Principles and Applications of Laser

Laser is the abbreviation of Light Amplification by the Stimulated Emission of Radiation. It is a device that creates a narrow and low-divergent beam[1] of coherent light, while most other light sources emit incoherent light, which has a phase that varies randomly with time and position. Most lasers emit nearly "monochromatic" light with a narrow wavelength spectrum. Fig.1 [1] is the spectrum of a helium neon laser, showing very high spectra purity.

Fig1. Spectrum of a helium neon laser

# 1 Principle of Lasers

The principle of a laser is based on three separate features: a) stimulated emission within an amplifying medium, b) population inversion of electronics and c) an optical resonator.

## Spontaneous Emission and Stimulated Emission

According to the quantum mechanics, an electron within an atom or lattice can have only certain values of energy, or energy levels. There are many energy levels that an electron can occupy, but here we will only consider two. If an electron is in the excited state with the energy E2 it may spontaneously decay to the ground state, with energy E1, releasing the difference in energy between the two states as a photon. [2] (see Fig.2a) This process is called spontaneous emission, producing fluorescent light. The phase and direction of the photon in spontaneous emission are completely random due to Uncertainty Principle. The angular frequency ω and energy of the photon is:

(1)
\begin{align} E_{2}-E_{1}=\hbar\omega \end{align}

where ћ is the reduced plank constant.

Conversely, a photon with a particular frequency satisfying eq(1) would be absorbed by an electron in the ground state. The electron remains in this excited state for a period of time typically less than 10-6 second. Then it returns to the lower state spontaneously by a photon or a phonon. These common processes of absorption and spontaneous emission cannot give rise to the amplification of light. The best that can be achieved is that for every photon absorbed, another is emitted.

(a)

(b)

Fig.2 Diagram of (a) spontaneous Emission; and (b) stimulated Emission

Alternatively, if the excited-state atom is perturbed by the electric field of a photon with frequency ω, it may release a second photon of the same frequency, in phase with the first photon. The atom will again decay into the ground state. This process is known as stimulated emission.[3] (see Fig.2b)

The emitted photon is identical to the stimulating photon with the same frequency, polarization, and direction of propagation. And there is a fixed phase relationship between light radiated from different atoms. The photons, as a result, are totally coherent. This is the critical property that allows optical amplification to take place.

All the three processes occur simultaneously within a medium. However, in thermal equilibrium, stimulated emission does not account to a significant extent. The reason is there are far more electrons in the ground state than in the excited states. And the rates of absorption and emission is proportional the number of electrons in ground state and excited states, respectively.[2,3] So absorption process dominates.

## Population Inversion of the Gain Medium

If the higher energy state has a greater population than the lower energy state, then the light in the system undergoes a net increase in intensity. And this is called population inversion. But this process cannot be achieved by only two states, because the electrons will eventually reach equilibrium with the de-exciting processes of spontaneous and stimulated emission.[4]

Instead, an indirect way is adopted, with three energy levels (E1<E2<E3) and energy population N1, N2 and N3 respectively. (see Fig.3a) Initially, the system is at thermal equilibrium, and the majority of electrons stay in the ground state. Then external energy is provided to excite them to level 3, referred as pumping. The source of pumping energy varies with different laser medium, such as electrical discharge and chemical reaction, etc.

In a medium suitable for laser operation, we require these excited atoms to quickly decay to level 2, transferring the energy to the phonons of the lattice of the host material. This wouldn’t generate a photon, and labeled as R, meaning radiationless. Then electrons on level 2 will decay by spontaneous emission to level 1, labeled as L, meaning laser. If the life time of L is much longer than that of R, the population of the E3 will be essentially zero and a population of excited state atoms will accumulate in level 2. When level 2 hosts over half of the total electrons, a population inversion be achieved.

