termined by the mixing of the atomic states by the optical ﬁeld see Refs. How to solve time dependent Optical Bloch Equations for a three level system? 0. Ghosh,* Lars Jönsson, and John W. 2 Feynman-Bloch Equations Assume deg = dge = d, the total Hamiltonian under the dipole approximation is: H = ~!0^¾ee ¡d^ ¢E = ~!0^¾ee ¡d¢E(^¾ge + ^¾eg) Using i~ O^_ = [O;H^]; the equations of motion in Heisenberg picture for ¾ij = h¾^iji are (note that the equations of motion for. In this paper, the general validity conditions for the. Bloch Equations with Relaxation • Differential Equation – Ordinary, Coupled, Non-linear • No analytic solution, in general. In the first one, the relaxation is in nature a non-Markovian process; one cannot obtain a set of differential equations for the perturbed bath-averaged components of the Bloch vector. 1 $\begingroup$ Is it possible to derive the optical Bloch equations for a 2-level-system driven by an oscillating EM-Field from the von Neumann equation for the density operator?. The coupled Maxwell-Bloch equations can be solved using a ﬂnite diﬁerence time domain (FDTD) method by directly discretizing the time and the space [26{28]. Then, we have. Optical Bloch equations with motion The motion of a two-level atom driven by a laser ﬁeld. The three. Sensitivity improvement of optical pumping atomic magnetometers using Bloch equations Malihe Ranjbaran * 1 , Mohammad Mahdi Tehranchi Dr , Seyedeh Mehri Hamidi Dr , Seyed mohammd hosein Khalkhali Dr. The marginal ray is an on-axis ray which travels from the center of an object to the edge of the stop and to the center of the image. for energy transfers, the form of the equations depends on that interpretation. It is shown that this system is integrable in the frameworks of the inverse scattering transformation method. Application of the phase-modulated pulsed light for advance spectroscopic measurements is the area of growing interest. The resulting electric polarization density of the medium 3. Also note that in the case of a so-called stratiﬁed medium (see, e. Two numerical schemes are developed for solutions of the bidimensional Maxwell–Bloch equations in nonlinear optical crystals. Quantum simple harmonic oscillator. Bloch–Redﬁeld equation when applied to optical excitation. Simple and intuitively appealing picture based on. 1 Introduction. Relationship to rate equation approach. Hi, I'm trying to derive the optical bloch equations for this system: But I'm not sure how to write down the original equation of motion of the … Press J to jump to the feed. Optical Bloch equations • 𝑖(𝑑11−𝑑22) 𝑖𝜕 = 2 𝑖𝑖 ℏ 𝜇𝑡𝜌21−𝜌21∗ − 𝑑11−𝑑22−𝑑11−𝑑220 𝜏, where 𝜏 is the lifetime of the upper level • This is because the population difference 𝜌11−𝜌22 would relax to its equilibrium value. Hello! In most of the textbooks that cover the optical bloch equations for a two-level system they only discuss the condition of when the laser is linearly polarized. We show that the classical. As an example of the application of the results obtained we describe the experiments on optical Bloch oscillation and breathing modes. – Numerical solutions for all cases. Maysenhölder, Acustica 78 (1993) 246-249. Does anyone know how the optical bloch equations for a two level system changes when the laser beam is circularly polarized?. Density Matrix Equations of Motion for a Two-Level Atom 6. , an atomic sample in a laser field. 19 May 2016. We probe this band structure by placing a Bose-Einstein condensate into excited Bloch states of an optical kagome lattice, and then measuring the group velocity through the atomic momentum distribution. The interaction of chirped femtosecond laser pulses with hybrid materials - materials comprised of plasmon sustaining structures and resonant molecules - is scrutinized using a self-consistent model of coupled Maxwell-Bloch equations. Lecture 1 Two-level atom in a radiation eld Our perception of the macroscopic world is dominated by light and matter. Optical Bloch Equations 6. Semiconductor Bloch equations. 3 Bloch Equations Atoms in low concentration show line spectra as found in gas-, dye- and some solid-state laser media. Optical Bloch equations • 𝑖(𝑑11−𝑑22) 𝑖𝜕 = 2 𝑖𝑖 ℏ 𝜇𝑡𝜌21−𝜌21∗ − 𝑑11−𝑑22−𝑑11−𝑑220 𝜏, where 𝜏 is the lifetime of the upper level • This is because the population difference 𝜌11−𝜌22 would relax to its equilibrium value. 