Laser Theory

Introduction

Flinn Scientific, Inc., sells two types of lasers: Helium-Neon (He-Ne) gas lasers and Visible Laser Diode (VLD) solid state lasers. These two types of lasers work by very different processes to generate the same result—Light Amplification by Stimulated Emission of Radiation (LASER).

Concepts

• Laser
• Stimulated emission of light

Safety Precautions

Please follow the safety guidelines described by the laser’s manufacturer. Never look directly at the laser light. For more information on laser safety, please refer to the “The Safe Use of Lasers,” Publication No. 10167.

Discussion

Laser Basics
A laser produces a strong beam of coherent (same phase and energy) photons by stimulated emission. Stimulated emission of a photon occurs when a photon of light interacts with an excited electron to produce another photon of light. For this to occur, the incident photon must have the same energy as the energy that the electron will release in its transition from the excited state back down to the ground state (or lower-energy state). The excited electron emits a photon of the same energy and in the same direction as the interacting photon, and the electron falls to its ground state. This produces two coherent photons, which can then interact with other excited electrons to produce two more coherent photons for a total of four photons, and so on. This theory was first proposed by Albert Einstein in 1917. During his work, Einstein discovered that the probability of an electron spontaneously emitting or absorbing a photon is equal. Therefore, in most cases, electrons will transition out of an excited state, via spontaneous photon emission, just as fast as other electrons are being energized to excited states. This leads to ordinary incoherent light (such as from a lightbulb filament). For Einstein’s theory to work there must be a surplus of excited electrons to interact with the emitted photons.

His theory became fact in 1960, with the development of the first laser—the ruby laser. The ruby laser used a technique known as optical pumping to obtain a surplus of excited electrons compared to ground-state electrons (a so-called population inversion). Optical pumping is a method that can be used on certain atoms that have metastable electron states (such as chromium for the ruby laser). Generally, an electron will not stay in an excited state for very long (only about 10^–8 seconds). A metastable state is an excited state with a much longer lifetime than an ordinary excited state (sometimes lasting as long as seconds, instead of nanoseconds). The electrons in chromium can transition from a normal excited state to a metastable excited state through a nonradiative transition (such as collisions with other atoms). This longer lifetime excited metastable electron state creates a population inversion because the probability of the electron remaining in this excited metastable state is greater than it returning to the ground state. When an electron does fall from the metastable state to the ground state and spontaneously emits a photon, this photon will have a very good chance of interacting with another electron in the longer-lifetime metastable state. The spontaneously emitted photon can then trigger another metastable electron to transition to the ground state and emit a photon of the same energy, phase, and direction. Often, the metastable excited state can not be reached by direct photon absorption. Therefore, the photons emitted as electrons fall from the metastable state to the ground state will not be absorbed by ground state electrons. This maintains the population inversion, and also allows the emitted photons to continuously interact with other metastable electrons and thus amplifies the emitted light (see Figure 1).

A helium-neon (He-Ne) laser cleverly produces a population inversion using collision pumping rather than optical pumping. A He-Ne laser consists of a glass tube containing 15% neon gas and 85% helium gas at a very reduced pressure (1/300 atmospheres). The helium atom electrons are excited to their first excited state (20.61 eV above the ground state) by an electric discharge in the tube. The second excited state for neon electrons is just above the energy level for the first excited state of helium electrons (20.66 eV). Therefore, the neon electrons can be excited to their second excited state when they collide with the excited helium atoms (the kinetic energy of the moving atoms is enough to provide the extra 0.05 eV of energy). The first excited state for neon electrons is 1.96 eV below the second excited state (or 18.70 eV above the ground state). Since the first excited state for the neon electrons is generally unoccupied, a population inversion is immediately created between the second excited state and the first excited state of the neon atom electrons. When an electron transitions from the second excited state to the first excited state, emitting a photon of 1.96 eV (wavelength 632.8 nm), there are plenty of other second-excited state electrons for this photon to interact with. Therefore, the photon stimulates the emission of other photons of the same energy level and in the same direction. When the electron reaches the first excited state, it quickly drops to the ground state via spontaneous emission through several transition states, and through collisions. The spontaneously emitted photons of different wavelengths travel in all directions and are eventually absorbed by the optic components of the laser. This maintains the population inversion between the second-excited state and the first-excited state (see Figure 2). It is possible for the neon atom electrons to gain enough energy from the electric discharge in the tube to be promoted to the appropriate energy level without the need for an excited helium collision. However, helium has a much greater ability (several orders of magnitude) to promote the electrons in neon to the appropriate energy level. Neon has ten electrons, compared to two for helium, so there are many different excited levels for each electron in neon. There is a low probability for an energetic electron (from the electric discharge) to excite a neon atom electron directly to the second excited state. Helium has a much better chance to reach its first excited state (just below the second excited state for neon) with the electric discharge. Once excited, the helium atom can supply just the right amount of energy to promote a neon electron to the second excited state when they interact. The maximum intensity of laser light is achieved when the ratio between helium and neon is about 6:1.

