Mach-Zehnder Interferometer

The Mach-Zehnder Interferometer has two input ports and two output ports. The light is split in the two arms of the input coupler of the interferometer, and they are later recombined in the output coupler of the interferometer. The optical length of the two arms is unequal, making the phase corresponding to delay in figure given below, to be a function of wavelength. The relative phase of the light in the two input ports of the output coupler is therefore a function of wavelength.

As the phase of the delay (d) is increased, the MZI cycles between the cross state, where most of the light appears in the waveguide on the same side as the input, and the bar state, where most the light moves to the waveguide on the other side. A typical application would call for a bar state at one specified wavelength, and a cross at another. For example, in a communication system where wavelength 1.3 um is being used for transmission, and 1.5 um is being used for reception on the same fibre, it would be useful to have a circuit that is in a bar state for 1.3, but in a cross at 1.5. In that way, most of the received light can be sent to the receiver, and not to the transmitter, without compromising the insertion loss between the transmitter and the fibre.

The ideal behaviour requires the couplers to be at a 3dB level. Over this large wavelength range, the coupler strength is a function of wavelength, but modest specs can still be obtained by designing the ideal 3dB point for 1.4 um. (It could be changed to 1.3 or 1.5 to minimize the insertion loss of the transmitter or receiver, at the expense of the other, if desired). This optimization is done (in 2D) in project Coupler14.bpd, to obtain the waveguide narrows distance of 5.4683. Next, the difference of length of the two arms is selected. The phase difference between the two arms will be

where L is the difference in the path length of the two arms, and n the modal index of the waveguide, here estimated as 1.485. As the path difference is increased, the MZI will cycle between cross and bar states, the crosses occurring at multiples of 2 p, and the bars interlacing. To obtain a circuit of minimum size, the minimum possible phase change between the design wavelengths, 1.5 and 1.3, is used. The transmission wavelength, 1.3, should be placed at a cross and the reception wavelength, 1.5, at an adjacent bar. If L is chosen such that

(bar state)

then the state at the Rx wavelength, 1.5, is very close to a cross:

and

(nearly cross)

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