Unit 2: Lasers and Applications - Subjective Questions

LASER stands for Light Amplification by Stimulated Emission of Radiation. It is a device that produces an intense, coherent, monochromatic, and highly directional beam of light.

The fundamental principle is stimulated emission. When an atom in an excited state interacts with a photon having energy

the atom is stimulated to return to the lower state . It emits another photon identical to the incident photon in frequency, phase, direction, and polarization.

The essential requirements of a laser are:

• Active medium: Provides atoms or molecules capable of stimulated emission.
• Pumping source: Supplies energy to excite the active medium.
• Population inversion: Ensures that more atoms occupy the upper laser level than the lower level.
• Optical resonator: Amplifies light through repeated reflection.

When optical gain exceeds cavity losses, a sustained laser beam is produced through the partially reflecting mirror.

Electrons in an atom can occupy only certain discrete energy states called energy levels. An electron cannot normally possess energy between two allowed levels.

If an electron moves between levels and , the energy of the absorbed or emitted photon is

where is Planck's constant and is the photon frequency.

• Absorption spectrum: An electron absorbs a photon and moves from a lower level to a higher level. Only photons whose energies match allowed energy differences are absorbed.
• Emission spectrum: An excited electron returns to a lower level and emits a photon of a definite frequency.
• Ground state: The lowest available energy state.
• Excited state: Any state with energy greater than the ground-state energy.

Because each element has a unique set of energy levels, it produces a characteristic line spectrum. Laser transitions also occur between selected discrete energy levels.

Consider two atomic energy levels and , where and . Radiation interacts with matter through three basic processes:

1. Absorption: An atom in absorbs a photon of energy and moves to . The incident radiation loses one photon.
2. Spontaneous emission: An atom in returns to without external stimulation and emits a photon. Its direction, phase, and polarization are random.
3. Stimulated emission: An incident photon of energy induces an excited atom to return to . The emitted photon is identical to the incident photon in frequency, phase, direction, and polarization.

Absorption reduces radiation intensity, while stimulated emission amplifies it. Spontaneous emission generally produces incoherent light, whereas stimulated emission is responsible for the coherent output of a laser.

In absorption, an atom initially in the lower energy state absorbs a photon and moves to the upper state . The condition for resonant absorption is

If is the population of the lower state and is the spectral energy density of incident radiation, the number of absorption transitions per unit time is

where is the Einstein coefficient of absorption.

Important features are:

• The absorption rate is proportional to the lower-state population.
• It is proportional to the radiation energy density.
• Absorption occurs efficiently only near the transition frequency.
• Photon energy is transferred to the atom.

In ordinary thermal equilibrium, absorption usually dominates stimulated emission because the lower energy level contains more atoms than the upper level.

Here, is the Einstein coefficient of spontaneous emission, is the coefficient of stimulated emission, and is the upper-state population. Stimulated emission is the central process underlying laser operation.

At thermal equilibrium, the populations of two levels and obey the Boltzmann distribution:

where and are level populations, and are degeneracies, is Boltzmann's constant, and is absolute temperature.

For non-degenerate levels,

Thus, under ordinary equilibrium conditions, the lower level contains more atoms than the upper level. Population inversion requires

or, more generally, . This cannot be achieved at positive thermal equilibrium. External energy must therefore be supplied through pumping. Population inversion is a non-equilibrium condition and is essential because it allows stimulated emission to exceed absorption, resulting in net optical gain.

Consider atoms in thermal equilibrium with radiation. Let and be populations of levels and , having degeneracies and .

The upward absorption rate is

The total downward rate is the sum of spontaneous and stimulated emissions:

At equilibrium, , so

Therefore,

Using the Boltzmann relation,

and comparing with Planck's radiation law,

we obtain

and

For non-degenerate levels, . These relations show that absorption and stimulated emission have equal probabilities for equal degeneracies, while spontaneous emission becomes more significant at higher frequencies.

A metastable state is an excited energy state with an unusually long lifetime, typically about , compared with about for an ordinary excited state. Atoms can therefore accumulate in a metastable state.

Population inversion is the condition in which the population of the upper laser level exceeds that of the lower laser level:

Their importance is as follows:

• Pumping raises atoms from the ground state to higher excited states.
• These atoms rapidly decay to the metastable state without significant laser emission.
• The long lifetime allows a large number of atoms to accumulate there.
• This accumulation establishes population inversion between the metastable upper laser level and a lower level.
• Under population inversion, stimulated emission exceeds absorption and optical amplification occurs.

A practical laser is usually designed as a three-level or four-level system because sustained population inversion is impossible in a simple two-level system under steady resonant pumping.

An optical resonant cavity consists of the active medium placed between two aligned mirrors:

• One mirror is almost fully reflecting.
• The other is partially reflecting and acts as the output coupler.

