Function Description

Each line describes a separate function. There is no limit to the number of segments that can be entered.

Each descriptor starts with a flag character followed by numbers.


Uniform Fill

Initially, the background refractive index is assumed to be 1.0. This function uniformly adds an incremental refractive index to the background.

b f

For example:
b 0.5
will add a uniform refractive index to the background material, bringing its refractive index from 1.0 to 1.5.





Piecewise Linear Distribution

This function can be used to describe a refractive index profile that linearly varies between the defined points.

l x1 f1 x2 f2 x3 f3 ..

Each point is described by the (distance, incremental index) pair. The incremental index is added to the background index. Since there is no limit to the number of points that can be on a single descriptor, this method allows one to describe any piece-wise linear refractive index profile.

For example:
l -2 0.1 0 0.1 2 0.05
would look like the function shown on the left.




Parabolic Distribution

A parabolic refractive index distribution follows the equation

The syntax is:

p f xr xc xa1 xa2

where xa1 and xa2 are the starting and ending limits (aperture) of the parabola/

For example:
p 0.1 2 0 -2 2
would look like the function shown on the left.

We can also only use a portion of the parabola using the xa1 and xa2 parameters. For example:
p 0.1 2 0 0 2
would look like the function shown on the left.




If the value of f is negative, the resulting parabola will be concaved. For example:
p -0.1 2 0 -0.5 2
would look like the function shown on the left.


Gaussian Distribution

A gaussian refractive index distribution follows the equation


The syntax can be summarized as:
g f w xc xa1 xa2


For example:
g 0.1 2 0 -10 10
would look like the function shown on the left.




We can also only use a portion of the gaussian using the xa1 and xa2 parameters. For example:
g 0.1 2 0 0 10
would look like the function shown on the left.







The function can also be negative. For example:
g -0.1 2 0 0 10
would look like the function shown on the left.

SUMMARY

DistributionSyntax
Uniform Fillb f
Piecewise linearl x1 f1 x2 f2 x3 f3 ..
Parabolicp f xr xc xa1 xa2
Gaussiang f w xc xa1 xa2