DOC-20250213-WA0003.

LASERS The word Laser stands for “Light Amplification by Stimulated Emission of Radiation“. It is a device which amplifies light. It has properties like Coherence, Unidirectionality, Monochromaticity, Intensity, etc. Interaction of an electromagnetic wave with matter leads to transition of...

LASERS The word Laser stands for “Light Amplification by Stimulated Emission of Radiation“. It is a device which amplifies light. It has properties like Coherence, Unidirectionality, Monochromaticity, Intensity, etc. Interaction of an electromagnetic wave with matter leads to transition of an atom or a molecule from one energy state to another. If the transition is from lower state to higher state it absorbs the incident energy. If the transition is from higher state to lower state it emits a part of its energy. Emission or Absorption takes through quantum of energy called photons. hν is called quantum energy or photon energy. h = 6.626×10-34 Joules Second is Planck’s constant and ‘ν’ is the frequency. If ∆E is the difference between the two energy levels, Then ∆E = (E2 - E1) Joule According to Max Planck, ∆E = hν = (E2-E1) ν = (E2 - E1)/h ….Hz. Three types of interactions, which are possible, are as follows: 1) Induced Absorption: Induced absorption is the absorption of an incident photon by an atomic system as a result of which the atomic system is elevated from a lower energy state to a higher state, wherein the difference in energy of the two states is the energy of the photon. Consider the atomic system having two energy states E1 and E2, E2 > E1. When a photon of energy hν is incident on an atom at level E1, the atom goes to a higher energy level by absorbing the energy. When an atom is at ground level (E1), if an electromagnetic wave of frequency ν is applied to the atom, there is possibility of getting excited to higher level (E2). The incident photon is absorbed. It is represented as Atom + Photon → Atom* Dr. Pratibha. S, Assistant Professor, BMSCE Page 1 2) Spontaneous Emission: The emission of a photon by the transition of an atomic system from a higher energy state to a lower energy state without the aid of an external energy is called spontaneous emission. Let ‘E1’ and ‘E2’ be two energy levels in a material, such that E2>E1. E1 is ground level and E2 is the higher level. hν =E2-E1 is the difference in the energy. The atom at higher level (E2) is more unstable as compared to that at lower level (E1). The life time of an atom is less in the excited state and atom emits the photon without the aid of any external energy while de- excitation. It is called spontaneous emission. The process is represented as Atom* → Atom + Photon The photons emitted in spontaneous emission may not have same direction and phase similarities. It is incoherent. Ex: Glowing electric bulbs, Candle flame etc. 3) Stimulated Emission: Stimulated emission is the emission of a photon by an atomic system under the influence of a passing photon of just the right energy due to which the atomic system transits from a higher energy state to a lower energy state. The photon thus emitted is called stimulated photon and will have the same phase, energy and direction of movement as that of the passing photon called the stimulation photon. Initially the atom is at higher level E2. The incident photon of energy forces the atom to get de-excited from higher level E2 to lower level E1. i.e. hν=E2–E1 is the change in energy. Dr. Pratibha. S, Assistant Professor, BMSCE Page 2  The incident photon stimulates the excited atom to emit a photon of exactly the same energy as that of the incident photons. The emitted two photons have same phase, frequency, direction and polarization with the incident photon and results in coherent beam of radiation. This kind of action is responsible for lasing action. Atom* + Photon → Atom + (Photon + Photon) Expression for energy density in terms of Einstein’s Coefficients Consider at any given instant of time, N1 be the number of atoms in the ground state of energy level E1 and N2 be the number of atoms in the excited state of energy level E2. Let radiation of frequency ν = (E2 – E1) / h and Eν be the energy density of radiation of frequency ν. Then Eν dν will be energy density of radiations whose frequencies lie in the range ν and ν + dν. Let us consider the absorption and two emission process 1) Induced absorption: Induced absorption is the absorption of an incident photon by atoms as a result of which the atom is elevated from a lower energy state to a higher state. The rate of absorption is proportional to N1Eν Rate of absorption = B12N1Eν........................................................... (1) Where ‘B12’ is the proportionality constant called Einstein Coefficient of induced absorption. 