Unit 2 - Notes

PHY109

Unit 2: Lasers and Applications

1. Fundamentals of Laser

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

Energy Levels in Atoms

According to quantum mechanics, electrons in an atom cannot possess arbitrary energy. They exist in discrete energy states or levels.

Ground State ( $E_1$ ): The lowest energy state where electrons usually reside. It is the most stable state.
Excited State ( $E_2$ ): Higher energy states. Electrons occupy these states only when supplied with external energy. The lifetime of a typical excited state is very short ( $\approx 10^{-8}$ seconds).
Transition: When an electron jumps from $E_2$ to $E_1$ , it releases energy as a photon ( $E = E_2 - E_1 = h\nu$ ).

2. Radiation-Matter Interaction

There are three distinct processes by which radiation interacts with matter regarding energy transitions.

A. Absorption of Light

An atom in the ground state ( $E_1$ ) absorbs a photon of energy $h\nu$ and transitions to an excited state ( $E_2$ ).

Condition: $h\nu = E_2 - E_1$
Process: $Atom + Photon \rightarrow Excited Atom$
The rate of absorption depends on the number of atoms in the ground state ( $N_1$ ) and the energy density of the incident radiation.

B. Spontaneous Emission

An atom in the excited state ( $E_2$ ) is unstable. It eventually returns to the ground state ( $E_1$ ) on its own, without any external inducement, emitting a photon.

Process: $Excited Atom \rightarrow Atom + Photon$
Characteristics: The emitted photons have random phase and direction. This produces incoherent light (e.g., standard light bulbs).

C. Stimulated Emission

This is the principle behind the LASER. If an atom is already in an excited state ( $E_2$ ), and a photon of energy $h\nu = E_2 - E_1$ passes by, it induces the atom to decay to $E_1$ immediately.

Process: $Excited Atom + Photon \rightarrow Atom + 2 Photons$
Result: One photon enters, two photons leave.
Characteristics: The emitted photon is identical to the incident photon in frequency, phase, polarization, and direction. This results in coherent amplification.

3. Einstein A and B Coefficients

Einstein established the mathematical relationship between the three processes. Let $N_1$ and $N_2$ be the number of atoms per unit volume in states $E_1$ and $E_2$ , and $\rho(\nu)$ be the energy density of radiation.

Rate of Stimulated Absorption: $R_{abs} = B_{12} N_1 \rho(\nu)$
Rate of Spontaneous Emission: $R_{spont} = A_{21} N_2$
Rate of Stimulated Emission: $R_{stim} = B_{21} N_2 \rho(\nu)$

Where:

$A_{21}$ = Einstein Coefficient for Spontaneous Emission.
$B_{12}$ = Einstein Coefficient for Absorption.
$B_{21}$ = Einstein Coefficient for Stimulated Emission.

Relations derived by Einstein:

$B_{12} = B_{21}$ (Probability of absorption equals probability of stimulated emission).
$\frac{A_{21}}{B_{21}} = \frac{8\pi h \nu^3}{c^3}$

Significance:
The ratio of spontaneous to stimulated emission is proportional to $\nu^3$ . This means at optical frequencies, spontaneous emission is dominant naturally. To make stimulated emission dominant (for lasing), we must create a Population Inversion.

4. Conditions for Lasing Action

To achieve laser output, specific conditions must be met to ensure stimulated emission dominates over absorption and spontaneous emission.

Population of Energy Levels (Boltzmann Law)

Under thermal equilibrium, the population of atoms decreases exponentially with energy:

N = N_0 e^{-E/k_B T}

Therefore, naturally,

N_1 > N_2

. Most atoms are in the ground state.

Metastable State

A normal excited state has a short lifetime ( $10^{-8} s$ ). A Metastable State is an excited state with a much longer lifetime ( $\approx 10^{-3} s$ ).

It acts as a temporary "storage" for electrons, allowing them to accumulate at the upper energy level.

Population Inversion

This is a non-equilibrium state where the number of atoms in the excited state is greater than the ground state ( $N_2 > N_1$ ).

Without inversion, incoming photons are simply absorbed.
With inversion, incoming photons trigger a cascade of stimulated emissions (Avalanche effect).

Excitation Mechanisms (Pumping)

The process of supplying energy to the medium to transfer atoms from lower to higher energy levels to achieve population inversion is called Pumping.

Optical Pumping: Using a light source (flash lamp) - Used in Ruby, Nd:YAG.
Electrical Discharge: High voltage accelerates electrons which collide with atoms - Used in He-Ne, $CO_2$ lasers.
Direct Pumping: Forward biasing a p-n junction - Used in Semiconductor lasers.

Resonant Cavity (Optical Resonator)

The active medium is placed between two mirrors:

High Reflector ( $M_1$ ): 100% reflecting.
Output Coupler ( $M_2$ ): Partially reflecting (e.g., 90-99%).
- Photons bounce back and forth, stimulating more emissions on each pass (Positive Feedback).
- Only light moving parallel to the axis remains in the cavity; other light escapes.
- A portion escapes through $M_2$ as the useful laser beam.

5. Properties of Laser Light

Monochromaticity: The light emitted has a single specific wavelength (or a very narrow bandwidth).
Coherence:
- Temporal Coherence: The waves maintain phase correlation over time.
- Spatial Coherence: The waves maintain phase correlation over different points in space (cross-section of the beam).
Directionality: The beam spreads very little (low divergence) and travels long distances without significant widening.
High Intensity: Immense energy is concentrated in a very small spatial region.

