Unit 2: Lasers and Applications

I. Orientation — Basis of laser operation

A laser—Light Amplification by Stimulated Emission of Radiation—converts supplied energy into an intense, coherent, and directional beam through stimulated emission inside an optical resonator.

• Governing principle: An incident photon can induce an excited atom to emit a second photon identical in frequency, phase, direction, and polarization.
• Essential requirements:
  • An active medium containing suitable atoms, ions, molecules, or charge carriers.
  • A pumping source that supplies energy.
  • Population inversion between selected energy levels.
  • A resonant cavity providing optical feedback.
• Photon energy:

E = hν = hc/λ

Here, E is photon energy, h is Planck’s constant, ν is frequency, c is the speed of light, and λ is wavelength.

A. Fundamentals of laser

Laser operation is controlled amplification rather than merely intense spontaneous illumination.

• Amplification: Stimulated photons trigger further identical emissions, producing a chain reaction.
• Threshold condition: Lasing begins when optical gain compensates for absorption, scattering, mirror transmission, and other cavity losses.
• Output formation: One cavity mirror is nearly fully reflecting; the partially reflecting output coupler transmits a fraction of the amplified radiation.
• Distinction from ordinary light: A lamp emits independently phased photons in many directions and wavelengths, whereas a laser organizes emission through feedback and stimulation.

II. Atomic Processes — Production and interaction of photons

Atomic energy structure determines whether incident radiation is absorbed or emitted and whether useful optical amplification can occur.

A. Energy levels in atoms

Bound electrons occupy discrete permitted energies rather than a continuous range.

• Transition condition:

E₂ − E₁ = hν

Here, E₁ and E₂ are lower and upper energy levels, and ν is the absorbed or emitted radiation frequency.

• Ground state: The lowest permitted energy state is normally the most populated.
• Excited state: Energy supplied by light, electricity, collisions, or chemical reactions raises a particle to a higher level.
• Level broadening: Collisions, finite state lifetime, and Doppler motion give practical transitions a small frequency width.

B. Radiation-matter interaction

Radiation interacts resonantly with matter when photon energy matches the separation between two allowed states.

• Possible events: The three basic processes are absorption, spontaneous emission, and stimulated emission.
• Transition probability: It depends on the atomic states, radiation energy density, and quantum-mechanical selection rules.
• Energy conservation: Every upward or downward transition exchanges energy hν with the electromagnetic field.

C. Absorption of light

Absorption transfers photon energy to a particle initially occupying a lower energy level.

• Process: An atom at E₁ absorbs a photon of frequency ν and moves to E₂.
• Rate:

Rabs = N₁B₁₂ρ(ν)

Here, Rabs is the absorption rate per unit volume, N₁ is the lower-level population, B₁₂ is the Einstein absorption coefficient, and ρ(ν) is spectral energy density.

• Laser consequence: Strong lower-level population causes absorption and opposes net optical gain.

D. Spontaneous emission of light

Spontaneous emission occurs when an excited particle decays without an external triggering photon.

• Rate:

Rsp = N₂A₂₁

Here, Rsp is the spontaneous-emission rate, N₂ is the upper-level population, and A₂₁ is the spontaneous-emission coefficient.

• Lifetime: For a single decay channel, the mean excited-state lifetime is τ = 1/A₂₁.
• Character: Emitted photons have random phases, directions, and polarization, producing incoherent radiation.
• Role in lasers: An initial spontaneous photon can seed stimulated amplification along a cavity mode.

E. Stimulated emission of light

Stimulated emission produces a second photon when resonant radiation encounters an excited particle.

• Rate:

Rst = N₂B₂₁ρ(ν)

Here, Rst is the stimulated-emission rate and B₂₁ is the Einstein stimulated-emission coefficient; the other symbols retain their previous meanings.

• Photon identity: The emitted photon matches the stimulating photon in frequency, phase, direction, and polarization.
• Optical gain: Because one photon effectively becomes two, repeated stimulated transitions amplify light.
• Competition: Net amplification requires stimulated emission to exceed resonant absorption.

F. Population of energy levels

The population of a level is the number of active particles occupying that energy state.

• Thermal equilibrium:

N₂/N₁ = (g₂/g₁)exp[−(E₂−E₁)/(kT)]

Here, g₁ and g₂ are level degeneracies, k is Boltzmann’s constant, and T is absolute temperature.

