Total Internal Reflection

Total Internal Reflection - TOTAL INTERNAL REFLECTION For...

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Unformatted text preview: TOTAL INTERNAL REFLECTION For an electromagnetic wave in a high index region incident upon a low index re— gion at an angle of incidence (01) greater than the critical angle [0c 2 sin’1(n2 / 711)], total internal reflection occurs. The total internal reflection process inherently includes a phase shift upon reflection and a lateral shift in the apparent point of reflection — the G005 Hanchen shift. For total internal reflection an exponentially decaying field exists in the lower refractive index material. If there is a small drop in refractive index across the boundary, then the evanescent field will extend over larger distances. If there is a large change in the refractive index across the boundary, the field will decay abruptly. The Goos-H'anchen shift may be viewed as the total internal reflection occurring at the 1 / e depth of the decaying field. The phase shift may be viewed as being due to the ex— tra distance light has to travel (into the evanescent field) in order to be reflected. These effects are apparent in the energy flow upon total internal reflection depicted in Fig. 1. X :2: ‘\ ”$“‘\ -0 4), 4.2x, 0 0 2x, 0.4x, 0.6x. 0.8).. 1.0M 1.2M Danna along muvha (m A. mun) Fig. 1 Poynting vector energy flow lines for total internal reflection for TE polarization with n1 = 1.5, 712 = 1, and 01 = 45°. A. Mahan and C. V. Bitterli, Appl. Opt. 17, 509 (1978). FRESNEL’S EQUATIONS - PHASE SHIFT UPON REFLECTION For an electromagnetic wave in a high index region incident upon a low index re- gion at an angle of incidence (01) greater than the critical angle [0,: = sin—1(n2 / 711)], total internal reflection occurs. In this case, the amplitude reflection coefficients become complex. For TE polarization (Er) _ n1c0391 —— jx/nfsinQQI—ng TE Ez' n1 cos 01 + j n1 sin2 01 -— n2 and for TM polarization 2 . . : 71200391 — jnl t/nilsmzfll—ng TM Ei n3 cos 01 + j m n? sin2 01 — 72% where j =' \/—1. The magnitude of these amplitude reflection coefficients is unity in each case. The phase shift (4)) upon total internal reflection is seen to be _ 2tan_1<\/n§1 sin2 01 — n2?) ¢TE - n1 cos 01 and vim/n:1 sin2 01 — 723) = 2 tan"1 ¢TM ( n3 cos 01 ...
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Total Internal Reflection - TOTAL INTERNAL REFLECTION For...

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