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# A TEXTBOOK OF APPLIED PHYSICS VOLUME I - SECOND EDITION ## Unit III ## 5. Laser ### 5.1 Introduction The Term LASER stands for Light Amplification by Stimulated Emission of Radiation. The discovery of the laser is one of the most important discoveries of the last century. The first successf...

# A TEXTBOOK OF APPLIED PHYSICS VOLUME I - SECOND EDITION ## Unit III ## 5. Laser ### 5.1 Introduction The Term LASER stands for Light Amplification by Stimulated Emission of Radiation. The discovery of the laser is one of the most important discoveries of the last century. The first successful operation of a laser was demonstrated by T. Maiman, using a ruby crystal in the USA in 1960. The first gas laser was fabricated by Ali Javan and his coworkers the following year. Since then, different types of lasers using solids, liquids, and gases have been developed. The immense use of lasers, from toys to warfare and from welding to surgery, has made it very popular. ### 5.2 Characteristics of Laser Light Like ordinary light, laser light is electromagnetic in nature, however, there are few characteristics of laser light not possessed by normal light. Some of these characteristics of laser light include: * **Directionality:** The laser beam is highly directional, having almost no divergence (except for the diffraction effect). The output beam of a laser has a well-defined wavefront, and therefore, it is highly directional. Due to its high directionality, a laser beam can be focused on a point by passing it through a suitable convex lens. If a laser beam of wavelength λ = 6000 Å and beam radius 2 mm is passed through a convex lens of focal length 5 cm, the area of the spot at the focal plane is of the order of: $a² = (πλ²/f²) × (5×10−2)²/(2×10−3)² = 7.1 × 10−10 m²$, which is extremely small. * **Monochromaticity:** The laser light is nearly monochromatic. In reality, no light is perfectly monochromatic, i.e., it is not characterized by a single wavelength λ or frequency v but instead is characterized by a spread in frequency Δv about the central frequency (or Δλ in case of wavelength λ). The monochromaticity of a light is defined by $Δv/v$ For perfect monochromaticity, Δv = 0, which is not attainable in practice, but the value of Δv is much smaller for lasers compared to ordinary light. For ordinary light Δv is of the order of 100 Hz, whereas for a laser, it is of the order of 500 Hz. Thus, for light of wavelength λ = 6000 Å or frequency v = 5 × 1014 Hz, $Δv/v$ = (5 × 1014 Hz)/(1010 Hz) = 2 × 10-5 for monochromaticity of ordinary light, $Δv/v$ = (500 Hz)/(5 × 1014 Hz) = 10-12 for monochromaticity of laser light. Thus, laser light is highly monochromatic compared to ordinary light. * **Coherence:** Laser radiation is characterized by a high degree of coherence, both spatial and temporal. In other words, a constant phase relationship exists in the radiation field of a laser light source at different locations and times. It is possible to observe interference effects from two independent laser beams. In fact, coherence is the main feature which distinguishes laser radiation from ordinary light, and the other characteristics (directionality, monochromaticity, and intensity) are related to the high degree of coherence. * **Intensity:** The laser beam is highly intense compared to ordinary light. Since the laser power is concentrated in a beam of very small diameter (≈ few mm), even a small laser can deliver very high intensity at the focal point of the lens. For example, if the power (P) of a laser beam is 1 watt, the intensity at the focal point is given by: $I = P/Area = 1 W/(πλ²f²) = 1 W/(7.0×10−10 m²) = 1.4 × 109 Wm-2$. Note that even a small power of 1 watt can give an intensity of 109 W/m², which is extremely large. ### 5.2 Absorption and Emission (Spontaneous and Stimulated) of Radiation To understand the principle of working of a laser, it is necessary to understand the radiative absorption and emission of photons in an atomic system. According to quantum theory, atoms exist only in certain discrete energy states, and absorption and emission of photons cause them to make a transition from one discrete energy state to another. Transition from one energy level to another can occur by stimulated absorption (or simply absorption), spontaneous emission, and stimulated (or induced) emission. We shall see that the stimulated emission is particularly important for a laser. ### 5.3 Relation Between Einstein's Coefficients In any transition process, two energy states are involved. Let us consider a system having two energy states, a lower state of energy E, with population N, and a higher state of energy E, with population N.. The population N, i.e., number of atoms per unit volume, in the energy state E, according to Boltzmann distribution law, is given by: $N = Ne-E/KT$ where N, is the population in the ground state (E = 0), k is the Boltzmann's constant, and T is the absolute temperature. From the above equation, it is clear that the population