Optical filters II Mar. 13, 2018

+ Acousto-optics tunable filters (pp. 143-146 2nd Ed, pp. 149-152 3rd Ed): Use RF signal to induce acoustic oscillation [equation] generate a Bragg grating that diffracts light.
Acoustic wave parameters - freq [equation], velocity [equation] and wavelength [equation].
RF signal induces strain [equation] where [equation] and [equation].
acousto-optical effect causes refractive index change [equation] where [equation] is photoelastic constant.
Select wavelength [equation]
Response time [equation] where [equation] is the optical beam diameter.
Operation - Use birefringent material to make a polarizing beam splitter. The resulting TE wave will be converted into TM wave if grating condition [equation] is satisfied. The polarizing beam splitter selects only TM waves.
Freq response [equation] where [equation], [equation] and [equation].

+ Mach-Zehnder (MZ) filter (pp. 135-139 2nd Ed, pp. 141-145 3rd Ed): Similar to Mach-Zehnder interferometer; replace beam splitter with directional coupler.
Directional coupler is a 2 ports device (pp. 108-112 2nd Ed, pp. 114-118 3rd Ed).
Its transfer function for straight thru (e.g. input 1 [equation] output 1) is [equation] and for cross over (e.g. input 1 [equation] output 2) is [equation] where [equation] is the coupling coefficient and [equation] is the coupling length..
By choosing appropriate [equation], we can construct a 3dB coupler (i.e. 50%/50% splitter).
For 3dB coupler, signal from each input port is split across 2 output ports. Phase shift of [equation] occurs when signal crosses ports, e.g. input port 1 to output port 2 or input port 2 to output port 1.
Two input ports separate freq depending on the phase difference between the two paths for input signals, e.g. signal at output port 1 satisfies [equation] for [equation];
signal at output port 2 satisfies [equation] for [equation].
Channel frequency spacing [equation]. (pp. 137, 138 2nd Ed, pp. 143, 144 3rd Ed)
Tunable output freq by RF, thermal or mechanical controls.
Cascading MZ to get more than 2 outputs.

Last Modified: March 11, 2018
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