422 Atomic and Optical Physics II, Spring 2013 View the complete course: http://ocw. Some of these features. So it's easy to see that those 2 numbers will be 12 and 11. However, the direct discretization of the Maxwell-Bloch equation is computationally ineﬁective, since it will result in. This physics course presents a general derivation of the master equation and the optical Bloch equations. The equations (2) have a well-known Bloch integral of. Maxwell's equations: EXP3_3: Displacement current, EMW in empty space, Maxwell's equations: Electromagnetic waves: EXP3_4: Energy and source of EMW, antennas, pressure, waves along cables; wave guides : Introduction into ray optics: EXP3_5: Geometric optics, chromatic dispersion, from wave to geometric optics: Reflection and refraction: EXP3_6. Applied Mathematics and Computation 219:8, 4082-4095. Various commercial mathematics and graphics packages were used for the calculations until we settled on MatLab as the optimum choice. We show that, in their unstable regime of operation, the "Maxwell-Bloch" equations that describe light-matter interactions and dynamics inside a bad-cavity-configured laser carry the same resonance properties as any externally driven mechanic or electric oscillator. Kannari, F & Obara, M 1990, ' Multilevel maxwell-bloch-equation description of ultrashort laser pulse amplification in inhomogeneously broadened XeCl media ', Journal of the Optical Society of America B: Optical Physics, vol. Bidégaray, A. Electromagnetic Waves propagating in an optical fiber consist of : - TE Modes. They consist of three first-order equations for the electric field in a single longitudinal cavity mode, which became nonlinear because the system oscillates between at least two discrete energy levels. where f(wo) is the contour of an inhomogeneously broad- ened line, Iml is the matrix element of the current of the resonance transition of a separate atom, and p is the density of the population inversion. Hence, the microscopic founded Bloch equations can be used for the description of high intensity optical experiments on light harvesting complex of photosystem II (LHC II). renormalization. The potential of the Bloch. The vector model of the Bloch equations 4. do not necessarily involve gyromagnetic spin systems. How is Optical Bloch Equations (physics) abbreviated? OBE stands for Optical Bloch Equations (physics). (47)] and the local-field correction 7(k) are related. Processes Resulting from the Intensity-Dependent Refractive Index 7. Section 6 presents the scaling arguments needed in homogenization, where we show that only a few Bloch waves contribute to the macroscopic ﬁeld. The homogeneously broadened single-mode laser equations are described as follows, dE dt = [(1 + i )E(t) + AP(t)] (1) dP dt = (1 i )P(t) E(t. (3) Dependingontheparticularquasimomentumkdistribution, an initially localized particle can propagate from site to site by means of the so-called Bloch tunneling, resulting in a ballistic spread over the whole lattice [28]. Optical bloch equations and circular polarization. Does anyone know how the optical bloch equations for a two level system changes when the laser beam is circularly polarized?. Carbon nanotube Bloch equations are proposed to analyze the many-body electron dynamics for optical interband transitions in carbon nanotubes. Although it was ﬁrst theoretical predicted in 1929 [66, 67], Bloch oscillations were not observable in natural crystals until 1993, due to the presence of lattice defects [65] 2. Classical Bloch equations and the limits of their applicability are derived from more general master equations. Split the resulting number "123" into 2 parts - 1 and 23. PACS numbers: 03. A vacuum is given an n value of 1. The system of equations for this specific problem is also known as the optical Bloch equations. equations are given in Section 4, and they are used in Section 5 to give a represen-tation of the general solution to Maxwell’s equations in periodic media. 