces from one incident pulse two transmitted pulses whose temporal separation depends on the waveguide geometry. In both examples, we apply our new modeling tool to investigate the near fields and find that near-field effects are critical in determining the performance characteristics of nanostructured devices. Furthermore, detailed observation and understanding of near-field phenomena in nanostructures may be applied to the design of novel photonic devices.

© 2001 Optical Society of America

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References

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    [CrossRef]
  5. J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1999 (4)

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by Cl2 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

F. Schreier, M. Schmitz, O. Bryngdahl, “Superliminal propagation of optical pulses inside diffractive structures,” Opt. Commun. 163, 1–4 (1999).
[CrossRef]

H. Ichikawa, “Analysis of femtosecond-order optical pulses diffracted by periodic structure,” J. Opt. Soc. Am. A 16, 299–304 (1999).
[CrossRef]

1998 (4)

1997 (1)

1995 (1)

1994 (1)

1982 (1)

1967 (1)

Allerman, A. A.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Arnold, D. W.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Asbill, R. E.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Bailey, C. G.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Brixner, B.

Bryngdahl, O.

F. Schreier, M. Schmitz, O. Bryngdahl, “Superliminal propagation of optical pulses inside diffractive structures,” Opt. Commun. 163, 1–4 (1999).
[CrossRef]

F. Schreier, M. Schmitz, O. Bryngdahl, “Pulse delay at diffractive structures under resonance conditions,” Opt. Lett. 23, 1337–1339 (1998).
[CrossRef]

Carter, T. R.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Chateau, N.

Cheng, C.-C.

Chou, H.-P.

Craighead, H. G.

Edwards, D. F.

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, San Diego, Calif., 1985).

Fainman, Y.

Gaylord, T. K.

Hugonin, J.-P.

Ichikawa, H.

H. Ichikawa, “Analysis of femtosecond-order optical pulses diffracted by periodic structure,” J. Opt. Soc. Am. A 16, 299–304 (1999).
[CrossRef]

H. Ichikawa, “Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method,” J. Opt. Soc. Am. A 15, 152–157 (1998).
[CrossRef]

H. Ichikawa, “Temporal apodisation by a grating in the resonance domain,” in EOS Topical Meeting on Diffractive Optics DO’99, J. Turunen, F. Wyrowski, eds., Vol. 22 of EOS Technical Digest Series (European Optical Society, Hanover, Germany, 1999), pp. 18–19.

Lopez, A. G.

Marom, D. M.

Matzke, C. M.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Moharam, M. G.

Salvekar, A. A.

Samora, S.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Scherer, A.

Schmitz, M.

F. Schreier, M. Schmitz, O. Bryngdahl, “Superliminal propagation of optical pulses inside diffractive structures,” Opt. Commun. 163, 1–4 (1999).
[CrossRef]

F. Schreier, M. Schmitz, O. Bryngdahl, “Pulse delay at diffractive structures under resonance conditions,” Opt. Lett. 23, 1337–1339 (1998).
[CrossRef]

Schreier, F.

F. Schreier, M. Schmitz, O. Bryngdahl, “Superliminal propagation of optical pulses inside diffractive structures,” Opt. Commun. 163, 1–4 (1999).
[CrossRef]

F. Schreier, M. Schmitz, O. Bryngdahl, “Pulse delay at diffractive structures under resonance conditions,” Opt. Lett. 23, 1337–1339 (1998).
[CrossRef]

Shames, P. E.

Sun, P.-C.

Sweatt, W. C.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Tyan, R.-C.

Tyan, Rongchung

Rongchung Tyan, “Design, modeling and characterization of multifunctional diffractive optical elements,” Ph.D. thesis (University of California, San Diego, La Jolla, Calif., 1998).

Vawter, G. A.

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by Cl2 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

Warren, M. E.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Wendt, J. R.

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by Cl2 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

Xu, F.

Zubrzycki, W. J.

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by Cl2 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

J. Vac. Sci. Technol. B (2)

W. J. Zubrzycki, G. A. Vawter, J. R. Wendt, “High-aspect-ratio nanophotonic components fabricated by Cl2 reactive ion beam etching,” J. Vac. Sci. Technol. B 17, 2740–2744 (1999).
[CrossRef]

J. R. Wendt, M. E. Warren, W. C. Sweatt, C. G. Bailey, C. M. Matzke, D. W. Arnold, A. A. Allerman, T. R. Carter, R. E. Asbill, S. Samora, “Fabrication of high performance microlenses for an integrated capillary channel electrochromatograph with fluorescence detection,” J. Vac. Sci. Technol. B 17, 3252–3255 (1999).
[CrossRef]

Opt. Commun. (1)

F. Schreier, M. Schmitz, O. Bryngdahl, “Superliminal propagation of optical pulses inside diffractive structures,” Opt. Commun. 163, 1–4 (1999).
[CrossRef]

Opt. Lett. (3)

Other (3)

H. Ichikawa, “Temporal apodisation by a grating in the resonance domain,” in EOS Topical Meeting on Diffractive Optics DO’99, J. Turunen, F. Wyrowski, eds., Vol. 22 of EOS Technical Digest Series (European Optical Society, Hanover, Germany, 1999), pp. 18–19.

