Lasers Notes FE Sem 1 Applied Physics | Mumbai University

This module starts from the three ways light and atoms interact (absorption, spontaneous emission and stimulated emission) and shows why population inversion and a resonant cavity are needed to build a laser. It then defines coherence length and coherence time, lists the special characteristics of laser light, and explains the construction and working of the He-Ne laser and the fibre laser. Finally it connects these ideas to real engineering uses: LiDAR, barcode readers and laser cutting, welding and drilling of metals. It carries course outcome CO1 and is a regular source of 5 and 6 mark questions in the end semester paper.

Summary

Spontaneous and stimulated emission: An atom in an excited state \(E_2\) can return to a lower state \(E_1\) on its own after a short lifetime (about \(10^{-8}\) s), emitting a photon of energy \(h\nu = E_2 - E_1\) in a random direction and with random phase; this is spontaneous emission and it gives incoherent light, as in an ordinary lamp. If instead a photon of exactly energy \(h\nu = E_2 - E_1\) passes the excited atom, it can force the atom to drop to \(E_1\) and emit a second photon that has the same frequency, phase, direction and polarisation as the incoming one. This is stimulated emission; one photon becomes two identical photons, which is the basis of light amplification. Absorption (stimulated absorption) is the reverse process, where a photon of energy \(E_2 - E_1\) lifts an atom from \(E_1\) to \(E_2\).

Population inversion and pumping: In thermal equilibrium the Boltzmann law \(N_2/N_1 = e^{-(E_2-E_1)/kT}\) makes the upper level far less populated than the lower one, so absorption dominates over stimulated emission. Laser action needs population inversion, a non-equilibrium state in which \(N_2 > N_1\) for the pair of laser levels. It is achieved with the help of a metastable state, a level whose lifetime (about \(10^{-3}\) s) is much longer than that of ordinary excited levels, so atoms pile up in it. The process of supplying energy to lift atoms to higher levels is called pumping; common methods are optical pumping (flash lamp or another laser), electrical discharge (gas lasers such as He-Ne), direct electrical injection (semiconductor lasers) and chemical reactions.

Active medium, active centre and resonant cavity: The active medium is the material (gas, solid crystal, liquid dye, semiconductor or doped fibre) in which population inversion is created and amplification takes place. The active centres are the specific atoms, ions or molecules in that medium that actually make the laser transition, for example neon atoms in the He-Ne laser or erbium ions in an erbium fibre laser. The resonant (optical) cavity is a pair of mirrors facing each other on either side of the active medium, one fully reflecting and the other partially reflecting. It sends photons back and forth through the medium many times so that stimulated emission builds up, it selects only those waves travelling along the axis, and it supports only wavelengths that satisfy \(2L = m\lambda\). The useful beam leaves through the partially reflecting mirror.

Coherence length and coherence time: Real light is emitted as wave trains of finite length. The average time for which a wave train keeps a constant phase relation is the coherence time \(\tau_c\), and the length of the wave train in that time is the coherence length \(L_c = c\,\tau_c\). Coherence time is related to the spectral width by \(\tau_c \approx 1/\Delta\nu\), so \(L_c \approx \lambda^2/\Delta\lambda\). Ordinary sources have coherence lengths of micrometres to millimetres, while a stabilised laser can have a coherence length of many metres or even kilometres. Larger coherence length means a purer, more monochromatic source.

Characteristics of lasers: Laser light is highly monochromatic (very narrow \(\Delta\lambda\)), highly coherent (both temporal and spatial coherence), highly directional (divergence of only about a milliradian, given by \(\theta = (r_2 - r_1)/(d_2 - d_1)\)) and of very high intensity or brightness because the energy is concentrated in a narrow beam. Many lasers also give polarised output. These properties come directly from stimulated emission and the axial selection made by the resonant cavity.

He-Ne laser: It is a four-level gas laser. A quartz tube about 30 to 80 cm long and a few mm in bore is filled with helium and neon in a ratio of about 10:1 at low pressure; helium is the pumped gas and neon provides the active centres. A high voltage DC discharge excites helium atoms to the metastable levels 19.81 eV and 20.61 eV. These collide with ground state neon atoms and transfer their energy (resonant energy transfer) to neon levels at 19.78 eV and 20.66 eV, which creates population inversion in neon. Neon atoms then make laser transitions: 632.8 nm (red, visible, the commonly used line), 3.39 μm and 1.15 μm (infrared). The lower laser levels empty quickly by spontaneous emission to a lower metastable level, which in turn empties by collisions with the tube walls, so the narrow tube is important. Mirrors at the ends (or outside Brewster windows) form the cavity; Brewster windows give plane polarised output. The laser is continuous wave with an output of a few mW.