(a)

(b)

Fig.3 Electron Transitions within (a) 3-level gain medium; and (b) 4-level gain medium

Because half of the electrons must be excited, the pump system need to be very strong. This makes three-level lasers rather inefficient. Most of the present lasers are 4-level lasers, see Fig.3b.[4] The population of level 2 and 4 are 0 and electrons just accumulate in level 3. Laser transition takes place between level 3 and 2, so the population is easily inverted.

In semiconductor lasers, where there are no discrete energy levels, a pump beam with energy slightly above the band gap energy can excite electrons into a higher state in the conduction band, from where they quickly decay to states near the bottom of the conduction band. At the same time, the holes generated in the valence band move to the top of the valence band.[5] Electrons in the conduction band can then recombine with these holes, emitting photons with an energy near the band gap energy.(see Fig.4)

Fig.4 Diagram of electron transitions of semiconductor gain medium

## Optical Resonator

Although with a population inversion we have the ability to amplify a signal via stimulated emission, the overall single-pass gain is quite small, and most of the excited atoms in the population emit spontaneously and do not contribute to the overall output[6]. Then the resonator is applied to make a positive feedback mechanism.

An optical resonator usually has two flat or concave mirrors, one on either end, that reflect lasing photons back and forth so that stimulated emission continues to build up more and more laser light. Photons produced by spontaneous decay in other directions are off axis so that they won’t be amplified to compete with stimulated emission on axis. The "back" mirror is made as close to 100% reflective as possible, while the "front" mirror typically is made only 95 - 99% reflective so that the rest of the light is transmitted by this mirror and leaks out to make up the actual laser beam outside the laser device.[7]

More importantly, there may be many laser transitions contribute in the laser, because of the band in solids or molecule energy levels of organics. Optical resonator also has a function of wavelength selector. It just make a standing wave condition for the photons:

(2)
\begin{align} L=n\lambda/2 \end{align}

where L is the length of resonator, n is some integer and λ is the wavelength. Only wavelengths satisfying eq(2) will get resonated and amplified.

# 2 Summary of Principles and Modes of Operation

As a summary, Fig.5 is the schematic diagram of the working process of lasers.[8]

Fig.5 Schematic Diagram of Laser Operation

The output of a laser may be a continuous constant-amplitude output (known as CW or continuous wave); or pulsed, by using the techniques of Q-switching, model-locking, or gain-switching. In many applications of pulsed lasers, one aims to deposit as much energy as possible at a given place in as short time as possible. Some dye lasers and vibronic solid-state lasers can produce light over a broad range of wavelengths; this property makes them suitable for generating extremely short pulses of light, on the order of a few femtoseconds (10-15 s).[1] The peak power of pulsed laser can achieve 1012 Watts.

# 3 Types of Lasers and Applications

According to the gain material, lasers can be divided into the following types. Several common used lasers are listed in each type.[1]

### Gas Lasers:

Laser Gain Medium Operation Wavelength(s) Pump Source Applications and Notes
Helium-neon laser 632.8nm Electrical discharge Interferometry, holography, spectroscopy, barcode scanning, alignment, optical demonstrations
Argon laser 454.6 nm, 488.0 nm, 514.5 nm Electrical discharge Retinal phototherapy (for diabetes), lithography, confocal microscopy, spectroscopy pumping other lasers
Carbon dioxide laser 10.6 μm, (9.4 μm) Electrical discharge Material processing (cutting, welding, etc.), surgery
Excimer laser 193 nm (ArF), 248 nm (KrF), 308 nm (XeCl), 353 nm (XeF) Excimer recombination via electrical discharge Ultraviolet lithography for semiconductor manufacturing, laser surgery

### Solid State Lasers:

Laser Gain Medium Operation Wavelength(s) Pump Source Applications and Notes
Ruby laser 694.3nm Flash Lamp Holography, tattoo removal. The first type of visible light laser invented; May 1960.
Nd:YAG laser 1.064 μm, (1.32 μm) Flash Lamp, Laser Diode Material processing, laser target designation, surgery, research, pumping other lasers. One of the most common high power lasers.
Erbium doped glass lasers 1.53-1.56 μm Laser diode um doped fibers are commonly used as optical amplifiers for telecommunications.
F-center laser Mid infrared to far infrared Electrical current Research