19 May 2016. Optical Bloch oscillations (BO) in waveguide arrays (WGAs) [1] is the optical analogue of the celebrated The remaining N 1 equations are to be satisfied by. The unorthodox solutions of the Bloch equations, which do not have the form of exponentially damped harmonic oscillations, are confined to rather small detunings \delta^2 = (\gamma-\gamma_t)^2/27 and small field strengths \Omega^2= 8 (\gamma-\gamma_t)^2/27, where \gamma and \gamma_t describe decay rates of the excited state (the total population relaxation rate) and of the coherence, respectively. The real-valued Maxwell-Bloch equations on R 3 are investigated as a Hamiltonian dynamical system obtained by applying an S 1 reduction to an invariant subsystem of a dynamical system on C 3. 2 Quantum mechanical approach 24 4 Solving the Coupled Equations 27. However, many other. Several theories have been proposed to explain this failure of the Bloch equations. Lecture 26 - Normal modes of ion lattice vibration, acoustic and optical modes. Lecture aims to explain: 1. Neumann system (T∗SU(2),ω c,H cn) is (g tg−1) t = [σ,Ad g(τ)]; g(t) : I−→ SU(2) while the Maxwell-Bloch equations can be rewritten in the form (g tg −1) t +c(g tg ) x = [σ,Ad (τ(x)]; g(t,x):I−→ SU(2). The Maxwell–Bloch equations, also called the optical Bloch equations describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. ρ= 1 2 (I+Xcosφsinθ+Ysinφsinθ+Zcosθ) = 1 2 (I+~rρ· ~σ) whereIis the identity matrix,~σis the 3-element ‘vector’ of Pauli Matrices (X,Y,Z), and~rρis the unit Bloch vector. In silicon quantum dots the EL depends on the size and the EL intensity is higher for smaller size [5]. In a recent experiment [ DevoeR. 2litrehotrod. The damped optical Bloch equations have been used to express the response of near-resonant atoms to an ap plied field. Rabi frequency small compared to spontaneous emission rate), a perturbative method to solve linear differential equations can be applied. As an example of the application of the results obtained we describe the experiments on optical Bloch oscillation and breathing modes. By rewriting the analytic solution in an alternate form, we are able to emphasize a number of unusual features:. For derivation of the equations see for example §7 of Atomic Physics by CJ Foot. The propagation of ultra-short optical pulses is. In this paper, according to the Bloch equation, the output signal was established. Daily Killer Sudoku Can you fill every row, column and 3x3 block with the digits 1 to 9?. In particular,. We show that, in their unstable regime of operation, the "Maxwell-Bloch" equations that describe light-matter interactions and dynamics inside a bad-cavity-configured laser carry the same resonance properties as any externally driven mechanic or electric oscillator. Sensitivity improvement of optical pumping atomic magnetometers using Bloch equations Malihe Ranjbaran * 1 , Mohammad Mahdi Tehranchi Dr , Seyedeh Mehri Hamidi Dr , Seyed mohammd hosein Khalkhali Dr. 1 we take a look onto an experiment from modern quantum optics. The optical Bloch equations are known in the literature in two very general limits in relation with the relaxation processes. In physics and chemistry, specifically in nuclear magnetic resonance, magnetic resonance imaging, and electron spin resonance, the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = as a function of time when relaxation times T1 and T2 are present. Published at The African Review of Physics 8(10) 65-68. The optical Bloch equations, which give the time evolution of the elements of the density matrix of an atomic system subject to radiation, are generalized so that they can be applied when transitions between pairs of states can proceed by more than one stimulated route. Department of Energy's Office of Scientific and Technical Information. Other example is the description of a cold atoms motion in an optical lattice with mathematical model based on the Gross-Pitaevskii equation [1]. Optical Bloch Equations (OBE) describe the coherent exchange of energy between a quantum bit (qubit) and a quasi-resonant driving field in the presence of a thermal bath. - Helical EH and HE modes contain both axial electric and magnetic fields. We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. (The parameters nj can also be interpreted as excitation densities with units of m −3; only in rate equation systems containing nonlinear terms, e. Semiconductor Bloch equations. optical matrix element Carrier dynamics. Bloch waves and Bloch band of Bose-Einstein Condensates in optical lattices are studied. The optical Bloch equations are derived for the simplest case of a pure nuclear