Useful components Apr. 19, 2018

Wavelength converters (sec 3.8): enable relocation and reuse of optical channels, adds to flexibility and efficiency.
Cross-gain modulation Cross-gain modulation - gain saturation in OA can lead to cross talk$\text{ }\to$ cross modulation, i.e. transfer modulation from$\text{ }{\lambda }_{1}$ to$\text{ }{\lambda }_{2}$ which is originally without modulation.
FWM - XPM causes cross talk among channels, e.g.$\text{ }{\omega }_{2}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\omega }_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\omega }_{3}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\omega }_{4}$ where$\text{ }{\omega }_{1}$ carries signal,$\text{ }{\omega }_{3}$ and$\text{ }{\omega }_{4}$ are pumps without modulation.
Extract$\text{ }{\omega }_{2}$ with a band pass filter.
Similar idea for optical freq shifter, except we use a dispersion-shifted fiber as the nonlinear medium.
Optical phase locked loop (OPLL) (sec 4.4.8): To lock on the phase of 2 lasers, i.e. syn. two clocks or local oscillators. Important for coherent detection.
E.g. Freq stabilization -- Use a hollow cathode lamp as calibrator for DFB lasers. When DFB laser lases at 1.296$\text{ }\mu m$ , a voltage is induced at the cathode lamp. This voltage is then feedbacked to lock freq of a master DFB laser. To lock freq of other lasers, a FP interferometer (FPI) is used at each node. The FPI biased by a feedback voltage so that it lets 1.296$\text{ }\mu m$ from the master DFB pass through to a photodetector (PD) that generates a biasing voltage for a slave DFB.
Optical directional couplers as external modulator (Fig. 3.58): when a section$\text{ }{L}_{o}$ of fibers becomes very close with a separation of$\text{ }d$ , light can transfer from 1 fiber to another through evanescent property of lightwave.
When applied voltage V=0, power is completely transferred to adjacent channels.
When$\text{ }V\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{V}_{s}$ , power stays in the same waveguide.

Directional coupler has 4 ports with relations$\text{ }{P}_{1out}/{P}_{1in}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\text{cos}}^{2}\left(\kappa {L}_{o}\right)$ and$\text{ }{P}_{2out}/{P}_{1in}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\text{sin}}^{2}\left(\kappa {L}_{o}\right)$ where$\text{ }\kappa$ is the coupling coef. and length parameter$\text{ }{L}_{c}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\pi /\left(2\kappa \right)$
Couple coef. decreases as d increases.
By setting coupling length$\text{ }{L}_{o}$ to be a fraction of$\text{ }{L}_{c}$ , we can make attenuator, splitter.
Power loss is about 3dB or$\text{ }\Gamma$ with the coupler called$\text{ }{\Gamma }^{1/2}$ coupler.
Ring resonators: $\text{ }1-\Gamma$ power coupled into the ring.
Ring has circumference of L and attenuation coef$\text{ }\alpha$
Light returns to coupler with modified amplitude ($\text{ }\text{exp}\left(\alpha L\right)$ ) and phase ($\text{ }\text{exp}\left(-j\beta L\right)$ ) factors which dep. on$\text{ }L$ and$\text{ }\lambda$
Freq. difference between max. and min.$\text{ }\Delta f\text{\hspace{0.17em}}=\text{\hspace{0.17em}}c/\left(2{n}_{eff}L\right)$ where$\text{ }{n}_{eff}$ is the weighted average index of waveguide and the substrate.
Ring resonator is a notch filter.
Optical equalizers (Sec 5.5.2): maintain equal gain for all channels. Output at each wavelength is measured and gain is adjusted, based on the measurement -- preferably, a dynamic wavelength equalizer (DWE).

Complete article on DWE fabricated by Silicon Light Machine

• Optical isolators (Sec 3.2): It is based on a set of cross polarizers with a magneto-optical material between them. It allows transmission of light in one direction.
Parameters - insertion loss$\text{ }L\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{P}_{in}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{P}_{T}\left(dB\right)$ and isolation$\text{ }I\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{P}_{in}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{P}_{R}\left(dB\right)$