Main Page/PHYS 4210/He-Ne Lasers

He-Ne Lasers

In this experiment we first align an open-ended laser. Then we set up some transverse mode patterns, and perform further exercises and experiments to understand how a laser works.

Key Concepts

Stimulated Emission Spontaneous Emission Stimulated Emission Incoherent/Coherent Radiation Einstein Coefficients Population Inversion Forbidden Transitions Metastable States LS coupling Electric dipole selection rules

Axial Modes TEM modes Spectral Width Atomic Lineshape Loss/Gain Coefficient Index of Refraction Brewster’s Angle Malus’s Law Fresnel-Arago Law Q-Switch

Reading and Exercises

• Read pages 94 to 105 from Preston-Dietz. Carry out Exercise 1 (pg. 100), Exercise 2 (pg. 103) and Exercise 3 (pg. 104), but do not submit them as part of your report.
• Continue with Exercise 4 (pg. 104).
• Read pages 100 to 112, on laser cavity modes.
• Do Exercise 1 (pp 111-112). 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, radius of curvature of the mirrors etc.

Use the polarizers to determine the polarization of laser.

Assume that the He-Ne 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 He-Ne laser. Discuss your results.

Brewster's Angle

Using the etalon, find an approximate value for the Brewster's angle. You can determine this by rotating the etalon 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 Q-switch 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 Q-switch as a device that quickly switches from absorbing to transmitting, suddenly reducing cavity losses.

The Q-switch 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, n₁ 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.

Set up the travelling microscope with the photo-detector at approximately 3 to 4 meters from the output coupler. Connect the detector to either a voltmeter or storage scope. Scan the beam to obtain the beam profile, i.e., transverse distance (x) versus intensity. Record the distance from the output coupler.

Note:If the storage scope is used to measure the intensity, you may have to use a cardboard to modulate (chop) the beam. Depending on the distance from the output coupler, you may want to use a NEUTRAL density (Wratten ND) filter to reduce to beam intensity.

Repeat your observations for the TEM_o1m mode. Remember that photodetectors are square-law 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 TEMoo 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/e² 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 w₀ 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.

Optional Further Experiments

Malus's Law

Malus’ law states that when a linearly polarized light beam of intensity I₀ 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 cos²Adependence.

Verification of the Fresnel-Arago Law

Fresnel-Arago 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 P₁ and P₂ 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.