Large-Scale Structures in Acoustics and Electromagnetics Proceedings of a Symposium (1996) / Chapter Skim
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4 NUMERICAL MODELING OF THE INTERACTIONS OF ULTRAFAST OPTICAL PULSES WITH NONRESONANT AND RESONANT MATERIALS AND STRUCTURES
4 NUMERICAL MODELING OF THE INTERACTIONS OF ULTRAFAST OPTICAL PULSES WITH NONRESONANT AND RESONANT MATERIALS AND STRUCTURES
Pages 89-102
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From page 89... ...
is given which includes both the Raman and the instantaneous Kerr nonlinear materials models to describe locally linear and nonlinear finite length corrugated optical waveguides for applications to gratingassisted couplers and beam steerers. We also describe another simulator under development which combines a multilevel atom materials model with our Maxwell's equations simulator to mode!
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From page 90... ...
It is believed that the successful development of semi-classical simulators that combine numerical quantum mechanical models of materials and macroscopic Maxwell's equations solvers will significantly affect the concept and design stages associated with novel nonlinear optics phenomena. The problem of accurate numerical modeling of the propagation of ultrafast pulses in nonlinear media and their use in NLO optical devices has been subject to increasing interest in recent years.
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From page 91... ...
technique-based simulation toot has been developed in two spatial dimensions to model the electromagnetic interaction of focused optical Gaussian beams incident on a corrugated surface coated with several layers of thin dielectric films and realistic metals. The technique is a hybrid approach that combines an intensive numerical method near the surface of the grating and that takes into account the optical properties of the dielectrics and metals, with a free space transform to obtain the radiated fields.
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From page 92... ...
These numerical solutions have been obtained in two space dimensions and time with a two-dimensional finite-difference time-domain (2D-FDTD) method, which combines a generalization of a standard, FDTD, fill-wave, vector, linear Maxwell's equations solver with a Lorentz linear dispersion model.
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From page 93... ...
The free space transform is one way to circumvent this problem. This transform takes a transverse component of the scattered field along a planar aperture near one of the four truncation boundaries in the simulation region and projects this field component onto a circle (in two dimensions, a sphere in three)
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From page 94... ...
Ne ar -to-f ar -field transform observation circle Scattered field region Sampling plane to generate equivalent sources Source planes Total field region Diffraction Grating r FDTD Simulation region Figure 4.1 The FDTD-Lorentz Medium simulator allows one to model locally scatterers such as realistic multilayered thin film diffraction gratings and yet produce far-field patterns with a near- to far-field transform 94
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From page 95... ...
The time from device conceptualization to fabrication and testing should therefore be enormously improved with numerical simulations that incorporate more realistic models of the linear and nonlinear material responses and the actual device geometries. It is felt that vector and higher dimensional properties of Maxwell's equations that are not currently included in existing scalar models, in addition to more detailed materials models, may significantly impact the scientific and engineering results.
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From page 96... ...
These numerical solutions have been obtained in two space dimensions and time with a nonlinear finitedifference time-domain :-FDTD) method that combines a generalization of the Lorentz linear dispersive medium-Maxwell's equations solver with a nonlinear Raman model and an instantaneous Kerr nonlinear model.
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From page 97... ...
The resulting fields have to satisfy a phase matching or Bragg condition resulting from the electromagnetic boundary conditions. Physically this means that because of the regular placement of the teeth in the corrugation section, the individual scattered fields will interfere constructively only along certain preferred directions and the "leaked" energy will appear in the form of pulsed beams that radiate at angles specified by the Bragg condition both into the air and into the substrate regions.
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From page 98... ...
Typical simulation geometries are shown in Figures 4.3 and 4.4. Since the electric field behavior near the edges of these metallic corrugations is significantly different between the two polarizations, the resulting radiated field structures reflect this difference.
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From page 99... ...
This effort is novel in that it combines a realistic material model that is quantum mechanically based with a full-wave, vector Maxwell's equations solver. The FDTD implementations of the Maxwell-Bloch modeling system in one space dimension and time have been accomplished (Ziolkowski et al., ~ 995)
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From page 100... ...
A SIT solution represents the nonlinear wave propagation dynamics in which a particular pulse shape, a carrier at the transition frequency with a hyperbolic secant envelope, having the appropriate high intensity completely loses its energy to a twolevel atom medium by stimulating it from its ground state into its excited state, and then is completely reconstructed in a coherent manner via stimulated emission by having the excited medium completely decay back into its ground state. This SIT pulse thus propagates through the highly nonlinear two-level atom medium with no change in its shape, i.e., as though the medium is transparent; it is a soliton solution of the semiclassical Maxwell-Bloch system.
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From page 101... ...
We discussed one such simulator which couples Maxwell's equations and a Lorentz linear dispersion mode! with a near- to far-field transform capability to generate the global far-field patterns associated with the scattering of optical Gaussian beams from diffraction gratings coated with multiple layers of realistic thin film dielectrics and metals.
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From page 102... ...
Examples from our efforts in this area, which have civilian and military relevance, have been given to illustrate what classes of simulators have been developed to model these structures. Future efforts in this area will require even more complete materials models appropriately integrated into the Maxwell equations solvers and the associated advanced HPC methods.
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