two-level system and for the more complex cases taking into account the presence of magnetic sub-states, hyperfine. Rare-earth-doped crystals can be modelled as inhomogeneously broadened two-level atoms. equations [2], [3] describe mode coupling in optical ﬁber as a ﬂow on the Poincaré sphere. Lecture aims to explain: 1. By combining the field-susceptibility technique with the optical Bloch equations, a general formalism is developed for the investigation of molecular photophysical phenomena triggered by nanometer scale optical fields in the presence of complex environments. Optical resonance for two level atoms A. equations of motion for tightly bound electron in one dimension to dx dt = 2 0a ~ sinka ~ dk dt = eE m ˝ dx dt: Take 0 = 1 eV, a = 2 A, E = 106V/cm, and ˝ = 10 14s. The Maxwell–Bloch equations, also called the optical Bloch equations, were first derived by Tito Arecchi and Rodolfo Bonifacio of Milan, Italy. BLOCH EQUATIONS 27 2. It is natural that with the heightened interest in few-mode and multimode optical ﬁber, researchers would attempt to generalize the Poincaré sphere description and Poole’s equations to a larger number of modes. The results may have potential applications in optical splitting and waveguiding devices and shed light on the coherent phenomena in optical lattices. 0= k(t= 0) across the Brillouin zone. Beam dynamics in this new type of optical structures is examined in detail for both one- and two-dimensional lattice geometries. Optical Bloch equations are widely used for describing dynamics in a system consisting molecules, electromagnetic waves, and a thermal bath. Now, we will make the deduction of Bloch's optical equations by examining the temporal dependence of the elements of the density operator matrix. (2012) Variational iteration method for solving the time-fractional diffusion equations in porous medium. We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. You will learn about various solutions of the optical Bloch equations, and you will discuss the quantum Monte Carlo wavefunction approach. The Effects of spectral deformation on soliton behaviour is studied. 2 The Hamiltonian 13 3 Bloch-Zener Oscillation Theory 19 3. 4392 Laird, Budimir, and Skinner: Derivation of the Bloch equations namics has subsided. in optical lattices; cf. Simply discussing what modifications make sense provides a strong plausibility argument for the optical Bloch equations. The Maxwell–Bloch equations, also called the optical Bloch equations describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. Two macroscopic variables were brought in to eliminate the summation symbol in terms of single mode and homogeneously broadening. 25 Optical Illusions That Prove Your Brain Sucks. Inthispaper,wehaveemployedthelastapproach to give details of the investigated QD-SOA [ , ]. It is a Bloch plane wave with slowly varying amplitude a(t,x). tem: Optical Bloch Equation Let the Hamiltonian be the system Hamiltonian H0 plus an interaction with an optical light ﬂeld: H = H0 ¡E(t)¢„ (1. (52) results in e(k, w) = 1 +. Since ancient Greek philosophy our conceptions of light and matter follow a capricious. The first is that the work formulated a longitudinal LLE equivalent to that of , deriving it from the Maxwell–Bloch equations (MBE) in the dispersive limit. They do not describe a physically-observable property of the system. Several theories have been developed to explain the phenomenon. In this paper, the general validity conditions for the. Optical Flow Estimation 3. (NMR) Bloch Equation Optical analogue: optical Bloch equation. Optical bloch equations and circular polarization. Sometimes they are called the equations of motion of nuclear magnetization. Kannari, F & Obara, M 1990, ' Multilevel maxwell-bloch-equation description of ultrashort laser pulse amplification in inhomogeneously broadened XeCl media ', Journal of the Optical Society of America B: Optical Physics, vol. The system of equations for this specific problem is also known as the optical Bloch equations. – Analytic solutions for simple cases. The optical Bloch equations are derived for the simplest case of a pure nuclear two-level system and for the more complex cases taking into account the presence of magnetic sub-states, hyperfine. 