2) Spontaneous emission: The emission of a photon by the transition of an atom from a higher energy state to a lower energy state without the aid of an external energy is called spontaneous emission. Spontaneous emission depends on N2 and independent of energy density. The rate of spontaneous emission = A21N2................................................................. (2) Where ‘A21’ is called proportionality constant called Einstein coefficient of spontaneous emission. 3) Stimulated emission: Stimulated emission is the emission of a photon by an atom under the influence of a passing photon of just the right energy due to which the atom transits from a higher energy state to a lower energy state The rate of stimulated emission is directly proportional to N2Eγ. The rate of stimulated emission = B21N2Eν ……………………(3) Where ‘B21’ is the proportionality constant called Einstein’s Coefficient of stimulated emission. At thermal equilibrium, Dr. Pratibha. S, Assistant Professor, BMSCE Page 3  Rate of absorption = (Rate of spontaneous emission + Rate of stimulated emission) B12N1E𝑣 = A21N2 + B21N2E𝑣 𝐵12𝑁1𝐸𝑣 = (𝐴21𝑁2 + 𝐵21𝑁2) 𝐵12𝑁1𝐸𝑣 = 𝑁2 (𝐴21 + 𝐵21) 𝑁1 𝐵12 𝐸𝛾 = [𝐴21 + 𝐵21 𝐸𝛾 ]................................................................(4) 𝑁2 −𝐸1 −𝐸2 According to Boltzmann’s equation, 𝑁1 = 𝑁0 𝑒 𝐾𝑇 and 𝑁2 = 𝑁0 𝑒 𝐾𝑇 𝐸2 −𝐸1 ℎ𝛾 𝑁1 ∴ =𝑒 𝐾𝑇 = 𝑒 𝐾𝑇 𝑁2 Substituting this in the above equation ℎ𝛾 𝑒 𝐾𝑇 𝐵12 𝐸𝛾 = [𝐴21 + 𝐵21 𝐸𝛾 ] ℎ𝛾 𝑒 𝐾𝑇 𝐵12 𝐸𝛾 − 𝐵21 𝐸𝛾 = 𝐴21 ℎ𝛾 𝐸𝛾 [𝑒 𝐾𝑇 𝐵12 − 𝐵21 ] = 𝐴21 𝐴21 𝐸𝛾 = ℎ𝛾 …………………………….(5) [𝑒 𝐾𝑇 𝐵12 −𝐵21 ] 𝐴 ( 21 ) 𝐵12 𝐸𝛾 = ℎ𝛾 ……………………..(6) 𝐵 [𝑒 𝐾𝑇 − 21 ] 𝐵12 Since the above equation is for an equilibrium state the radiation density ‘Eγ’ is same as given for a blackbody by Max Planck. According to Planck’s radiation law 8𝜋ℎ𝛾3 1 𝐸𝛾 = [ ℎ𝛾 ]……………(7) 𝑐3 (𝑒 𝐾𝑇 −1) Comparing equations (6) and (7) we get, 𝐴 8𝜋ℎ𝛾3 𝐵21 (𝐵21 ) = and = 1, gives the relation between Einstein’s coefficients. 12 𝑐3 𝐵12 Where ‘ν’ is the frequency of the radiation, ‘c’ velocity of light, ‘k’ Boltzmann’s constant and T is thetemperature of the atomic system 𝐴 ( 21 ) 𝐵12 𝐸𝛾 = [ ℎ𝛾 ]……………….(8) (𝑒 𝐾𝑇 −1) This is the expression for energy density. Dr. Pratibha. S, Assistant Professor, BMSCE Page 4  Condition for laser action: 1) Meta Stable State: It is the special type of excited state where in the life time of atom is more than the normal excited state. This state plays an important role in lasing action. In metastable state, atoms stay of the order of 10-3 to 10-2 second. In normal excited state other than metastable atom stay of order of 10-8 to10-9 seconds. It is possible to achieve population inversion condition in certain atomic system which possesses a metastable state. 2) Population Inversion: It is the state of the atomic system at which the population of a higher energy level is greater than that of the lower energy level. Let E1, E2, E3 be the energy levels of the atomic system E3>E2>E1. E2 is the metastable state of the atomic system. Atoms get excited from the state E1 to E3 by means of external source and stay there for short time. These atoms undergo spontaneous transitions to E2 and E1. The atoms at the state E2 stay for longer time. A stage is reached in which the number of atoms at state E2 is more than the number of atoms at E1 which is known as population inversion. Requisites of a Laser System: a. The pumping process: It is the process of supplying energy to the medium in order to transfer it to the state of population inversion is known as pumping process Dr. Pratibha. S, Assistant Professor, BMSCE Page 5   Optical Pumping: It is the process of exciting atoms from lower energy level to higher energy level by using high intensity light or by operating flash tube as an external source called optical pumping.  Electrical pumping: It is the process of exciting atoms from lower energy level to higher energy level by using dc power supply as an external source called electrical pumping. b. Active medium: It is a medium which supports population inversion and promotes stimulated emission leading to light amplification  Active centers: In a medium consisting of different species of atoms only small fraction of the atoms of a particular type are responsible for stimulated emission and consequent light amplification they are known as Active centers c. Laser cavity. An active medium bounded between two mirrors is called as a laser cavity. Gallium-Arsenide Laser Semiconductor laser: A Semiconductor diode laser is one in which the active medium is formulated by semiconducting materials. Dr. Pratibha. S, Assistant Professor, BMSCE Page 6  Construction: Gallium-Arsenide Laser is a single crystal of GaAs consists of heavily doped n-type and p-type. The diode is very small size with sides of the order of 1mm. The width of the junction varies from 1-100μm. The top and bottom surfaces are metalized and Ohmic contacts are provided for external connection. The front and rear faces are polished. The polished faces functions as the resonant cavity. The other two faces are roughened to prevent lasing action in that direction. Working: Energy level diagram of p-n junction Ga-As semi-conductor diode Laser (a) Before b i a s i n g (b) after biasing  The energy band diagram of heavily doped p-n junction is as shown. At thermal equilibrium the Fermi level is uniform.  