is maximum in the ground state and decreases exponentially as one goes to higher energy states. For our considered system, using Boltzmann distribution law, we have: $N₂/N₁ = e-(E2-E₁)/kT$ or $N = N₁e-(E2-E₁)/kT$ . Using the relation E₂ - E₁ = hv, we get: $N₂ = N₁e-hu/kT$. In a closed system under thermal equilibrium, the net rate of emissions must equal the net rate of absorptions. That is, $Rst + Rsp = Ras$. Using Eqs. (5.1), (5.2), and (5.3), we get: $B₁₂UN₁ + A₂₁N₂ = B₂₁UN₂$ or $u = (N₂A₂₁)/(N₁B₁₂-N₂B₂₁)$ $u = (N₂A₂₁)/(N₁B₁₂ - 1)$ or $u = (N₂B₂₁/N₁)/(1 - N₂B₂₁/N₁)$. Substituting the value of (N₂/N₁) from Eq. (5.7), we get: $u = (A₂₁/B₂₁)/(e^{hv/kT} - 1)$. The energy density u, from Planck's radiation law, is given by: $u = (8πν³/c³)/(e^{hv/kT}-1).$ Where c is the speed of light in free space. Comparing Eqs. (5.8) and (5.9), we get: $B₁₂ = B₂₁$. The expressions are called Einstein's relations, and the coefficients A and B are called Einstein's A and B coefficients. Absorption and stimulated emissions are mutually reverse processes, and their probabilities are equal, i.e., B₁₂ = B₂₁ . ### 5.4 Population Inversion Consider an optical medium having two energy states E, and E, (E, <E) with population N, and N₂, respectively. Under normal conditions, Boltzmann distribution law requires N₁ > N₂, i.e., the population of atoms in the lower energy state E, must be greater than that in the higher energy state E. When radiation is passed through the medium, at any given time, numerous absorption and emission processes occur. Each absorption process attenuates the incident light wave, whereas each stimulated emission amplifies it. Unlike light waves generated by stimulated emission, light waves generated by spontaneous emission exhibit a random phase. The small number of spontaneously emitted photons, which accidently have the same phase as that of the photons generated by stimulated emission, aid the lasing action. Laser operation, i.e., amplification of incident light wave, requires that stimulated emission is dominant compared to absorption. We know, $Rst = B₁₂uN₁$ and, $R_{ab} = B₂₁uN₂$. Consider the ratio $Rst/R_{ab} = (B₂₁uN₂)/(B₁₂uN₁) = (N₂/N₁)$. It is evident from the above equation that the ratio depends only on the population of the atoms in the excited state and the ground state. On the basis of the above ratio, consider the following cases: (i) N, > N: That is, population of the atoms in the ground state is higher than that in the excited state. In this case, absorption is dominant, and hence, the intensity of light wave decreases exponentially. (ii) N, = N: That is, population of atoms in the ground state is equal to that in the excited state. In this case, absorption and stimulated emission are in equilibrium, and hence, the intensity of light wave remains constant. (iii) N, <N: That is, population of atoms in the excited state is more than that in the ground state. This condition, known as population inversion, is the most important case and must be achieved for lasing action. In this case, stimulated emission is dominant, and hence, the intensity of incident light increases, i.e., the incident light wave is amplified. From Eq. (5.7), we have: $N₂/N₁ = e-hu/kT$. Which can also be expressed as: $N₁/N₂ = e^{hu/kT}$. In normal situations, N₁>N₂ for E, <E,. However, to achieve optical amplification, i.e., lasing action, it is essential to create a non-equilibrium distribution of atoms such that the population of the upper energy level is greater than that of the lower energy level (N₂>N₁, for E,>E₁). Achieving Population Inversion: Pumping The process of raising the atoms or molecules of the active medium to a higher energy state, so as to achieve population inversion, is called pumping. Commonly used methods of pumping are: (i) optical pumping, (ii) electric excitation, (iii) inelastic atom-atom collision, (iv) chemical reactions, and (v) direct conversion. (i) Optical Pumping: In this method, a highly intense radiation from an optical flash tube is incident on the active medium, raising the atoms to a higher energy state through stimulated absorption. Normally, the radiation is given out in the form of short flashes. Maiman used this method of pumping in ruby laser, and it is still widely used in solid-state lasers. For better efficiency, the active material is placed inside a helical flash lamp. (ii) Electrical Excitation: In this method, an electric discharge is used to excite the atoms of the active material. The method is normally used in gas lasers, e.g., He-Ne, Argon gas laser, etc. An extremely high electric field (≈ several kV/m) accelerates the electrons emitted by the cathode towards the anode. Collisions between these high energy electrons and the atoms of the active medium raise them to the higher energy level, producing population inversion. (iii) Inelastic Atom-Atom Collision: In some cases, the active medium has two types of atoms (He-Ne). An electric discharge initially excites one type of atom. These excited atoms then collide inelastically with