# physics

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Mode spacing and gain coefficient: A Nd microchip laser has an index of refraction 1.78 and a cavity length of 3.20 mm. Mirrors of reflectivity 0.997 and 0.975 are mounted directly on the faces of the chip. The emission lineshape of the laser transition can be considered to be Lorentzian, with a linewidth of 4.80 THz. a) Calculate the frequency spacing between modes of the laser and the frequency width of the modes. (8 pts) b) Calculate the number of modes within the transition linewidth. (9 pts) c) Given the loss coefficient of 0.4 m-1 for the chip; calculate the gain coefficient at lasing threshold. (13 pts)

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