HW1 solutions

# HW1 solutions - 1.1 Gaussian beams Consider two identical...

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Unformatted text preview: 1.1 Gaussian beams Consider two identical spherical mirrors A and B that have been aligned to be focal directly face each other as in Figure 1Q1. The two mirrors and the space in between them (the optical cavity) form an optical resonator because only certain light waves with certain frequencies can exit in the optical cavity. The light beam in the cavity is a Gaussian beam. When it starts at A its wavefront is the same as the curvature of A . Sketch the wavefronts on this beam as it travels towards B , at B , as it is then reflected from B back to A . If R =25 cm, and the mirrors are of diameter 2.5 cm, estimate the divergence of the beam and its spot size (minimum waist) for light of wavelength 500 nm. Figure 1Q1 Solution Let D = diameter of the mirror, from Figure 1Q1, tan θ = ( D /2)/ R gives θ = arctan( D /2 R ) = arctan(0.05) = 0.05 rad. Divergence is 2 θ or 0.1 rad. Divergence 2 θ and spot size 2 w o are related by 2 θ = 4 λ π (2 w o ) and depends on the wavelength of interest. Taking λ = 500 nm, and, 2 w o = 4 λ π (2 θ ) = 4(500 × 10- 9 m) π (0.1) = 6.4 × 10- 6 m or about 6 micron. 1.7 Phase changes on TIR Consider a light wave of wavelength 870 nm traveling in a semiconductor medium (GaAs) of refractive index 3.6. It is incident on a different semiconductor medium (AlGaAs) of refractive index 3.4, and the angle of incidence is 80 ° . Will this result in total internal reflection? Calculate the phase change in the parallel and perpendicular components of the reflected electric field. Solution Two confocal spherical mirrors reflect waves to and from each other. F is the focal point and R is the radius. The optical cavity contains a Gaussian beam Wave front Spherical mirror 2 θ Optical cavity Spherical mirror A B R F L R a First calculate the critical angle: θ c = arcsin(3.4/3.6) = 70.8 ° . The angle of incidence ....
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HW1 solutions - 1.1 Gaussian beams Consider two identical...

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