50, 1269 ( 1983)], it was found that the optical Bloch equations could not satisfactorily explain the signal that was observed for free-induction decay in the impurity ion cyrstal Pr3+:LaF3. In silicon quantum dots the EL depends on the size and the EL intensity is higher for smaller size [5]. Bidégaray, A. 3 – 7 have remarkable structural properties. Since we are dealing with a single time displacement between two frames, ¢t = 1 and thus disappears. Find books. 1 $\begingroup$ Is it possible to derive the optical Bloch equations for a 2-level-system driven by an oscillating EM-Field from the von Neumann equation for the density operator?. 1 we take a look onto an experiment from modern quantum optics. Expanded Course Description: Quantum Mechanics Schroedinger wave equation and time-dependent perturbations; Fermi’s Golden Rule; Density matrix formalism-decay rates and. 3 Bloch Equations Atoms in low concentration show line spectra as found in gas-, dye- and some solid-state laser media. So it's easy to see that those 2 numbers will be 12 and 11. dM~ dt = M~ ⇥ B~ Mx ˆi+My ˆj T 2 (Mz M 0) ˆk T 1 + Dr2M~. Since ancient Greek philosophy our conceptions of light and matter follow a capricious. Numerical simulation results are given for an off-axis 3-pulse. We extend to more than one spatial dimension the semiclassical full-wave vector Maxwell-Bloch equations for the purpose of achieving an adequate and rigorous description of ultrashort pulse propagation in optical waveguides containing resonant nonlinearities. 08 Lens Equations. (2012) A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D. The Bloch equations as originally applied to nuclear magnetic. They are analogous to the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. By studying the linear stability of the constant solutions of these four equations we observe various regimes, from stable, to modulational unstable, and unstable at all frequencies. IMAGING EQUATIONS The imaging equations can be derived by tracing the chief and marginal rays of an optical system. Beam dynamics in this new type of optical structures is examined in detail for both one- and two-dimensional lattice geometries. Bloch waves and Bloch band of Bose-Einstein Condensates in optical lattices are studied. I will review here Bloch's theorem, and how we can use it to treat this periodic system. Press question mark to learn the rest of the keyboard shortcuts. Topics to be covered include: translational symmetry and Bloch's theorem, rotational symmetry and group representation, electron-electron interaction and Hartree-Fock equations, APW, OPW, pseudopotential and LCAO schemes of energy band calculations, Boltzmann equation and thermoelectric phenomena, optical properties of semiconductors. Optical resonance for two level atoms A. Hence, the microscopic founded Bloch equations can be used for the description of high intensity optical experiments on light harvesting complex of photosystem II (LHC II). The optical properties of such systems are examined with the example of periodic sinusoidal gratings. electrons after optical excitation Graphene Bloch equations. 5 Polarization States of Light 14 1. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten suitably microstructured ﬁlament. To understand your results, we will use Bloch's theorem. 2 the important "dressed state" model is. And this is sort of the subject of master equation open system dynamics. Request PDF | Optical Bloch Equations | To set the stage, in Sect. Carbon nanotube Bloch equations are proposed to analyze the many-body electron dynamics for optical interband transitions in carbon nanotubes. A particularly attractive technique translates. Overview of optical fiber communication – Historical development, The general system, advantages of optical fiber communications. The optical properties of silicon quantum dots specially the EL is affected by different factors such as the preparation methods and conditions (laser ablation, deposition. With these polarizations as the source term, the Maxwell equation for the signal field is solved both in the frequency and time regions. 3 In the case where n t and n t are constants, Eq. This yields equations which determine the proﬁles wj. Phase- and polarization-controlled two-photon rabi oscillation of the biexciton state in a semiconductor quantum dot In this paper, the optical Bloch equations describing the mechanism of cavity QED are investigated to obtain the transfer function of the Rabi oscillation with the. Such equations, analogous to the Maxwell-Bloch or optical Bloch equations, lack one of the beautiful and most useful features of the Bloch equations. H|ψi = E(1) |ψi ⇒ Difference equation −J ψ(xj−1)+ψ(xj+1) = E(1) ψ(xj) Bloch band (N= 31) 0 10 20 30 k −3 −2 −1 0 1 2 3 E k (1) /J Solution [ﬁnite lattice (Nsites)] ψk(xj) = sin h π(k+1)j N+1 i ⇒ |ψki = q 2 N+1 PN j=1 sin h π(k+1)j N+1 i |xji Energy eigenvalues [0 ≤ k

