LASER PRINCIPLES & TYPES (SEMESTER - V):
1. LASER: Meaning and Physical Basis
Definition: LASER is the acronym for Light Amplification by Stimulated Emission of Radiation.
In 1917, Albert Einstein published an important paper on the thermodynamic equilibrium between matter and cavity radiation. He showed that a complete description of the interaction of atoms with radiation requires three processes: absorption, spontaneous emission and stimulated emission. The transition rates of these processes are related mathematically through the Einstein A and B coefficients.
1.1 Thermal equilibrium and the Boltzmann distribution
Consider a cavity containing black-body radiation and atoms with two non-degenerate energy levels E₁ and E₂, where E₂ > E₁. If the atomic system is in equilibrium with radiation at temperature T, the populations N₁ and N₂ obey the Boltzmann distribution:
N₁ = N₀ exp(-E₁/kT)
N₂ = N₀ exp(-E₂/kT)
N₁/N₂ = exp[(E₂ - E₁)/kT] = exp(hν/kT) > 1 (1)
Thus the lower level is more heavily populated than the upper level at thermal equilibrium. In other words, N₁ > N₂. This population distribution is the opposite of the population inversion required for laser action.
Notation: k is the Boltzmann constant, h is Planck's constant, ν is the radiation frequency, and hν = E₂ - E₁.
1.2 The three radiation-matter interactions
Figure 1. Absorption, spontaneous emission and stimulated emission in a two-level system.
Stimulated absorption. An atom in the lower state E₁ absorbs an incident photon of energy hν = E₂ - E₁ and moves to E₂. The upward transition rate is proportional to the radiation energy density u(ν) and to the lower-state population N₁.
R₁₂ = B₁₂ N₁ u(ν) (2)
B₁₂ is the Einstein coefficient for stimulated absorption and measures the probability of an induced transition from level 1 to level 2.
Spontaneous emission. An excited atom in E₂ may return to E₁ without an external photon. The emitted photon has energy hν, but its direction, phase and polarization are random.
R₂₁(spontaneous) = A₂₁ N₂ (3)
Stimulated emission. A photon of energy hν can induce an excited atom to move from E₂ to E₁. The emitted photon is identical to the stimulating photon in frequency, phase, direction and polarization. This duplication of photons is the basis of optical amplification.
R₂₁(stimulated) = B₂₁ N₂ u(ν) (4)
The total downward transition rate is therefore the sum of stimulated and spontaneous emission:
R₂₁(total) = B₂₁ N₂ u(ν) + A₂₁ N₂ (5)
1.3 Einstein relations
At thermal equilibrium, the total upward transition rate equals the total downward transition rate:
B₁₂ N₁ u(ν) = B₂₁ N₂ u(ν) + A₂₁ N₂
u(ν) = (A₂₁/B₂₁) / [(B₁₂/B₂₁)(N₁/N₂) - 1] (6)
Planck's black-body radiation formula is
u(ν) = [8Ï€hν³/c³] / [exp(hν/kT) - 1] (7)
For equations (6) and (7) to be identical for all temperatures and frequencies, the coefficients must satisfy the Einstein relations:
B₁₂ = B₂₁ (8)
A₂₁/B₂₁ = 8Ï€hν³/c³ (9)
Physical meaning: Equation (8) states that, for non-degenerate levels, stimulated absorption and stimulated emission are equally probable. Equation (9) relates spontaneous and stimulated emission. For degenerate levels, the more general relation is g₁B₁₂ = g₂B₂₁.
2. Basic Components of a Laser
Every practical laser requires an amplifying medium, a source of energy to produce population inversion and an optical resonator to provide feedback and a directed output.
Figure 2. Essential components and working arrangement of a laser.
2.1 Active medium
The active medium, also called the amplifying medium, contains active centres such as atoms, molecules or ions that can be excited to higher energy states and can amplify light by stimulated emission. It is normally enclosed within an optical resonator.
Common forms of active media include:
Gases or mixtures of gases.
Crystals or glasses doped with suitable ions.
Liquids containing laser dyes.
Semiconductor junctions.
