Model Answer (Paper code: AR-7112) M. Sc. (Physics) IV Semester Paper I: Laser Physics and Spectroscopy Section I Q1. Answer (i) (b) (ii) (d) (iii) (c) (iv) (c) (v) (a) (vi) (b) (vii) (b) (viii) (a) (ix) (c) (x) (c) Q2. Answer Section II Population inversion exists whenever more atoms are in an excited atomic state than in some lower energy state. Lasers can produce coherent light by stimulated emission only if a population inversion is present. A population inversion can be achieved only through external excitation of the atomic population. The excitation mechanism is a source of energy that excites, or "pumps," the atoms in the active medium from a lower to a higher energy state in order to create a population inversion. In gas lasers and semiconductor lasers, the excitation mechanism usually consists of an electrical-current flow through the active medium. Solid and liquid lasers most often employ optical pumps; for example, in a ruby laser, the chromium atoms inside the ruby crystal may be pumped into an excited state by means of a powerful burst of light from a flash lamp containing xenon gas. Further pumping serves only to excite as many downward transitions as upward transitions, since the probability of absorption is equal to the to the probability of stimulated emission for a given transition. For a population inversion to be produced, energy absorption must occur for a transition different from the transition undergoing stimulated- thus the need for at least a three level system. If T 32 is the transition rate for the transition from 3 2 and T 21 is the transition rate for the transition from 2 1, then the a necessary condition is that T 32 > T 21 For obtaining population inversion a minimum pump power is required and is given by W pt T T For a three level system, one can write 32 32 T 21 T 21
N = N 1 + N 2 + N 3 N 1 + N 2 where we have assumed that the atoms from level 3 drop down to level 2 so quickly that level 3 is essentially unpopulated. And since, N = N 2 N 1 and for population inversion it should be positive, one can write N N 2 N1 N N and N 2 2 It is clear the population of the upper level (N 2 ) should be more than 50 % for the laser action. Q3. Answer (i) Consider a laser which is oscillating on a rather large number of longitudinal modes. Under ordinary circumstances, the phases of these modes will have random values. Let s now suppose that the oscillating modes, while still having equal or comparable amplitudes, are somehow made to oscillate with some definite relation between their phases. Such a laser is referred to as mode locked, and the process by which the modes are made to adopt a definite phase relation is referred to as mode locking The methods of mode-locking can be divided into two categories: (1) Active-mode-locking, in which the mode-locking element is driven by an external source. (2) Passive mode-locking, in which the element which induces mode-locking is not driven externally and instead exploits some non-linear optical effect such as saturation of a saturable absorber or non-linear refractive index change of a suitable material.
(ii) The frequency spacing of the longitudinal mode in the cavity is given by c 2L where, c is the velocity of light and L is the length of the cavity. Putting, c = 3 x 10 8 m/s, and L = 1.5 m so, ν = 2 x 10 8 Hz Q4. Answer (i) A longitudinal mode has its nodes located axially along the length of the cavity, whereas Transverse modes, with nodes located perpendicular to the axis of the cavity, may also exist. A longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces. All other wavelengths are suppressed by destructive interference. A transverse mode of a beam of electromagnetic radiation is a particular electromagnetic field pattern of radiation measured in a plane perpendicular (i.e., transverse) to the propagation direction of the beam. (ii) The distance of separation between consecutive lines is 2 2 L For a single mode oscillation λ has half the width of gain profile Therefore the length L=λ 2 /2μ λ Putting μ=1, λ = 6328 x 10-10 m, L = 2 x 10-3 nm L = 10 cm Q5. Answer The grating equation is (a+b)sin = nλ If the nth order of wavelength λ 1 coincide with (n+1)th order of λ 2 Then (a+b)sin = nλ 1 = (n+1)λ 2 n 1 1 2 n Here, λ 1 =5400 Å, λ 2 =4050 Å n 1 5400 4050 n = 3 n Putting the value of n and = 30 in the first equation, we get (a+b)sin30 = 3 x (5400 x 10-8 cm) (a+b) = 3.24 x 10-4 cm
Number of lines per cm = 1 4 3. 24 10 = 3086 Q6. Answer (i) If a light quantum hv o hits a molecule, an elastic scattering process, i.e., Rayleigh scattering of quanta with energy hv o, has the highest probability. The inelastic process, during which vibrational energy is exchanged, has a much lower probability; is called Raman scattering. It emits quanta of energy hv o hvs,. At ambient temperature most molecules are in their vibrational ground state. According to Boltzmann s law, a much smaller number is in the vibrationally excited state. Therefore, the Raman process, which transfers vibrational energy to the molecule and leaves a quantum of lower energy (hv o hvs) has a higher probability than another process where molecule from the excited state after getting exited return back to the lower energy level by leaving a quantum of higher energy (hv o + hvs). The Raman lines