Interaction of Electromagnetic Radiation: Quantum Structures

Interaction of Electromagnetic shaft of light Quantum StructuresPreparation and ikon of Quantum dust Infr ard Photo Detector and Its Application in night Vision DevicesSubmitted byMangala Gowri MFocus of the study during this flowing was to get wind interaction of electromagnetic beam of light with quantum structures.Interband diversity and intraband enactment constituentic number 18 ii types of mutation possible in semiconductors. Intraband enactments be unique for the quantum semiconductor structures. Intraband conversions amid the quantized nix levels are possible depending on several parameters. The ring wavelength depends on effective masses of the carriers, parameters like size, shape and composition of the quantum structures. practical observations made on quantum structures like quantum goods and quantum dots were very interesting. The first look observation of infrared absorption betwixt conduction subbands of n-doped GaAs/AlGaAs quantum substanti all ys was inform in 1985. It was confirmed that intersubband varietys between electronic deposits of quantum wells are inexpugnablely polarized along the confinement potence cathexis. 1 Therefore light whose polarization has lot along the confinement potential command gets absorbed. Therefore light must carry a polarization comp one and only(a)nt perpendicular to the quantum well layers. 1 This is the strong limitation for the quantum well infrared photo detectors. On the other hand, quantum wires and quantum dots theoretically do not have this limitation on the polarization manner of incident radiation sickness. For quantum well polarization, direction radiation should not be form (perpendicular) to the confinement potential direction, whereas this type of normal incidence is allowed for quantum dots.Oscillator StrengthOscillator effectivity is a dimensionless quantity that expresses the fortune of absorption or emission of radiation in transitions between might level s of an atom or molecule. 2 When an electronic transition occurs an oscillating dipole chip give be induced by interaction of electric domain of a aim of the organization with electromagnetic radiation. The following model explains the mechanism of transition in a organisation in general. approximate an electron changes its energy from En to Em by changing its situate from n to m. During the transition it will be in a democracy which is superposition of the two states. = an + bm hazard that the electron in the state n is a2 and probability that it is in state m is b2 so that at any era a2 + b2 =1. We put up see that expectation value mn oscillates at frequency nm = , nm is the transition frequency.mn is the oscillator strength as the strength of the palpitation is proportional to the expectation value of intermediate state. It is also called the transition hyaloplasm broker. For allowed transitions mn is a nonzero value and for forbidden transitions it is zero.Transi tion Dipole issueTransition dipole twinkling is the dipole here and now associated with the transition between two states. It is a complex vector quantity. It encodes phase factors associated with the two states. The direction of this dipole arcminute is the polarization of the transition. The polarization of the transition determines the interaction of the administration with electromagnetic radiation with a given polarization. Square of the dipole moment of transition gives the strength of the transition.Transition dipole moment is off- cut matrix element of position operator multiplied by the interpretericles kill. Classically, dipole moment is product of charge and separation between the two charges. In the presence of an electric field, the two charges will experience a personnel office in opposite direction so that a torque acts on the dipole. Similarly, during transition, coupling between an electromagnetic wave and transition dipole moment of the frame depends on th e charge distri thoion within the system, strength of the field and the relative polarization of the field and the transition. Also transition dipole moment depends on the geometries and relative phases of the two states involved in transition. The concept of transition dipole moment is very useful to determine whether a transition is allowed or not. If the integral defining transition dipole moment is nonzero, that transition is allowed.Perturbation TheoryTo understand the mechanism of interaction between the system and electromagnetic radiation, we adopt quantum mechanical perturbation theory. Incident radiation is case-hardened as a perturbation. Electromagnetic radiation provides a time strung-out potential, which assists quantum jumps between energy levels. So total Hamiltonian of the system has two parts, one is time independent and another is time dependent. If time dependent part is small compared to time independent part, then that jackpot be enured as a perturbation.Co nsidering two level system, where a and b are two eigen states of unperturbed Hamiltonian H0. The two states are orthonormal. Any other state of the system burn be written as a additive combination of those two states.