Brewster_cavity_help.txt

This function is an extension of the original Cavity function. It adds the ability to 
model astigmatic cavities, with the astigmatism arising from tilted and curved mirrors 
and Brewster-cut crystals. The cavity is assumed to be a ring with two curved mirrors 
bracketing the nonlinear crystal. The ring is assumed to be planar so the in-plane and 
out-of-plane mode profiles are independent of one another and can be computed separately. 
The mode profiles for the two planes are both computed and displayed whenever the 
function is run. The function also allows user specification of a disturbance to the 
cavity. Disturbances can be either a tilt or a displacement of the mode in the plane of 
the cavity, and they can be located anywhere in the cavity. This calculation is useful in 
understanding how tilting a cavity mirror shifts the mode or how refraction in a tuning 
prism shifts the mode. This knowledge is useful in deciding how to tweak the alignment of 
a cavity or where to place a mode selecting aperture in the cavity.
				
When a beam is reflected from a curved mirror at an in-plane angle-of-incidence the 
effective curvature of the mirror is less than the actual radius of curvature in the 
in-plane direction and greater than the actual radius of curvature in the out-of-plane 
direction. The cavity is astigmatic even if the crystal faces are perpendicular to the 
beam.
				
When a beam enters a crystal through Brewster cut input face the beam diameter 
immediately expands be a factor of n in the in-plane direction. The radius of curvature 
immediately increases in the in-plane direction by a factor of n cubed, and in the 
out-of-plane direction by a factor of n. These changes are reversed on exiting the 
crystal through a Brewster output face. 
				
The astigmatism of a Brewster cut crystal can be offset to a degree by adjusting the 
angle-of-incidence of the curved mirrors.
				
The function inputs are:
- Wavelength.
- Crystal length. This is the physical length of the optical path through the crystal.
- Crystal refractive index.
- Mirror radius of curvature. This is the manufacturers radius of curvature, not an 
effective radius of curvature.
- Mirror angles-of-incidence. This the in-plane angle-of-incidence on the two curved 
mirrors.
- Leg1 length. This is the physical length of the light path between the curved mirrors 
that includes the crystal. The crystal is located midway between the curved mirrors.
- Leg2 length. This is the physical length of the path between the curved mirrors that 
does not include the crystal.
				
- Disturbance type and location. The disturbance can be either a beam tilt or a beam 
displacement and it can be located anywhere in the cavity, including in the crystal, as 
specified by "Disturbance dist. from L mirr."
				
The function outputs are:
- Plots of the mode diameter, either FWHM or 1/e^2 as selected by the user. The in-plane 
and out-of-plane diameters are both plotted.
				
- Plots of the beam radius of curvature. Both in-plane and out-of-plane curvatures are 
plotted. There is a step of n for the out-of-plane radius of curvature on entering or 
exiting the crystal. For the in-plane radius of curvature the step is n for non-Brewster 
crystal and n cubed for a Brewster crystal.
				
- Optional plot of mode shift due to a specified disturbance. At the location of a tilt, 
the in-plane slope of the mode displacement changes by the specified tilt magnitude. At 
the location of an offset the in-plane mode displacement changes by the specified offset. 
The disturbed mode is the mode of the disturbed cavity. Multiple disturbances can be 
modeled individually, and then the individual mode displacement around the cavity can be 
summed to find the effect of multiple disturbances.
				
Form outputs include the in-plane and out-of-plane Rayleigh range, mode waist diameter at 
the crystal midpoint, mode waist diameter in leg2 of the cavity. The outputs "L mir beam 
diam" and "L mir rad curv" give the beam diameter and radius of curvature just inside the 
curved input mirror. This is necessary information for launching a beam that matches the 
cavity mode. The "Crystal input beam diam" and "Crystal input rad curv" can similarly be 
used to launch a mode matched beam at the crystal input face. The round trip time output 
is the Gouy phase accumulated in one pass of the full cavity. The vert. mirror separation 
and horiz mirror separation are useful in setting up the curved mirrors for a Brewster 
crystal. They are the mirror separations in the direction normal to the mode and parallel 
to the mode necessary to achieve the specified input leg1 length. The Brewster angle 
output is arctan(n).