Download Gaussian Beams: Properties, Intensity Distribution, and Experimental Measurement - Prof. L and more Lab Reports Physics in PDF only on Docsity! Experiment 0– Gaussian beams 1 Experiment 0 Properties of a Gaussian Beam 1 Introduction We will look at the intensity distribution of a laser beam. The out- put of a laser is different than that of most other light sources. The laser resonator determines the spatial characteristics of the laser beam. Most Helium Neon (HeNe) lasers have spherical-mirror Fabry-Perot res- onators that have Hermite-Gaussian spatial modes. Usually only the lowest order transverse resonator (TEM00) mode oscillates, resulting in a Gaussian output beam. 2 Background - see Hecht, Chap. 13, Pedrotti, Chap. 27 The irradiance (proportional to the square of the electric field) of a Gaussian beam is symmetric about the beam axis and varies with radial distance r from the axis as I(r) = I0 exp(−2r 2/w2) (1) Here w is the radial extent of the beam where the irradiance has dropped to 1/e2 of its value on the beam axis, I0, and is a function of position along the beam. A Gaussian beam has a waist, where w0 is smallest. It either diverges from or converges to this beam waist. This divergence or convergence is measured by the angle θ which is subtended by the points on either side of the beam axis where the irradiance has dropped to 1/e2 of its value on the beam axis, this is the place where the electric field has dropped by 1/e. Under the laws of geometrical optics a bundle of rays (a beam) con- verging at an angle of θ should collapse to a point. Because of diffrac- Experiment 0– Gaussian beams 2 tion, this does not occur. However, at the intersection of the asymptotes that define θ, the beam diameter reaches a minimum value d0 = 2w0, the beam waist diameter. The variation of the beam waist w as a function of propagation distance z is: w(z) = w0 √ 1 + ( z z0 )2 (2) with the Rayleigh length z0 given by: z0 = πw2 0 λ (3) A TEM00 mode w0 depends on the beam divergence angle as w0 = λ/πθ, (4) where λ is the wavelength of the radiation. The product w0θ is constant for a Gaussian beam of a particular wavelength. A beam with a very small beam waist w0 requires the divergence θ must be large, while for a highly collimated beam with small θ the beam waist w0 must be large. The most important characteristic of the beam is the wavefront or surface of constant phase. The wavefront is flat (infinite radius of cur- vature) at the waist w0, then grows to a minimum radius at z0 and returns to flat at infinity. The Radius of Curvature of the wavefront is given by R(z) = z √ 1 + (z0 z ) 2 . (5) 3 Experiment Please be very careful when using a laser. Parallel light gets focused and that can happen with a laser beam focused by your eye lens onto your retina. In the following experiments, you will find the divergence of your laser θ, the beam waist of the laser w0. Use the appropriate limit (z >> z0) of Eq. (2) to define the divergence angle θ in terms of the other parameters (see Figure 1). Use the diverging lens to have a large laser beam. Take the pho- todetector and place the small aperture on it. You will measure the Gaussian profile of the laser using a scanning detector and the computer interface. The data will be in the form of a tex file with two columns of
