3.9 It is rare for a mode of an etalon to exactly match the frequency of one of

Question

3.9 It is rare for a mode of an etalon to exactly match the frequency of one of the modes of the laser. However, twisting the etalon slightly will change the optical path length and allow the modes to overlap. (a) Consider an etalon 2.5 mm thick. Assume that it will be used in a 488 nm laser, has an index of refraction of n = 1.58, and has both surfaces coated so that they have reflectances of 90%. Use a computer program to generate several plots of the transmittance spectrum for this Fabry-Perot etalon. Construct the plot so that all the transmittance spectra can be seen and compared (the plot should look similar to Figure 3.9). Generate spectra for 0 radians, e, = 0.004 radians. = 0.008 radians, and , = 0.012 radians. Put transmittance (T) on the y-axis and wavelength on the x-axis. (b) Considering the results of Exercise 3.8, generate an equation that predicts how many degrees an etalon must be twisted in order to move the etal radians free spectral range of the etalon. Solve the equation for the conditions given in Exercise 3.8. Is the answer consistent with your computer results?

Explanation / Answer

Transitions in states and means that machines moves to the right as long as 0 or 1 is on the tape. The machine starts by writing a blank symbol to delimit the left-hand edge of the tape Stage 1 is implemented by states through : , , if the first symbol of input is , and if the first input symbol was . To simplify the figure we don’t show the reject state or transitions going to reject state. These transitions occur implicitly whenever a state lacks an outgoing transition for a particular symbol. Example, on # is such a transition

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