the second type of atom, transferring energy from the excited atoms to the unexcited atoms. Thus, the second type of atom also gets excited, creating population inversion in them. (iv) Chemical Pumping: In chemical lasers, the energy required for excitation is obtained from a suitable chemical reaction. For example, in a chemical laser, hydrogen and fluorine combine to form hydrogen fluoride, and this chemical laser produces an infrared laser beam of over 2 MW. (v) Direct Conversion: In semiconductor lasers and light-emitting diodes (LED), direct conversion of electrical energy into radiation takes place. The two-level atomic systems are, however, not suitable for achieving population inversion. Because if B₁₂ = B₂₁, the probabilities of absorption and stimulated emission are equal, keeping the population of the two states unchanged. For achieving population inversion, three or four energy level atomic systems are used. The energy level diagrams of such systems are shown in Fig. 5.4. These atomic systems are characterized by the presence of a central metastable state in which atoms spend an unusually long time. It is the transition from this metastable state that the stimulated emission, or lasing action, takes place. ### 5.5 Components of a Laser System A laser system requires three essential components for its operation. These are: (i) An active medium in which the lasing action takes place. (ii) An energy source, or the pumping source, which excites the atoms to a higher energy state, achieving the population inversion. (iii) A resonant cavity, or optical cavity, to provide the feedback for laser oscillations. The active medium may be solid, liquid, or gas. In most lasers, the active medium is enclosed in a cavity formed by two mirrors (plane or curved) facing each other. One of the mirrors of the cavity is 100% reflecting, while the other mirror is partially transparent to allow some of the radiations to pass through. The optical cavity is analogous to an oscillator as it provides positive feedback of the photons by reflection, at the mirrors, at either end of the cavity. Therefore, the area enclosed inside the optical cavity is also called an optical resonator. After multiple passes through the cavity due to reflection at the mirrors, light amplification becomes very large. One of the mirrors is partially transparent, and the laser output is obtained through this mirror. A schematic diagram representing essential components and their arrangement is shown in Fig.5.5. ### 5.6 Ruby Laser Ruby laser is a three-level solid-state laser and it was the first laser fabricated by Maiman in 1960. Ruby crystal, which is a crystal of Al₂O, with some Al³+ ions replaced by Cr³+ ions, has been known to the mankind for hundreds of years, as a naturally occurring precious stone. For the laser, the ruby crystal is grown from a molten mixture of Al₂O, and Cr₂O. Typical Cr³+ concentration in the crystal is nearly 0.05 weight per cent. In the ruby crystal, Cr³+ ions are the active components. Ruby crystal is taken in the form of a cylindrical rod of 5 to 10 cm length and 5 mm in diameter. One end of the rod is completely polished while the other end is made partially reflecting. Hence, the ends work as the cavity mirrors. The energy levels of Cr³+ ions responsible for the lasing action is shown in Fig. 5.6. It has three energy levels E₁, E₂, and E,. The uppermost level E, consists of two bands F₁ and F₂. The states in these bands have extremely small lifetimes of the order of 10−⁹ s. The second energy level E₂ is a metastable state and has a lifetime of the order of 10−³ s, several orders of magnitude longer than that of E,. The level E₂, in fact, has two sublevels of difference of nearly 14 Å. The transition from E, to E₂ is non-radiative while a transition from E₂ to E₁ is radiative and is responsible for the lasing action. The ruby rod is placed inside a xenon flash lamp as shown in Fig.5.7. The light from the flash lamp pumps the Cr³+ ions to the energy bands 4F, and 4F. The ions in these bands make a rapid non-radioactive decay to the metastable state E. Due to the longer lifetime in this level, the number of Cr³+ ions keeps on increasing. Subsequently, population inversion takes place between the levels E₂ and E,. When the required population inversion is reached, lasing action is initially triggered by spontaneously emitted photons which are available in the system and spontaneous incoherent red fluorescence, typical of ruby, with a peak near 6940 Å, is produced. But as the pumping energy is increased and the population inversion exceeds the threshold, stimulated emission starts and coherent laser light with a sharp peak at 6943 Å is produced. Because of the sublevels in E₂, some other wavelengths are present, particularly for spontaneous transitions, but for stimulated transitions, the wavelength 6943 Å dominates other lines. The stimulated emission depopulates the level E₂ at a faster rate than the pump rate, momentarily stopping the lasing action. However, before the output falls