conopix.lc: Conoscopy of liquid crystal cell: pixel calculation

In uniaxialOptics: Modelling multilayer anisotropic stacks

Description

Computes m pixels in the conoscopy (interference) figure of a liquid crystal cell. Multiple (l) wavelengths can be computed simultaneously for the same stack. See conopix.stack for more details

Usage

conopix.lc(lambda, lc, eolc, eelc, db,eb,dt,et,x, y,
az0 = pi/4, i = 1, method = "ko")

Arguments

lambda	vector of wavelengths, in metres, length = l
lc	a list containing at least depthz (sublayer depths) ,a vector of length n, and two n x m matrices, tilt and twist, which define m director profiles. The function lc\_switching\_sequence() in the EricksenLeslie package provdes just such a list. It is assumed that tilt[1] and tilt[m] are defined at the edge of the LC film, ie at the bottom and top of the end sublayers, whereas every other tilt/twist is defined in the middle of its sublayer.
eolc	ordinary relative permittivity of the LC. Either a complex scalar, or a complex vector of length l if dispersion is to be included
eelc	extraordinary relative permittivity of the LC. See eo.
db	vector, length nt, of depths for the top isotropic layers
eb	relative permittivity of the top layers. Either a complex vector of length nt or a complex nt x l matrix if dispersion is to be included
dt	vector, length nb, of depths for the bottom isotropic layers
et	relative permittivity of the top layers. See et
x	vector, length m, of pixel x-coordinates to compute
y	vector, length m, of pixel y-coordinates to compute
az0	scalar, angle between the polarizers transmission axis and the x-axis
i	index of tilt,twist matrices to extract - ie director profile at seqeunce index i.Defaults to 1
method	which underlying method to use. Currently "ko" for Berreman 4x4 treatment, and "lien" for Jones treatment

See Also

optics.lc, conopix.stack, conorect.lc

Examples

glass <- 1.52^2 + 0.0i
ito <- 3.8 + 0.08i
nz <- 48
d <- 5e-6
eolc <- 1.52^2 + 0i
eelc <- 1.68^2 + 0i
di <- c(0,30e-9)
ei <- c(glass,ito)

lc <- list(depthz=c(0.5,rep(1,nz-2),0.5) * d/nz,
           tilt=matrix(seq(0,pi/2,l=nz),ncol=1),
           twist=matrix(seq(0,0,l=nz),ncol=1))

lambda <- c(632.8e-9,500e-9,400e-9)

numap <- .55/1.52 # numerical aperture, in glass, of ~50X lens
x <- seq(-numap,numap,l=100)
y <- x


cko <- conopix.lc(lambda,lc,eolc,eelc, di,ei,rev(di),rev(ei), x, y,  method="ko")

clien <- conopix.lc(lambda,lc,eolc,eelc, di,ei,rev(di),rev(ei), x, y,  method="lien")

#define matrix plotting function for convenience
mp <- function(x,y,add=FALSE,lty=1,...){
  col <- rainbow(ncol(y))
  if (add){
    matlines(x,y,type='l',lty=lty,col=col,...)
  } else {
    matplot(x,y,type='l',lty=lty,col=col,...)
  }
}

mp(x,cko$crossed,xlab='x', ylab=expression(Irradiance),ylim=c(0,1),
   main ="x=y section through HAN cell conoscopy figure")

mp(x,clien$crossed,xlab='x', ylab=expression(Irradiance),add=TRUE,lty=2)

legend(x="bottomright",leg=lambda*1e+9,title=expression(lambda),lwd=1,
       col= rainbow(3),
       bg="#eeeeee")

legend(x="bottomleft",leg=c("ko","lien"),title="method",lty=c(1,2),
       bg="#eeeeee")

uniaxialOptics documentation built on May 2, 2019, 5 p.m.