glmtscatt package¶
Submodules¶
glmtscatt.constants module¶
Module with some of the physical constants used to calculate all kinds of properties used in other modules from this package.
@author: Luiz Felipe Machado Votto
glmtscatt.field module¶
glmtscatt.frozenwave module¶
Specific Frozen Wave parameters
@author: Luiz Felipe Machado Votto
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glmtscatt.frozenwave.axicon_omega(degree, axicon)¶
glmtscatt.glmt module¶
glmtscatt.specials module¶
Module for declaring special functions to be used in GLMT.
@author: Luiz Felipe Machado Votto
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glmtscatt.specials.d2_riccati_bessel_j(degree, argument)¶ Second order derivative of Riccati-Bessel function of first kind
\[\Psi_n''(x) = \frac{(1+n^2-x^2)\Psi_n^{(1)}(x)}{x},\]where \(\Psi_n^{(1)}\) is the Spherical Bessel function of first kind.
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glmtscatt.specials.d2_riccati_bessel_y(degree, argument)¶ Second order derivative of Riccati-Bessel function of second kind
\[\xi_n''(x) = \frac{(1+n^2-x^2)\Psi_n^{(4)}(x)}{x},\]where \(\Psi_n^{(4)}\) is the Spherical Bessel function of fourth kind.
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glmtscatt.specials.d_riccati_bessel_j(degree, argument)¶ Derivative of Riccati-Bessel function of first kind
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glmtscatt.specials.d_riccati_bessel_y(degree, argument)¶ Derivative of Riccati-Bessel function of second kind
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glmtscatt.specials.fac_plus_minus(n, m)¶ Calculates the expression below avoiding overflows.
\[\frac{(n + m)!}{(n - m)!}\]
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glmtscatt.specials.legendre_p(degree, order, argument)¶ Associated Legendre function of integer order
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glmtscatt.specials.legendre_pi(degree, order, argument, overflow_protection=False)¶ Generalized associated Legendre function pi
\[\pi_n^m(x) = \frac{P_n^m(x)}{\sqrt{1-x^2}}\]
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glmtscatt.specials.legendre_tau(degree, order, argument, mv=True)¶ Returns generalized Legendre function tau
Derivative is calculated based on relation 14.10.5: http://dlmf.nist.gov/14.10
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glmtscatt.specials.memoize(function)¶
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glmtscatt.specials.riccati_bessel_j(degree, argument)¶ Riccati-Bessel function of first kind
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glmtscatt.specials.riccati_bessel_radial_i(degree, argument)¶
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glmtscatt.specials.riccati_bessel_radial_s(degree, argument)¶
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glmtscatt.specials.riccati_bessel_y(degree, argument)¶ Riccati-Bessel function of second kind
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glmtscatt.specials.squared_bessel_0(argument, scale)¶ Squared value for order 0 regular Bessel function