Experiment 0: Gaussian Beams1 BackgroundThe irradiance of a Gaussian beam is symmetric ab out the beam axis and varieswith radial distance r from the axis asI(r) = I0exp(−2r2/w20) (1)Here, w0is the radial extent of the beam w here the irradiance has droppedto 1/e2of its value on the beam axis, I0.A Gaussian beam has a waist, where w0is smallest. It either diverges fromor converge s to this beam waist. This divergence or convergence is measuredby the angle θ which is subtended by the points on either side of the beam axiswhere the irradiance has dropped to 1/e2of its value on the beam axis.Under the laws of geometrical optics, a bundle of rays (a beam) converging atan a ngle of θ should collapse to a po int. However, real be ams of waves (for whichthe uncertainty principle holds) do not behave this way. At the intersection ofthe a symptotes that define θ, the b e am diameter reaches a minimum valued0= 2w0(the beam waist diameter).2z02z0Figure 1:1The variation of the beam waist as a function of propagation distance z is:w(z) = w0s1 +zz02, (2)where the “Rayleigh length” z0is given by:z0= πw20λ, (3)and λ is the wavelength of the radiation.The beam wais t w0depends on the beam diver gence angle asw0=2λπθ. (4)2 ExperimentCAUTION: Please b e very careful when using a laser. DO NOT lo ok directlyinto the laser aperture, and be especially careful when bending down to alignoptics.The goal of this lab is to mea sure the transverse spatial profile of the Gaus-sian beam emitted by the laser to compute the divergence angle θ, beam waistw0, and Rayleigh length z0. However, the computer measures light intensity asa function of time, not detector distance. Therefore, you must first calibrate thescanner displacement vs time. Use the appr opriate detector slit to increase thespatial resolution. Adjust for a reduction in photodetector signa l by increasingthe amplifier gain.Rather than give explicit instructions on how to determine θ, w0, and z0,we expect you to design a procedure of your own, using only the transverseintensity profiles you measure in this lab. Be creative, if necessary
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