Photons traveling along the cavity axis are reflected repeatedly through the active medium. Each passage causes further stimulated emissions, producing optical amplification. The cavity performs the following functions:

• Provides positive optical feedback.
• Increases the effective interaction length between light and the active medium.
• Selects photons traveling nearly parallel to the axis, improving directionality.
• Supports only certain longitudinal resonant modes.
• Allows part of the amplified light to emerge as the laser output.

For a cavity of length and refractive index , the resonance condition is

where is an integer. The frequency spacing between adjacent longitudinal modes is

Laser oscillation occurs when the round-trip optical gain equals or exceeds the total round-trip losses.

Pumping is the process of supplying external energy to the active medium to produce population inversion. Important mechanisms include:

• Optical pumping: Light from a flash lamp or another laser excites the active atoms. It is used in ruby and many solid-state lasers.
• Electrical discharge: Energetic electrons collide with gas atoms and excite them. It is used in the He-Ne laser.
• Current injection: Forward-biased electrons and holes recombine across a semiconductor junction. It is used in semiconductor lasers.
• Energy-transfer pumping: One species is excited first and transfers energy through collisions to the lasing species. In the He-Ne laser, helium transfers energy to neon.
• Chemical pumping: Energy released in a chemical reaction creates excited molecules.
• Gas-dynamic pumping: Rapid expansion produces a non-equilibrium distribution of molecular energy levels.

The pumping method is selected according to the active medium, required output power, efficiency, and mode of operation.

The sequence of lasing action is:

1. The pumping source transfers energy to the active medium.
2. Atoms are raised to higher energy states.
3. They rapidly decay to a metastable upper laser level.
4. Atoms accumulate in this level and establish population inversion.
5. A spontaneously emitted photon traveling along the cavity axis initiates stimulated emission.
6. Identical photons move back and forth between the cavity mirrors.
7. Repeated stimulated emissions amplify the radiation.
8. A fraction escapes through the partially reflecting mirror as the laser beam.

If is the gain coefficient, is the active-medium length, and are mirror reflectivities, and is the internal loss coefficient, the round-trip threshold condition is

Therefore, the threshold gain is

Below threshold, losses exceed amplification. At threshold, gain balances losses. Above threshold, sustained coherent oscillation and measurable laser output are obtained.

Laser light has the following important properties:

• High monochromaticity: It has a very narrow range of wavelengths because laser emission occurs through selected transitions and cavity modes.
• High coherence: The emitted waves maintain a fixed phase relationship. Temporal coherence refers to phase correlation over time, while spatial coherence refers to correlation across the wavefront.
• High directionality: The beam has very small angular divergence because the resonator favors propagation along its axis.
• High intensity: Energy is concentrated within a narrow beam and a small spectral range. Focusing can produce extremely high power density.
• Definite polarization: Many lasers produce strongly polarized light because of cavity design or properties of the active medium.

Ordinary light is generally polychromatic, incoherent, highly divergent, comparatively weak, and randomly polarized. These distinctive laser properties enable precision measurement, high-speed communication, material processing, and holography.

A ruby laser is a three-level solid-state laser. Its active medium is synthetic ruby, consisting of doped with a small amount of ions.

Construction:

• A cylindrical ruby rod has optically polished parallel ends.
• One end is fully reflecting and the other is partially reflecting.
• A xenon flash lamp, usually arranged helically around the rod, provides optical pumping.
• A reflector directs lamp radiation into the rod.

Working:

1. Blue-green light from the flash lamp excites ions from the ground state to broad higher energy bands.
2. The ions rapidly make non-radiative transitions to a metastable level.
3. Population inversion is established between the metastable level and the ground state.
4. Stimulated emission occurs from the metastable level to the ground state.
5. The cavity amplifies the radiation, producing red light of wavelength approximately .

Limitations:

• As a three-level laser, more than half of the active ions must be excited.
• It requires intense pumping and has low efficiency.
• It commonly operates in pulsed mode rather than continuous mode.

The Nd:YAG laser is a four-level solid-state laser. Its active medium is yttrium aluminium garnet, , doped with ions.

Construction:

• An Nd:YAG crystal rod forms the active medium.
• It is optically pumped using a flash lamp or laser diode.
• The rod is placed between a fully reflecting mirror and a partially reflecting output mirror.
• Cooling is provided for high-power operation.

Operation:

1. Pump radiation excites ions from the ground level to higher pump bands.
2. The ions rapidly decay non-radiatively to the metastable upper laser level.
3. Population inversion develops between the metastable level and a lower laser level.
4. Stimulated transition produces radiation of wavelength approximately .
5. Ions in the lower laser level quickly decay to the ground state, maintaining population inversion.

