The Operation of an Important "Light Guiding Device"

Introduction:

In many optical systems a series combination of two tapered plates differing in index of refraction is used as a simple beam deflector.  We present here a representative set of data on the deflection caused by such a taper plate combination that was prepared with a simple MATLAB program. (The MATLAB programs are appended.)  We assume that the direction of the incident light defines a reference axis and the output deviation or deflection is measured with respect to that axis.  The angular deviation of each of the three planes of interest are measured with respect to the direction orthogonal to the direction of the incident light as illustrated below.

Device schematic:

 

Definitions of terms used in this discussion: n1: First tapered plate index of refraction n2: Second tapered plate index of refraction b1: First block angle b2: Second block angle a : Interface angle

Two particular device examples:

Device calculations:

Deflection as function of n2 and b1 (b2= b1) with a  fixed at 30° -- i.e. a slab oriented at an angle b1 wrt the direction orthogonal to the horizontal axis.

Deflection as function of n2 and b1 (b2= b1) with a  fixed at 30° -- i.e. a slab oriented at an angle b1 wrt the direction orthogonal to the horizontal axis. Note the general result that there is no deviation when the slab is homogeneous -- i.e. when  n2 = n1

Deflection as function of n2 and b1 (b2= b1) with a  fixed at 0° -- i.e. a slab oriented at an angle b1 wrt the direction orthogonal to the horizontal axis and the interface parallel to that direction.

Deflection as function of n2 and b2 with b1 and a  fixed:

 
 

MATLAB programs:

"deflection.m" the function that computes deflection by three planar surfaces
"plotit_30.m" the function that plots the data in the first graph above.
"plotit_0.m" the function that plots the data in the second graph above.
"plotit_trap.m" the function that plots the data in the third graph above.