### Metal-vapor Lasers:

Laser Gain Medium Operation Wavelength(s) Pump Source Applications and Notes
Helium-cadmium (HeCd) metal-vapor laser 441.563 nm, 325 nm Electrical discharge in metal vapor mixed with helium buffer gas. Printing and typesetting applications, fluorescence excitation examination (ie. in U.S. paper currency printing)
Copper vapor laser 510.6 nm, 578.2 nm Electrical discharge Dermatological uses, high speed photography, pump for dye lasers

### Other types of lasers:

Laser Gain Medium Operation Wavelength(s) Pump Source Applications and Notes
Dye lasers Depending on materials, usually a broad spectrum Other laser, flashlamp Research, spectroscopy, birthmark removal, isotope separation.
Free electron laser A broad wavelength range (about 100 nm - several mm) Relativistic electron beam Atmospheric research, material science, medical applications

# 4 History and Extension

In 1917 Albert Einstein first raised the concepts of probability coefficients (later to be termed 'Einstein coefficients') for the absorption, spontaneous emission, and stimulated emission of electromagnetic radiation. It was confirmed in 1940s. [1]

In 1953, Charles H. Townes and graduate students James P. Gordon and Herbert J. Zeiger produced the first microwave amplifier, a device operating on similar principles to the laser. In 1955 Prokhorov and Basov suggested an optical pumping of multilevel system as a method for obtaining the population inversion, which later became one of the main methods of laser pumping. Townes, Basov, and Prokhorov shared the Nobel Prize in Physics in 1964.

The first working laser was made by Theodore H. Maiman in 1960.[9] He used a solid-state flashlamp-pumped synthetic ruby crystal to produce red laser light at 694 nm wavelength. Maiman's laser, however, was only capable of pulsed operation due to its three-level pumping scheme. Later in 1960 the Iranian physicist Ali Javan made the first gas laser using helium and neon. It was the first continuous-light laser. The concept of the semiconductor laser diode was proposed by Basov and Javan. And the first laser diode was demonstrated by Robert N. Hall in 1962.

Numerous types of lasers have been invented since then and applied widely. Today they are still being improved to get better features, such as maximum peak output power and minimum output pulse duration.

As an interesting extension, femtosecond laser can be used to change the color of metals. This is a pretty new discovery by Chunlei Guo and Anatoliy Vorobyev in 2007. [10] They permanently change the aluminum, which is normally silver-colored, to gold, grey and black. And they can also turn gold black.(See Fig.6)

Fig.6 From left, aluminum turned a gold color, titanium turned to blue, and platinum turned gold.

Their trick is to etch the metals' surfaces with pits of different lengths and create other tiny shapes using a powerful laser. These tune the surfaces to absorb particular wavelengths of light, and reflect only the desired color — or almost no light in the case of black.

## References:

[1]http://en.wikipedia.org/wiki/Laser
[2] http://en.wikipedia.org/wiki/Spontaneous_emission
[3] http://en.wikipedia.org/wiki/Stimulated_emission
[4] http://en.wikipedia.org/wiki/Population_inversion
[5] http://www.rp-photonics.com/semiconductor_lasers.html
[6] http://www.mellesgriot.com/pdf/CatalogX/X_36_2-5.pdf
[7] http://www1.union.edu/newmanj/lasers/Laser%20Theory/laser_theory.htm
[8] http://common.ziffdavisinternet.com/encyclopedia_images/LASER.GIF
[9] T.Maiman,, "Stimulated optical radiation in ruby". Nature vol187, 4736(1960): 493–494
[10] A Vorobyev and C. Guo, "Colorizing metals with femtosecond laser pulses", App.Phys.Lett. vol92, 041914 (2008)