• Normal distribution: Since E₂ > E₁, thermal equilibrium generally gives fewer particles in the upper state.
• Dynamic population: Pumping raises particles, while radiative and non-radiative decay remove them from excited levels.

G. Einstein A and B coefficients

Einstein coefficients quantify the probabilities of the three radiation–matter interactions.

• Coefficient meanings: A₂₁ describes spontaneous emission, B₂₁ stimulated emission, and B₁₂ absorption.
• Equilibrium relations:

g₁B₁₂ = g₂B₂₁
A₂₁/B₂₁ = 8πhν³/c³

Here, g₁ and g₂ are degeneracies; all remaining symbols have their previously defined meanings.

• Frequency dependence: The second relation shows that spontaneous emission becomes comparatively important at high frequencies.
• Physical implication: Absorption and stimulated emission are fundamentally linked rather than independently adjustable processes.

III. Conditions for Laser Oscillation — Gain, feedback, and pumping

Sustained laser action requires stored excitation, excess upper-state population, and repeated passage of resonant light through the active medium.

A. Metastable state

A metastable state is an excited level whose transition to lower levels is weak or quantum-mechanically restricted.

• Long lifetime: Its lifetime is commonly much longer than the roughly nanosecond lifetime of ordinary excited states.
• Energy storage: Pumped particles accumulate because they enter the state faster than they leave it.
• Laser importance: Accumulation makes population inversion achievable with practical pumping power.
• Example: Chromium ions in ruby remain about milliseconds in the metastable level before the 694.3 nm laser transition.

B. Population inversion

Population inversion is the non-equilibrium condition in which the upper laser level contains more appropriately weighted particles than the lower level.

• Gain condition:

N₂/g₂ > N₁/g₁

Here, N₁ and N₂ are level populations, while g₁ and g₂ are their degeneracies.

• Necessity: Without inversion, absorption equals or exceeds stimulated emission.
• Three-level system: The lower laser level is the ground state, so more than half the particles may need excitation.
• Four-level system: The lower laser level rapidly empties, allowing inversion at lower pump power.

C. Resonant cavity

A resonant cavity provides optical feedback by placing the active medium between two aligned mirrors.

• Mirror arrangement: One mirror is highly reflecting, while the output coupler is partially transmitting.
• Resonance condition:

2nL = qλ

Here, n is refractive index, L is cavity length, q is an integer mode number, and λ is vacuum wavelength.

• Mode selection: Only standing-wave frequencies satisfying the cavity condition receive strong repeated amplification.
• Directionality: Photons traveling near the cavity axis undergo the greatest number of passes and dominate the output.

D. Excitation mechanisms

Excitation mechanisms supply the external energy needed to create and maintain population inversion.

• Optical pumping: Flash lamps or other lasers excite solid-state media, as in ruby and Nd-YAG lasers.
• Electrical discharge: Electron collisions excite gas atoms, as in the He-Ne laser.
• Current injection: Forward bias injects electrons and holes into a semiconductor junction.
• Other methods: Chemical reactions, gas expansion, and electron beams are used in specialized high-power lasers.
• Efficiency requirement: Pump energy must exceed threshold losses without causing unacceptable heating or damage.

E. Lasing action

Lasing action is the complete regenerative sequence from pumping to coherent output.

• Sequence:
  1. Pumping raises particles to higher energy states.
  2. Rapid decay transfers them to a metastable upper laser level.
  3. Population inversion develops.
  4. A photon initiates stimulated emission.
  5. Cavity reflections multiply resonant photons.
  6. The output coupler releases part of the beam.
• Threshold: Below threshold, spontaneous emission dominates; above threshold, stimulated emission rises sharply.
• Operation modes: Lasers may operate continuously or in pulses through techniques such as Q-switching.

F. Properties of laser

Laser radiation has distinctive spatial, temporal, spectral, and intensity characteristics.

• Monochromaticity: Emission occupies a narrow spectral width around a principal wavelength.
• Coherence: Photons maintain predictable phase relationships over time and across the beam.
• Directionality: Small angular divergence allows the beam to travel long distances with limited spreading.
• High intensity: Energy concentrated into a narrow beam and short pulse can produce very high power density.
• Polarization: Cavity design and optical components can produce a strongly polarized output.
• Focusability: Low divergence permits focusing to microscopic spots for machining and data storage.

