lecture3-4

# lecture3-4 - LECTURES 3-4 Uniform plane waves vs Gaussian...

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[email protected] 2011-414-spring Uniform plane waves vs. Gaussian beams Reference planes Ray vectors Ray transfer matrices (ABCD matrices) Building blocks Some examples LECTURES 3-4

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[email protected] 2011-414-spring UNIFORM PLANE WAVES Characterization of waves: Frequency (or free-space or vacuum wavelength ) Amplitude Phase Polarization Direction of propagation Constant-phase surface is plane plane wave (PW) + Const field amplitude at const-phase plane uniform PW Wave velocity = 1/  Refractive index n = c /
[email protected] 2011-414-spring METHODS OF BEAM PROPAGATION ANALYSIS Uniform plane waves: Planar constant phase surfaces Uniform field intensity on constant-phase surfaces ABCD matrices Gaussian beams (diverging): Spherical diverging constant-phase surfaces Non-uniform field intensity on the constant-phase surface ABCD law Diffraction of waves

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[email protected] 2011-414-spring RAYS Rays are normal to wave fronts: Lens example
[email protected] 2011-414-spring RAY VECTORS On a reference plane at z: Ray Position: (x, y) Slope: ( ) = (x’, y’) dz dy , dz dx (x,y) z ' y ' x y x R = 4 x 4 propagation matrices

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[email protected] 2011-414-spring UNIFORM PLANE WAVES Three assumptions 1. Rotationally symmetric and coaxial systems optical axis Reference plane - z Constant phase surfaces Propagation direction ray UPW z
[email protected] 2011-414-spring UNIFORM PLANE WAVES 2. Meridional rays only (ignore skew rays) 3. Paraxial rays rays close to and approximately parallel to the optical axis | |< 0.09 radian ( <5 ), then sin ~ , cos ~1, tan ~ r << system cross section r / L << 1 Paraxial approximation – Gaussian optics Optical axis z axis

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[email protected] 2011-414-spring UNIFORM PLANE WAVES Basic laws Homogeneous medium: Rays follow straight lines Smooth surface: Law of reflection ( i = r ) Snell’s law (n 1 sin 1 = n 2 sin 2 ) n 1 n 2 r

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lecture3-4 - LECTURES 3-4 Uniform plane waves vs Gaussian...

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