Fibre laser: Here the active medium is the core of an optical fibre doped with rare earth ions such as erbium (\(Er^{3+}\)), ytterbium (\(Yb^{3+}\)) or neodymium (\(Nd^{3+}\)). Pump light from semiconductor laser diodes (for example 980 nm for erbium) is launched into the fibre, usually into an inner cladding in a double-clad design so that a large pump power can be used. The pump creates population inversion in the dopant ions, and the emitted light is guided along the core by total internal reflection. Fibre Bragg gratings written into the fibre at its two ends act as the mirrors, one highly reflecting and one partially reflecting, forming the resonant cavity. An erbium fibre laser emits near 1550 nm and an ytterbium fibre laser near 1060 nm. Fibre lasers are compact, efficient, need little cooling because of their large surface area, and give a high quality beam that is easily delivered through a flexible fibre.

Applications: LiDAR (Light Detection and Ranging) sends short laser pulses, measures the time \(t\) for the reflected pulse to return and finds the distance as \(d = ct/2\); by scanning the beam it builds a 3D point cloud used in mapping, autonomous vehicles, forestry and atmospheric studies. A barcode reader sweeps a low power laser beam (He-Ne 632.8 nm or a red diode laser) across the code; dark bars absorb and white spaces reflect, a photodetector turns the reflected light into an electrical pulse train, and a decoder converts the bar widths into the product number. In metal work, the high intensity and focusability of lasers (CO2, Nd:YAG and fibre lasers) are used for cutting, welding, drilling fine holes, marking and surface hardening, with a small heat-affected zone and no tool wear.

Mind map

Working of the He-Ne laser step by step

Important definitions

Formulas

Key points to remember

• Three processes: absorption, spontaneous emission (incoherent) and stimulated emission (coherent, basis of the laser).
• LASER stands for Light Amplification by Stimulated Emission of Radiation.
• In equilibrium N2 is far less than N1; laser action needs population inversion, which is a non-equilibrium state.
• A metastable state is essential for population inversion; a two-level system cannot give steady inversion.
• He-Ne laser: helium is pumped, neon lases; He:Ne about 10:1; lines 632.8 nm, 1.15 μm and 3.39 μm; continuous output.
• He-Ne is a four-level laser, so inversion is easier than in a three-level laser like ruby.
• Narrow discharge tube helps the 1s metastable neon atoms return to the ground state through wall collisions.
• Brewster windows make the He-Ne output plane polarised.
• Fibre laser: rare-earth doped core, diode pumping, fibre Bragg gratings as mirrors, excellent beam quality and cooling.
• Coherence length of a laser is much larger than that of an ordinary source because its line width is very small.
• LiDAR distance = c x time / 2, because the pulse travels to the target and back.
• Lasers in metal work give narrow kerf, small heat-affected zone, no tool wear and easy automation.

Solved examples

Example 1. Calculate the ratio of populations of the upper and lower levels of the 632.8 nm transition of a He-Ne laser at room temperature (300 K). What does the result show?

Energy gap: \(\Delta E = hc/\lambda = (6.63\times10^{-34})(3\times10^{8})/(632.8\times10^{-9}) = 3.14\times10^{-19}\) J (about 1.96 eV). Thermal energy: \(kT = 1.38\times10^{-23}\times300 = 4.14\times10^{-21}\) J. Exponent: \(\Delta E/kT = 3.14\times10^{-19}/4.14\times10^{-21} = 75.9\). Ratio: \(N_2/N_1 = e^{-75.9} \approx 1.1\times10^{-33}\). The upper level is practically empty in thermal equilibrium, so population inversion cannot occur naturally; external pumping is essential.

Example 2. A He-Ne laser emits at 632.8 nm with a line width of 0.01 nm. Find the coherence length and coherence time.

