Arrayed Waveguide Grating Router 4

Arrayed Waveguide Grating Router 4 - Arrayed Waveguide...

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Unformatted text preview: Arrayed Waveguide Grating Router 4 Arrayed waveguide grating routers are used in fiber optic network telecommu- nications 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 conve- niently implemented as silica waveguides on a silicon wafer. The most basic operation of an arrayed waveguide grating. router is perhaps as a demultiplexer. This mode may be visualized by considering two wavelengths in the cen- ter waveguide of the series of input channel waveguides. As these waves propagate across the input slab waveguide region their wavefronts expand to fill all of the waveguides in the arrayed waveguide region. The waves for each wavelength propagate individually in the waveguides of the array. As they approach the output slab waveguide region they each recombine to form a single converging wavefront. The arrayed channel waveguides are spaced d apart at the output slab waveguide. Each wavefront propagates a distance L f across the output slab waveguide and converges to a output channel waveguide. The first wavelength enters one of the output channel waveguides. The second wavelength enters a separate output channel waveguide. The output channels are spaced Ax apart. The angular dispersion for a wave of frequency f in the output slab waveguide region is given by d9 _ m A2 N 916), E _ _ st MC}. for small angles of deviation. The quantity m is the diffraction order, A is the center wavelength (enters the center input channel waveguide and exits the center output chan- nel waveguide), N31 is the effective index of the slab aneguide, NC}, is the effective index of the channel waveguides, and Ngflh is the group velocity index of the channel waveg— uides given by Ng,ch = N6}, — A chh/dA. For a particular practical arrayed waveguide grating router, d = 25 pm, L f = 10.00 mm, m = 100, NS; = 1.4529, NC}, = 1.4513, and Ngfih = 1.4752. With this arrayed waveguide grating router, it is desired to demutliplex two C-band channels whose (ITU standard) frequencies are f1 = 195.0 TH z and f2 = 195.1 TH 2. Calculate, showing all work, the needed spatial separation, Am, between output waveguides to accomplish this. ‘ Express your answers accurately to five significant figures. Put your answer in the space provided below. Spatial separation between output channels, Am :2 um. ARRAYED WAVEGUIDE GRATING ROUTER Arrayed Waveguide Grating Region Input Slab 10m , Waveguide Region Output Slab Waveguide Region 1 cm Input Output Ports . Pons ARRAYED-WAVEGUIDE \_/ INPUT/OUTPUT WAVEGUIDE : SUB WAVEGUIDE \/ 3 C 3% E : i d Li I: Arrayed Waveguide Grating Router 4 Input channels f1 = 195.0 THz —> A] : c/f = 1537,40nm f2 = 195.1 THz —» 12 = c/ f = 1536.61 nm ‘ ! Angular dispersion d0 m A2 NM 3? Z ' stchch m = 100 NW = 1.4752 NS; = 1.4529 d = 25 pm Nch = 1.4513 L f = 10.00 mm and so d9 m A2 NW _= ____=_. -5 =—1.244 1—3 df NsldCNch 220633x10 rad/0H2 6 1 X 0 deg/0H2 Angle between adjacent output channel waveguides Angle = g A f and from geometry ‘ A11: and so d6 Ax = 37Afo therefore Ax = (2.20633 x 10—5md/GH2) (100 GHz) (10,000 pm) = 22.0633 um ...
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