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## 6.6 Waveforms

Global variable: group Waveforms

In Angora, a time waveform is defined as a self-contained structure that can be used by other structures; such as a Hertzian dipole source or a plane-wave injector. The library of available time waveforms will be expanded in the future. Please send any comments, suggestions, and requests to help@angorafdtd.org.

An example usage of Waveforms:

 Waveforms: { GaussianWaveforms: ( { … } ); DifferentiatedGaussianWaveforms: ( { … } ); … … }; 

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### 6.6.1 Gaussian Waveforms

Sub-variable of Waveforms: list GaussianWaveforms

This variable is used to define Gaussian time waveforms given by the formula

The peak, 10%-amplitude (-20 dB power), and 1%-amplitude (-40 dB power) frequencies in the spectrum of the Gaussian are , respectively.

Gaussian waveforms are defined as follows:

 Waveforms: { GaussianWaveforms: ( { waveform_tag = "my_waveform"; amplitude = 1.0; tau = 2.1291e-15; delay = 3; }, { … … } ); }; 
Sub-variable of GaussianWaveforms: string waveform_tag

This is the string tag by which the waveform will later be referred to by another structure that requires a time waveform in its definition.

Sub-variable of GaussianWaveforms: floating-point amplitude (default: 1.0)

This specifies the variable in the above equation defining the Gaussian waveform.

Sub-variable of GaussianWaveforms: floating-point tau (units: sec)

This specifies the variable in the above equation defining the Gaussian waveform.

Sub-variable of GaussianWaveforms: floating-point delay (default: 0.0)

This specifies the variable in the above equation defining the Gaussian waveform.

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### 6.6.2 Differentiated-Gaussian Waveforms

Sub-variable of Waveforms: list DifferentiatedGaussianWaveforms

This variable is used to define differentiated Gaussian time waveforms, given by the formula

where are the (physicists’) Hermite polynomials.

The peak frequency in the spectrum of the differentiated-Gaussian is , the 10%-amplitude (-20 dB power) frequencies are and ; and the 1%-amplitude (-40 dB power) frequencies are and .

Differentiated Gaussian waveforms are defined as follows:

 Waveforms: { DifferentiatedGaussianWaveforms: ( { waveform_tag = "my_waveform"; amplitude = 1.0; tau = 2.1291e-15; delay = 3; n_diff = 3; }, { … … } ); }; 
Sub-variable of DifferentiatedGaussianWaveforms: string waveform_tag

This is the string tag by which the waveform will later be referred to by another structure that requires a time waveform in its definition.

Sub-variable of DifferentiatedGaussianWaveforms: floating-point amplitude (default: 1.0)

This specifies the variable in the above equation defining the differentiated Gaussian waveform.

Sub-variable of DifferentiatedGaussianWaveforms: floating-point tau (units: sec)

This specifies the variable in the above equation defining the differentiated Gaussian waveform.

Sub-variable of DifferentiatedGaussianWaveforms: floating-point delay (default: 0.0)

This specifies the variable in the above equation defining the differentiated Gaussian waveform.

Sub-variable of DifferentiatedGaussianWaveforms: integer n_diff

This specifies the order of differentiation in the above equation defining the differentiated Gaussian waveform.

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### 6.6.3 Modulated-Gaussian Waveforms

Sub-variable of Waveforms: list ModulatedGaussianWaveforms

This variable is used to define sinusoidally-modulated Gaussian time waveforms, given by the formula

where the function is a sinusoidal function, being either or .

The peak frequency in the spectrum of the modulated-Gaussian is , the 10%-amplitude (-20 dB power) frequencies are ; and the 1%-amplitude (-40 dB power) frequencies are . A MATLAB script named ‘mod_gaussian_wf.m’ is distributed as part of the Angora package, which calculates the center frequency and the time constant of a modulated-Gaussian waveform that has the desired lower and upper cutoff wavelengths, and the desired amount of attenuation at these wavelengths. It also outputs the -40 dB wavelength and the suggested maximum spatial time step in the simulation (which is the -40 dB wavelength divided by 15). This script is installed in the directory ‘$(prefix)/share/angora/’ (see Compilation and Installation). If Angora was installed without any $(prefix) configuration option, the default location is ‘/usr/local/share/angora/’. This script can also be downloaded directly from the Angora website (link here).

Modulated Gaussian waveforms are defined as follows:

 Waveforms: { ModulatedGaussianWaveforms: ( { waveform_tag = "my_waveform"; modulation_type = "sine"; amplitude = 1.0; tau = 2.1291e-15; f_0 = 5.8929e14; delay = 3; phase = 90; differentiated = false; }, { … … } ); }; 
Sub-variable of ModulatedGaussianWaveforms: string waveform_tag

This is the string tag by which the waveform will later be referred to by another structure that requires a time waveform in its definition.

Sub-variable of ModulatedGaussianWaveforms: string modulation_type

If assigned "sine", the modulation function in the above equation becomes a sine. If assigned "cosine", it becomes a cosine.

Sub-variable of ModulatedGaussianWaveforms: floating-point amplitude (default: 1.0)

This specifies the variable in the above equation defining the modulated Gaussian waveform.

Sub-variable of ModulatedGaussianWaveforms: floating-point tau (units: sec)

This specifies the variable in the above equation defining the modulated Gaussian waveform.

Sub-variable of ModulatedGaussianWaveforms: floating-point f_0 (units: Hz)

This specifies the modulation frequency in the above equation defining the modulated Gaussian waveform.

Sub-variable of ModulatedGaussianWaveforms: floating-point delay (default: 0.0)

This specifies the variable in the above equation defining the modulated Gaussian waveform.

Sub-variable of ModulatedGaussianWaveforms: floating-point phase (units: degrees, default: 0.0)

This specifies the extra phase in the above equation defining the modulated Gaussian waveform. This phase should be specified in degrees, which is then converted internally to radians, which are the actual units of .

Sub-variable of ModulatedGaussianWaveforms: boolean differentiated (default: false)

If set to true, the waveform in the above equation is differentiated once with respect to time.

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This document was generated by Ilker Rafet Capoglu on December 12, 2012 using texi2html 1.82.