lecture10-11

lecture10-11 - LECTURE 10-11 GAUSSIAN BEAMS Expressions in...

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Expressions in terms of E o , I o and P Beam radius w(z) Radius of curvature of cons. phase surface R(z) Half angle of beam divergence Rayleigh range z R Complex radius of curvature q(z) ABCD law LECTURE 10-11: GAUSSIAN BEAMS
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PLANE WAVES Can light be transported without spreading around? Plane waves: Rays direction of travel No angular spread Energy extends over all of space
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SPHERICAL WAVES Can light be transported without spreading around? Spherical waves: Originates from a single point Rays diverge in all angular directions
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GAUSSIAN BEAMS Can light be transported without spreading around? Paraxial waves: Rays – only small angles with the z axis Gaussian Beams: All power - within a small cylinder around beam axis Intensity distribution is a circularly symmetric Wavefronts are planar near the beam waist spherical far from the waist Rays thin pencil of rays (PW nature but with paraxial rays)
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GAUSSIAN BEAMS Can light be transported without spreading around? Paraxial waves: Rays – only small angles with the z axis Non-uniform field intensity on the constant-phase surface Non-uniform spherical waves near and parallel to axis Plane wave traveling along the z Modulated by a complex envelope A(r) - slowly varying function of position
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3/32” 2.4 mm Brass plate ~ 0.5 mm 1.3 mm
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GAUSSIAN BEAM
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GAUSSIAN BEAM Sinusoidal fields: sin t, cos t, e +j t UPW going in +z in free space: e +j( t-kz) UPW going in +z in medium index n: e +j( t-knz) Radially diverging, uniform waves: e +j( t-kr) Radially diverging uniform waves with constant power, in air: (1/r) e +j( t-kr)
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lecture10-11 - LECTURE 10-11 GAUSSIAN BEAMS Expressions in...

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