We can get even more detailed! Now suppose you want to model FTIR for the case where a curved surface comes into near-contact with a flat surface. For example, you might have a slab of silica with light totally internally reflecting off the inside of the bottom surface.  You then might want to know how much light is coupled out when a slightly curved surface is brought into contact with the planar surface.

We’ll start with the original “TIR NSC example.ZMX” file, and this time we’ll add a new object (Object 4) of type “Standard Lens” with the following properties:

Comment: bottom lens
Ref Object: 1
Y Position: -25
Z Position: 50
Tilt About X: 90
Material: SILICA
Radius 1: 2.00000E+5
Clear 1: 20
Edge 1: 20
Thickness: 5
Clear 2: 20
Edge 2: 20

It will also be useful to set the Opacity of this lens object to 10%, as we did with the top slab previously.

Note that for the present example we want to see the changing FTIR effects over the beam, so we have chosen a very shallow curved surface with a 200-meter radius of curvature (ROC).

Now we’ll add a bottom detector.  Select and copy the “top slab detector” and paste it at the bottom of the NSC Editor spreadsheet (so the new detector becomes Object 5).  We’ll need to change a few things.  First, the Comment for this new detector should read “bottom detector”.  Second, we’ll change the “Ref Object” to “4”.  Finally, we need to change the “Z Position” of this new bottom detector to “1”.  This is what the NSC editor spreadsheet should look like:

Note that this lens just touches the bottom of the silica slab, but it does so at just one, infinitesimally tiny point.  Here is a Shaded Layout of our setup (note that I’ve rotated the image a little bit, to give a better view of the bottom detector inside the bottom lens):

Clear the detectors and trace rays.  You’ll notice that the rays are totally internally reflected everywhere, except in a very small area around the infinitesimal contact point.  This small area shows where the surface of lens comes within the glue distance (1.0nm in our case) of the top slab, where ZEMAX considers the two objects to be touching and so the rays are completely transmitted within this small area.

In order to see FTIR effects, once again we must do so with the help of coatings.  We’ll use the same trick we used for the wedge, but this time instead of a linear tapered coating, we’ll need to define a slightly more complicated spherical-sag tapered coating. 

First thing we need to do is convert our lens from a curved surface to a flat one, because, remember, the lens needs to make direct contact over its entire surface with the top slab.  To do this, we change the “Radius 1” value of our bottom lens (Object 4) to 0.000.

We now need to create a tapered coating to simulate the sag of a 200m ROC sphere, which is 40mm in diameter.  First step is to fit a 200m ROC circle to a polynomial (for the range 0 < r < 20mm, where r is the radial distance). 
 
Note that ZEMAX takes the radial distance value, r, in lens units (which in our case are mm) but it converts these to thickness units that are in microns.  Effectively, ZEMAX will apply a factor of 0.001 to our sag measurement when calculating coating thickness.

Therefore, to model a 200m ROC sphere, we need to fit the surface sag of a 200mm ROC sphere.  The equation for the surface sag of a sphere is

s = R - (R² - r²)^1/2

where s is the surface sag, R is the ROC of the sphere, and r is the radial coordinate.

I chose to fit this spherical lens shape to a 4th degree polynomial, but you are free to choose any number, up to 20th order, for a polynomial fit in ZEMAX tapered coatings.  Because we want a radially-symmetric coating, we’ll use a Radial Taper (RT) this time.

Here are a few lines that need to be added to the coating.dat file:

TAPR LENS
RT 0 1.350545e-7
RT 1 -1.964583e-7
RT 2 2.5000646e-3
RT 3 -7.6597998e-9
RT 4 1.5947742e-8

COAT 200mm_LENS
AIR 1 1 0 LENS

After adding these lines to coating.dat and then saving the file, return to ZEMAX and click to “Reload Coating File” once again.  Change the coating on Object 4, Face 1, to “200MM_LENS,” as shown below:

Clear the detectors and trace rays once more.

Results for the two detectors are shown below:

Note that the curved surface has drained power from the center of the beam, and note also that 58% of the beam is now drained out of the top slab.