Beam Profile of a Helium-Neon Laser

Matt Whitrock
Laser Teaching Center
Summer 2004

Advisors: Prof. Harold Metcalf and Dr. John Noe


Project Goal

The goal of this project was to accurately measure the width of the HeNe laser at different distances and cross-sections. This can be accomplished using a photodiode, translation stage, and multimeter.


The HeNe Laser - Basic concepts

The HeNe laser emits a beam of coherent light that has a Gaussian intensity profile. The Gaussian intensity profile is defined by the equation

I(r)=I0exp  
-2r2
W02
 

where I is the intensity at a point distance r from the maximum intensity I0, and w is the beam radius. The beam radius is the distance between I0 and I0/e2.

(Fig. 1) A Gaussian intensity profile

(Fig. 1) A Gaussian intensity profile


As the beam propagates, the beam begins to diverge, causing the beam width to increase. This results in a wider intensity profile and a smaller value for I0. A beam that is tightly focused when it exits the cavity will diverge more rapidly than a beam that is fairly wide when exiting the cavity.


Photodiode

Semiconductors doped with impurities are termed p and n semiconductors. A p-type material will have excess holes (a deficiency of valence electrons), whereas a n-type material will have excess valence electrons. A p-n junction is created when p-type and n-type materials are placed in contact with each other. The p-n junction will allow current to easily flow in one direction (forward-biased) but not in the other (reverse-biased). At the junction, electrons move from the n-type material to combine with holes in the p-type material, creating a depletion region near the junction. The p-n junction is the basic diode.

(Fig. 2a, 2b) Diagrams of p-n junction

(Fig 2a, 2b)Diagrams of p-n junction


A photodiode is a reverse-biased p-n junction. In a reverse-biased p-n junction, a reverse voltage is applied, pushing the charge of the p-type side in the negative direction. This forces the electrons coming from the n-type material to travel "uphill" to get to the p-side material. When no light hits the photodiode, the potential of the depletion layer equals the applied voltage, and the only current present is a very small thermal current. However, when light hits the photodiode, a current flows across the junction.

Photodiodes are fairly accurate when used to measure light intensity, and generally have a very fast response time.


Setup

Although the distances and alignments used to obtain data varied, all the measurements were taken using a similar setup. The laser used was a red Melles-Griot cylindrical HeNe model # 25-LHR-991-249, putting out ~10mW. The beam was directed toward a Thorlabs DET110 photodetector with a 100μm pinhole attached on the front. The photodetector was mounted on a translation stage with adjustments marked in increments of mils. The photodetector was connected to a RadioShack mulltimeter catalog #22-805. For measurements taken at a distance of 93.5", a mirror was used, and two mirrors were used to take measurements at 157.25". The mirrors were necessary in order to create a longer beam. The mirrors were fairly clean but were not 100% reflective and had a few small scratches.


Procedure

For each set of measurements the entire setup was aligned to determine where the maximum intensity was. The stage adjustment was then turned toward 0 until the multimeter displayed a reading of zero. At distances of 6/32", 9", and 25", measurements were then taken across the entire profile at intervals of one mil. At 93.5", measurements were taken at intervals of 2 mils, and at 157.25' measurements were taken in increments of 5 mils. The data was input into a Quattro Pro spreadsheet and used to create various graphs of detector position versus light intensity.

At 9" an extra set of measurements was intentionally taken that did not go directly through the center of the beam.


