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How Lasers Work

Physical Characteristics of Lasers and How They Work

The uniqueness of laser light in contrast to natural light which is emitted from the sun or from a hot wire in a light bulb arises from only two characteristic properties of laser radiation: 1) MONOCHROMATISM and 2) COHERENCE. Based on these two characteristics, it is possible to generate light fields with unbelievable short duration, extremely tight focusing and exorbitant irradiances.

Light Absorption: Photonic Energy to Electronic Energy

To understand how laser light is generated, one has to first have an idea on how light is generated. The simple Bohr planetary model of the atom is adequate, to explain the mechanisms. Here the electrons move on distinct orbits around the nucleus, which have certain energy levels (Fig. 1).

Under normal conditions, the electrons stay in the lower ground state E1. If energy is transferred to the atom, the electrons are excited to a higher level. The various ways in which energy can be transferred to the electrons is by:

  1. the impact of two atoms (heat),
  2. the impact of accelerated free electrons (gas discharge),
  3. the release of internal energy due to exothermal chemical reactions or
  4. absorbing an incoming photon (Fig. 2 top).

In the last case, the energy of the photon, which will be absorbed, has to be identical to the energy gap between the upper and lower level of the electron. The frequency ν (or color) of the photon is determined by its energy E. The relationship between energy and frequency of a photon is given by Heisenberg’s equation:

E = hν = E2 - E1

were h is the so-called Plank constant. Using

hν = c/λ

one can calculate the wavelength λ of the photon as a function of the energy gap:

λ = hc  / (E2-E1)

c is the speed of light.

Light Emission: Electronic Energy to Photonic Energy

In the same way the photon is absorbed by exciting the atom, it can be spontaneously emitted when the electron drops down to the ground state (Fig. 2 middle). The emission process is of a statistical nature, which means, the electron relaxes at any time within an average life time T, and a photon will be emitted in any direction. The only way to influence this emission process is to send another photon to the atom with an energy corresponding to the energy gap between the ground level and the excited level. In that case, the excited electron will be stimulated to relax down to the ground state and emit an identical photon with the same energy and the same direction (Fig. 2 bottom). Moreover, these two photons now have the same phase, which means, the amplitude of the electromagnetic field of both photons, are identical at the same place within the same time. This condition of two or more photons which are in phase is called coherence.

Stimulated Emission of Photons

This process of stimulated emission provides the basis for a second important mechanism: the doubling of the number of photons after one stimulated emission. In other words, the process of stimulated emission acts as an amplifier. If a sufficient number of excited atoms exist, an avalanche of coherent photons will be generated. This process is called Light Amplification by Stimulated Emission of Radiation (LASER).

However, an important condition to start the amplification process is to have more atoms with their electrons in the excited upper level than in the ground state. This unnatural configuration is called population inversion.

Population Inversion

Typically, in one atom, the distribution of electrons as a function of energy follows the so called Boltzman's law of thermodynamic distribution.

In this law, the higher the energy level, the lower its population density by electrons (Fig. 3). On the other hand, light amplification will occur only when the upper level has a higher population than the ground state. This condition, called population inversion, never happens in nature, and that is the reason why no natural light source emits laser radiation. One mechanism, which leads to population inversion is called optical pumping. Herein, the energy for excitation can be delivered by:

  1. an external light source (typical example: Nd:YAG-Laser),
  2. an electrical excitation due to a gas discharge (typical examples: HeNe-Laser, Ar-Ion Laser, Excimer Laser),
  3. an electron injection (Diode Lasers) or
  4. a chemical reaction.

Because the probability of exciting an electron into the upper level (by irradiating light into the active medium) equals the probability of stimulating emission (by forcing an excited electron to the ground state), it is impossible to achieve population inversion on a two level system, regardless of how intense the pumping light happens to be. At the most, an equal population of both levels will exist.

The easiest way to achieve population inversion by optical pumping is to introduce a third energy level to redirect the energy pathways (Fig. 4a).