To further strengthen the output of coherent laser light from a He-Ne laser, highly reflective mirrors are placed at each end of the tube. The back mirror is almost perfectly reflecting whereas the front mirror is about 99% reflecting, letting about 1% of the beam pass through (which is what is seen). The light passes back and forth between the mirrors many times stimulating more photons and producing a nearly parallel beam of light with little divergence (the laser beam is said to be highly collimated) (see Figure 3). The Visible Laser Diode (or VLD) is a solid state laser that uses a semiconductor chip to generate laser light. Semiconductor chips are made from silicon which has been doped (adding a controlled amount of impurities) in order to change the electrical properties of the semiconductor. A p-type semiconductor has positive “holes”—the doping agent has an incomplete valence and thus produces extra positive charges (or holes) in the lattice crystal. A n-type semiconductor has extra negative charge because the doping agent has an extra valence electron. For a semiconductor laser, n-type and p-type semiconductors are sandwiched together and at the pn-junction (the region where the semiconductor changes from a p-type to an n-type semiconductor), there is an active layer known as the depletion region. The active layer for many semiconductor lasers is gallium arsenide crystals since the p-type semiconductor is doped with gallium and the n-type semiconductor is doped with arsenic. The entire “laser chip” is generally about 1 to 2 mm thick and the active layer is only about 0.5 mm thick. The depletion region has a very high resistance when no external electric voltage is supplied so it prevents the positive “holes” and the negative electrons from diffusing across from the p-type to the n-type semiconductor, and vice versa. When a voltage is applied across the semiconductor chip, with the positive electrode on the p side and the negative electrode on the n side, the resistance is lowered. This allows the electrons to diffuse to the positive electrode and “holes” to the negative electrode. When the electrons and “holes” meet, they recombine and release energy in the form of photons. Under normal conditions, the light would be incoherent and the semiconductor chip would be a simple light emitting diode (LED). However, if the proper current is applied, the light traveling parallel to the active layer can stimulate the emission of other photons (resulting from an electron-hole recombination). These photons will also travel parallel to the active layer and together produce a coherent parallel laser beam (see Figure 4). Laser Characteristics

General Characteristics
He-Ne lasers produce an orange-red beam at a wavelength of 632.8 nm (632.8 x 10^–9 m). VLD lasers produce a deep red beam at a wavelength of 635–680 nm. The exact wavelength produced by a VLD laser depends on the geometry of the individual laser crystal and the operating temperature. All the lasers sold by Flinn Scientific are designed to be operated between –20 and +50 °C, at altitudes up to 3 km, and at humidities up to 99%. Some common laser terms are explained.

Power is proportional to the intensity (I = P/area) of the laser beam and is measured in units of energy divided by time, millijoules per second (mJ/sec), which is equal to milliwatts (mW). How much power is delivered in a given response time is important in laser safety issues. A general response time is about one quarter of a second (0.25 sec). The power of each of the lasers Flinn Scientific sells is listed: Beam diameter is the diameter of the laser beam. This is also called the cross section. It is measured between points near the outer edge of the beam where the intensity is about 86% of the intensity at the center of the beam.

Divergence is a measure of how much the beam spreads out or diverges as it travels away from the laser (the beam forms a cone instead of a cylinder). To determine the divergence, measure the beam diameter at a distance several meters from the laser. Divide the beam diameter by the distance from the laser to determine the angle of divergence in radians. Divergence is generally measured in milliradians (mRad) so multiply by 1000 to determine the angle of divergence in mRad. For example, if the beam diameter was measured to be 12 mm and that measurement was taken 10 m away from the laser, then the angle of divergence would be 1.2 mRad. A typical divergence for the lasers sold by Flinn is about 1 mRad; the laser beam diverges 1 mm for every 1000 mm of travel.

