• Mach-Zehnder interferometry is used to make wavelength dependent These devices can be either active or passive.
  • A layout of 2 x 2 passive MZI is shown in 7.3.1. It consists of three stages
  1. 3-dB splitter
  2. Phase shifter
  3. 3-dB



  • Initially a 3 dB directional coupler is used to split input signals. The middle stage, in which one of waveguide is longer by ∆L to given a wavelength dependent phase shift between the two arms. The third stage is a dB coupler which recombines the signals at
  • Thus input beam is splitted an phase shift it introduced in one of the paths, the recombined signals will be in phase at one output and out of phase at other output. The output will be available in only one

Output powers


  • The output powers are given by –

Pout, 1 = Eout,1 + E* out,1                                                                                                         … (7.3.1)

Pout, 2 = Eout,2 + E* out,2                                                                                                         … (7.3.2)

The optical output powers are square of respective optical output field strengths.


                                 … (7.3.3)

                                 … (7.3.4)


∆L = Difference of path lengths,


  • If all the power from both input should leave the same output port (any of output port) then, there is need to have  and

                                                            … (7.3.5)

= π


  • The length difference in interferometer arms should be


… (7.3.6)



… (7.3.7)



∆v is frequency separation of two wavelengths ηeff is effective refractive index in waveguide

Example 7.3.1 : ln 2 x 2 MZIs, the input wavelengths are separated by 10 GHz. The silicon waveguide has ηeff = 1.5. Compute the waveguide length difference.

Solution : Given :       ∆v = 10 GHz = 10 x 109 Hz

ηeff = 1.5 The length difference is given by

… (7.3.8)


∆L = 10 mm                                                                                      … Ans.