Let us assume that we have a ground state, E1, and an upper pumping level, E3, where the electrons are excited by absorbing the pumped light. After the natural life time of the upper level, T3 terminates, the electrons decay into the ground state. or they make a transition into the third state which has a little lower energy level E2. If the life time T2 of this intermediate level E2 is larger than the life time of the upper level E3, the electrons which are pumped into E3 will accumulate in level E2. Because the pumped light will not lead to stimulated emission into the intermediate state, we will achieve population inversion in E2 when more than 50 percent of the atoms are excited.

Another, more efficient way to generate population inversion is by introducing a fourth level, which acts as the lower laser level (new E2).  Provided, the life time, T4 of the upper pumping level  (E4) is much shorter than the life time of the upper laser level (new E3) and the lower laser level (new E2) decays quickly into the ground state (new E1), one can achieve population inversion from the earliest electrons which are excited by the pumped light, and this inversion is independent of the pumping rate. This is the most efficient way to produce laser radiation (Fig. 4b).

Laser Components and Modes of Laser Operation

To build a laser we need only a few components. First we need an active medium, which can be a transparent solid state, a gas or a liquid. The medium has to be pumped by an external pumping source, which can be, for example, an intense arc lamp or another laser. In order to direct the stimulated emission process into one direction, we need a feedback mechanism, which is provided by two mirrors which force the light to oscillate back and forth through the excited laser medium (Fig. 5).

Regarding operation time, lasers are divided into continuous wave (cw) and pulsed systems. Continuous wave is usually defined as a period, which lasts longer than 250 ms. The emission time is controlled by an external shutter; or the laser system can be completely turned on and off.

With pulsed laser systems, usually the pumping process, or optical devices inside the oscillator, determines the pulse duration of the laser output. Pulsed lasers are subdivided into so-called free running lasers, q-switched lasers and mode coupled lasers. In the following section we will analyse the different types of pulsed laser systems.

Free Running Mode

When the laser is pumped by a flash lamp, the laser runs in the so-called, “Free Running-Mode”. This means pulse duration is roughly determined by the duration of the pump flash, which is in the range of several hundred microseconds (1 µs = 10-6 s) to milliseconds (1 ms = 10-3 s). A main characteristic of a free running pulse is its spiking. The emitted pulse consists of many short and intense spikes, each with only a few µs duration (Fig. 6). This is caused by a nondeterministic interplay of stimulated emission and excitation.

Q-switch Mode

Usually, the duration of a flash lamp pulse cannot be set shorter than a few µs. If laser pulse durations in the nanosecond regime (1 ns = 10-9 s) are needed, one has to make use of the so-called “Q-switch” principle. The optical pumping is supported by an optical switch which reduces the quality (Q) of the resonator. As a consequence, the stimulated emission process is stopped. Only when the optical switch is opened, the highly accumulated inversion can be cleared by a giant laser pulse. The stored pump energy is then released by stimulated emission within several ns (Fig. 7).

Mode Locking

For the generation of picosecond pulses (1 ps = 10-12 s) or even femtosecond pulses
(1 fs = 10-15 s), the laser has to be “Mode Locked”. The axial laser modes, which are light waves with a slightly different frequency or wavelength, have to be synchronized or locked in a fixed phase. When their phases are fixed, they interfere in such a way that their amplitude either adds up or annihilates (Fig. 8).

The interference of these modes generates very short, but intense amplitudes. These packages of highly intense waves oscillate inside the resonator and partially leave it at the output mirror (Fig. 9).

The duration and the amplitude of these wave packages depend on the number of modes which are generated and locked inside the resonator. The more modes that are locked, the shorter and more intense the pulses are.

