[R] how to fit gauss beam?

[Thomas Hunger]

Hello,

I am having a hard time fitting a gauss beam using R. In 
gnutplot I did something like

$ w(z) = w0 * sqrt(1+(z/z0)**2)
$ fit w(z) 'before_eom.txt' using 1:2 via w0, z0

to obtain w0 and z0. Now I want to do the same in R. I tried 
a linear model like this (r = radius, z = distance):

beam <- function(z) {
  sum(sqrt(1 + z**2))
}

lm(r ~ I(beam(z)), data = before_eom)

Which gives nonsensical answers ...

Then I tried a nonlinear model:

d <- read.table ("before_eom.tab", header=T)
z <- d$d
r <- d$minor * 1e-6

beam<- function(p) {
  M <- 1.1
  sum((r-M*p[1]*sqrt(1 + (z/p[2])**2))^2)
}

out <- nlm(beam, p=c(400, 0.1), hessian=TRUE)
out$estimate

This is very sensitive to the starting values and gives 
nonsensical answers as well...

Is there a simple way to translate the gnuplot fit into R?

Thanks,
Thomas