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The mathematical function that describes the Gaussian beam is a solution to the Paraxial form of the Helmholtz Equation . The solution, in the form of a Gaussian Function , represents the Complex amplitude of the Electric Field , which propagates along with the corresponding Magnetic Field as an Electromagnetic Wave in the beam. MATHEMATICAL FORM For a Gaussian beam, the complex electric field amplitude, measured in Volt s per Meter , at a distance ''r'' from its centre, and a distance ''z'' from its waist, is given by : where : is the Imaginary Unit , and : is the Wave Number (in Radians per meter). The functions ''w''(''z''), ''R''(''z''), and ζ(''z'') are parameters of the beam, which we define below. The corresponding time-averaged intensity (or irradiance) distribution, measured in Watt s per Square Meter , is | ||
| Where ''w''(''z'') Is The Radius At Which The Field Amplitude And Intensity Drop To 1/''e'' And 1/''e''<sup>2</sup>, Respectively This Parameter Is Called The Beam Radius Or Spot Size Of The Beam ''E''<sub>0</sub> And ''I''<sub>0</sub> Are, Respectively, The Electric Field Amplitude And Intensity At The Center Of The Beam At Its Waist, Ie <math>E 0 \equiv E(0,0)</math> And <math>I 0 \equiv I(0,0)</math> The Constant <math>\eta \,</math> Is The | "http://wwwinformationdelightinfo/encyclopedia/entry/characteristic_impedance" class="copylinks">Characteristic Impedance of the medium in which the beam is propagating For free space, <math> \eta = \eta_0 \approx 377 \ \mathrm{ohms} </math> |
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