Week 16

1. What is meant by population inversion and what happens to the population inversion under steady state conditions of lasing action?

2. Current is passed through a wire that heats up to a temperature of 1900K. A spectral range of light is emitted from the hot wire, the average wavelength being 1micron. Assuming that the wire was integrated into some optical feedback system calculate the ratio of rates of spontaneous : stimulated emission.

3. Show that the relationship between the Einstein coefficients is the same when the lineshape function is considered when compared to a single frequency approximation. (Hint: the lineshape function appears in the spontaneous decay rate only).

Week 17

1. A Helium Neon laser operates at 633nm in the TEM₀₀ mode in a confocal cavity with no aperture. If the spot size on the feedback mirrors is 0.5mm, what is the length of the cavity? If the cavity length is now increased to 1.24m and the stimulated emission linewidth is 1.5 GHz, estimate the number of axial modes detected in the laser output.

2. A Nd:YAG crystal (length 5cm, diameter 0.5cm, r.i.=1.5) is the active medium in a laser cavity with mirror reflectivities of 100% and 95% directly on the rod ends. The spontaneous transition time is 5.5 X 10^-4 s, and has a spectral width of 0.7nm and a centre wavelength of 1064nm. Estimate the threshold population density assuming no cavity losses and hence the pump power threshold. In a high power pumped laser a Nd:YAG glass laser rod will often be used in preference to a crystal – why? Are there any disadvantages in using a glass laser rod?

Week 18

1. An electro-optic modulator is constructed from a material that has a r.i. of approximately 1.5. Estimate the highest possible modulation frequency for a crystal 2mm thick, stating any assumptions or approximations made.

2. What do you notice about the polarisation directions of the various components of light in the type of phase matching that we have studied in the non-linear optical effect.

3. Derive an expression for the phase matching angle for an optically non-linear crystal in terms of the ordinary and extraordinary r.i. s of both the fundamental and second harmonic component. ADP has r.i 1.4943 and 1.4603 for the ordinary and extraordinary components respectively at 1.06?m, and r.i. 1.5132 and 1.4712 for the ordinary and extraordinary components respectively at 0.53microns. Calculate the phase matching angle for ADP.

Week 19

1. A photo-conductive material is deposited on a substrate - the substrate completely absorbs incident light and has the same r.i. as the photo-conductive material (n=1.4). Determine the average carrier generation rate in the photo-conductive material given the following conditions.
Irradiance =100μW/m² @ 632nm, area of slab=100mm², thickness of slab=100microns, quantum efficiency=0.6, and an absorption coefficient of 1000m^-1.
What extra considerations are required if the r.i. of the substrate is different to that of the photo-conductive layer?

2. A photomultiplier has a ‘pure metal’ cathode with an area of 100mm², and a work function of 1.3eV. The detector is used in an experiment where it is cooled down to –77^oC and is required to have a minimum bandwidth of 20Hz for detecting light of wavelength 1micron. Write down an expression for the dark current and calculate the dark current at this temperature. Explain why the expression for the minimum detectable power is independent of the detected photo-current. Calculate how this value changes if the detector is at room temperature.

Each electrode of the photomultiplier emits 10 secondary electrons for every electron that falls on the electrode. Calculate the minimum detectable power under these conditions if the quantum efficiency is 0.4. (Hint: the figure for the secondary electron generation is only implying something about multiplication noise.)

Week 20

1. A photodiode is used in reverse bias to detect modulated light. The detection circuit can be approximated to a resistor (over which the voltage signal is measured) and a capacitor (diode capacitance). By considering the response time due to carrier drift and the electrical response time of the circuit, calculate the maximum frequency response if the diode capacitance is 10pF (at this optimum response time) and a resistor of 100 ohms is used.

2. A planar optical light waveguide is used to carry optical signals between two points 100m apart. The waveguide core has r.i.=1.48 and the cladding r.i=1.47 for the light being transmitted down the guide. The light entering the waveguide has its polarisation in the plane of the waveguide. The light propagating down the guide is derived from a laser operating at 1500nm with a linewidth of 10nm. Calculate if the modal or material dispersion is the dominant dispersion factor if the material dispersion factor l² d²n/dl² = -.0010.
All other things remaining the same, what linewidth would the laser have if the modal and material dispersion factors were equal.
In what types of fiber and under what conditions might we expect material dispersion to be a dominant dispersion factor?