R/vswf.gwg.r

In wendellopes/rvswf: RVSWF: Expansion in Vector Spherical Wave Functions written in R

#' General expression for wave guides.
#' 
#' @details This expression does not take in account the value of the Fourier 
#' transform of azimuthal component. It does not depend on the position of the
#' expansion, only on the wave vector.
#' @param gamma The transversal component of the wave vector \eqn{\gamma}.
#' @param kz The longitudinal component of the wave vector \eqn{k_z}.
#' @param lmax The maximum value of \eqn{l} of the expansion.
#' @return The values \eqn{A} and \eqn{B}.
#' @include vswf.qlm.r
#' @export
#' @seealso \code{\link{vswf.cwg}}, \code{\link{vswf.rwg}}.
#' @examples 
#' th<-pi/3
#' u<-vswf.gwg(sin(th),cos(th),10)
#' plot(Re(u$A),type='b')
#' points(Im(u$A),type='b',pch=4,col='red')
#' plot(Re(u$B),type='b')
#' points(Im(u$B),type='b',pch=4,col='red')
vswf.gwg<-function(gama,kz,lmax,code="C"){
   if(!code%in%c("C","R")){
      stop("Code must be \"C\" or \"R\"")
   }
   if(code=="C"){
      dummy<-rep(0,lmax*(lmax+2)+1)
      u<-.C("vswf_gwg",
            gamma=as.double(gama),
            kz=as.double(kz),
            lmax=as.integer(lmax),
            A=as.complex(dummy),
            B=as.complex(dummy))
      return(data.frame(A=u$A,B=u$B))
   }else{
      k<-sqrt(gama^2+kz^2)
      LMAX=lmax*(lmax+2)+1
      #----------------------------------------
      u<-vswf.qlm(kz/k,lmax)
      Qlm<-u$Qlm
      dQlm<-u$dQlm
      ll<-u$l
      mm<-u$m
      llp1<-1/sqrt(ll*(ll+1))
      llp1[1]<-0
      #----------------------------------------
      A<-2*(1i^ll)*((k/gama)^2)*Qlm*mm*llp1
      B<-2*(1i^(ll-1))*dQlm*llp1
      return(data.frame(A,B))
   }
}