Because of very high doping on n- side, the Fermi level is pushed in to the conduction band and electrons occupy the portions of the conduction band that lies below the Fermi level and on p-side, the Fermi level lies within the valence band and holes occupy the portions of the valence band that lies above the Fermi level.  A suitable forward bias is applied to overcome the potential barrier. As a result electrons from n-region and holes from p-region injected into the junction.  The current begins to flow following which there will be a region in junction in which the population inversion can be achieved.  Initially concentration of electrons in the energy levels at the bottom of the conduction band will be less than that of energy levels at top of valence band. So that the recombination of electrons and holes result only in spontaneous emission then junction works as LED. Dr. Pratibha. S, Assistant Professor, BMSCE Page 7   When the current exceeds the threshold value, population inversion is achieved in the active region which is formulated in the junction.  At this stage the photons emitted by spontaneous emission triggers stimulated emission, over a large number of recombination leading to build up laser.  Since the energy gap of GaAs is 1.4eV, the wavelength of emitted light is 8400 A o. Properties of laser: i. Coherence: The emitted radiation after getting triggered is in phase with the incident radiation. ii. Monochromaticity: The laser beam is highly monochromatic than any other radiations. iii. Unidirectionality: Laser beam travels in only one direction. It can travel long distance without spreading. iv. Focus ability/ Intensity: A laser beam can be focused to an extremely fine spot. Applications of laser: 1) Lasers in Defense - Laser range finder in defense A high power pulsed laser (Nd-YAG) beam is directed towards the enemy target from the transmitter. The beam bounces back from the surface of the target as a reflection. A part of the reflected beam is received as a signal by the receiver. The unwanted noise signal will be filtered by the optical filter and pure signal is amplified by the photomultiplier in the receiver. The range finders high speed clock measures the exact time of incident and reflection of the pulse and then convert it in to distance. 2) Medical Applications- Eye Surgery and Skin Treatment a) Eye Surgery: LASIK, which stands for laser in-situ keratomileusis, is a popular surgery that can correct vision in people w h o are nearsighted or farsighted, or who have astigmatism. It’s one of many vision correction surgeries that work by reshaping your cornea, the clear front part of your eye, so that light focuses on the retina in the back of your eye. Dr. Pratibha. S, Assistant Professor, BMSCE Page 8  b) Skin Treatment: Laser therapy is also used cosmetically to:  remove warts, moles, birthmarks, and sun spots  remove hair and tattoos  lessen the appearance of wrinkles, blemishes, or scars Laser toning and tightening is a non-surgical cosmetic correction method that uses lasers to penetrate the deeper layers of the skin. Skin damage due to sun burning or aged skin is removed by directing an intense wavelength of light. Most of the times CO 2, Yttrium Aluminium-Garnet lasers are used. Carbon dioxide (CO2) lasers make shallow cuts. They’re often used for superficial Cancers, such as skin cancer. 3) Laser printers: Laser printers were invented at XEROX in 1969 by Gary Stark weather. It is a printer linked to a computer producing good-quality printed material by using a semiconductor diode laser to form a pattern of electrostatically charged dots on a photoconductor drum, which attracts toner (or dry ink powder). The toner is transferred to a piece of paper and fixed by a heating process.  Charging: In older printers, a corona wire positioned parallel to the drum in more recent printers, a primary charge roller, projects an electrostatic charge onto the photoreceptor (otherwise named the photoconductor unit), a revolving photosensitive drum or belt, which is capable of holding an electrostatic charge on its surface while it is in the dark.  Exposing: A laser printer uses a laser because lasers are able to form highly-focused, precise, and intense beams of light, especially over the short distances inside of a printer. The laser is aimed at a rotating polygonal mirror which directs the light beam through a system of lenses and mirrors onto the photoreceptor drum, writing pixels at rates up to sixty- five million times per second Dr. Pratibha. S, Assistant Professor, BMSCE Page 9   Developing: As the drums rotate, toner is continuously applied in a 15-micron-thick layer to the developer roll. The surface of the photoreceptor with the latent image is exposed to the toner-covered developer roll. Toner consists of fine particles of dry plastic powder mixed with carbon black or coloring agents. The toner particles are given a negative charge inside the toner cartridge, and as they emerge onto the developer drum they are electrostatically attracted to the photoreceptor's latent image (the areas on the surface of the drum which had been struck by the laser). Because negative charges repel each other, the negatively-charged toner particles will not adhere to the drum where the negative charge (imparted previously by the charge roller) remains.  