Changes

*A FORTRAN program has been written which simulates rays exiting the laser aperture and then focused through a fused silica lens. We are able to determine the smallest spot size attainable as a function of the distance away from the lens.

*A FORTRAN program has been written which simulates rays exiting the laser aperture and then focused through a fused silica lens. We are able to determine the smallest spot size attainable as a function of the distance away from the lens.

[[File:r0(2)r0(1).jpg|right|thumb|Original Beam Profile]]

[[File:r0(2)r0(1).jpg|right|thumb|Original Beam Profile]]

[[File:r2.jpg|right|thumb|Focused Beam Profile]]

[[File:r2.png|right|thumb|Focused Beam Profile]]

*Taking the X and Y projections of the focused beam and fitting them with a Gaussian distribution, we are able to attain the <math>\sigma_{X}\,</math> and the <math>\sigma_{Y} \,</math>.

*Taking the X and Y projections of the focused beam and fitting them with a Gaussian distribution, we are able to attain the <math>\sigma_{X}\,</math> and the <math>\sigma_{Y} \,</math>.

*Assuming a Gaussian distribution at the waist of the beam, we now find the FWHM (full width at half maximum) by the following relation, <math>\mathrm{FWHM} = 2 \sqrt{2 \ln 2}\ \sigma. </math>  

*Assuming a Gaussian distribution at the waist of the beam, we now find the FWHM (full width at half maximum) by the following relation, <math>\mathrm{FWHM} = 2 \sqrt{2 \ln 2}\ \sigma. </math>  

*The smallest value of <math>\mathrm{FWHM_{X}}</math> and <math>\mathrm{FWHM_{Y}}</math> were 1.49mm and 0.552mm respectively.

*The smallest value of <math>\mathrm{FWHM_{X}}</math> and <math>\mathrm{FWHM_{Y}}</math> were 1.49mm and 0.552mm respectively.

*The Rayleigh Length,<math>\mathrm{Z_{R}}</math> is defined as the distance from the beam waist along the axis of propagation to the point where its cross section is doubled. Taking <math>\mathrm\omega_{0}</math> as the beam waist, and using the <math>\mathrm{FWHM}</math> as its value we are looking for the point where <math>\mathrm{FWHM} = 2 \sqrt{2 \ln 2}\ \omega_{0}. </math>

*The Rayleigh Length,<math>\mathrm{Z_{R}}</math> is defined as the distance from the beam waist along the axis of propagation to the point where its cross section is doubled. Taking <math>\mathrm\omega_{0}</math> as the beam waist, and using the <math>\mathrm{FWHM}</math> as its value we are looking for the point where <math>\mathrm{FWHM} = 2 \sqrt{2 \ln 2}\ \omega_{0}. </math>