planar: Multilayer Optics

## ----load, echo=FALSE,results='hide'-----------------------------------------
library(knitr)
library(ggplot2)

opts_chunk$set(fig.path="gaussianbeam/", cache=TRUE, cache.path="gaussian/",
               warning=FALSE,error=FALSE,message=FALSE)
library(ggplot2)
theme_set(theme_minimal() + theme(panel.border=element_rect(fill=NA)))


## ----setup, results='hide', echo=FALSE----------------------------------------
library(planar)
library(ggplot2)
library(plyr)


## ----pw---------------------------------------------------------------
struct <- list(wavelength=632.8,
               thickness=c(0,50,50,0),
               epsilon=c(1.5^2, epsAu(632.8)$epsilon, 1.1^2, 1.0^2))

## first, check the plane wave result
results <- multilayer(epsilon=as.list(struct$epsilon),
                      wavelength=struct$wavelength, thickness=struct$thickness, d=1,
                      angle=seq(0, pi/2, length=2e3), polarisation='p')

enhancement <- results$Mr.perp[[2]] + results$Mr.par[[2]]
maxi <- max(enhancement, na.rm=T)
spp <- results$angle[which.max(enhancement)]

qplot(results$angle*180/pi, enhancement, geom="line")+
  labs(x="incident angle /degrees", y=expression("|E|"^2))

## ----depth---------------------------------------------------------------
xyz <- as.matrix(expand.grid(x=c(0, 5000, 10000), y=0, 
                             z=seq(-100, 500, length=100)))

res <- gaussian_near_field_layer(xyz, epsilon=struct$epsilon,
                              wavelength=struct$wavelength, 
                              thickness=struct$thickness,
                              w0=5e3, alpha=spp, maxEval=500)

xyz <- data.frame(xyz, field=res)

ggplot(xyz, aes(z, field, colour=factor(x)))+
  geom_vline(xintercept=cumsum(struct$thickness), linetype="dotted") +
  geom_line() + scale_y_log10()+
  scale_x_continuous(expand=c(0,0))+
  labs(x=expression("z /nm"), y=expression(log("|E|"^2)), 
       colour=expression("x /nm")) 


## ----waist---------------------------------------------------------------

simulation <- function(w0=10){
  w0 <- w0*1e3
  xyz <- as.matrix(expand.grid(x=seq(-5*w0, 5*w0+5000,length=100), y=0, z=51))
  
  res <- gaussian_near_field_ml(xyz, epsilon=struct$epsilon,
                                wavelength=struct$wavelength, 
                                thickness=struct$thickness,
                                w0=w0, alpha=spp, maxEval=600)
  
  data.frame(xyz, field=res)
}

params <- data.frame(w0=c(2, 5, 10, 50, 1e2, 500, 1e3))
all <- mdply(params, simulation)

ggplot(all, aes(x/w0/1000, field, group=w0, colour=factor(w0)))+
  geom_line() + 
  geom_vline(aes(xintercept=0),lty=2) +
  geom_hline(aes(yintercept=maxi),lty=3) +
  annotate("text", label="plane-wave", y=maxi, x=-2.5, vjust=1, fontface="italic") +
  labs(x=expression(x/w[0]), y=expression("|E|"^2), 
       colour=expression(w[0]/mu*m)) +
  coord_cartesian(xlim=c(-5,5)) + theme_minimal()+
  guides(colour=guide_legend(reverse=TRUE)) +
  theme(panel.background=element_rect(fill=NA))


## ----map-----------------------------------------------------------------
w0 <- 2000
xyz <- as.matrix(expand.grid(x=seq(-3*w0, 5*w0, length=50), 
                             y=seq(-3*w0, 3*w0, length=50),
                             z=51))
res <- gaussian_near_field_ml(xyz, epsilon=struct$epsilon,
                              wavelength=struct$wavelength, 
                              thickness=struct$thickness,
                              w0=w0, alpha=spp, maxEval=600)

m <- data.frame(xyz, field=res)

p <-   ggplot(m, aes(x/1e3, y/1e3, fill=field))+
  geom_raster(interpolate=TRUE) +
  scale_x_continuous(expand=c(0,0))+
  scale_y_continuous(expand=c(0,0)) +
  labs(x=expression("x /nm"), fill=expression("|E|"^2), 
       y=expression("y /nm")) +
  coord_fixed() + theme_minimal()

p