The number of modes is limited by the spectral bandwidth of the laser medium. The broader its spectrum, the more modes can be generated, and the shorter the laser pulse can be. Some laser crystals, for example Titanium: Sapphire, can stimulate 10,000 modes, which results in pulse widths of only a few femtoseconds. Ytterbium based crystals, which are commonly used in ophthalmic applications at wavelengths around 1040 nm, are able to generate pulse widths of a few hundred femtoseconds.

Because the wave package oscillates inside the laser resonator with the speed of light, mode locked lasers have very high pulse rates. At a resonator length of typically 2 meters (m) (the resonator usually is folded, so the box of the laser machine can be shorter), the light needs for one full oscillation (4 meters takes) only 4/300,000 km/s = 13 ns, which results in a repetition rate of 1/13 ns = 75 MHz.

Need for an Amplifier with Most Femtosecond Lasers

MHz repetition rate pulses cause problems in placing each single pulse to a different place. Common scanner systems are too slow. Moreover, laser oscillators can produce pulse energies up to several hundred nJ which is, depending on the focusing optics, too low to reach the threshold of photodisruption.

As a consequence, currently all commercially available ophthalmic laser systems  need a power amplifier to get enough pulse energy for surgical applications, except the LD from Ziemer.

The oscillator, usually a diode pumped solid state or fiber laser, seeds the amplifier with low energy pulses. Because MHz repetition rate are too high to process, an optical switch (Electro-Optic Modulator (EOM) or Acousto-Optic Modulator (AOM)) selects the pulses and reduces the pulse rate to typically several hundred kHz. Moreover, the oscillator pulses are optically stretched to several picoseconds. Making the pulses longer reduces their peak power. If the pulses would be amplified directly, the optical components of the amplifier would be damaged by photodisruption.

The power amplifier consists of a second laser crystal or a laser fiber which is optically pumped by another pump diode. The seed pulses from the oscillator depopulate the inversion by stimulated emission and will tus be amplified by a factor of 100 to 1,000.  Finally, the amplified pulses are compressed by an optical compressor to several hundred fs and pulse energies to several µJ (Fig. 10).

Content Overview

Light Absorption: Photonic to Electronic Energy
Light Emission: Electronic to Photonic Energy
Stimulated Emission of Photons
Population Inversion
Laser Components & Modes of Laser Operation

© by Holger Lubatschowski, 2012

Figure 1
Bohr’s Planetary Model, were the Electrons are orbiting around the Nucleus. If an electron transfers from von level E2 to the lower level E1 it emits a photon with energy E2-E1 Vice versa an electron can be lifted from the lower state E1 to the exited s
Figure 2
Population of the electrons of a simple two level system in the Bohr Planetary Model. Top: absorption of a photon, middle: the emission of a photon and bottom: the stimulated emission of a photon.
Figure 3
Population of two energy levels of an atom as a function of energy. The population density of the upper level E2 is always smaller than the population of the lower level E2.
Figure 4a
Three level system to achieve population inversion for the laser transition from level E2 to E1.
Figure 4b
Four level system, achieving inversion for the laser transition from E3 to E2.
Figure 5
Schematic drawing of the main components of a laser oscillator
Figure 6
Relaxation oscillations (spicking) of a Nd:YAG laser (source:http://photon.physnet.uni-hamburg.de/ilp/sengstock/research/dynamics-of-multimode-lasers/)
Figure 7
Principle of Q-switching. Top: in cw mode the laser output power is proportional to the optical pump power. Bottom: while the quality of the laser resonator is low, the stimulated emission process is stopped and optical pumping leads to high population in
Figure 8
Principle of Mode Locking:  Four different modes in a resonator (top) and their interference to contribute to either annihilation or higher amplitudes (bottom).
Figure 9
Oscillating wave inside a resonator generated by a Mode-Locker (left). A transparent mirror (right) couples out a fraction of the oscillating wave every time when it is reflected at the resonator wall.
Figure 10
Schematic diagram of an oscillator–amplifier laser system. (Source: http://en.wikipedia.org/wiki/Chirped_pulse_amplification)
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