IV. Representative Laser Systems — Construction and operation

Laser systems are classified mainly by active medium and pumping method, which determine wavelength, efficiency, output mode, and application.

A. Ruby laser

The ruby laser is a three-level, optically pumped solid-state laser.

• Active medium: Synthetic sapphire, Al₂O₃, contains approximately 0.05% trivalent chromium ions, Cr³⁺.
• Pumping: A xenon flash lamp surrounds the ruby rod and excites chromium ions into broad absorption bands.
• Transition: Non-radiative decay fills a metastable level; stimulated transition to the ground state produces red light at 694.3 nm.
• Output: Its high threshold favors intense pulsed operation.
• Limitation: Three-level operation makes it less efficient than common four-level lasers.

B. Nd-YAG laser

The Nd-YAG laser is a four-level solid-state laser using neodymium ions in yttrium aluminium garnet.

• Active medium: Nd³⁺ ions are embedded in Y₃Al₅O₁₂.
• Pumping: Flash lamps or laser diodes, commonly near 808 nm, excite the neodymium ions.
• Output transition: The principal infrared wavelength is 1064 nm.
• Advantages: Four-level operation gives lower threshold, good efficiency, and continuous or pulsed output.
• Uses: High beam quality supports welding, drilling, range finding, and precision medical procedures.

C. He-Ne laser

The He-Ne laser is a gas laser pumped by an electrical discharge through a helium–neon mixture.

• Energy transfer: Excited helium atoms collide resonantly with neon atoms and populate neon’s upper laser levels.
• Transition: The best-known output is the red 632.8 nm line, although infrared transitions also occur.
• Construction: A narrow discharge tube, Brewster windows, and two cavity mirrors form the optical system.
• Performance: It provides stable, coherent, low-power continuous output with excellent beam quality.
• Applications: Alignment, interferometry, barcode scanning, and laboratory demonstrations exploit its stability.

D. Semiconductor laser

A semiconductor laser produces light through electron–hole recombination in a forward-biased direct-band-gap junction.

• Active region: Injected electrons and holes recombine in a thin junction or quantum-well layer.
• Photon energy: The approximate emitted energy equals the band gap, so λ ≈ hc/Eg, where Eg is band-gap energy.
• Cavity: Cleaved parallel crystal faces or fabricated gratings provide optical feedback.
• Advantages: Semiconductor lasers are compact, efficient, directly modulatable, and compatible with integrated electronics.
• Examples: GaAs-based devices emit in the near infrared; other compound semiconductors cover visible and communication wavelengths.

V. Technological Use — Engineering and wavefront recording

The controllability of laser wavelength, phase, direction, and power enables precision measurement, manufacturing, communication, and three-dimensional imaging.

A. Applications of laser in engineering

Engineering applications exploit either concentrated energy or coherent, accurately directed radiation.

• Manufacturing: Focused lasers cut, drill, weld, engrave, harden, and additively process metals, ceramics, and polymers.
• Metrology: Interferometers measure displacement, surface flatness, strain, and vibration with wavelength-scale sensitivity.
• Communication: Semiconductor lasers carry high-bandwidth signals through low-loss optical fibres.
• Surveying and sensing: Laser range finders and LiDAR determine distance from pulse travel time, d = ct/2, where d is distance and t is round-trip time.
• Electronics: Lasers support photolithography, resistor trimming, circuit inspection, and optical data storage.
• Safety consideration: High-power and invisible beams require wavelength-rated eyewear, enclosures, and controlled beam paths.

B. Holography

Holography records and reconstructs both the amplitude and phase information of light scattered by an object.

• Recording: A coherent laser beam is divided into an object beam and a reference beam; their interference pattern is stored on a photosensitive or digital medium.
• Hologram: The recorded pattern resembles fringes rather than an ordinary image because it encodes wavefront information.
• Reconstruction: Illumination by the original or equivalent reference beam diffracts from the pattern and recreates the object wavefront.
• Three-dimensional effect: Different viewing positions receive different wavefront directions, producing parallax and depth.
• Types: Transmission holograms are viewed using transmitted laser light, while reflection holograms can often be viewed using suitable white light.
• Engineering uses: Holographic interferometry reveals microscopic deformation, vibration, stress, and defects through changes in interference fringes.