scholarly journals CAPHE: Time-domain and Frequency-domain Modeling of Nonlinear Optical Components

2012 ◽  
Author(s):  
Martin Fiers ◽  
Thomas Van Vaerenbergh ◽  
Joni Dambre ◽  
Peter Bienstman
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Nonlinear Optical ◽  
Domain Modeling ◽  
Optical Components

scholarly journals Time-domain and frequency-domain modeling of nonlinear optical components at the circuit-level using a node-based approach

2012 ◽  
Vol 29 (5) ◽  
pp. 896 ◽  
Author(s):  
Martin Fiers ◽  
Thomas Van Vaerenbergh ◽  
Ken Caluwaerts ◽  
Dries Vande Ginste ◽  
Benjamin Schrauwen ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Nonlinear Optical ◽  
Domain Modeling ◽  
Optical Components

Time-domain modeling of electromagnetic diffusion with a frequency-domain code

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. F1-F8 ◽  
Author(s):  
Wim A. Mulder ◽  
Marwan Wirianto ◽  
Evert C. Slob
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Hermite Interpolation ◽  
Computational Grid ◽  
Skin Depth ◽  
Domain Modeling ◽  
Time Domain Modeling ◽  
Robust Multigrid ◽  
Selection Of

We modeled time-domain EM measurements of induction currents for marine and land applications with a frequency-domain code. An analysis of the computational complexity of a number of numerical methods shows that frequency-domain modeling followed by a Fourier transform is an attractive choice if a sufficiently powerful solver is available. A recently developed, robust multigrid solver meets this requirement. An interpolation criterion determined the automatic selection of frequencies. The skin depth controlled the construction of the computational grid at each frequency. Tests of the method against exact solutions for some simple problems and a realistic marine example demonstrate that a limited number of frequencies suffice to provide time-domain solutions after piecewise-cubic Hermite interpolation and a fast Fourier transform.

scholarly journals A frequency‐space 2-D scalar wave extrapolator using extended 25-point finite‐difference operator

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 289-296 ◽  
Author(s):  
Changsoo Shin ◽  
Heejeung Sohn
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Time Domain ◽  
Difference Operator ◽  
Rapid Development ◽  
Synthetic Seismograms ◽  
Domain Modeling ◽  
Time Migration ◽  
Space Frequency ◽  
Grid Points

Finite‐difference frequency‐domain modeling for the generation of synthetic seismograms and crosshole tomography has been an active field of research since the 1980s. The generation of synthetic seismograms with the time‐domain finite‐difference technique has achieved considerable success for waveform crosshole tomography and for wider applications in seismic reverse‐time migration. This became possible with the rapid development of high performance computers. However, the space‐frequency (x,ω) finite‐difference modeling technique is still beyond the capability of the modern supercomputer in terms of both cost and computer memory. Therefore, finite‐difference time‐domain modeling is much more popular among exploration geophysicists. A limitation of the space‐frequency domain is that the recently developed nine‐point scheme still requires that G, the number of grid points per wavelength, be 5. This value is greater than for most other numerical modeling techniques (for example, the pseudospectral scheme). To overcome this disadvantage inherent in space‐frequency domain modeling, we propose a new weighted average finite‐difference operator by approximating the spatial derivative and the mass acceleration term of the wave equation. We use 25 grid points around the collocation. In this way, we can reduce the number of grid points so that G is now 2.5. This approaches the Nyquist sampling limit in terms of the normalized phase velocity.

Quasi-analytical method for frequency-to-time conversion in CSEM applications

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. E357-E363 ◽  
Author(s):  
Ali Moradi Tehrani ◽  
Evert Slob ◽  
Wim Mulder
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Diffusion Time ◽  
Basis Functions ◽  
Time Range ◽  
Late Time ◽  
Square Root ◽  
Domain Modeling ◽  
The Time Domain ◽  
Exponential Part

Frequency-to-time transformations are of interest to controlled-source electromagnetic methods when time-domain data are inverted for a subsurface resistivity model by numerical frequency-domain modeling at a selected, small number of frequencies whereas the data misfit is determined in the time domain. We propose an efficient, Prony-type method using frequency-domain diffusive-field basis functions for which the time-domain equivalents are known. Diffusive fields are characterized by an exponential part whose argument is proportional to the square root of frequency and a part that is polynomial in integer powers of the square root of frequency. Data at a limited number of frequencies suffice for the transformation back to the time. In the exponential part, several diffusion-time values must be chosen. Once a suitable range of diffusion-time values are found, the method is quite robust in the number of values used. The highest power in the polynomial part can be determined from the source and receiver type. When the frequency-domain data are accurately approximated by the basis functions, the time-domain result is also accurate. This method is accurate over a wider time range than other methods and has the correct late-time asymptotic behavior. The method works well for data computed for layered and 3D subsurface models.

Frequency‐domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 626-632 ◽  
Author(s):  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Equations Of Motion ◽  
Domain Modeling ◽  
Multiple Sources ◽  
State Equations ◽  
Migration Imaging ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

The migration, imaging, or inversion of wide‐aperture cross‐hole data depends on the ability to model wave propagation in complex media for multiple source positions. Computational costs can be considerably reduced in frequency‐domain imaging by modeling the frequency‐domain steady‐state equations, rather than the time‐domain equations of motion. I develop a frequency‐domain approach in this note that is competitive with time‐domain modeling when solutions for multiple sources are required or when only a limited number of frequency components of the solution are required.

scholarly journals Sponge boundary condition for frequency‐domain modeling

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1870-1874 ◽  
Author(s):  
Changsoo Shin
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Rayleigh Waves ◽  
Seismic Waves ◽  
Domain Modeling ◽  
Seismic Modeling ◽  
Artificial Boundary ◽  
Diffusion Term ◽  
S Waves ◽  
Artificial Boundaries

Several techniques have been developed to get rid of edge reflections from artificial boundaries. One of them is to use paraxial approximations of the scalar and elastic wave equations. The other is to attenuate the seismic waves inside the artificial boundary by a gradual reduction of amplitudes. These techniques have been successfully applied to minimize unwanted seismic waves for time‐domain seismic modeling. Unlike time‐domain seismic modeling, suppression of edge reflections from artificial boundaries has not been successful in frequency‐domain seismic modeling. Rayleigh waves caused by coupled motions of P‐ and S‐waves near the surface have been a particularly difficult problem to overcome in seismic modeling. In this paper, I design a damping matrix for frequency‐ domain modeling that damps out seismic waves by adding a diffusion term to the wave equation. This technique can suppress unwanted seismic waves, including Rayleigh waves and P‐ and S‐waves from an artificial boundary.

Sign in / Sign up

Export Citation Format

Share Document