Chapter4_Integrated_Optic_Waveguide.ppt

1、Chapter 4Integrated Optic Waveguide,4.1 Dielectric Slab Waveguide,n3,n2,n1,d,Trapping of light ray in a waveguide,n2 n3,q,4.2 MODES IN THE SYMMETRIC-SLAB WAVEGUIDE,Range of for bound waves:,Propagation factor,Longitudinal propagation factor,Define the effective index of refraction:,4.2.1 Mode Condit

2、ion,The two boundaries (upper and lower) form a cavity. A cavity is resonant when the round trip phase shift is 2m (where m = 1,2,3 ). = m2 (4.10),4.2.2 TE and TM Polarization,TE polarization (Transverse Electric) This is the same as perpendicular polarization (s).,TM polarization (Transverse Magnet

3、ic) This is the same as parallel polarization (p).,(4.11),where we used the relationship,4.2.3 TE Mode Chart,Example,Consider an AlGaAs Laser Diode,For the TE0 mode the calculations yield the table:,(1),(2),(3),(4),(5),(6),q,n,eff,tan(hd/2),hd,2,p,n,1,cosq,d/l,80.4,3.550,0,0,3.757,0,82,3.565,0.651,1

4、.155,3.148,0.367,84,3.580,1.261,1.780,2.364,0.753,86,3.591,2.161,2.275,1.578,1.442,88,3.598,4.653,2.718,0.789,3.445,90,3.600,3.142,0,4.2.4 Higher Order Modes,(4.12),(4.13),q,n,eff,D(d/l),(d/l)2,80.4,3.550,0.836,0.836,1.672,82,3.565,0.998,1.365,2.363,84,3.580,1.329,2.082,3.410,86,3.591,1.991,3.433,5.

5、424,88,3.598,3.980,7.425,11.40,90,3.600,(d/l)0,0,0.367,0.753,1.442,3.445,(d/l)1,TE0,TE1,TE2,TE3,TE4,TE5,d/l,neff,q,Example: Let d = 1.64 m, = 0.82 m.,Find , neff, and the number of allowed modes. From the mode chart (next slide):,TE Mode Chart,d/l,neff,q,In general, the m-th mode cuts off (no longer

6、 propagates) when d/l satisfies:,(4.14),In a multimode waveguide: Lower-ordered rays travel with larger angles than higher-ordered rays.,TE0, TM0,TE1, TM1,d/l,q,neff,4.2.5 TM Mode Chart,Degenerate mode,Single mode propagation is obtained by satisfying (4.17),and polarizing the light as TE or TM.,cos

7、(hy),TE0,TE1,sin(hy),y,y,e-a(y-d/2),e-a(y-d/2),d/2,-d/2,4.2.6 Mode Pattern,cos(hy),TE2,TE3,sin(hy),y,y,d/2,-d/2,e-a(y-d/2),4.3 Modes In The Asymmetric Waveguide,d,n3,n2,n1,z,y,Example: Letn1 = 2.29 ZnS (zinc sulfide) n2 = 1.5 glass n3 = 1.0 air,TE0,TM0,d/l,neff,q,4.4 Coupling To The Waveguide,4.4.1E

8、dge Coupling,(4.21),Define the fractional refractive index change as:,Assume that n1 and n2 are nearly equal. Then,Finally,Cladding Modes Consider rays beyond the critical angle, ( c),These rays may be guided as cladding modes. (At the inner boundary there is partial reflection),4.4.2Prism Coupling,

9、gap,n1,n2,TE0 field in the film,p,np,n3 = air,Ep prism field,Prism,4.4.3Grating Coupling,4.5 Dispersion And Distortion In The Slab Waveguide,4.5.1Waveguide Dispersion,n1,n2,n1 n2,Axial mode,L2,n2,c,Higher order mode,L1,4.5.2Multimode Distortion ( Modal Distortion ),Axial mode travel time:,For the cr

10、itical angle ray,The total path of the critical angle ray is then,The total delay is,(4.27),The total pulse spread is given by,4.6 Integrated Optic Components,4.6.1 Passive Devices,Integrated Optic Directional Coupler,Substrate,L,P1,P2,P3,P4,For an ideal (lossless) coupler the relative output powers

11、 are given by: P2/P1 = cos2 (pL/2Lc) (4.30) P3/P1 = sin2 (pL/2Lc) (4.31) where Lc is called the coupling length. Any splitting ratio between the two output ports is possible by appropriate choice of length L.,Example: If the actual length L of the coupling region is Lc /2, compute the output couplin

12、g. P2/P1 = cos2 (p/4) = (0.707)2 = 0.5 P3/P1 = sin2 (p/4) = (0.707)2 = 0.5 50% of the power exits both of the output ports. Since 10 log P2/P1 = 10 log 0.5 = -3 dB this is a 3-dB coupler.,integrated optic power splitters,4.6.2 Active Devices Light Control Devices Beam Switches Modulations Light Conv

13、ersion Devices Light Sources (Transmitters) Photodetectors (Receivers),The electrooptic switch,As in the passive coupler, the power distribution is given by: P2/P1 = cos2 (pL/2Lc) P3/P1 = sin2 (pL/2Lc) L is the interaction length and Lc is the coupling length.,The interaction length L is set equal to the coupling length Lc,P2/P1 = cos2 ( /2) = 0 P3/P1 = sin2 ( /2) = 1,Mach-Zehnder Modulator,Optoelectronic int