Coherence length: \(L_c = \lambda^2/\Delta\lambda = (632.8\times10^{-9})^2/(0.01\times10^{-9}) = 4.004\times10^{-13}/1\times10^{-11} = 0.040\) m = 4.0 cm. Coherence time: \(\tau_c = L_c/c = 0.040/3\times10^{8} = 1.33\times10^{-10}\) s.

Example 3. A laser source has a frequency spread of 1 MHz. Find its coherence time and coherence length.

\(\tau_c = 1/\Delta\nu = 1/(1\times10^{6}) = 1\times10^{-6}\) s. \(L_c = c\tau_c = 3\times10^{8}\times1\times10^{-6} = 300\) m. Such a long coherence length is possible only with a highly monochromatic laser.

Example 4. A 5 mW He-Ne laser emits light of wavelength 632.8 nm. How many photons does it emit per second?

Energy of one photon: \(E = hc/\lambda = 3.14\times10^{-19}\) J. Number per second: \(n = P/E = 5\times10^{-3}/3.14\times10^{-19} = 1.59\times10^{16}\) photons per second.

Example 5. A LiDAR unit receives the echo of a laser pulse 2 μs after sending it. How far is the object?

The pulse travels to the object and back, so \(d = ct/2 = (3\times10^{8}\times2\times10^{-6})/2 = 300\) m.

Example 6. The spot diameters of a laser beam are 4 mm and 6 mm at distances 2 m and 4 m from the laser. Find the angular divergence.

Radii: \(r_1 = 2\) mm, \(r_2 = 3\) mm. \(\theta = (r_2 - r_1)/(d_2 - d_1) = (3-2)\times10^{-3}/(4-2) = 0.5\times10^{-3}\) rad = 0.5 mrad. (If the question defines divergence using diameters, \(\theta = (D_2 - D_1)/(d_2 - d_1)\) gives 1 mrad as the full angle; state the definition used.)

Example 7. A semiconductor laser has a band gap of 1.43 eV. Find the wavelength of the emitted light.

\(\lambda = hc/E_g = (6.63\times10^{-34}\times3\times10^{8})/(1.43\times1.6\times10^{-19}) = 1.989\times10^{-25}/2.288\times10^{-19} = 8.69\times10^{-7}\) m, about 869 nm (near infrared). Using the short cut \(\lambda(\mu m) = 1.24/E(eV)\) gives 0.867 μm, the small difference being rounding of constants.

Example 8. At what temperature would the population of the upper level be 1/e of the lower level for a transition of wavelength 694.3 nm?

Condition: \(N_2/N_1 = e^{-1}\), so \(\Delta E/kT = 1\) and \(T = \Delta E/k\). \(\Delta E = hc/\lambda = 1.989\times10^{-25}/694.3\times10^{-9} = 2.865\times10^{-19}\) J. \(T = 2.865\times10^{-19}/1.38\times10^{-23} = 2.08\times10^{4}\) K. Even such an enormous temperature only gives \(N_2 < N_1\); inversion is never reached thermally.

Important questions and answers

Q1. Distinguish between spontaneous and stimulated emission. (4 marks)

Spontaneous emission: (1) occurs on its own without any external photon; (2) emitted photons have random phase, direction and polarisation; (3) light is incoherent and polychromatic; (4) rate depends only on N2; (5) example: sodium lamp, LED. Stimulated emission: (1) needs an incident photon of energy \(E_2 - E_1\); (2) emitted photon is identical to the incident photon in frequency, phase, direction and polarisation; (3) light is coherent, monochromatic and directional; (4) rate depends on N2 and on the energy density of the incident radiation; (5) gives light amplification, as in a laser.

Q2. What is population inversion? Why is it necessary for laser action and how is it achieved? (5 marks)

Population inversion is the state in which more atoms are in a higher energy level than in a lower one (N2 > N1). In equilibrium the Boltzmann law \(N_2/N_1 = e^{-(E_2-E_1)/kT}\) gives N2 much less than N1, so an incident photon is more likely to be absorbed than to cause stimulated emission and the light is attenuated. Only when N2 > N1 do stimulated emissions outnumber absorptions and the light is amplified. It is achieved by pumping (optical, electrical discharge, injection current or chemical) together with a metastable state: atoms are raised to a short-lived level, quickly drop to a metastable level where they stay for about \(10^{-3}\) s and accumulate, while the lower laser level is kept nearly empty. Three-level and four-level schemes are used; four-level schemes reach inversion more easily because the lower laser level is above the ground state.

