Properites of Helium Neon Lasers

Aaron Hansen, Ian Nelson

University of Minnesota - School of Physics and Astronomy

Minneapolis, MN 55455

Abstract

We studied the properties of an open cavity helium-neon laser including the laser amplification model parameters, transverse Hermite-Gaussian mode beating, oscillation at 640.1nm, and spontaneous emission from the gain medium. Experimental results are compared to theoretical laser models and to typical helium neon laser parameters.

Introduction

A helium neon laser works by utilizing two main components: a gain medium which acts as an optical amplifier and two mirrors which act as an optical resonator.

The gain medium acts as an amplifier by exciting the helium and neon gas mixture with a DC voltage. From this excited state spontaneous de-excitation occurs which releases a photon at a random time and in a random direction. These spontaneous emissions are not used in the lasing action. However, the excitation of the helium is crucial to the operation of the laser because some of the excited helium atoms will collide with the neon atoms and force them into a metastable state. This metastable state is different from other neon excitation levels because it has a relatively long lifespan. This process of bringing the neon atoms into a metastable state is called optical pumping.

The consequence of this metastable state is that the optical pumping will produce a population inversion, which is simply a state where there are more neon atoms in the excited metastable state then in any other states. The next key concept in lasing is stimulated emission. Stimulated emission is a phenomenon where a photon incident on an excited atom of the same energy will cause the atom to de-excite and produce a 'clone' photon. This 'clone' has the same energy, polarization, and phase as the original photon. When stimulated emission is combined with a population inversion the result is a cascading effect which produces many photons of the same energy, polarization, and phase.

The final component of the laser is the mirrors which act as an optical resonator. By placing a mirror at each end of the gain medium boundary conditions are imposed on the photons which exist within the laser cavity. Only those photons which satisfy the wavelength condition as shown in equation 1, where 'L' is the distance between the mirrors and 'n' is an integer index, will be allowed within the laser cavity. The high reflectivity of the mirrors also allow the photons of the laser beam to make multiple passes through the gain medium, increasing the circulating power in the laser cavity.

.(1)

a) The first part of our experiment deals with the amplification properties of our laser. By treating the gain medium as a black box amplifier we can determine the gain, loss, and saturation power by studying the output power as a function of some added loss.

b) The second part of our experiment deals with the modes which are allowed within the laser cavity. In addition to the longitudinal modes which were discussed earlier, there are also transverse modes which can exist within the laser cavity. These transverse and longitudinal modes oscilate at a frequency which is function of the cavity length.

c) The third part of our experiment deals with lasing at wavelengths other than 632.8nm. Most HeNe lasers operate at 632.8nm due to the high gain associated with the energy level. This however is not the only transition which can be exploited for use in a laser. The 640.1nm transition is also available for lasing in the gain medium but is normally not present in the beam due to gain competition.

d) The final portion of our experiment deals with the spontaneous emissions from the gain medium. By studying the spontaneous emissions of the helium and neon gas mixture we can observe exactly which transitions are used in the lasing action.

Theory

a) To study the lasing parameters of our laser we need to introduce a controllable loss in the system. This is accomplished by placing a glass slide inside of the laser cavity. This glass slide introduces a loss through Fresnel reflection, which is a loss that is a function of the index of refraction of the slide and the angle of incidence. This loss is described in equation 2.

.(2)

.

.

.

By measuring the beam's angle of incidence on the slide and the output power from the laser we can then find the gain (g0), saturation power (Ps), and the loss due to air and the slide (a)by using equation 3..

.(3)

.

b) The modes within the laser cavity oscillate in the terrahertz range, which is too high of a frequency for most detectors to measure. The superposition of these high frequency waves produces a much slower beat frequency in the megahertz range, which is measurable with a reasonably fast detector.

The transverse modes that we are studying are Hermite-Gaussian modes, which are found by solving the wave equation in rectangular coordinates. The frequency difference between a mode of index m and n and the 00 mode is given by equation 4.

.(4)

.

In addition to transverse modes, longitudinal modes also exist within the laser cavity. The frequency differrence between two adjacent longitudinal mode is given by equation 5.

.(5)

.

Thus, by adding equation 3 and 4 we find the total beat frequency which is shown in equation 6.

.(6)

.

c) To observe oscillation at 640.1nm the 632.8nm line must be suppressed. On way of supressing the 632.8nm line while leaving the 640.1nm line intact is to use a Fabry-Pérot resonator. A Fabry-Pérot is simply tow opposing mirrors which allow an incident light beam to self interefere while being reflected between the mirrors. The distance at which a beam will self interfere depends on the wavelength of light. Thus, the distance at which the 632.8nm wavelength will self interfere will leave the 640.1nm line intact.

d) The difference between the spontaneous emission spectra with and without lasing is very small but by performing a spectral subtraction we can see exactly which transitions are involved in lasing.