2.2 Pumping source
A pump source supplies energy to the active medium and raises particles from lower states to excited states. The method is called pumping. A solid laser is commonly pumped with intense light from a flash lamp or another laser. Gas lasers are often pumped by an electric discharge, typically at several kilovolts per metre.
Other pumping methods include:
Inelastic atom-atom or electron-atom collisions.
Direct current injection across a semiconductor junction.
Chemical reactions in liquid or gas systems.
Optical pumping using an intense lamp or another laser.
2.3 Optical cavity
The optical cavity is formed by two mirrors placed on a common optical axis. One mirror is highly reflecting; the other is partially transmitting. Photons travel repeatedly through the active medium, causing further stimulated emission. The partially transmitting mirror allows a fraction of the amplified radiation to emerge as the laser beam. Mirrors may use metallic or dielectric coatings.
Ruby Laser
The Ruby laser was the first successful solid-state laser. It was demonstrated by Theodore H. Maiman in 1960 and operates as a three-level laser system. Its output is normally pulsed.
3.1 Construction
Figure 3. Schematic construction of a Ruby laser.
The active medium is a synthetic ruby crystal: aluminium oxide, Al₂O₃, doped with a small concentration, approximately 0.05%, of trivalent chromium ions, Cr³⁺. Chromium ions replace some Al³⁺ ions in the crystal lattice and act as the active centres. Aluminium and oxygen form the host lattice; the chromium ions provide the laser action and also give ruby its red colour.
The crystal is made into a cylindrical rod, typically about 5 cm long and 1 cm in diameter in the laboratory arrangement shown in the source notes. Its end faces are polished flat, parallel and normal to the axis. One end is fully reflecting and the other is partially reflecting.
A helical xenon flash lamp surrounds the rod and is connected to a high-voltage pulsed power supply. A reflecting enclosure directs pump light toward the rod. Because much of the pump energy becomes heat, a suitable cooling arrangement is required.
3.2 Energy-level scheme
Figure 4. Simplified three-level energy scheme of the Ruby laser.
Replacement of Al³⁺ by Cr³⁺ produces broad absorption bands in the blue and green regions of the visible spectrum. In the simplified diagram, E₁ is the ground state, E₃ represents the broad pump band and E₂/E₂′ represent metastable states.
When the flash lamp is fired, blue and green pump light is absorbed by Cr³⁺ ions, raising them from E₁ to the broad absorption band E₃. The ions then lose energy to the crystal lattice and fall rapidly to the metastable states by non-radiative transitions. The energy released during this step appears as heat.
The metastable level has a lifetime of the order of milliseconds, much longer than an ordinary excited state. Intense pumping therefore allows more ions to accumulate in the metastable state than remain in the ground state, producing population inversion.
3.3 Working and laser output
A spontaneously emitted photon near 694.3 nm can initiate stimulated emission from other excited Cr³⁺ ions. The new photons have the same frequency, phase, direction and polarization. Photons travelling along the rod axis are reflected repeatedly by the end mirrors, so the intensity grows rapidly. A short, intense, coherent red pulse emerges through the partially reflecting mirror.
Because the pump source is a flash lamp, Ruby-laser output is not smooth. It often appears as a train of narrow, high-intensity pulses called spikes. Each spike may last approximately 10⁻⁶ s or less.
Figure 5. Schematic spiking in the output of a pulsed Ruby laser.
3.4 Drawbacks and applications
Important drawbacks of the Ruby laser are:
A high pump-light threshold is required because it is a three-level laser.
A significant fraction of the pump energy is converted into heat.
Continuous pumping is difficult with the conventional xenon flash-lamp arrangement, so the laser normally operates in pulses.
Modern Ruby-laser cavities usually use external mirrors, one highly reflecting and the other partially reflecting. Typical pulse energies range from about 15 J to 100 J. Ruby lasers are high-power sources of pulsed coherent radiation and have been used in interferometry, plasma diagnostics, holography and laser ranging.
Reference distances noted in the source: Mean Earth-Moon distance: approximately 384,400 km. Mean Earth-Sun distance: approximately 149,600,000 km.
Helium-Neon Laser
The Helium-Neon, or He-Ne, laser was the first successful gas laser and one of the most widely used four-level lasers. Ali Javan and collaborators achieved the first He-Ne laser operation in 1960; the work was reported in 1961. The familiar visible output wavelength is 632.8 nm.