Results

(Fig. 3) Intensity Profile @ 6/32"
(Fig. 3) Intensity Profile @ 6/32"


(Fig. 4) Intensity Profile @ 6/32"
(Fig. 4) Intensity Profile @ 9"


(Fig. 5) Intensity Profile @ 9" + Off-Axis Profile (uncorrected)
(Fig. 5) Intensity Profile @ 9" + Off-Axis Profile (uncorrected)


(Fig. 6) Intensity Profile @ 9" + Off-Axis Profile (corrected)
(Fig. 6) Intensity Profile @ 9" + Off-Axis Profile (corrected)


(Fig. 7) Intensity Profile @ 25"
(Fig. 7) Intensity Profile @ 25"


(Fig. 8) Intensity Profile @ 93.5" (logarithmic)
(Fig. 8) Intensity Profile @ 93.5" (logarithmic)


(Fig. 9) Intensity Profile @ 157.25"
(Fig.9) Intensity Profile @ 157.25"


(Fig. 10) Beam Diameter vs. Distance w/ Manufacturer Specifications
(Fig. 10) Beam Diameter vs. Distance w/ Manufacturer Specifications


Summary of Data



Distance (inches) Distance (cm) Width (mils) 2W (mm)
6/32 0.476 14.3 0.726
9 22.86 13.63 0.692
9 (off-axis) 22.86 14.12 0.717
25 63.5 20.04 1.02
93.5 237.5 60.84 3.09
157.25 399.4 102.3 5.20

Discussion

The first set of data (Fig. 3), taken at 6/32", appears to be fairly Gaussian on the sides, but near I0 the curve has a flat top. The green data points show the derivative, which in an ideal Gaussian intensity profile would have point symmetry.

The data taken on-axis at 9" (Fig. 4) is much closer to an ideal Gaussian curve, with virtually no noticeable deviation from the curve of best fit. The off-axis curve at the same distance (Fig. 5) is similarly close to its curve of best fit, but is significantly shorter and also slightly shifted to one side. Multiplying the off-axis curve by I0(a)/I0(b), where I0(a) is the I0 value of the on-axis curve and I0(b) is the I0 value of the off-axis curve, adjusts the second curve so it can be aligned with the first curve without canging the shape of the curve to one that is not Gaussian. After shifting the second curve slightly, the two intensity profiles were shown to be nearly identical, as were their widths (Fig. 9). It is therefore possible to measure the width of a Gaussian beam without going directly through the center of the beam. This is true because, for the Gaussian intensity profile:

e-k(x2+y2)=e-k(x2)+e-k(y2)

The data taken at 25" (Fig. 7) fits the Gaussian intensity profile of best fit even more closely than the data from 9" does. By this point I0 has started to decrease significantly.

At 93.5" (Fig. 8) I0 had decreased to the point that a 330KΩ resistor was needed in order to get meaningful results. Using the 330KΩ resistor produced data points whose values differed by nearly 4 orders of magnitude. A logarithmic plot of this data shows that the Gaussian intensity profile is a parabola when a logarithmic scale is used for the y axis.

At 157.25" (Fig. 9) I switched to a 1.8MΩ resistor to maintain accurate measurements. The measurements here were affected by a small resudual voltage that was accounted for, as well as minor aberrations in the 1st surface mirrors that were used. However, the graph of the intensity profile was still very accurate.

The spotsize graph (Fig. 10) shows the estimated manufacturer specifications for beam divergence as well as the beam width calculations that I made. The initial beam width values are lower than the manufacturer's specifications indicate, so as a result the beam diverges more rapidly as it propagates. This is illustrated by the 93.5" and 157.25" calculated beam width values. The actual spotsize figures, shown by the solid line, fit a line whose slope is significantly greater than the slope of the manufacturer's specifications' line. Using these calculations, the actual beam width (2w) at distance=0 is .62mm, as opposed to the specified value of .70mm.


Future Research

In the immediate future I plan to do the following:

  • Create intensity profiles of an Airy pattern, specifically to analyze its center;
  • Create intensity profiles of optical vortices.

Special Thanks

I would like to thank Dr. Metcalf and Dr. Noe for their guidance and vast amounts of knowledge, and I would also like to thank Jon Wu, Danielle Bourguet, Anirudh Ramesh, Yaagnik Kosuri, Azure Hansen, Yiyi Deng, Lidiya Mishchenko, Rita Kalra, and Jose Mawyin, all of whom have been in the lab at one time or another while I was working, and all of whom managed to collectively keep me focused on the task at hand.


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