Main Page/PHYS 4210/HeNe Lasers
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HeNe Lasers
In this experiment we first align an openended laser. Then we set up some transverse mode patterns, and perform further exercises and experiments to understand how a laser works.
Key Concepts


Reading and Exercises
 Read pages 94 to 105 from PrestonDietz, The Art of Experimental Physics, John Wiley and Sons,1991. Carry out Exercise 1 (pg. 100), Exercise 2 (pg. 103), Exercise 3 (pg. 104), and Exercise 4 (pg. 104) and submit them as part of your report, either in the introduction or as an appendix as you deem appropriate.
 Read pages 100 to 112, on laser cavity modes.
 Do Exercise 1 (pp 111112). Do not forget to answer the last question of the exercise: Calculate the frequency difference between two adjacent axial modes TEM_{oom} & TEM_{oo(m+1)}.
Experiments
Aligning the laser
Align the laser until it begins lasing. The TA will discuss techniques to accomplish this.
When you are successful with the aligning process, and lasing is achieved, try varying the distances between the mirrors (using the adjusting screws on the laser mount) that still supports lasing. Record, in your lab book, the aligning process used, maximum, minimum and 'best' distances between the mirrors.
What the radius of curvature of the mirrors which form the optical cavity?
Use the polarizers to determine the polarization of laser.
Assume that the HeNe produces 3 mW of laser output power and that the electrical data given applies to your gas discharge tube. Compute the efficiency, in percent, for converting electrical energy to red laser light energy with this HeNe laser. Discuss your results.
Brewster's Angle
Using the glass plate provided, find an approximate value for the Brewster's angle. You can determine this by rotating the glass plate until lasing stops. Only at the Brewster's angle does lasing resume.
Knowing that the tangent of the Brewster's angle is the ratio of the refractive indices of the lasing medium to air, determine the refractive index of the glass medium.
Every resonant laser cavity has a characteristic quality factor or Q that measures the internal losses. The higher the Q, the lower the losses.
A Qswitch pulse can be made by blocking one end of the mirror, then exciting the medium and then quickly unblocking the mirror. Stimulated emission will quickly drain the stored laser energy from the cavity in a short pulse with peak power much higher than the laser can produce. One can think of a Qswitch as a device that quickly switches from absorbing to transmitting, suddenly reducing cavity losses.
The Qswitch pulse length is given by
where t is the round trip time (back and forth in the cavity), and R is the output mirror reflectivity ( >98% ).
Therefore
where L is the distance between the mirrors, n_{1} is the refractive index of the medium, and c is the speed of light. Pulse length can then be written as
Using the data from your laser, what is the theoretical value for the pulse length?
TEM Modes
Set up a camera with the screen at about 1 to 2 meters from the output mirror. Adjust the output coupler screws (or any other adjustments) to produce the TEM_{00m}, TEM_{10m}, TEM_{01m}, .... modes. Photograph or sketch a few of them.
Beam Profile of the TEM_{oom} and the TEM_{10m} modes
Realign the beam to produce the TEM_{oom} mode.
You will use a rotating mirror and a photodiode monitored on an oscilloscope to observe the profile of the laser beam.
Be sure to ensure the photodiode is not saturating when the laser is aligned onto it. If it is, switch the scale of the photodiode amplifier to a lower gain setting.
Repeat your observations for the TEM_{o1m} mode. Remember that photodetectors are squarelaw detectors, i.e., the current density J is proportional to the square of the electric field. (See Preston for details). Sketch the beam profiles for both modes.
Beam Profile or Shape
A laser beam has a certain profile with most energy concentrated at the center. The beam has the following form
Figure 1  Amplitude distribution across laser beam oscillating in the TEM_{oo} mode.

where w is the radius of the beam. The Gaussian function, exp [ (r/w)^{2} ] falls to 1/e, when r = w, i.e.,
Since the energy is proportional to the square of the amplitude, the beam radius, or SPOT SIZE, w, is defined as that distance from the axis where the power has dropped to 1/e^{2} of its value at the center. Twice that distance, 2w, is the beam diameter.
The beam radius, w, is the function of distance along the axis. If we call x the axial distance measured from the midpoint between the two (concave) mirrors, then the parameter w is given by
where λ is the wavelength and w_{0} is the minimum beam radius between mirrors.

Note that from w_{x} above; at x = 0, w_{x} = w_{o}.
From Preston (equation 21, p. 102),
Calculate w_{o} and w_{x}.
From your observations of the beam profile for the TEM_{oom}, determine w_{x}, the beam radius. How does your calculated value compare with the experimental value? Explain any differences.
Malus's Law
Malus’ law states that when a linearly polarized light beam of intensity I_{0} passes through a linear polarizer with its axis rotated by angle A from the light beam polarization, the emergent intensity I is given by
Use the rotatable polarizer and photodiode detector to verify this law quantitatively. Make detector readings at several values of angle A and record them in a neat table in your notebook. Graph your data to demonstrate the expected cos^{2}Adependence.
Verification of the FresnelArago Law
FresnelArago law state that two coherent light rays which are polarized right angles to each other will not mutually interfere.
Use the laser to set up the Michelson interferometer as shown below to form an interference pattern.
Insert polarizers P_{1} and P_{2} such that their axes of polarization is in the same direction. You may have to make slight adjustments to retain the interference pattern. Now, rotate ONE of the polarizers through 90º. Verify that the law is true. Try to take pictures of the resulting effect and include them with your report.