4.1 Construction
Figure 6. Schematic construction of a Helium-Neon laser.
The active medium is a low-pressure mixture of helium and neon gases, with helium in excess. The source notes use a He:Ne ratio of approximately 5:1; practical mixtures commonly fall in the range 5:1 to 10:1. The mixture is enclosed in a narrow glass discharge tube.
Electrodes connected to a high-voltage power supply establish an electric discharge through the gas. The tube ends are sealed by mirrors that form the optical cavity. One mirror is highly reflecting, while the output mirror transmits a small fraction, about 1% in the arrangement described in the notes, of the laser intensity.
4.2 Energy transfer and population inversion
Figure 7. Simplified energy-transfer and laser-transition scheme of a He-Ne laser.
The electric discharge ionizes part of the gas and accelerates free electrons. Inelastic collisions raise helium atoms to long-lived metastable states near 20.61 eV and 20.66 eV above the helium ground state.
These helium metastable energies are very close to selected excited states of neon. During nearly resonant collisions, helium transfers its excitation energy to neon. This mechanism populates the upper neon laser level much more efficiently than direct electron impact alone.
The transition from the upper neon level to the lower laser level is allowed and produces the 632.8 nm line. The lower laser level is rapidly depopulated through lower states to the ground state. Consequently, the upper level becomes more heavily populated than the lower level, establishing the population inversion required for stimulated emission.
4.3 Frequency and wavelength of the red laser line
For the simplified levels used in the notes:
hν = E₂ - E₁ = (20.66 - 18.70) eV = 1.96 eV
ν = (E₂ - E₁)/h = 1.96/(4.1357 × 10⁻¹⁵) ≈ 4.74 × 10¹⁴ Hz
λ = c/ν = hc/(E₂ - E₁) ≈ 632.8 nm = 6328 Ã…
Correction: The handwritten numerical frequency was written with an incorrect exponent. The physically correct value for 632.8 nm light is approximately 4.74 × 10¹⁴ Hz.
4.4 Optical amplification and output
Light at 632.8 nm travels repeatedly between the two cavity mirrors. On each pass, it induces further stimulated emission and the resonant field grows. The highly reflecting mirror returns almost all of the light, while the partially reflecting mirror transmits a small fraction as a narrow, monochromatic laser beam.
4.5 Merits of the He-Ne laser
It is a well-established and widely used gas laser that provides a few milliwatts of continuous-wave visible output.
It is comparatively simple, inexpensive and reliable.
Its excellent beam quality makes it useful in student laboratories, alignment systems and optical experiments.
By choosing mirrors that are highly reflecting only over a selected wavelength range, a desired transition can be favoured.
5. Gas Lasers Compared with Solid-State Lasers
The essential differences between the two lasers described in these notes are summarized below.
Feature | Ruby laser | Helium-Neon laser |
Active medium | Cr³⁺ ions in Al₂O₃ crystal | Low-pressure helium-neon gas mixture |
Level scheme | Three-level system | Four-level system |
Pumping | Optical pumping by xenon flash lamp | Electric discharge plus resonant He-to-Ne energy transfer |
Main output | Pulsed coherent red light | Continuous-wave coherent red light |
Wavelength | 694.3 nm | 632.8 nm |
Threshold | Relatively high | Relatively low |
Typical use | High-energy pulses, holography and ranging | Alignment, student laboratories and optical experiments |
Gas lasers generally give highly directional, narrow-line radiation because the gaseous medium is free from crystal imperfections and experiences less thermal distortion and scattering. Electric-discharge pumping can operate continuously throughout the gas. In addition, the rapidly emptied lower level of a four-level gas laser reduces the pump power required to maintain population inversion.
6. Conclusion
A three-level solid-state laser such as the Ruby laser usually obtains population inversion through intense optical pumping, often from a flash lamp. Because the lower laser level is the ground state, a large fraction of the active ions must be excited before amplification begins.
A four-level gas laser such as the He-Ne laser uses an electric discharge and resonant energy transfer to populate an upper neon state. The lower laser level is rapidly depopulated, so continuous operation and population inversion are easier to maintain. The sharp atomic levels of gases also favour efficient, monochromatic output.
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