Apparatus

The laser that we use for this experiment is a Melles Griot 05-LHB-670. The laser used in this experiment uses a Brewster window to terminate the gain medium. The Brewster window functions as a polarizer for the laser. This polarization is necessary when measuring the power output because while the total power will remain constant, the power output at a particular polarization will drift randomly over time for lasers without Brewster windows. This random polarization combined with the polarizing angled glass slide would produce a much more inconsistent power output.

a) To measure the laser parameters a glass microscope slide on a rotating mount was inserted between the Brewster window and the output mirror. The Brewster angle which minimizes Fresnel reflection for this setup is approximately 56º. From this angle the slide was rotated to produce a loss in the laser as a function of the angle of incidence. The power output at the front of the laser was measured with a photodiode and a Thorlabs PM100D optical power meter. The setup for this experiment is shown in figure 1.

.(figure 1)

.

.

.

.

.

b) To measure the beat modes the output mirror was positioned to give the laser a certain resonator length 'd'. Adjusting the alignment of the output mirror allowed us to select the different transverse HG modes of the laser. A 1GHz spectrum analyzer was used to measure the beat frequencies produced by the longitudinal and transverse HG modes at each distance 'd'.

c) To set up a Fabry-Pérot resonator an additional mirror on a translation stage was added behind the output mirror. The translation stage allowed the Fabry-Pérot's mirror distance to be finely controlled in order to suppress the 632.8nm line without affecting the 640.1nm line.

d) To observe the spontaneous emission spectrum a spectrometer is oriented towards the gain medium out of the path of the laser beam. Two spectra, one with lasing and another without lasing are taken and a spectral subtraction is performed between them. The resulting spectrum shows exactly which transitions are involved in the lasing process.

Results

a) The laser amplification parameters power measurement data was taken at one degree microscope slide steps between 45º and 64º. An additional measurement of the power output was taken without the slide inserted into the cavity. Using equation 1 a chi-squared reduction fit was used to find the index of refraction of the slide n, the saturation power Ps, the gain g0, and the loss term a. Fits were performed for both inhomogeneous (α=1/2) and homogenous (α=1/2) broadening. The measurement without the slide was used for a fit of equation 1 without the Fresnel loss and glass slide loss terms, leaving only the loss in air a0 term. This 'no slide' fit was then used to determine the glass slide loss term a1 by simply subtracting a0 from the calculated loss term a found in the fits with the glass slide. The measured and predicted values of the power output are shown in figure 2.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

The fit parameters for the inhomogeneous and homogenous fits are shown in table 1. The expected value for the saturation power is in the range of 30-100mW, but this parameter is highly dependent on the particular laser in question. From this saturation power alone we can rule out homogenous broadening, as a saturation power of 331mW is very unlikely. The expected value of g0 is very roughly in the range of .12-.15 m-1, but this value is highly dependent on many factors including gain medium composition, laser diameter, and gas pressure [3]. Without knowing more about the specifications of our gain medium we cannot determine the accuracy of our g0 measurements, but we can say that they are within a reasonable range of what we would expect. The expected value for a0 is between .012-.015 [3]. This value is highly dependent on the cavity length and mirrors but we can see that our measurement of a0=.017 for inhomogeneous broadening is a bit high but within reasonable expectations. The value of a0=.0066 for homogenous broadening is smaller than we would expect, leading us to once again rule out homogenous broadening. The expected value for a1 is approximately .007 [3]. This value is only dependent on the particular microscope slide used in the experiment, and because most microscope slides have very similar properties we would not expect our measurement to deviate far from this value. The value of a1=.0073 for inhomogeneous broadening is what we would expect from a typical microscope slide. The value of a1=.006 for homogenous broadening is lower than what we would expect from a typical microscope slide.

.

.

.

.

.

b) The Beat modes data was taken at 12 distances over approximately 6.25cm measured from an arbitrary point past the gain tube's Brewster window. At each distance every frequency that was observed was recorded. Incomplete modes and modes which did not belong to a longitudinal or transverse Hermite-Gaussian mode were removed from the data set. To compare the data to the theoretical model the arbitrary distance offset was used as a fitting parameter for a chi-squared reduction. The results of this fit is shown in figure 3. For this fit the reduced chi-squared is 1.01.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

One extension of this project is to measure the speed of light using the frequency of a longitudinal mode as a function of cavity distance. By using equation 5 and the k=-1, m+n=0 mode, c can be found to be (2.991 ± .005)x108 m/s , which is 1.20σ from the accepted value of 2.997x108 m/s .

c) The spectrometer measurement taken when lasing at 640.1nm is shown in figure 4. A peak at approximately 635nm can be seen which is most likely the 635.2nm 3s² → 2p³ transition. The presence of this 635nm line may explain the relative weakness of the 640.1nm line, as both transitions use the 3s² neon state and would therefore undergo gain competition.

.

.

.

.

.

.

.

.

.

.

