1. A very narrow laser beam in air is shone into a sphere of solid glass that has a uniform
refractive index n>1 and radius ? . The beam makes an angle a in air with the normal to
the surface of the sphere.
Sketch the path of the beam in the circular cross-section of the sphere defined by the
normal and the beam direction, and show all reflected and transmitted rays.
Explain why the beam cannot become a bound whispering gallery ray propagating around
the inside the glass-air surface of the sphere.
2. An asymmetric, multimode, step-profile slab waveguide has a core index of 1.49. The
cladding index above the core has value 1.47 and the cladding index below the core has
value 1.48. Rays propagate in the core in the x-z plane and make an angle ?z relative to
the z-axis along the centre of the waveguide.
(a) Determine the range of (positive) values of ?z in degrees for which only bound rays
will propagate along the waveguide.
(b) How many different types of rays can propagate along the waveguide?
Sketch a typical path for each type of ray.
(c) Determine the values of ?z in degrees that delineate between the 3 types of ray paths.