1. Tilted etalon
An etalon is essentially a Fabry-Perot interferometer of fixed spacing. Since the spacing is fixed, so is the wavelength it transmits. However, the transmitted wavelength of an etalon (or other interference filter) can be tuned by changing the angle of incidence of the light.
We shall explore this by using a slab of glass as our etalon. The slab has flat, parallel sides and an index of refraction m = 1.5. If we want it to serve as an etalon (at normal incidence) for lo = 442 nm (the blue HeCd laser line), how thick should it be? What is the contrast for this etalon? (Not so great!) The resolving power? (Also not so great!) Now tilt the slab so that the light is incident at an angle q. What is the new value of the resonant wavelength? How has the contrast changed? How far can you shift the resonant wavelength by tilting the slab? The effect of tilting a multilayer interference filter is similar, so such a filter can be used over a (small) range of wavelengths.
2. Lummer-Gherke plate
Fig. 15.7 (pg. 457) in your textbook shows a Lummer-Gherke plate, which produces a large number of parallel output beams. It uses multiple reflection at internal angles just less than the critical angle in a parallel-sided plate of thickness d, length L and refractive index m. What is the phase difference between adjacent beams, as a function of the output angle q? What is the resolving power (inverse of the limit of resolution)?
3. Polarization dependence
In class, when we looked at the number of modes which propagate in a slab waveguide we assumed that the light was ^ polarized. Would we get a different number of allowed modes for ||-polarized light? Usually there is more loss (due to absorption and scattering) in the cladding than in the core. That being the case, which type of polarization will travel farther down the fiber before being attenuated to an unacceptable degree?
4. Slab waveguide
To get a feel for the magnitudes of the quantities involved in an electro-optic integrated circuit, consider a slab waveguide made of a thin layer of Ga0.67In0.33As (m = 3.37) on a GaAs substrate (m = 3.30), using a wavelength typical for optical communications (l = 1.3 µm). What is the numerical aperture for this waveguide? What is the minimum thickness for the film in order for the wave to propagate? What should the thickness be in order that the film act as a single-mode waveguide? If we make the film 100 µm thick, how many modes will propagate? What will be the smallest reflection angle (measured from the interface normal) in that case? What will be the spread in arrival times among the various modes for a multi-mode pulse that travels a distance of 1 cm? What happens if we use HeNe laser light instead? (Hint: what about absorption?) How about if we cap the Ga0.67In0.33As layer with GaAs? How do these numbers compare to the corresponding values for a slab of SiO2 (m = 1.45) surrounded by air? What can we do to the SiO2 slab to improve its dispersion (pulse-spreading) characteristics? (Hint: think about real optical fibers.)