Because it is a four-level laser, Nd:YAG has a lower threshold and higher efficiency than ruby. It can operate continuously or in pulses and is used in cutting, welding, drilling, range finding, medicine, and optical instrumentation.

The He-Ne laser is a gas laser that commonly emits visible red light at .

Construction:

• A narrow discharge tube contains a low-pressure mixture of helium and neon, typically with more helium than neon.
• Electrodes connected to a high-voltage supply produce an electrical discharge.
• Brewster windows reduce reflection and help produce plane-polarized light.
• A fully reflecting mirror and a partially reflecting mirror form the resonant cavity.

Working:

1. Electrons in the discharge excite helium atoms to metastable states.
2. Excited helium atoms collide with neon atoms.
3. Because certain helium and neon energy levels are nearly equal, resonant collisions transfer energy efficiently to neon.
4. Population inversion is established between suitable excited neon levels.
5. Stimulated transitions in neon produce laser radiation, including the red line.
6. Neon atoms subsequently decay through lower levels, while helium returns to the ground state.

The He-Ne laser provides a stable, continuous, coherent, low-divergence beam and is widely used in alignment, interferometry, barcode scanning, and laboratory experiments.

A semiconductor injection laser, or laser diode, converts electrical energy directly into coherent light. It is formed from a forward-biased - junction made of a direct-band-gap semiconductor such as GaAs.

Principle and construction:

• Under heavy forward bias, electrons are injected from the -region and holes from the -region into a thin active region.
• Opposite cleaved faces of the semiconductor act as partially reflecting mirrors, forming a Fabry-Pérot cavity.
• Heterojunction structures confine both carriers and photons to the active layer.

Working:

1. Carrier injection creates a high concentration of electrons and holes.
2. At sufficiently high current, population inversion develops between conduction-band and valence-band states.
3. Electron-hole recombination emits photons with energy approximately equal to the band gap:

4. Photons traveling parallel to the junction stimulate further recombination.
5. Above the threshold current, gain exceeds losses and coherent light emerges from a cleaved face.

Laser diodes are compact, efficient, rapidly modulated, and suitable for optical-fiber communication, optical storage, sensing, and printing.

Ruby requires strong pumping because its lower laser level is the ground state. Nd:YAG has a lower threshold due to its four-level scheme. He-Ne offers excellent frequency and beam stability, while semiconductor lasers provide the greatest compactness, electrical efficiency, and modulation speed.

Lasers are used extensively in engineering because of their high intensity, directionality, coherence, and monochromaticity.

• Material processing: High-power lasers perform cutting, welding, drilling, engraving, surface hardening, cladding, and additive manufacturing.
• Metrology: Interferometers measure displacement, surface flatness, strain, refractive index, and very small dimensional changes.
• Alignment and surveying: Low-divergence beams provide accurate reference lines for construction, tunneling, and machine installation.
• Optical communication: Semiconductor lasers transmit high-bandwidth data through optical fibers with low loss.
• Remote sensing: LIDAR measures distance, atmospheric composition, topography, and object velocity.
• Data storage and printing: Lasers read and write optical discs and are used in laser printers and barcode scanners.
• Electronics manufacturing: They trim resistors, mark components, inspect wafers, and fabricate microstructures.
• Non-destructive testing: Holographic interferometry reveals deformation, vibration, cracks, and structural defects.
• Range finding: Pulsed lasers determine distance using the time-of-flight relation

where is the round-trip travel time.

The choice of laser depends on wavelength, output power, pulse duration, beam quality, and the material being processed.

Holography is a technique for recording and reproducing both the amplitude and phase information of a light wave scattered by an object. The recorded interference pattern is called a hologram.

Recording procedure:

1. A coherent laser beam is expanded and divided by a beam splitter into an object beam and a reference beam.
2. The object beam illuminates the object and is scattered toward a photosensitive plate.
3. The reference beam reaches the same plate directly.
4. The two coherent beams interfere and produce a fine fringe pattern.
5. The photographic plate records the intensity distribution

where and represent the object and reference waves.

6. After development, the plate becomes a hologram.

Although a photographic detector directly records only intensity, interference with the known reference wave encodes the object's phase information in the fringe structure. High coherence and mechanical stability are essential during exposure.

Reconstruction:

• The developed hologram is illuminated with a beam similar to the original reference beam.
• The recorded fringe pattern behaves like a complex diffraction grating.
• It diffracts the incident light and reconstructs the original object wavefront.
• An observer sees a virtual three-dimensional image behind the hologram. Under suitable geometry, a real image may also be formed in front of it.
• Viewing the hologram from different positions reveals different perspectives and produces parallax.

Holography versus photography:

Applications include three-dimensional imaging, security labels, data storage, microscopy, pattern recognition, and holographic interferometry for detecting small deformations and vibrations.