Mode refers to the distribution of light in the laser beam. Flinn sells lasers that operate in what is known as the TEM₀₀ mode. TEM₀₀, the lowest order transverse electric and magnetic mode, is the most widely used mode because it produces a Gaussian distribution throughout the entire beam cross-section. This is the preferred mode for holography.

Irradiance is the power density of the laser beam. It is generally measured in terms of power per unit area (i.e., mW/cm²). Many laser safety measurements are listed in terms of irradiance.

Coherence length is the distance the laser beam can travel while its photons remain in phase with one another. For He-Ne lasers, the coherence length is about 10 to 20 cm, while the coherence length for VLD lasers is only a few centimeters. A longer coherence length is better for interferometry and holography experiments.

Light from a laser differs from ordinary light in four important ways:

1. Small Divergence. The beam from a laser does not spread out nearly as much as light from an ordinary source. Therefore, instead of dissipating rapidly, the energy from the light is concentrated in a narrow beam.
2. Monochromatic. Light from a laser is monochromatic (one color) because it consists of a single wavelength. White light from an ordinary light source contains the full range of colors in the visible spectrum.
3. Coherence. Light from a laser is coherent, or in phase. Light consists of oscillating electric and magnetic fields perpendicular to each other and to the direction the light is traveling. The length between the peaks or troughs in the electromagnetic fields is defined as the wavelength. In a coherent light source, such as a laser, the peaks and troughs of the oscillating electric and magnetic fields are in line with each other. In an ordinary light source, the peaks and valleys of the electromagnetic waves are not lined up; they are out of phase.
4. High Intensity. Laser light is very intense because all of its energy is concentrated in a small radius. Light from a typical classroom laser is relatively safe if used as intended.

Differences Between the Laser Beam Generated by He-Ne and VLD Lasers
The laser beam emitted from a VLD laser is different from that produced by a He-Ne laser in three important ways: the shape of the beam, the visibility of the beam and the coherence length of the beam.

The beam that is emitted from a round capillary tube, such as that present in the He-Ne lasers, has a round cross section (discounting divergence). That emitted from a rectangular slab, such as that in the VLD lasers, has an elliptical cross section. This elliptical cross section is corrected by placing a special lens over the laser aperture.

The wavelength given off by a VLD laser is about 635–680 nm, which is a much deeper red than the red-orange light with wavelength 632.8 nm produced by a He-Ne laser. The human eye is less sensitive to the deep red of the VLD laser than to the redorange of the He-Ne laser and the beam from a VLD laser appears about ¼ as bright as that from a He-Ne laser.

As mentioned in the section on laser characteristics, the coherence length of a typical He-Ne laser is about 10–20 cm, while the coherence length of a VLD laser is only a few cm. The VLD lasers that Flinn sells have a coherence length of about 5 cm which makes them suitable for use in holography or interferometry experiments; however, the longer coherence length found with the He-Ne lasers is better for these types of applications.

What to Look for in Selecting a Laser
Since individual needs for a laser differ, several factors should be considered when planning a laser purchase. The amount of output power required is one of the most important issues. If the laser is to be used for general classroom applications or student laboratory activities, a low-power laser such as the He-Ne laser is sufficient. The brighter beams of the medium-power lasers, such as the laser pointers, are better for use in lecture halls. All the lasers Flinn sells are rugged, will have a long life, will be resistant to shock, and will withstand hard usage from several generations of students. The solid state VLD laser pointers can be expected to operate trouble-free for at least 10,000 hours. Other factors to consider include beam diameter, beam divergence, polarization and modulation.

Overall, if a school can afford to purchase only one laser for general use and communications, it should be a modulated solidstate VLD laser pointer. If the laser is needed for general use as well as holography and demonstrations in a brightly lit room, the one laser to purchase is a He-Ne laser.

References

Laser Teaching Supplement; Metrologic Instruments: Blackwood, NJ, 1993; pp 2–10.

Tipler, Paul A.; Physics for Scientists and Engineers, 3rd Ed., Vol. 2; Worth Publishers: New York, 1990; pp 1244–1250.