.

d) The spectrometer data taken from the spontaneous emissions of the lasing medium is shown in figure 5. The 632.8nm lasing line is produced by the 3s² → 2p4 neon transition. All three peaks at 595nm, 609nm, and 668nm are the transitions from the 2p4 neon state to lower energy states. The intensity of these peaks is much higher with the lasing action present due to the stimulated emission, which forces more neon atoms in the 2p4 state. The valleys at 633nm and 640nm can be explained as simply being a depletion of the 3s² neon state. The 3s² state is used in the lasing action and is therefore unavailable for spontaneous emission when the lasing action is present.

.

.

.

.

.

.

.

.

.

.

.

.

Analysis

a) The reduced chi-squared for the inhomogeneous amplification parameters fit is 2.20. The reduced chi-squared for the homogeneous amplification parameters fit is 3.01. We expect inhomogeneous broadening so the better fit to the inhomogeneous prediction is encouraging. Figure 6 shows a chi plot for each data point by decreasing slide angle. The x-axis of this chi plot also corresponds to time during the experiment. There is a clear increasing sinusoidal trend to the errors in both the inhomogeneous and homogenous data points. One possible cause of this simply the drift of the optical equipment. During the experiment it was noted that over time the optical equipment could drift from their original alignment at a rate high enough to be significant on the experimental time scale. The other source of this error may be the glass slide used to cause Fresnel reflection. As the slide's angle was changed the location that the beam would strike the glass surface would change, therefore any small imperfections in the glass surface could appear and disappear as the measurements were taken. This explanation could account for how well the timescale of the error aligns with the experimental timescale.

.

.

.

.

.

.

.

.

.

b) The reduced chi-squared for the beat modes fit is 1.01. From the chi for each data point plot in figure 7 we can see that at higher cavity distances the error increases significantly. This is mainly due to the convergence of many modes towards a single frequency. At distances very close to the end of the stability region higher resolution is needed to differentiate the converging frequencies. To account for this systematic error the data points with high chi values at high distances were removed from the final data set. The chi plot also reveals a tendency towards negative error, which is most likely simply due to a frequency offset at the spectrum analyzer.

.

.

.

.

.

.

.

.

.

.

Discussion and Conclusion

We measured the laser amplification amplification model parameters, the transverse Hermite-Gaussian mode beating, lasing at 640.1nm, and the spontaneous emission from the gain medium. By the method of an introduced adjustable loss the laser amplification parameters for the Melles Griot 05-LHB-670 were found to be a saturation power of Ps=(103 ± 30)mW, and a gain of g0=(1.6601 ± .0006)x10¨¹ m¨¹. These parameters are within expected values for a typical helium-neon laser. The main source of systematic error in this experiment was due to the imperfections in the glass slide and the drift of the optical equipment, which when combined produced relatively large fluctuations in the power output of the laser.

The transverse Hermite-Gaussian mode beating frequencies were measured for a range of distances and the measured data was compared to the theoretical model. The measured data fit the theoretical curve with a reduced chi-squared of 1.01. As an additional check and as an extension of this experiment the speed of light was measured using a longitudinal beat mode. The speed of light was measured to be (2.991 ± .005)x108 m/s , which is 1.20σ from the accepted value of of 2.997x108 m/s .

Lasing at 640.1nm was measured using the method of a Fabry-Pérot mirror. An additional line was observed at 635.2nm with the Fabry-Pérot. The presence of this second line at 635.2nm indicates how extremely precise the Fabry-Pérot method of suppression is, as we were able to suppress the 632.8nm line without suppressing either of the relatively weak 640.1nm and 635.2nm lines. At the same time, it showed how the Fabry-Pérot method must be aligned precisely in order to work, as the best that could be done with the equipment available did not manage to suppress the 632.8nm line to below the intensity of the other two. The limiting factors on measuring lasing at 640.1nm relates to the loss in the system. To observe lasing at the weaker laser lines they need to be brought as high above the lasing threshold as possible. New mirrors and a setup which allowed the mirrors to be brought closer to the laser tube would decrease the overall loss in the system and allow stronger lasing at 640.1nm and other weaker lines.

The spontaneous emission lines from the gain medium were measured and a spectral subtraction was performed between the measurements with and without lasing action present. The spectrometer readings gave insight into the population dynamics inside the gain medium, namely that the optical pumping and stimulated emissions created many more neon atoms in the 2p4 state. The depletion of the 3s² neon state due to stimulated emission was also observed in the spectral subtraction.

References

[1] Bob Mellish, Wikipedia editor

[2] Dan Li, 'Laser Mode', Laser Teaching Center Department of Physics & Astronomy Stony

Brook University, 'http://laser.physics.sunysb.edu/~dli/hnwork.html'

[3] Henningsen, J 2011, 'Teaching laser physics by experiments' American Journal of Physics , vol 79,

no. 1, pp. 85-93.

[4] Saleh, B.E.A, Teich, M.C., 'Fundamentals of Photonics: 2nd Edition', Wiley Interscience

2007

[5] Steve Lympany, 'Module 1-7: Optical Cavities and Modes of Oscillation', Central Carolina

Community College, Engineering Technologies