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__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: ( { … } ); … … };

6.6.1 Gaussian Waveforms | ||

6.6.2 Differentiated-Gaussian Waveforms | ||

6.6.3 Modulated-Gaussian Waveforms |

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__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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__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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__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*.