Lecture 5

Tunable Filters

Δf defines as the frequency difference between the lowest- and the highest-frequency channels and  f as the spacing between channels. The maximum number of equally spaced channels can be calculated as N max = Δf /  f. The access time is the speed which a tunable filter can be reset from one frequency to another. This should be in the unit of microsecond. The filter’s transfer function T(f) is not generally equal to unity due to its internal losses.

Tunable Filters Good filters should be independent to light polarizations. Tunable-filters have an advantage over the coherent-detection due to that. With the help of lithography, the low cost filter can be fabricated, but the fiber loss attachment exists. However, with other methods, high-cost processes are involved and that is the great barrier to develop such a technology.

Tunable Filters Wavelength selective filters might be categorized into: 2-port filter 1  N WDM filter

Tunable Filters 4-port add-drop filter

Crosstalk

Filters for WDM Requirements: Center wavelength near 1.55 μm or 1.3 μm. Some local network might have a center wavelength of 0.8 μm. Frequency Spacing: about 100 GHz. Number of channels: having been increased to more than 256. Tuning speed: less than 1 μs.

Some of tunable filters Fabry-perot filters Mach-Zehnder chain Grating Acousto-optic tunable filter (AOTF) Electro-optic tunable filter (EOTF)

Fiber Fabry-Perot Filter

Consider a single mirror

Fiber Fabry-Perot Filter After a round trip

Fiber Fabry-Perot Filter After two round trips After N round trips

Fiber Fabry-Perot Filter At steady state (N  ∞)

Fiber Fabry-Perot Filter At steady state (N  ∞)

Fiber Fabry-Perot Filter Plot T vs 

Fiber Fabry-Perot Filter

We can find the bandwidth of the peak by looking at the denominator expression for T.

Fiber Fabry-Perot Filter Another important parameter to characterize a FP filter is the finesse, F. This can determine the maximum number of channels in WDM system.

Example If we have 10 channels with 100 GHz spacing for each channel. What shoud the length of FPI filter be?

Example Consider a Fabry Perot filter with an air cavity of length L and R = 0.99 for each mirror, with a free spectral range of 3.2 THz. (a) What is L in μm? (b) For the value of L determined in (a), what is the wavelength λ 0 nearest 1.53  m for which the transmittance is a maximum.

Mach-Zehnder Chain

Example Consider a 7-stage MZ chain with a FSR of 3.2 THz produced in single mode fiber with n = 1.46 for the fundamental mode and a transmittance maximum for λ 1 = 1.53  m. What is the shortest and longest path difference for any interferometer in the chain?

Gratings Spatial period d diffracted waves interface

Example Find the allowed mode and angles for each mode for I =30 , = 1.53 μm, and d = 1.61 μm.

Gratings

Calculating wavelength dependence of focused spot position.

Example From previous example, if channel spacing is 100 GHz. What should be a value of h?

Spectral resolution Spectral resolution is an ability to separate light into wavelength components.

Gratings