are referred to as Stokes lines and anti-stokes lines, respectively. Fig. below shows the Stokes lines are caused by quanta of lower energy whereas; the anti-stokes lines are caused by the quanta of higher energy. Since the intensities of Stokes line are higher than those of anti-stokes lines, therefore Stokes lines are usually recorded as Raman spectrum. (ii) Fluorescence: Fluorescence occurs when a molecule in the lowest vibrational energy level of an excited electronic state returns to a lower energy electronic state by emitting a photon. This process is called Fluorescence. The lifetime of an excited singlet state is approximately 10-9 to 10-7 sec and therefore the decay time of fluorescence is of the same order of magnitude. If fluorescence is unperturbed by competing processes, the lifetime of fluorescence is the intrinsic lifetime of the excited singlet state. The quantum efficiency of fluorescence is defined as the fraction of molecules that will fluoresce. Phosphorescence: When molecules absorb light and go to the excited state they have two options. They can either release energy and come back to the ground state immediately or undergo other non-radiative processes. If the excited molecule undergoes a non radiative process, it emits some energy and come to a triplet state where the energy is somewhat lesser than the energy of the exited state, but it is higher than the ground state energy. Molecules can stay a bit longer in this less energy triplet state. This state is known as the metastable state. Then metastable state (triplet state) can slowly decay by
emitting photons, and come back to the ground state (singlet state). When this happens it is known as phosphorescence. As phosphorescence originates from the lowest triplet state, it will have a decay time approximately equal to the lifetime of the triplet state (ca. 10-4 to 10 sec).therefore phosphorescence is often characterized by an afterglow which is not observed for fluorescence. Factors influencing the fluorescence Fluorescence is dependent on light exposure and temperature. The fluorescence decreases at high exposure. Fluorescence is indirectly correlated with temperature. As the temperature increases, the fluorescence decreases. Fluorescence can also be quenched by using some fluorescence quencher material. Q7. Answer (i) The absorption of radiation (UV or visible) corresponds to the excitation of outer electrons. There are three types of electronic transition which can be considered; 1. Transitions involving p, s, and n electrons 2. Transitions involving charge-transfer electrons 3. Transitions involving d and f electrons (not covered in this Unit) When an atom or molecule absorbs energy, electrons are promoted from their ground state to an excited state. Some possible electronics transitions are shown below in the molecules These transitions can be monitored using UV-Visible absorption spectroscopic technique. (ii) The difference between fluorescence and phosphorescence: When light is supplied to a sample of molecules, we immediately see the fluorescence. Fluorescence stops as soon as we take away the light source. But phosphorescence tends to stay little longer even after the irradiating light source is removed. Fluorescence takes place when excited energy is released, and the molecule comes back to the ground state from the singlet-excited stage. Phosphorescence takes place when a molecule is coming back to the ground state form the triplet excited state (metastable state). The energy released in the fluorescence process is higher than that in the phosphorescence. In fluorescence, the absorbed amount of energy is released back but, in phosphorescence, released energy is lower than what is absorbed.
Q8. Answer Monochromator is used to separate and transmit a narrow portion of the optical signal chosen from a wider range of wavelengths available at the input. In the simplest case the monochromator is composed from two slits (entrance and exit) and a dispersion element (prism or diffraction grating). In both these elements, one takes advantage of the dependence of the refraction angle (prism) or the reflection angle (grating) on the radiation wavelength. In the case of prism, the larger the photon energy (shorter wavelength) the smaller is the refraction angle. The main goal of the entrance slit is to define the geometric properties of the investigated irradiation. The dispersion or diffraction is only controllable if the light is collimated, that is if all the rays of light are parallel, or practically so. The goal of the prism is to disperse the light into a rainbow. At the exit slit, the colors of the light are spread out (in the visible this shows the colors of the rainbow). Schematic diagram Single monochromator: In single monochromator there is only one dispersing element i.e. grating is used Schematic diagram double monochromator: In double monochromator there are two dispersing element i.e. grating is used
Advantage of double monochromator: The main advantage of double monochromator over single monochromator is that it reduces stray light i.e. unwanted light to go to the detector. Other advantage it that because of an addition grating the dispersion is larger and we get much resolve spectra in the double monochromator than from single monochromator.