Rongchung Tyan, “Design, modeling and characterization of multifunctional diffractive optical elements,” Ph.D. thesis (University of California, San Diego, La Jolla, Calif., 1998).

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, San Diego, Calif., 1985).

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Figures (9)

Fig. 1
Fig. 1

Nanostructured PSM design for Si/SiO2 material system. The grating period is Λ=0.6 µm, the fill factor is F=0.5, and the refractive indices are n1=3.48,n2=1.44, and nsub=1.44 for operation at λ=1.523 µm.

Fig. 2
Fig. 2

Reflected intensity versus wavelength calculated by using RCWA for TE- and TM-polarized illumination incident on the PSM structure shown in Fig. 1.

Fig. 3
Fig. 3

Pulse propagation at the design wavelength (λ=1.523 µm) through the PSM: (a) shape of the TE incident (t=-0.25 ps) and reflected (t=0.30 ps) pulses, (b) shape of the TM incident (t=-0.25 ps) and transmitted (t=0.30 ps) pulses, (c) magnitude and phase of the complex TE reflection coefficient of the PSM across the bandwidth of the incident pulse, (d) magnitude and phase of the complex TM transmission coefficient of the PSM across the bandwidth of the incident pulse.

Fig. 4
Fig. 4

Pulse propagation at the offset wavelength (λ=1.18 µm) through the PSM: (a) shape of the TE incident (t=-0.25 ps) and reflected/transmitted (t=0.30 ps) pulses, (b) shape of the TM incident (t=-0.25 ps) and reflected/transmitted (t=0.30 ps) pulse, (c) magnitude and phase of the complex TE reflection coefficient of the PSM across the bandwidth of the incident pulse, (d) magnitude and phase of the complex TM transmission coefficient of the PSM across the bandwidth of the incident pulse.

Fig. 5
Fig. 5

Modeling results showing TE- and TM-polarized optical pulses with center wavelength at the design wavelength (λ=1.523 µm) interacting with the PSM. Each frame shows one period of an infinite periodic structure: (a) TE and (b) TM wide views at t=-0.2 ps showing the incident pulses approaching the PSM structure, (c) TE and (d) TM magnified views of fields inside the PSM structure at t=0.05 ps (note the different internal field configurations for the two polarizations), (e) TE wide view of the reflected pulse and (f) TM wide view of the transmitted pulse in the substrate at t=0.3 ps.

Fig. 6
Fig. 6

One-dimensional subwavelength grating structure that supports two modes for incident pulses with center wavelength of λ=0.92 µm. The structure is composed of alternating layers of materials having refractive indices n1=3.57 and n2=1.63, and widths w1=0.2 µm and w2=0.5 µm, respectively. The depth of the structure is d=250 µm. The black rectangle represents the modeling domain consisting of one period.

Fig. 7
Fig. 7

Ultrashort pulse propagating through the two-mode waveguide structure shown in Fig. 6. Each frame shows the intensity in one period of an infinitely periodic structure at various times: (a) t=-0.3 ps, incident pulse approaching the structure from below (the pulse peak arrives at the front of the structure at t=0), (b) t=1.3 ps, pulse propagating inside the structure, where two distinct modes with different transverse profiles are clearly visible, (c) t=3.5 ps, two transmitted pulses observed after exiting the structure, with temporal separation of Δt=1.37 ps.

Fig. 8
Fig. 8

Profile through the center of the grating period at t=3.5 ps [corresponding to Fig. 7(c)] for a TE-polarized pulse with FWHM=167 fs incident on the structure shown in Fig. 6. Each waveguide mode couples to an output pulse, producing two transmitted pulses from one incident pulse. The z position of the peak and the FWHM for each pulse are shown.

Fig. 9
Fig. 9

Profile through the center of the grating period at t=3.5 ps for a TE-polarized pulse with FWHM=167 fs incident on a structure similar to that of Fig. 6 but with high- and low- refractive-index material widths w1=0.25 µm and w2=0.45, respectively. The z position of the peak and the FWHM for each pulse are shown.

Equations (9)

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

E(r, t)={aˆ0p(r, t)exp[-j(k0·r-ω0t)]}n=-δ(t-nΔT),
E˜(r, ω)={aˆ0P˜(r, Ω)exp[-jk0·r]}n=-δ(Ω-nδω),
P˜(r, ω)-p(r, t)exp(-jωt)dt
δω=2πΔT.
p(r, t)=exp-t-kˆ0·rνg-t022τ2,
P˜(r, ω)=2πτ exp-jωkˆ0·rνg+t0exp-τ2ω22.
E˜(r, ω)=aˆ02πτ exp-jkˆ0·r-jΩkˆ0·rνg+t0×exp-τ2Ω22n=-MMδ(Ω-nδω),
E(r, t)=12π -E(r, ω)exp(jωt)dω.
E(r, t)=12π n(r, t; ωn)δω.

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