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Entry  Mon Jul 7 14:42:33 2014, Harry, Update, General, Beam Waists 16x
    Reply  Mon Jul 7 18:11:04 2014, Koji, Update, General, Beam Waists 
Message ID: 10139     Entry time: Mon Jul 7 14:42:33 2014     Reply to this: 10144
Author: Harry 
Type: Update 
Category: General 
Subject: Beam Waists 

I was finally able to get a reasonable measurement for the beam waist(s) of the spare NPRO.


I used a razorblade setup, pictured below, to characterize the beam waist of the spare 1064nm NPRO after a lens (PLCX-25.4-38.6-UV-1064) in order to subsequently calculate the overall waist of the beam. The setup is pictured below:



After many failed attempts, this was the apparatus we (Manasa, Eric Q, Koji, and I) arrived with. The first lens after the laser was installed to focus the laser, because it's true waist was at an inaccessible location. Using the lens as the origin for the Z axis, I was able to determine the waist of the beam after the lens, and then calculate the beam waist of the laser itself using the equation wf = (lambda*f)/(pi*wo) where wf is the waist after the lens, lambda the wavelength of the laser, f the focal legth of the lens (75.0 mm in this case) and wo the waist before the lens.

We put the razorblade, second lens (to focus the beam onto the photodiode (Thorlabs PDA255)), and the PD with two attenuating filters with optical density of 1.0 and 3.0, all on a stage, so that they could be moved as a unit, in order to avoid errors caused by fringing effects caused by the razorblade.

I took measurements at six different locations along the optical axis, in orthogonal cross sections (referred to as X and Y) in case the beam turned to be elliptical, instead of perfectly circular in cross section. These measurements were carried out in 1" increments, starting at 2" from the lens, as measured by the holes in the optical table.


Once I had the data, each cross section was fit to V(x) = (.5*Vmax)*(1-erf((sqrt(2)*(x-x0))/wz))+c, which corresponds to the voltage supplied to the PD at a particular location in x (or y, as the case may be). Vmax is the maximum voltage supplied, x0 is an offset in x from zero, wz is the spot size at that location in z, and c is a DC offset (ie the voltage on the PD when the laser is fully eclipsed.) These fits may all be viewed in the attached .zip file.

The spot sizes, extracted as parameters of the previous fits, were then fit to the equation which describes the propagation of the spot radius, w(z) = wo*sqrt(1+((z-b)/zr)^2)+c, w(z) = w0*sqrt(1+((((z-b)*.000001064)^2)/((pi*w0^2)^2))) where wo corresponds to beam waist, b is an offset in the z. Examples of these fits can be viewed in the attached .zip file.

Finally, since the waists given by the fits were the waists after a lens, I used the equation wf = (lambda*f)/(pi*wo), described above, to determine the waist of the beam before the lens.



note: I was not able to open the first measurement in the X plane (Z = 2in). The rest of the plots have been included in the body of the elog, as per Manasa's request.



Y_plane_measurement_1_(Z_2in).png X_plane_measurement_6_(Z_7in).pngX_plane_measurement_5_(Z_6in).pngX_plane_measurement_4_(Z_5in).pngX_plane_measurement_3_(Z_4in).pngX_plane_measurement_2_(Z_3in).pngX_plane_measurement_1_(Z_2in).pngX_Waist_fit.png


The X Waist after the lens (originally yielded from fit parameters) was 90.8 27.99 ± .14 um. The corresponding Y Waist was 106.2 30.22 ± .11 um.

After adjustment for the lens, the X Waist was 279.7 907.5 ± 4.5 um and the Y Waist was 239.2 840.5 ± 3.0 um.

edit: After making changes suggested by koji, these were the new results of the fits.


Attached you should be able to find the razor blade schematic, all of the fits, along with code used to generate them, plus the matlab workspace containing all the necessary variables.

NOTE: Rana brought to my attention that my error bars need to be adjusted, which I will do as soon as possible.

Attachment 2: erFitFinal2.zip  142 kB  Uploaded Tue Jul 8 13:44:49 2014
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