MZI

Question 1

What is an interferometer?

Answer 1

An interferometer is a device that works by combining two or more sources of light to create an interference pattern, which can be measured and analysed.

Question 2

What is an MZI?

Answer 2

An MZI or Mazh-Zehnder Interferometer is a device where light is spli into two different paths and then recombined. The paths may vary in length or group index. This leads to a different response at the end of the MZI compared to the beginning.

Question 3

Describe the MZI wavelength response?

Answer 3

For a wideband signal or pulse

β = (2πn_eff)/λ

β being the propagation constant

The transmission is expressed via the equation:

I_o/I_i =1/2+〖1/2 cos〗⁡(2π/λ (n_eff2 L₂-n_eff L₁ ) )

If there is a phase difference between the two arms, the transmission spectrum will have a sinusoidal response with wavelength as described above.

Question 4

What is the FSR of an asymmetric MZI with a difference in length ∆L?

Answer 4

FSR=λ²/(n_g ∆L)

Question 5

MZIs require a phase difference to function as sensors, modulators, and other devices. Where can this phase difference come from?

Answer 5

The phase difference can either come from a difference in the physical length of the arms, or a difference in the group refractive index in the two arms.

This divides MZIs into two types, asymmetric and symmetric.

Question 6

FSR of a symmetric MZI

Answer 6

FSR=λ²/∆n_g L)

Question 7

How can you derive the insertion loss from the MZI transmission spectra?

Answer 7

The “insertion loss” is the loss in dB at the wavelength with the maximum transmission. It is the difference between 0 and the max value of the transmission.

Question 8

How do you derive the extinction ratio from an MZI transmission spectrum?

Answer 8

The “extinction ratio” is the ratio of the minimum and maximum transmission, expressed in dB.

Question 9

What affects the transmission spectra of real devices?

Question 10

How does an MZI work?

Answer 10

1. Beam is split equally into two arms
2. The beams propagate through each arm, and depending on the difference in optical path length, may arrive at the combiner with a relative phase change
3. The beams recombine to give an output where the phase difference is converted into a change in amplitude

Question 11

How can an MZI be used as a modulator?

Answer 11

In a Mach-Zehnder interferometer, a change in the refractive index of a waveguide can change the phase in one of the MZI arms, and can be converted into a change in light intensity.

The refractive index of a waveguide can be controlled electrically using a variety of different electro-optic mechanisms.

Question 12

Describe MZI as a thermo-optic modulator

Answer 12

The thermo-optic modulator is a device where a wire is placed just above the waveguide heats up the waveguide when a current is passed through the wire

As the refractive index of silicon changes with temperature, a phase shift is produced.

In practice this is a very slow modulation mechanism, and high speed modulators (for 10-100 Gbit/s) use different modulation mechanisms

Question 13

Describe an MZI as a sensor

Answer 13

MZIs can convert small changes in length, refractive index into larger, more easily measurable optical intensity changes.

Question 14

Describe Step 1 of MZI

Answer 14

A light beam with an electric field amplitude E_i is launched into the input waveguide.

At the splitter, the light power is split equally into the two output waveguides.

If I_i=1/2 cϵ₀ E_i²

and if I₁=1/2 cϵ0 E₁²

Since the power is splitting evenly, I₁=I_i /2, then

E₁=E₂=E_i/√2

Question 15

Describe Step 2 of MZI

Answer 15

The beams propagate through each arm:

Assuming no Losses

The electric field in each branch is equal to 0.707E_i where E_i is the incident electric field.

Question 16

Describe Step 3 of MZI

Answer 16

The beams recombine:

The output electric field is a fraction of the input field from the splitter.