Optical computers require microscopic optical switches to turn signals on and of

Question

Optical computers require microscopic optical switches to turn signals on and off. One device for doing so, which can be implemented in an integrated circuit, is the Mach-Zender interferometer seen in the figure on the next page. Light from an on-chip infrared laser ( lambda = 1.050 mu m ) is split into two waves that travel equal distances around the arms of the interferometer. One arm passes through an electro-optic crystal, a transparent material that can change its index of refraction in response to an applied voltage. Suppose both arms are exactly the same length and the crystal's index of refraction with no applied voltage is also 1.549. With no voltage applied, is the output bright (switch closed, optical signal passing through) or dark (switch open, no signal)? What is the first index of refraction of the electro-optic crystal larger than 1.549 that changes the optical switch to the state opposite the state you found in part a? Express your answer using four significant figures.

Explanation / Answer

A) The output is dark since the path difference of the wave is a half-integer number of wavelengths.

B) The crystal changes the path lenght to xn, where x is the length of the arms, so the path difference between the two arms is xn - x = x(n-1) so this needs to be an integral number of wavelengths for constructive interference (assuming no phase change).
For first index of refraction, x(n-1) =wavelength

n-1 =1.05/6.7 =0.157

n =1.157

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