Q3. Explain the terms: active medium, active centre, pumping and resonant cavity. (4 marks)

Active medium: the material in which inversion and amplification occur, such as He-Ne gas mixture, ruby crystal, doped fibre. Active centre: the atoms or ions in the medium that make the laser transition, such as neon atoms or \(Er^{3+}\) ions. Pumping: supplying energy to raise atoms to higher levels and obtain inversion, by optical, electrical, injection or chemical means. Resonant cavity: two parallel mirrors, one fully and one partly reflecting, enclosing the medium; it provides feedback for repeated stimulated emission, selects axial direction and wavelengths satisfying \(2L = m\lambda\), and lets the beam out through the partial mirror.

Q4. Define coherence length and coherence time and give the relation between them. (3 marks)

Coherence time \(\tau_c\) is the average time over which a light wave maintains a constant phase. Coherence length \(L_c\) is the distance travelled by the wave in that time, i.e. the length of an unbroken wave train. Relation: \(L_c = c\tau_c\); also \(\tau_c = 1/\Delta\nu\) and \(L_c = \lambda^2/\Delta\lambda\). A laser has a large coherence length (metres or more) compared with an ordinary lamp (micrometres to millimetres).

Q5. State the characteristics of laser light. (4 marks)

(1) Monochromatic: very narrow line width, of the order of 0.001 nm or less for a He-Ne laser compared with about 0.1 nm or more for a gas discharge lamp line. (2) Coherent: constant phase relation in time and across the beam, giving large coherence length. (3) Directional: divergence about 1 mrad, so the beam stays narrow over long distances. (4) High intensity: energy concentrated in a tiny area; can be focused to a spot of micrometre size. (5) Often polarised (e.g. He-Ne with Brewster windows). These properties arise from stimulated emission and feedback in the resonant cavity.

Q6. With a neat energy level diagram explain the construction and working of a He-Ne laser. (6 marks)

Construction: a long narrow quartz discharge tube (length 30 to 80 cm, bore 2 to 8 mm) is filled with He and Ne in about 10:1 ratio (He about 1 mm Hg, Ne about 0.1 mm Hg). Electrodes connected to a high voltage DC supply produce a discharge. Two mirrors at the ends, one fully reflecting and one partially reflecting, form the resonator; Brewster windows may be used. Working: electrons in the discharge excite He atoms to metastable levels \(2^3S\) (19.81 eV) and \(2^1S\) (20.61 eV). These collide with ground state Ne atoms and transfer energy to the Ne 2s (19.78 eV) and 3s (20.66 eV) levels by resonant transfer, since the energies nearly match. Ne atoms pile up in 3s and 2s while 2p and 3p are almost empty, producing inversion. Laser transitions: 3s to 2p gives 632.8 nm (red), 3s to 3p gives 3.39 μm, 2s to 2p gives 1.15 μm. Ne atoms in 2p fall to 1s by spontaneous emission (about 600 nm) and from 1s to the ground state by collisions with the tube walls, which keeps the lower level empty. Output: continuous, coherent, a few mW. Energy diagram: draw He levels on the left (ground, 19.81, 20.61 eV) and Ne levels on the right (ground, 1s, 2p, 3p, 2s, 3s) with collision transfer arrows and the three laser lines. Uses: alignment, barcode scanners, holography, interferometry.

Q7. Explain the construction and working of a fibre laser. State its advantages. (5 marks)

Construction: a long single mode optical fibre whose core is doped with rare earth ions (\(Er^{3+}\), \(Yb^{3+}\) or \(Nd^{3+}\)) is the active medium. Semiconductor laser diodes supply pump light, coupled into the fibre (often into an inner cladding of a double-clad fibre). Fibre Bragg gratings at the two ends act as mirrors: one with near 100 percent reflectivity at the laser wavelength, the other partially reflecting for output. Working: pump photons (e.g. 980 nm for erbium) are absorbed by the dopant ions and raise them to an upper level; they relax to a long-lived upper laser level, giving population inversion. Spontaneous photons guided along the core cause stimulated emission; the gratings feed the light back repeatedly so it is amplified, and the output leaves through the partial grating (near 1550 nm for Er, about 1060 nm for Yb). Advantages: high efficiency, excellent beam quality, compact and rugged, easy cooling due to large surface to volume ratio, flexible beam delivery, long life and low maintenance. Uses: cutting and welding of metals, marking, telecommunications, medical surgery.