6. Specific Laser Systems

A. Ruby Laser (First successful laser - T. Maiman, 1960)

Type: Solid State, 3-Level Laser.
Active Medium: Synthetic Ruby Rod ( $Al_2O_3$ doped with $0.05\%$ Chromium ions $Cr^{3+}$ ).
Pumping Source: Xenon flash lamp (Optical Pumping).
Working:
1. Flash lamp excites $Cr^{3+}$ ions from ground state ( $E_1$ ) to high energy bands ( $E_3$ ).
2. Ions decay rapidly (non-radiative) to the Metastable State ( $E_2$ ).
3. Population inversion occurs between $E_2$ and $E_1$ .
4. Stimulated emission occurs from $E_2 \rightarrow E_1$ .
Output: Pulsed Red Light ( $\lambda = 694.3$ nm).
Drawback: High power consumption; pulsed only (not continuous).

B. Nd-YAG Laser

Type: Solid State, 4-Level Laser.
Active Medium: Yttrium Aluminum Garnet (YAG) crystal doped with Neodymium ( $Nd^{3+}$ ) ions.
Pumping: Krypton arc lamp or Laser Diodes.
Working:
1. $Nd^{3+}$ ions pumped to $E_4$ .
2. Decay to metastable state $E_3$ .
3. Lasing transition occurs between $E_3$ and $E_2$ (where $E_2$ is an intermediate state above ground).
4. $E_2$ decays rapidly to Ground ( $E_1$ ), keeping $E_2$ empty.
Advantage: Easier to maintain population inversion than 3-level systems (because lower laser level is not the ground state).
Output: Infrared ( $\lambda = 1.064 \mu m$ ). Can be Continuous Wave (CW) or Pulsed.

C. He-Ne Laser

Type: Gas Laser, 4-Level.
Active Medium: Mixture of Helium and Neon (10:1 ratio) in a quartz tube.
Role of Gases: Helium is the pumping agent; Neon is the lasing agent.
Pumping: Electrical Discharge.
Working:
1. Electrons collide with Helium atoms, exciting them to metastable states $F_2$ and $F_3$ .
2. Resonant Energy Transfer: Helium atoms collide with Neon atoms, transferring energy because He states match Ne excited states ( $E_4, E_6$ ).
3. Population inversion is achieved in Neon.
4. Transition from Neon levels $E_6 \rightarrow E_3$ produces the laser light.
Output: Continuous Red Light ( $\lambda = 632.8$ nm).
Uses: Lab experiments, barcode scanners, alignment.

D. Semiconductor (Diode) Laser

Type: Solid State, Injection Laser.
Active Medium: p-n junction diode (e.g., Gallium Arsenide - GaAs).
Pumping: Direct pumping (Forward Bias Voltage).
Working:
1. Heavily doped p and n regions.
2. When forward biased, electrons are injected into the conduction band and holes into the valence band at the junction (Active Region).
3. Population inversion exists between the conduction band and valence band.
4. Recombination of electron and hole releases a photon ( $E_g = h\nu$ ).
5. Polished ends of the crystal act as the cavity mirrors.
Output: Depends on bandgap. GaAs produces IR ( $\approx 840$ nm). GaAsP produces visible red.
Advantages: Tiny, high efficiency, cheap, easily modulated.

7. Applications of Lasers in Engineering

1. Mechanical / Manufacturing:

Laser Cutting/Drilling: Precise cutting of metals and ceramics.
Laser Welding: High precision welding (e.g., in electronics or automotive) with minimal heat-affected zones.

2. Communication:

Fiber Optics: Semiconductor lasers serve as the light source for carrying data over long distances with low loss.

3. Medical:

Ophthalmology: LASIK eye surgery (cornea reshaping).
Surgery: Laser scalpel for bloodless surgery (cauterizes as it cuts).

4. Metrology & Surveying:

LIDAR: Remote sensing for mapping and autonomous vehicles.
Interferometry: Measuring extremely small distances or vibrations.

5. Consumer Electronics:

Barcode readers, Laser printers, Optical disk drives (CD/DVD/Blu-ray).

8. Holography

Definition: Holography (Greek holos = whole, graph = writing) is a technique used to record and reconstruct a 3D image of an object. Unlike photography which records only intensity, holography records both the intensity and phase of light.

Principle: Based on Interference and Diffraction.

Construction of a Hologram (Recording)

A laser beam is split into two parts:
- Reference Beam: Goes directly to the photographic plate.
- Object Beam: Illuminates the object and reflects onto the photographic plate.
The two beams superimpose on the plate.
Due to coherence, they create an interference pattern (constructive and destructive interference zones).
This pattern is recorded on the film. The developed film is called a Hologram. It looks like random noise to the naked eye.

Reconstruction of the Image

The hologram is illuminated by the Reference Beam (same wavelength and angle as recording).
The hologram acts as a diffraction grating.
The light diffracts to reconstruct the wavefront that originally came from the object.
Result: The observer sees a virtual 3D image appearing behind the hologram (parallax exists—you can look around the object).

Comparison: Photography vs. Holography

Feature	Photography	Holography
Dimensions	2D	3D
Information	Amplitude (Intensity) only	Amplitude and Phase
Lens	Required	Not required (Lensless)
Film Fragment	Destroying film destroys image	Small piece can reconstruct whole image