lecture12

# lecture12 - PHYSICAL INTERPRETATION wo w2 z E(r z Eo e e w...

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PHYSICAL INTERPRETATION  2 2 1 2 tan 2 (, , ) () R r z kr jk z j z wz R z o o w Er z E e e e     Field Field amplitude at z=0 Variation of the amplitude with r Longitudinal phase factor Radial phase factor

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RADIUS OF CURVATURE Radius of curvature of the constant-phase surface: R(z) Planar constant-phase surfaces ? R  at z=0 and at z Minimum radius of curvature : at z = z R R = R min = 2z R , at z = z R Gouy phase : z z z ) z w ( 1 z ) z ( R 2 R 2 2 o } { ) w z ( tan ) z ( 2 o 1
The total optical power carried by the beam: integral of the optical intensity over any transverse plane (at z) ½ Peak intensity x beam area GAUSSIAN BEAM: TOTAL POWER

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GAUSSIAN BEAM 2 2 w / r 2 2 2 o o e ) z ( w w I ) z , , r ( I
Irradiance (power per until area) I 0 (or intensity), on axis, at beam waist Total power P (or P) carried by the beam GAUSSIAN BEAM 2 2 w / r 2 2 2 o o e ) z ( w w I ) z , , r ( I 2 2 w / r 2 2 e w P 2 ) z , , r ( I 2 o | ) z , , r ( E | 2 1 ) z , , r ( I ) 2 /( | E | I o 2 o o |E| Fundamental Gaussian beam with peak beam irradiance I 0

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POWER THROUGH A HOLE OF SIZE a 2 2 w / a 2 a e 1 P / P Beam radius at screen : w z a P P a
POWER THROUGH A HOLE OF SIZE a

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POWER THROUGH A HOLE OF SIZE a aP a /P P a /P 1w 86.5% -0.63dB 1.5w 98.9% -0.43dB 2.0w 99.97% -0.001dB 3.0w 99.99999%
Complex radius of curvature, q(z) Re[q(z)] = z = distance to the waist Im[q(z)] = z R = Rayleigh range = w o 2 / Re[1/q(z)] = 1/R(z)=1/ Radius of curvature Im[1/q(z)] = - /( w 2 (z)) ~ /(beam radius) 2 R 2 jz z 1 ) z ( w j R 1 ) z ( q 1 )] jz z ( 2 /[ jkr )] z ( kz [ j 2 R 2 ) z ( w / r )) z ( R 2 /( jkr )] z ( kz [ j 2 R 2 R 2 2 2 2 e e z z ' C e e e z z ' C E

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lecture12 - PHYSICAL INTERPRETATION wo w2 z E(r z Eo e e w...

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