A beam of vacuum wavelength travels inside a medium of index and totally reflects…

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

What an Instrument Can See, Ch The boundary as a two-port

Problem

A beam of vacuum wavelength λ0=633 nm\lambda_0=633\ \mathrm{nm} travels inside a medium of index n1=1.45n_1=1.45 and totally reflects from its plane boundary with air at θi=50∘\theta_i=50^\circ. Given dδsdθi=2sin⁡θisin⁡2θi−n2,n≡n2n1,\frac{d\delta_s}{d\theta_i} = \frac{2\sin\theta_i}{\sqrt{\sin^2\theta_i - n^2}}, \qquad n\equiv\frac{n_2}{n_1}, where δs\delta_s is minus the phase of rsr_s (the Fresnel-rhomb sign, which makes δs\delta_s positive), and the Goos-Hanchen shift along the face, Ds=λi2πcos⁡θidδsdθiD_s = \dfrac{\lambda_i}{2\pi\cos\theta_i}\dfrac{d\delta_s}{d\theta_i}, the chapter's formula written for this sign of δs\delta_s, with λi=λ0/n1\lambda_i=\lambda_0/n_1 the wavelength in the incident medium, find the lateral shift of the s-polarised beam.

Browse the problem library