to zero, the population again builds up in the level E₂ exceeds the threshold value and the lasing action restarts. This process occurs many times before the pumping flash ends. Hence, the output consists of a series of spikes as shown in Fig. 5.8; this process is referred to as spiking of the laser. Since the flash lamp operation is pulsed, the laser output is also pulsed, i.e., the laser beam is emitted in the form of pulses, lasting a few milliseconds. A large amount of energy is dissipated in the ruby rod, and it has to be cooled for efficient continuous operation. Liquid nitrogen is circulated for this purpose. ### 5.7 Helium-Neon Laser The He-Ne laser was the first successfully operated gas laser, brought in operation in 1961 by Javan, Bennet, and Harroit. Unlike ruby laser, this laser gives out a continuous laser beam. By selecting proper resonator mirrors, laser beams of wavelengths 6328 Å, 33913 Å, and 11523 Å can be produced. It is a low power laser with a typical output power of a few milliwatts and is a four-level laser. Construction: The He-Ne laser consists of a long (length 10 to 100 cm) and narrow (diameter 2 to 10 mm) discharge tube filled with helium and neon gases with typical partial pressures of 1 mm Hg (1 torr) and 0.1 mm Hg (0.1 torr) respectively. The lasing action takes place due to the transitions in neon atoms, while the helium atoms help in the excitation of neon atoms. The ends of the cavity are enclosed by two concave mirrors. One of the mirrors is 100% reflecting at the lasing frequency while the other is partially reflecting. Earlier, the mirrors used to be sealed inside the glass, but the tubes do not last long since the seal gets eroded. Therefore, as shown in Fig. 5.9, now an external mirror arrangement is preferred. The glass tube is closed by windows which are tilted at the Brewster angle. Such windows allow the light waves with electric fields in the plane of the paper to pass through without any reflection. The light waves with electric fields perpendicular to the plane of the paper are reflected away from the cavity. With such windows, the output laser beam thus gets linearly polarized. Inside the gas cell, there are electrodes connected to the terminals of a de power supply. Lasing Action: The energy levels of He and Ne are shown in Fig. 5.10. When an electrical discharge is passed through the gas, high-energy electrons produced in the tube collide with the gas atoms. As the concentration of helium atoms is higher, the probability of collision with He atoms is higher than that with the neon atoms. These collisions excite the helium atoms to the higher energy states. The helium atoms tend to accumulate in the metastable states E, and E, with respective lifetime of 10−⁴ and 5×10−³ s. The energy levels E and E of neon atoms have almost the same energy as the levels E and E of the helium atoms. Due to collisions between helium and neon atoms, the excited helium atoms excite the neon atoms to the levels E, and E. We can represent this process as: He* (E) + Ne (E) → He (E) + Ne* (E) He* (E) + Ne (E) → He (E) + Ne* (E). Where the letters in parentheses refer to the corresponding energy levels of gases. Depending upon the energy levels involved in the transition, the major transitions are as follows: (i) The 6328 Å Transition: When the lasing transition is from E→E, the wavelength of the produced laser beam is 6328 Å. The level En is 3S, and E is 2P. This is the most commonly obtained laser beam in He-Ne laser. The lifetime of E is of the order of 10−⁸ sec, while that of E is 10⁻⁷ sec, hence, population inversion build-up is possible between these two levels. (ii) The 33913 Å Transition: The transitions from E →E produce a lasing beam of 33913 Å (or 3.3913 µm). The upper level is same in this case and in the 6328 Å transition. (iii) The 11523 Å Transition: This is the output wavelength of the first He-Ne laser. The transition from E → E produces photons beams of 11523 Å (or 1.1523 µm) wavelength. * He-Ne laser is widely used in laboratories where highly coherent and monochromatic sources are needed. It is also used in supermarket scanners, printers, Fourier transform spectrometers, holography, etc. ### 5.8 Applications of Lasers Lasers are being used extensively nowadays in every field of life, from toys to warfare. Some of the important applications are mentioned below: * Communication: In optical communication, laser is used as an optical carrier signal. Because of the large bandwidth, the information carrying capacity of laser light is enormous. The rate at which the information can be transmitted is proportional to bandwidth and the bandwidth is proportional to the carrier frequency which is of the order of 10¹⁵ Hz for the optical signals. High bandwidth together with low transmission loss, immunity to interference, signal security, reliability, etc., make optical communication the most advantageous mode of information transmission. * Laser is used in LIDAR (Light Detection and Ranging). It is used as a range finder. The transit time of