S15HeNeLaser
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Properties of a HeNe Laser
Eng Hock Lee and Joshua Miller
School of Physics and Astronomy University of Minnesota - Twin Cities
Minneapolis, MN 55455
May 15, 2015
Abstract
We studied the underlying properties of the amplification model and transverse Hermite-Gaussian mode of an open cavity Helium-Neon laser. The goal of this project was to better understand optical physics through the use of lasers. A glass slide outside the cavity of a Melles Griot Helium-Neon laser gain tube 05-LHB-670 reflects in an angle dependent manner and tunes the gain. The output power distribution as a function of the angle of the slide was measured.
Introduction
LASER (Light Amplification by Stimulated Emission of Radiation) has been revolutionizing technology industries since their development in 1960 [1]. Ranging from lasers for heavy steel cutting to Krypton Fluoride excimer lasers for advanced eye surgery, lasers have been a state-of-the-art technology that transform our every-day lifestyle. On the other hand, Helium-Neon (HeNe) gas lasers have many industrial and scientific uses due to their effective low cost and ease of operation. The uniqueness of the HeNe gas laser also comes from the 10:1 ratio of Helium to Neon gas mixture, which makes lasing possible since excess excited helium atoms are constantly assisting Neon atoms in achieving an excited state by transferring energy through collisions.
Theory
Given by Henningsen [2], the theoretical frame work for analyzing the spatial beam properties can be deduced to z- dependent Gouy phase. It can be shown that the beat frequency of Hermite-Gaussian (HG) transverse mode between mode
and the lowest order mode to be
where and is the radius of curvature of internal and external output mirror, respectively. Parameters m and n are the indices of transverse mode, which can be determined by the intensity distribution of the laser beam. The inverse tangent term comes from Gouy phase shift factor, which is a phase shift of
; experienced by laser beam when it passes through a focus [3].
The beat frequency can be obtained through the superposition of longitudinal and transverse modes, namely
Since the transverse mode is independent of its frequency, this implies that there can exist in several longitudinal modes k for a given transverse mode m and n.
For the amplification model experiment, the goal is to determine the characteristic parameters of the !HeNe laser. For simplicity, the details of the glass slide of internal reflection and optical amplification of the microscopic mechanism are neglected. This can be considered a good approximation to our experiment [2]. If we introduce the small gain coefficient
power transmission coefficient of the output mirror t, gain length L, and the additional loss per double pass a, we can obtain an expression for the output power
where is the saturation power of the laser, and is the broadening types of the atomic transition. For the case of !HeNe laser, =1 and =1/2 represent homogeneous and inhomogeneous broadening, respectively. Homogeneous broadening is a type of emission spectrum in which all atoms radiate with equal probability [4]. Inhomogeneous broadening is a type of emission spectrum in which different atoms radiate with different probability [4]. For the additional loss factor a, it can be expanded into three parameters,
where
is the resonator loss in the absence of the glass slide, is the absorption and scattering loss of the slide, and is the loss due to reflection of the slide. and depend on the material of which we have little to no control over. However,
can be determined from the Fresnel reflection equation and can be expressed as [2]
where n is the refractive index of the glass slide and is the incident angle of the slide shown in Figure 1. We emphasize that the incident angle of the glass slide is the angle between the beam axis and the normal axis of the glass slide. By measuring the output power,
as a function of the incident angle of the glass slide, parameters . , , and can be determined from a fit to equation (3).
Experimental Setup
The setup for amplification model experiment is shown in figure 1. The laser tube is mounted with the Brewster flat surface window facing horizontally to the beam plane, such that the reflected light beam caused by Brewster window travels only within the beam plane. The output mirror and glass slide were fixed at 12.5 cm and 5 cm away from the Brewster window along the beam's axis, respectively. A power photo-detector was placed 5 cm away from the back of the output mirror to detect the transmitted light beam. In addition, instead of relying on the reading from the precision rotation stage, we collected angle measurements of the glass slide with the aid of the blackboard located by the side of the experiment setup as our preference, since both methods provide similar uncertainty. By determining the distance from the glass slide to point a and the distance ab allowed us to obtain the angle
. Using trigonometry, we obtained
Where is the incident angle of the glass slide in degrees. A metal ruler is placed along the blackboard to determine the distance ab as the glass slide rotated.
The next experiment involved measurement of beat frequency vs. various cavity length. The output mirror was attached on the linear translational stage, which allowed the output mirror to move along the beam axis shown in figure 2. At the back of the output mirror was a convex lens to focus the laser beam on the photodetector. The photodetector detected and sent laser signals to a Rigol DSA815 spectrum analyzer to analyze the laser's frequency domain. The output mirror started off at 3.71 cm away from the Brewster window, and for each increment of 0.254 cm the corresponding frequencies were measured, up until the maximum distance of 5.08 cm has been reached. The procedure was preformed for transverse modes m+n=0,1,2.
