Arrayed Waveguide Grating Router 2

Arrayed Waveguide Grating Router 2 - Arrayed Waveguide...

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Unformatted text preview: Arrayed Waveguide Grating Router 2 Arrayed waveguide grating routers are used in fiber optic network telecommuni- cations as multiplexers, demultiplexers, add-drop filters, and as N X N switches. The device, shown in the attached figure, consists of an array of channel waveguides with the optical path length of adjacent waveguides differing by a constant value. At the ends of the array of waveguides are input and output region slab waveguides. These slab wave- guide regions, in turn, are connected to input and output channel waveguides that are linked to individual optical fibers. The arrayed waveguide grating router can be conven- iently implemented as silica waveguides on a silicon wafer. The most basic operation of an arrayed waveguide grating router is perhaps as a demultiplexer. This type of operation may be characterized by considering multiple wavelengths in the input slab waveguide region incident at an angle 0,- on the input to the arrayed waveguide grating region. The wavelengths are launched into all of the chan- nel waveguides of the arrayed waveguide region. The length of each channel waveguide is AL longer than the channel waveguide below it. Each wavelength propagates indi— vidually in the channel waveguides of the array. As the waves approach the output slab waveguide region they each recombine (constructively interfere) to form a single wave- front propagating at an angle 6 in the output slab waveguide region. The condition for this constructive interference is given by the grating equation for the arrayed waveguide grating router which is N,,(/\)dsm6,- + Nch()\)AL + Nsl()\)dsz'n0 = mA, where NS; is the effective index of the slab waveguide, NC}, is the effective index of the channel waveguides, A is the freespace wavelength, d is the spacing between adjacent channel waveguides at the input and output slab waveguide regions, and m is the diffrac— tion order (an integer). For the center wavelength A0, the angles of incidence and diffrac- tion are 6,- = 0 = 0 and so Nch()\0)AL = on. For small angles of incidence and diffraction, calculate the angular dispersion dfi/dA for a wave of wavelength /\ (near the center wavelength A0) in the output slab waveguide region. Express your answer as a function of only m, d, N31, Nch, and NM}, where Ngach = Nch — A chh/dA is the group velocity of the wave in the channel wave— guide. Put your final answer in the space provided. d0 A l d' ' —— = ngu ar 1spers1on d)‘ ARRAYED WAVEGUIDE GRATING ROUTER Arrayed Waveguide Grating Region Input Slab 1cm Waveguide Region Output Slab Waveguide Region 1cm input Output Ports Ports ARRAYED-WAVEGUIDE \_/ INPUT/OUTPUT WAVEGUIDE : SLAB WAVEGUIDE \/ 3 4? > 9 > : x d Lf AX ¢ E i: E ’7 C ’7,_ Arrayed Waveguide Grating Router 2 Grating equation for the arrayed waveguide grating router Nsl()\) dsin 0,- + Nch()\) AL + stOx) dsin 0 = mA Differentiating with respect to wavelength (101- stl(/\) r ._ 1\51()\)dc036z dA+ dA chh(,\) d0 _ stl()\) ______A _ A L+Nsl(/\)dco.30d)\+dsm0 A dsin0i+ =m Since 0i is a constant, d6i /d)\ = 0. Solving for da/dA gives d9 __ 1 stl(A) , i chh(/\) stl()\) , d/\ ‘ st(/\)dco.30lm d/\ dsme' d/\ M d,\ dsmgl Since the angles 6,- and 6 are small, then do _ 1 chm) dA “ st(/\)d[m dA AL] Using AL 2 m Ao/Nch, this becomes fl_ 1 [m_m/\0chh()\)] d/\ — Nsl()\)d Nch d)\ Using Ngach = Nch — /\ dNCh/dA and since A 2 A0, then fi_ mNg,ch dA — Nslchh ...
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This note was uploaded on 04/29/2008 for the course ECE 4500 taught by Professor Gaylord during the Spring '08 term at Georgia Institute of Technology.

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Arrayed Waveguide Grating Router 2 - Arrayed Waveguide...

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