A strontium titanate right-angle prism (np = 2.32) is used as an input coupler to couple light of 9050 A (vaccum) wavelength into a Ta ˚ 2O5 waveguide
(n = 2.09) from an air beam. The face of the prism makes an angle of 45◦ with
the surface of the waveguide. The β of the lowest-order mode in the waveguide
is 1.40 × 105 cm−1.
(a) Make a sketch of the coupler labeling the significant angles φ1, φ2, φ3,
etc. Use these labels in your calculations in part b.
(b) What angle must the input laser beam (in air) make with the surface of
the waveguide in order to be coupled into the lowest-order mode?
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