(0) = Ca a + Cb bCa and Cb are constants, which include information about probability of finding the system in respective states.Suppose we are curious to know the state of the system after a time t. If there is time dependent perturbation, (t) is once again superposition of the two states. Not only the two states evolve with time, but also coefficients Ca and Cb are also exits of time. If we eject determine Ca(t) and Cb(t) we can understand the system at time t. Several mathematical stairs lead us toa = Andb = Where a and b are time derivatives of Ca(t) and Cb(t) respectively.Both of the above equations taken together are tantamount(predicate) to time dependent Schrodinger equation for a two level system.The diagonal matrix elements of H vanish.Therefore,a = b = With Considering that H is small, above equations can be solved by a exercise called successive approximations. present we also consider that perturbation is having sinusoidal time dependence. past And In the first order we have is the driving frequency and 0 is the transition frequency.If and 0 are very close to each other flake term in the square brackets dominates. So we can say + 0 0 We drop first term and after simplificationThe transition probability gives the probability that a particle started from the initial state will reach at final state in time t.We can see here that transition probability as a function of time oscillates sinusoidally.Fig Transition probability as a function of time, for sinusoidal perturbation.Maximum value of probability is . The probability of rising to the maximum value is much less than 1 for small perturbation. Another function to observe here that the probability of transition is highest when 0.Fig Transition probability as a functio n of driving frequency.Thus as time goes on width of the peak becomes narrower and height of the peak becomes higher. That means that the system will undergo transition with higher probability.Emission and Absorption of RadiationAn electromagnetic wave consists of transverse oscillating electric and magnetic fields. An atom reacts primarily to the oscillating electric element of radiation. Assume that an atom is subject to a sinusoidally oscillating electric field. Consider that the field is polarized along z direction.Then the perturbing Hamiltonian is written asNote Considering that the period of oscillation of the field is long compared to the time taken by the charge to move around within the atom we adopt electrostatic regulation for Vab that is equal to ThenWhere P = is transition dipole moment. is an odd or regular function of z. We consider that the diagonal matrix elements of H vanish. Then the interaction of radiation with the system is governed by precisely the kind of oscillatory perturbation with Vab Note P is off-diagonal matrix element of z component of dipole moment operator qr.Transition probability is proportional to the energy density of the perturbing fields. And we see that the probability is proportional to time.If incident radiation is monochromatic, transition probability oscillates. However, if the system is exposed to incoherent spread of frequencies that flopping constitution disappears. The transition rate will be a constant.In the calculations, we have assumed that the direction of propagation of perturbing radiation is y direction and it is polarized along z axis. However, in practice the system (like quantum well, quantum dot) is exposed to a radiation coming from all directions and with all possible polarizations. Then the energy of the field is shared equally among these different modes. So in the order of we have to substitute the average of P.n2 with n is the direction of polarization of radiation. Average is over all polarizations and all incident directions.Quantum WellA quantum well can be considered as idealized square, finite and rhombohedral potential well. It is now evident that absorption of radiation by quantum well depends on the direction of the transition dipole moment and direction of polarization of incident radiation. It can be shown that the wave function of quantum well is a even function in ground state and it is alternatively even or odd in higher states.In order to P be nonzero a and b should be of opposite parity since z is odd. In addition, direction of P depends on a and b. Since the wavefunction of the quantum well has only z component, transition dipole moment will also be directed along the z direction i.e. along the direction of potential Vwell(z).In the case of normal incidence, the polarization of radiation is perpendicular to the walls of the well barrier or to the potential. The n that refers to polarization direction of radiation is in xy plane.So choosing cylind rical polar coordinates, we haveAnd . Thus, .Then, Which implies that normal incidence in quantum wells is forbidden.The polarization selection rules for transitions in quantum wells are summarized below.Quantum DotQuantum dot is a quantum structure, which is confined three dimensionally. Thus, the confinement potential has all the three x, y, z components. Similarly the wave functions representing the states of quantum dot have x, y, z components. So the scalar product between transition dipole moment and the polarization direction of incident radiation will not be equal to zero.Average of is not zero in quantum dots. Thus, the quantity in quantum dots is nonzero. There is no restriction for direction of polarization of radiation theoretically. in time though normal incidence intraband absorption is forbidden in quantum wells, they are allowed in quantum dots. This is major fact of great interest in the outgrowth of infrared photodetectors.I attended a two-day collaborators sh op class organized by Centre of ART, SIT, Tumkur from 20-02-2014 to 21-02-2014.Study Plan In the undermentioned half year, focus of the study will be MOCVD growth process of quantum dots.Signature of the CandidateSignature of the Guide(Manala Gowri M) (Prof. (Dr.) Ganesh N. Raikar)ReferencesA. Weber. Intraband Spectroscopy of Semiconductor quantum dots, 1998.2. http//en.wikipedia.org/wiki/Oscillator_strength3. Proefschrift. Optical Properties of Semiconductor Quantum Dots, 20114. Griffith. D.J, intromission to quantum Mechanics, 2nd Ed, Pearson Education Inc, 2006.