Results
We utilized a 45 cm radius of curvature 98.5% reflectivity external output mirror throughout the amplification model experiment. The glass slide was tuned at an angle at which the laser tube began to lase and the reflected beam can be seen on the blackboard. A distance ab = 16 cm and the output power were recorded. This process was repeated for 2 cm distance increments, and the corresponding output power was recorded. Note that we adjusted the precision rotational stage to obtain a precise distance ab. After the data collection was done, an additional measurement was taken without the of glass slide present.
For the amplification model, the resulting data are shown in the table above. The saturation power is highly dependent on the supply voltage of the laser tube, and its expected value is believed to fall somewhere within the range of 30-100 mW. However, our saturation power result for both homogeneous and inhomogeneous are considerably low but still within its expected range. Next, the expected small gain coefficient
given by Henningsen [2] is 0.1 , and this value is largely depends on gas composition, pressure, and the diameter of the laser tube. Because these conditions are not well known it is therefore difficult to determine the exact value. Yet our
value for inhomogeneous broadening is somewhat smaller but considerably close to the expected value. For the resonator loss in the absence of the glass slide
, the value depends on the cavity length and the properties of the output mirror, and the expected value is 0.015 [2]. From here we can expect
=0.0083 is unlikely to be true and therefore the homogeneous broadening is ruled out. Finally, the expected value for the absorption and scattering loss due to the glass slide is 0.007 [2]. This comes from the properties of the glass slide. Our result
=0.0163 shows that it is about twice the amount of the expected value. This difference is assumed to be expected since the glass slide properties vary from brand to brand.
For the transverse Hermite-Gaussian experiment, the same output mirror is utilized from the previous experiment. A beat frequency vs. cavity length plot of k=0,±1, ±2, ±3 for each m+n value is presented in the right side of figure 3. However, the limit on the spectrum analyzer can only allow to observe frequencies within the range below 500 MHz, therefore the beat frequencies beyond the range limit were not be considered. Besides that, transverse modes m+n equals 3 or higher could not be detected by the spectrum analyzer due to the overlapping with the background noise signals, thus resulting in the missing observed data points of (-2,3) in figure 3. Because the beat frequencies are separated by a discrete distance, changing its cavity distance will not deviate the beat frequencies, therefore the chi squared value of all (k,m+n) modes would be identical. We performed chi squared analysis on the randomly chosen (1,0) modes, and obtained the reduced chi-squared value of 0.96.
Analysis
For the amplification model experiment, the reduced chi-squared values for homogeneous and inhomogeneous broadening are 1.01 and 1.32 respectively. We ruled out homogeneous broadening since our predicted parameter values do not match with the expected values, hence the inhomogeneous broadening was accepted as our final result. Figure 4 showed the graph of chi as a function of number of data points for both homogeneous and inhomogeneous broadening. As we can see, an obvious sinusoidal trend in each graph clearly indicates the present of a systematic error in our experiment. Our assumption was the poor condition of the laser tube. In our case, the laser tube has been used many times over the years by the previous MXP groups and it was believed that the condition of the laser tube has been worn down over time. For example, the observed maximum output power without the presence of glass slide is 0.265 mW, which is 10 times smaller than the product specification shown in the website. For this reason, we suspected the internal parameters of the laser tube would be slightly inaccurate and hence produce the second order effect.
For the transverse Hermite-Gaussian mode experiment, the reduced chi squared is 0.96. The chi graph in figure 5 showed our observed data and calculated data are well fitted. However, despite the observed data agreeing with the calculated data, the maximum distance the linear translational stage can move has restricted our ability to observe the beat frequency beyond the maximum distance. This is rather unfortunate because it is said that at the cavity distance of roughly 45 cm, the associated beat frequencies converge into a single beat frequency. And at distance beyond 45 cm, the cavity region became unstable and the laser beam would become unpredictable [2].
Conclusion
In summary, we determined the Melles Griot Helium-Neon laser gain tube 05-LHB-670 undergoes inhomogeneous broadening in our amplification model experiment. We obtained the laser's parameters
=32±4mW, x
, and x agrees with the expected value, except the disagreement on parameter x. For the transverse Hermite-Gaussian mode experiment, we concluded with the agreement of the theoretical fit and the experimental results. A good proposal for a future project would be the measurement of beat frequencies at the cavity distance beyond the unstable region; it would be an interesting project to explore the behavior of the beat frequencies at that region. Another interesting proposal would be the use of a 1 m radius of curvature output mirror instead of a 45 cm radius of curvature for the beat frequency experiment, and again it would be an interesting project to investigate those beat frequencies at the unstable region and beyond.
References
[1] Steen, W. M., and J. Mazumder. "Prologue." \textit{Laser Material Processing}. 4th ed. London: Springer, 2010. 1. Print.
[2] Jes Henningsen, "Teaching Laser Physics by Experiments" American Journal of Physics 79, 85 (2011);
[3] Hariharan, P. (1996). Letter The Gouy phase shift as a geometrical quantum effect. \textit{Journal of Modern Optics}, 219-222.
[4] Saleh, Bahaa E. A., and Malvin Carl Teich. \textit{Fundamentals of Photonics}. 1st ed. New York: Wiley, 1991. 100. Print.
[5] Figure from Lee, Eng Hock