THEORY EXAMINATION (SEM–IV) 2016-17 LASER SYSTEMS AND APPLICATIONS

LASER SYSTEMS AND APPLICATIONS (NOE043)

SECTION – A

(10 × 2 = 20 Marks | Short Answers)

(a) de-Broglie wavelength of an electron

For an electron of energy V eV:

λ=h2meV=12.27V A˚\lambda = \frac{h}{\sqrt{2meV}} = \frac{12.27}{\sqrt{V}} \ \text{Å}λ=2meV​h​=V​12.27​ A˚ 

(b) Objective of Davisson–Germer experiment

To experimentally verify the wave nature of electrons and confirm de-Broglie’s hypothesis through electron diffraction.

(c) Unmodified radiation in Compton scattering

Unmodified radiation refers to scattered X-rays having the same wavelength as incident radiation, occurring when photons scatter without energy transfer.

(d) Stimulated emission of radiation

It is the process in which an incident photon forces an excited atom to emit another photon of the same frequency, phase, and direction, forming the basis of laser action.

(e) Role of optical cavity in a laser

The optical cavity provides multiple reflections, enhances stimulated emission, ensures directionality, and helps in achieving population inversion.

(f) Why two-level pumping is not suitable for lasing

In a two-level system, population inversion cannot be achieved because absorption and stimulated emission occur at the same rate.

(g) Spiking in ruby laser

Spiking refers to initial high-intensity pulses produced due to rapid depletion and recovery of population inversion during laser start-up.

(h) Gain medium in excimer lasers

The gain medium is an excited dimer (excimer) such as ArF, KrF, or XeCl formed temporarily during laser action.

(i) Role of Q-switching

Q-switching allows storage of energy in the gain medium and its sudden release, producing very high-power, short laser pulses.

(j) Characteristics of a hologram

A hologram:

Stores amplitude and phase information

Produces a 3D image

Each part contains information of the whole object

SECTION – B

(Attempt Any Five | 5 × 10 = 50 Marks)

(a) Heisenberg Uncertainty Principle & Binding Energy

The uncertainty principle states:

ΔxΔp≥h4π\Delta x \Delta p \ge \frac{h}{4\pi}ΔxΔp≥4πh​

Significance:

For microscopic particles, uncertainty is significant

For macroscopic bodies, it is negligible

Binding Energy of Electron:
Using uncertainty principle, minimum energy of electron in atom is obtained, showing stable bound states exist.

(b) Components and Principle of Laser + Coherence Length

Main Components:

Active medium

Pumping source

Optical resonator

Principle:
Population inversion + stimulated emission → coherent laser beam.

Coherence Length:

L=cΔν=3×1083000=1×105 mL = \frac{c}{\Delta \nu} = \frac{3\times10^8}{3000} = 1\times10^5 \text{ m}L=Δνc​=30003×108​=1×105 m 

(c) Advantages of Four-Level Lasers & Threshold Power

Advantages:

Easier population inversion

Lower threshold pumping power

Continuous operation possible

Threshold Pumping Power (3-level):
Derived using rate equations; it is higher than four-level systems due to ground-state pumping.

(d) Classification of Lasers Based on Medium

Solid-state lasers (Ruby, Nd:YAG)

Gas lasers (He-Ne, CO₂)

Liquid lasers (Dye lasers)

Semiconductor lasers

Each has specific advantages and limitations regarding efficiency, wavelength range, and power.

(e) CO₂ Laser – Construction & Photon Calculation

Construction: Gas mixture of CO₂, N₂, He
Working: Energy transfer from N₂ → CO₂ → laser emission

Number of photons:

E=hcλE = \frac{hc}{\lambda}E=λhc​ N=PEN = \frac{P}{E}N=EP​

(Substituting given values gives total photons per second.)

(f) Mode Locking

Mode locking forces all longitudinal modes to oscillate in phase, producing ultra-short pulses (picoseconds).

(g) Dye Lasers

Dye lasers use organic dyes in liquid form as gain medium.

Features:

Wide tunability

High efficiency

Short pulse generation

(h) LIDAR – Principle & Applications

Principle:
Laser pulses are emitted and reflected from targets; distance is calculated using time of flight.

Applications:

Atmospheric monitoring

Range finding

Pollution measurement

Remote sensing

 SECTION – C

(Attempt Any Two | 2 × 15 = 30 Marks)

3) Particle in a One-Dimensional Box

Schrödinger Equation:

−h28π2md2ψdx2=Eψ-\frac{h^2}{8\pi^2m}\frac{d^2\psi}{dx^2}=E\psi−8π2mh2​dx2d2ψ​=Eψ

Eigenvalues:

En=n2h28mL2E_n=\frac{n^2h^2}{8mL^2}En​=8mL2n2h2​

For L = 1 Å:

E1=37.6 eV,E2=150.4 eVE_1 = 37.6\ \text{eV}, \quad E_2 = 150.4\ \text{eV}E1​=37.6 eV,E2​=150.4 eV

This proves energy levels are discrete.

4) Solid-State Lasers & Alexandrite Laser

Alexandrite Laser:

Tunable solid-state laser

Chromium-doped BeAl₂O₄ crystal

Advantages over Nd:YAG:

Wider tunability

Higher peak power

Better thermal properties

Applications: medical, spectroscopy, research.

5)

(i) Lasers in Drilling, Cutting & Melting

Lasers provide high precision, minimal heat-affected zone, and non-contact machining.

(ii) Laser Characteristics for Length Measurement

High coherence

Monochromaticity

Directionality

Method: Interferometry using stable laser source.