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Arrayed Waveguide Grating Router 1

Arrayed Waveguide Grating Router 1 - Arrayed Waveguide...

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Unformatted text preview: Arrayed Waveguide Grating Router 1 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 A2: apart. The angular dispersion for a wave of frequency f in the output slab waveguide region is given by d9 _ m A2 NW}, 87 ‘ _ NS; cha for small angles of deviation where m is the diffraction order, /\ is the center wavelength (enters the center input channel waveguide and exits the center output channel wave- guide), N s; is the effective index of the slab waveguide, NC}, is the effective index of the Channel waveguides, and Ngfih is the group velocity index of the channel waveguides given by Ngflh = Nch —- A chh/dA. For a particular practical arrayed waveguide grating router, d = 25 pm, L f 2 9381 pm, Ax = 25 pm, m = 118, /\ = 1553.81 nm, NS; = 1.4529, Nch = 1.4513, and Ngfih = 1.4752. For this arrayed waveguide grating router, calculate in deg / GH 2, showing all work, the magnitude of the angular dispersion in the output slab waveguide region for small angles of deviation. Calculate the magnitude of the frequency separa— tion in GHz and the freespace wavelength separation in nm between adjacent output channel waveguides. Express your answers accurately to five significant figures. Put your answers in the spaces provided below. Angular dispersion = deg / GH 2. Frequency separation between channel waveguides = CH z. Wavelength separation between channel waveguides = nm. ARRAYED WAVEGUIDE GRATING ROUTER Arrayed Waveguide Grating Region Input Slab 1cm Waveguide Region Output Slab Waveguide Region 1 cm 4—“, Input Output Ports Ports lNPUT/OUTPUT WAVEGUIDE JUUUUL/L/k “ Ax Lf SLAB WAVEGUIDE 9 WWWW _ ARMYED-WAVEGUIDE Arrayed Waveguide Grating Router 1 Angular dispersion d6 _ _m,\2Ng,ch df _ stdCNch m = 118 A = 1553.81 nm Ngfih = 1.4752 NS; = 1.4529 d = 25 ,um Nah = 1.4513 Lf = 9381 ,um Ax = 25 ,um and so /\2 C d9 —m—Ngi = —2.6593 X 10—5rad/GHz = —1.5237 x 10‘3deg/GHZ E : st dCNch Angle between adjacent output channel waveguides Angle = 93 = 2.665 x 10*3md = 0.1569 deg = Q A f Lf df Frequency separation Ax d0 ‘1 Wavelength separation (using /\ = c/ f ) 1 A2 d/\=c ——-—— df=— ——df=0.80703nm f2 C ...
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Arrayed Waveguide Grating Router 1 - Arrayed Waveguide...

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