Q8. What is LiDAR? Explain its principle and give applications. (4 marks)

LiDAR (Light Detection and Ranging) is a remote sensing technique that uses laser pulses to measure distance. Principle: a pulsed laser (often near infrared) sends a short pulse to a target; a photodetector receives the back-scattered light and a timer measures the round-trip time t; distance \(d = ct/2\). A scanning mirror moves the beam and GPS plus an inertial unit record position and orientation, so millions of distance points form a 3D map (point cloud). Applications: self-driving cars and robots, topographic and city mapping, forestry, archaeology, flood modelling, speed guns and atmospheric pollution studies.

Q9. Explain the working of a laser barcode reader. (4 marks)

A barcode is a pattern of dark bars and light spaces of different widths that encodes a number. In the reader, a low-power laser (He-Ne at 632.8 nm or a red diode laser near 650 nm) produces a narrow beam, which a rotating polygon mirror or oscillating mirror sweeps across the code. Dark bars absorb the light and white spaces reflect it, so the reflected intensity varies with the pattern. A lens collects the reflected light onto a photodiode, which produces a train of electrical pulses whose durations match the bar and space widths. A decoder circuit converts the pulses into digits and sends them to the computer, which looks up the product and price. The laser's directionality and monochromaticity give a sharp spot and good contrast, so codes can be read from a distance and at an angle.

Q10. Describe the applications of lasers in metal work. (4 marks)

Because a laser beam can be focused to a tiny spot with power densities above \(10^{6}\) W/cm², it can melt or vaporise metals. Cutting: CO2 and fibre lasers cut steel and aluminium sheets with a narrow kerf and smooth edges, often assisted by an oxygen or nitrogen jet. Welding: deep, narrow welds with a small heat-affected zone, used in car bodies and electronics; welding is possible without contact. Drilling: very fine holes in hard materials (turbine blades, fuel injectors) by pulsed Nd:YAG lasers. Marking and engraving: permanent serial numbers and logos. Surface hardening and cladding: local heating improves wear resistance. Advantages: no tool wear, high precision, easy automation and CNC control, works on hard and brittle materials.

Exam tips

• For the He-Ne question always draw the energy level diagram with the 19.81 and 20.61 eV helium levels and the 632.8 nm, 1.15 μm and 3.39 μm neon lines; this diagram alone carries 2 marks.
• Write the full form of LASER and LiDAR once; examiners look for it.
• In population inversion answers, quote the Boltzmann equation and explain why a metastable state is required.
• In numericals convert nm to m and eV to J (1 eV = 1.6 x 10^-19 J) before substituting; give the final unit.
• For LiDAR remember the factor 2 in d = ct/2.
• For the fibre laser mention the three key parts: doped core, diode pump and fibre Bragg grating mirrors.
• Tabulate differences (spontaneous vs stimulated emission) in at least four points for a 4 mark question.

FAQs

Why is helium needed in the He-Ne laser if only neon lases?

Neon is hard to excite directly and selectively. Helium is easily excited by the discharge to long-lived metastable levels whose energies almost match the upper neon laser levels, so helium efficiently transfers energy to neon by collisions and creates the inversion.

Why can't population inversion be obtained in a two-level system?

In a two-level system pumping raises atoms from E1 to E2, but the same pump radiation also causes stimulated emission from E2 to E1. At best the two populations become equal, never inverted. A third (metastable) or fourth level is needed.

Is a laser more powerful than a bulb?

Not always in total power; a 5 mW He-Ne laser emits far less power than a 60 W bulb. Its intensity is much higher because the power is concentrated in a very narrow beam and a tiny spot.

What decides the colour of a laser?

The energy gap between the upper and lower laser levels of the active centre, through \(\lambda = hc/(E_2 - E_1)\); the cavity then selects the exact modes within that line.

These notes follow the University of Mumbai first-year engineering syllabus (NEP 2020, Applied Physics) and were prepared with AI help and checked.