Transferring: A sheet of paper is then rolled under the photoreceptor drum, which has been coated with a pattern of toner particles in the exact places where the laser struck it moments before. The toner particles have a very weak attraction to both the drum and the paper, but the bond to the drum is weaker and the particles transfer once again, this time from the drum's surface to the paper's surface.  Fusing: The paper passes through rollers in the fuser assembly under high temperatures and pressure are used to permanently bond the toner to the paper. One roller is usually a hollow tube (heat roller) and the other is a rubber-backed roller (pressure roller). 4) Barcode scanner: A barcode is a printed series of parallel bars or lines of varying width that is used for entering data into a computer system. A barcode scanner is a device with lights, lenses, and a sensor that decodes and captures the information contained in barcodes. Laser scanner uses laser light source along with oscillating mirrors or rotating prisms to scan the laser beam back and forth across the barcode. Photodiode measures the reflected light from the barcode by generating an analog signal which will be converted to digital signal later. Dr. Pratibha. S, Assistant Professor, BMSCE Page 10  Most barcodes display a twelve-digit number, usually printed underneath as a backup for possible complications. Here are what the numbers represent: First two number: Indicates the country code. Following 5 Numbers on the Right: Product Code. This part of the code is unique to the individual product. Following 5 Numbers: The Manufacturer Code. The five numbers are a unique code that identifies the manufacturer or distributor of the product. Final Number: Check Digit (a Self-Policing System). The final digit of a barcode number is a computer check digit which makes sure the barcode is correctly composed. However, there are a variety of diverse types of barcodes. The most common type is UPC or Universal Product Number restricted to around 20 alphanumerical characters. Any more than that would need a QR (2D Barcode) code. Important Questions and numerical problems: 1. Derive the expression for energy density of radiation in terms of Einstein's A and B Coefficients. 2. Explain the terms with neat diagrams, (i) Population inversion, (ii) Metastable state &, (iii) Resonant cavity. 3. Explain the terms with neat diagrams, (i) Induced absorption, (ii) Spontaneous emission, (iii) Stimulated emission. 4. Explain the three possible ways through which radiation and matter interaction can take place 5. Describe with energy band diagram the construction & working of Semiconductor diode LASER along with applications. 6. With the help of a sketch describe the principle, construction and working of the LASER Printer. 7. Discuss the applications of LASER in bar-code scanner. 8. Find the ratio of population of two energy levels in a LASER if the transition between them produces light of wavelength 6493 Å, assuming the ambient temperature at 27°C. 9. Find the ratio of population of two energy levels in a medium at thermal equilibrium, if the wavelength of light emitted at 291 K is 6928 Å. 10. The ratio of population of two energy levels out of which one corresponds to metastable state is 1.059 × 10−30. Find the wavelength of light emitted at 330 K. 11. Find the ratio of population of two energy levels in a medium at thermal equilibrium, if the wavelength of light emitted at 300 K is 10-6m. Also find the effective temperature when energy levels are equally populated. 12. The average power output of a LASER beam of wavelength 6500 Å is 10 mW. Find the number of photons emitted per second by the LASER source. 13. The average power of a LASER beam of wavelength 6328 Å is 5 mW. Find the number of photons emitted per second by the LASER source. 14. A pulsed LASER has an average power output 1.5 mW per pulse and pulse duration is 20 ns. The number of photons emitted per pulse is estimated to be 1.047 ×108. Find the wavelength of the emitted LASER. 15. A pulsed LASER with power 1 mW lasts for 10 ns. If the number of photons emitted per pulse is 5 ×107. Calculate the wavelength of LASER. 16. A pulsed LASER has an average power output 1.5 mW per pulse and pulse duration is 20 ns. The number of photons emitted per pulse is estimated to be 1.047 ×1010. Find the wavelength of the emitted LASER. Dr. Pratibha. S, Assistant Professor, BMSCE Page 11