LASER MODES

“Lasers are amazing devices which emit beams of light powerful enough to vaporize a bulldozer, yet are so precise that they can be used in delicate optical surgery, provided the surgeon remembers to change the setting on the laser to ‘delicate optical surgery’ from ‘vaporize bulldozer.”
- Dave Barry, Haverford alumnus, on the topic of lasers

Introduction and Background
Dave Barry is right about one thing: Lasers are useful. Their applications are myriad and diverse- but in all cases lasers are useful for the simple reason that they emit light with a narrowly defined wavelength with a well-defined direction, as opposed to the traditional light bulb, which emits a broad spectrum of light wavelengths in diffuse directions. (Scientifically, we call this temporal coherence—a well-defined frequency of light is emitted with a well-defined phase—and spatial coherence—the light is also emitted in a highly parallel beam.) However, the wavelength distribution of laser light is more complicated than you might initially think. Rather than emitting at a single wavelength, the laser instead emits light at several distinct wavelengths, in a relatively tight, Gaussian distribution centered at the ideal wavelength.
This distribution of wavelengths has important ramifications – but primarily for people who have to spend a lot of time with lasers. As long as your CD player is working, you don’t need to worry too much about the results of this distribution. Rather, as a physics student, you should be concerned with the causes of this distribution, many of which turn out to be (surprise!) quantum mechanical.
In this laboratory you will use a Fabry-Perot interferometer to measure the intensity of light emitted from the laser as a function of frequency. You should find that the radiation is not monochromatic, but rather that the radiation is concentrated in certain discrete modes that are characteristic of the laser cavity.
Additional References:
• Donald O’Shea, W. Russell Callen, and William Rhodes, Introduction to Lasers and Their Applications, pp. 126-131 (Reserve Reading)
• Yariv, Introduction to Optical Electronics, Holt, Reinhart and Winston, New York, 1975. (Reserve Readings)
• Lengyel, Introduction to Laser Physics, John Wiley and Sons, New York, 1966. (Reserve Readings)
• T. Kallard, Exploring Laser Light, pp. 1-6
• Frank J. Blatt, Modern Physics, pp. 191-198

The Helium-Neon Laser
The word laser stands for light amplification by stimulated emission of radiation. The Helium-Neon laser is commonly used in instructional laboratory experiments and applications. This laser utilizes many of the same strategies as other lasers do to cause stimulated emission of light. The basic idea is as follows: the laser consists of a container of Helium and Neon gas atoms (normally in a 10:1 ratio), with mirrors at both ends and a voltage applied along its length. When the voltage is applied, an electric discharge causes electrons to strike the Helium atoms and raise them to the excited 1s12s1 state. (See Fig. 1.) The goal is what is called a population inversion, where more Helium atoms are in an excited state than in the ground state. This happens because the excited state is metastable — atoms in that state decay relatively slowly to the ground state, so that the excitation process causes them to accumulate in the excited state.

Figure 1 Energy levels for the Helium-Neon laser. This exact energy level diagram shows the more commonly used red lasing line. The energy level diagram for the green lasing line used here is similar. Source: http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter4a_files/image024.gif

Once the helium atoms are excited, the neon atoms come into play. The energy needed to excite helium to the 1s12s1 state is almost exactly the same as the energy needed to excite the neon to its 2p55s1 state. Once the helium population is successfully inverted, excited helium atoms will strike neon atoms and transfer their energy to the neon (the helium atoms then return to their ground state). Since the 2p55s1 neon excited state is more stable than those below it, there is a buildup of neon atoms in this state, while the atoms in other states decay to the ground state. Once a photon is released from the decay of the neon 2p55s1 state to the neon 2p53p1 state through ordinary random emission of a photon (called spontaneous emission), this photon can interact with another neon atom and force it to de-excite in the same way. When a photon stimulates emission of a second photon in this fashion, the second photon is emitted with exactly the same energy, phase and direction as the first. This purely quantum mechanical effect is called stimulated emission.
Many of the photons simply escape from the sides of the cavity, never to be seen again. However those that happen to travel along the axis of the cavity and have the correct frequency to interfere constructively after reflection by the mirrors will survive for a long time, and can induce even more neon atoms to radiate photons into the same state, thus forming a phase coherent and parallel beam. Thus, a standing wave develops between the two mirrors at either end of the cavity. The allowed wavelengths are those for which the cavity length is an integral number of half wavelengths.
Photons are not trapped in the cavity completely, or no useful laser would exist, but most photons must be reflected at the mirrors in order to maintain constructive interference. For this reason, the mirrors are usually 99% reflective at the front mirror, and 99.9% at the back one (from Exploring Laser Light by T Kallard). This means that a particular photon will reflect about 100 times, giving a high probability to induce stimulated emission, before emerging from the front mirror and leaving the cavity. This abbreviated discussion is not meant to substitute for reading in the library!

Line Broadening Effects and Laser Modes
Since a laser works by producing many identical photons, each with the same frequency E/h, the light from a laser exhibits that frequency. For the laser used in this experiment (UniPhase model #1674P), the listed wavelength of emission is 543.5 nm. Thus, its plot of intensity versus wavelength should be zero everywhere except at a wavelength of 543.5 nm. However, several effects combine to produce broadening of the emitted spectral line.
Figure 2 shows a plot of intensity versus frequency that demonstrates the presence of more than one wavelength. The peaks are a result of longitudinal laser modes, as we will explain shortly. This plot also shows a high level of resolution, with ten laser modes visible. Although eight to ten laser modes are typical, you most likely will not be able to attain such high resolution. The broadening occurs from a variety of effects, two of the most important of which are Doppler broadening and lifetime broadening