transmitted and reflected pulses of laser light is recorded, and the distance of the reflecting object is estimated. This method is widely used for finding range and detecting obstacles in fog, smoke, and underwater. Large range finders are used for military surveillance. Optical radars are used in airplanes, ambulances, police cars, etc. * In high-speed photography, lasers are useful because they can detect fast-moving bullets and missiles. * Laser is also used in holography which can be said to be a kind of three-dimensional photography. A normal photograph represents a two-dimensional recording of a three-dimensional scene. A hologram produces a three-dimensional image of a three-dimensional scene. A hologram also records the phase of the reflected light in addition to the amplitude of the reflected light. A hologram reproduces the image using a process called reconstruction. The availability of coherent laser radiation has made the reconstruction possible. The holographic pattern recognition is used for identifying fingerprints, postal address, etc. Holograms are also used as data storage devices. * Medical Applications: A narrow and intense beam of laser is used for destroying cancerous tissues. It is also used for other kinds of surgery. During these processes, the heat generated seals up capillaries and blood vessels preventing blood loss. For certain internal surgeries, the laser beam is carried to the spot through an optical fiber. * The most successful application of laser has been in eye surgery for the treatment of detached retina by ophthalmologists. Very low power lasers of short pulse duration are used for this purpose. * Industrial Applications: Lasers are used for cutting, welding, drilling, etc. Because the laser beams can be focused onto a fine spot, it is particularly suitable for welding of fine wires, contacts in miniature assemblies, drilling holes, etc. It is used in aircraft and automobile industries to cut sheets of metals and alloys of a thickness about 5 mm or less. Using lasers, holes as small as 10 µm in diameter can be drilled. Drilling of fine holes using lasers is done in diamonds, watch jewels, etc. * Lasers are used in many purposes in the electronics industry—for the manufacture of electronic components and integrated circuits. Lasers are used to perforate, divide silicon slices, selective evaporation, production of masks for integrated circuits, trimming of thick and thin film resistors, etc. * Scientific Research Applications: Lasers are used for the determination of chemical and crystalline structures of molecules, i.e., laser spectroscopy. It is also used extensively in Raman spectroscopy to investigate the molecular structure. It is used to produce irreversible chemical changes in laser photochemistry. * It is used in non-linear optics, when a strong beam of laser light interacts with a medium, it polarizes the medium. The polarization P is given by: $л = сЕ + СЕ² + c E +......(5.23)$ Where E is the electric field associated with the incident radiation, c is the dielectric susceptibility of the medium and c₁, c₂,….are higher orders of susceptibilities. With the normal incident light, only the first term which is linear in E, can be activated. The non-linear (or higher order) terms which give the non-linear effects in E can be activated only by the radiations having extremely high electric field E. Only a giant pulse of lasers are capable of producing such fields. * Laser Induced Nuclear Fusion: Nuclear fusion is the process by which stars produce their energy and scientists have been attempting to carry out nuclear fusion in the lab. One of the difficulties for nuclear fusion to occur is the requirement of very high temperature (~ 10⁸ K). This is necessary to overcome the coulombic repulsion between the nuclei so that they fuse together. With the availability of high power laser pulses, creation of such high temperatures seems achievable. Many countries are developing laser enabled nuclear fusion facilities. * Applications in Metrology: The characteristics of lasers, such as coherence, low divergence, and monochromaticity, have been used in metrology. The He-Ne laser is the most widely used laser because of its visible output, low power and low cost. Lasers are used for precision distance measurement, calibration testing comparison with standards, etc. Optical interference techniques using laser as a parallel monochromatic source has been used for the determination of the diameter of very thin wires to detect small variations in surface smoothness, etc. Laser scanning gauges to measure the roundness and diameter have been made. The laser beam is generally considered to be very directional, monochromatic, and coherent. The properties of laser light have allowed for its widespread use in many fields of science, engineering, and medicine. The invention of this technology has led to a plethora of improvements in many facets of modern life, including but not limited to, telecommunications, medicine, manufacturing, and scientific research.