= −(cec∗ g M +c. Could you show me the Eq. 422 Atomic and Optical Physics II, Spring 2013 View the complete course: http://ocw. edu/8-422S13 Instructor: Wolfgang Ketterle In this lecture, the. Then,the optical Bloch equations for the density operators are solved under the external pump-fields, in terms of which the nonlinear polarization is evaluated. For in- stance, the solutions of associated linear systems obey. However, the direct discretization of the Maxwell-Bloch equation is computationally ineﬁective, since it will result in. needs to be modelled by extending Bloch equations beyond the Hartree-Fock approximation (Boltzmann equation) Anisotropic carrier distribution. BLOCH EQUATIONS 27 2. 3 Complex Numbers and Monochromatic Fields 6 1. Mathematical Modeling of Bloch NMR to Solve the Schrodinger Time Dependent Equation Solutions of the Schrödinger are not new in Physics. The resulting electric polarization density of the medium Lecture 12 1. do not necessarily involve gyromagnetic spin systems. - EH and HE Modes. The equations of motion are a numerically tractable. To solve the KdV equation in COMSOL Multiphysics, users can add PDEs and ODEs into the software interface via mathematical expressions and coefficient matching. 5 Optical Bloch equations 6 Applications J. Several theories have been proposed to explain this failure of the Bloch equations. Talanina and C. Simple and intuitively appealing picture based on. the nonlinear Schrodinger equation in one-dimension – linear and nonlinear dispersion – self-phase modulation – optical phase conjugation – optical bistability – pulse compression – temporal solitons – stimulated light scattering – two-level-atom approximation and the optical Bloch equations – Rabi oscillations – the. The first version is very intuitive, but rather slow. 2 Energy Density and Energy Flux 5 1. The course will conclude with a discussion of unraveling open system quantum dynamics. Optical Bloch equations • 𝑖(𝑑11−𝑑22) 𝑖𝜕 = 2 𝑖𝑖 ℏ 𝜇𝑡𝜌21−𝜌21∗ − 𝑑11−𝑑22−𝑑11−𝑑220 𝜏, where 𝜏 is the lifetime of the upper level • This is because the population difference 𝜌11−𝜌22 would relax to its equilibrium value 𝜌11−𝜌220 with the time constant 𝜏 after the field 𝜇𝑡 is turned off. 422 Atomic and Optical Physics II, Spring 2013 View the complete course: http://ocw. , Brambilla M. MATLAB Release. I am trying to solve the optical block equations for three level system which are time dependent, which i generated using the "Atomic Density Matrix" package. Download books for free. These equations on R 3 are bi-Hamiltonian. is an artiﬁcial “torque” vector having compo-nents t,0, t. They are analogous to the. The latter method is used to determine the time dependence of the mean momentum of a two-level atom subjected to monochromatic coherent light for general values of various. Two macroscopic variables were brought in to eliminate the summation symbol in terms of single mode and homogeneously broadening. Optical fiber wave guides- Introduction, Ray theory transmission, Total Internal Reflection, Acceptance angle, Numerical Aperture, Skew rays. It is well known that the Maxwell–Bloch equations[1] de-scribe the propagation of short (< 10 9 s) optical pulses in a resonant two-level media. They do not describe a physically-observable property of the system. Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. We present a microscopic optical-Bloch-equation model for N two-level atoms being driven by a monochromatic radiation field. Neumann system (T∗SU(2),ω c,H cn) is (g tg−1) t = [σ,Ad g(τ)]; g(t) : I−→ SU(2) while the Maxwell-Bloch equations can be rewritten in the form (g tg −1) t +c(g tg ) x = [σ,Ad (τ(x)]; g(t,x):I−→ SU(2). resonance have wide application to a variety of physical effects thar. 7 Elementary Theory of Coherence 25 References and Suggested Readings 29. Simulating the KdV Equations with Equation-Based Modeling. The simplest atomic model is of course the two-level-atom which is governed by the Bloch optical equations. "23" will be result of "first number plus second number". (3) More precisely, the above equation is equivalent to the system (1), if we impose the constraint Tr(g. 12714 [gr-qc] View in: ADS Abstract Service. Split the resulting number "123" into 2 parts - 1 and 23. So, let's analyze. The potential of the Bloch. Coherent Regime: Optical Bloch Equations 77 5-4. a(kw) = 2CWQ (-iw + r)2+ Q[Q + 2CJ(k)] Equation (54) together with Eq. The index of refraction value of a material is a number that indicates the number of times slower that a light wave would be in that material than it is in a vacuum. The system of equations for this specific problem is also known as the optical Bloch equations. (The parameters nj can also be interpreted as excitation densities with units of m −3; only in rate equation systems containing nonlinear terms, e. dephasing. We hereby provide such an analysis, by deriving the relevant framework from first principles. In order to simplify the evaluation, the light field in the Haken laser equation was expanded in the standing wave form. Beam propagation in the crystals can be described by the Maxwell-Bloch equations. 2 the important "dressed state" model is. Justiﬁcation of coupled-mode equations for optical lattices – p. By studying the linear stability of the constant solutions of these four equations we observe various regimes, from stable, to modulational unstable, and unstable at all frequencies. The course will conclude with a discussion of unraveling open system quantum dynamics. A model system consisting of an array of transversely magnetized. Bourgeade, P. Properties of the Light Emitted by the Atom. y ( x) = 1 + x + 3 2 x 2 + y ( 3) ( 0) 6 x 3 + …. They describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008). 1 Semi-classical Theory. Optical bloch equations and circular polarization. Be the first to review “Numerically Solving Maxwell Bloch Equations using Nested Runge Kutta” Cancel reply. Other example is the description of a cold atoms motion in an optical lattice with mathematical model based on the Gross-Pitaevskii equation [1]. The second version uses the hamiltonian. Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008). We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. Bidégaray, A. Rare-earth-doped crystals can be modelled as inhomogeneously broadened two-level atoms. (a) Put these equations in dimensionless form, measuring distance in units of a and measuring time in units of ˝. In particular, Bloch-Zener oscillation and a di erent type of Bloch-dipole-Zener oscillation are obtained by the eld-evolution analysis. This physics course presents a general derivation of the master equation and the optical Bloch equations. An extended analytic approach is considered for this coupled equations. 2018-05-31. in optical lattices; cf. Optical bistability and multistability devices are widely used in the areas of optoelectronics such as optical memory, optical transistor, all-optical logic gate, and all-optical switching due to their ability of harnessing optical nonlinear characteristics [1-4]. 0 is simulated and the wake characteristics are compared to the single phase results at the same Reynolds. resonance have wide application to a variety of physical effects thar. 0= k(t= 0) across the Brillouin zone. Could you show me the Eq. The Maxwell–Bloch equations, also called the optical Bloch equations describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. This file was created by the Typo3 extension sevenpack version 0. Optical Communication Notes Pdf – OC Notes Pdf. Steady-State Response of a Two-Level Atom to a Monochromatic Field 285 6. For atoms in an optical lattice, the “electric” and “mag-netic” forces are the inertial Coriolis forces, if we describe the motionin aframe movingwith the lattice which islin-early accelerated and/or rotated, respectively. - TM Modes. A transfer function is the basis for further control system design. 12714 [gr-qc] View in: ADS Abstract Service. Inthispaper,wehaveemployedthelastapproach to give details of the investigated QD-SOA [ , ]. Does anyone know how the optical bloch equations for a two level system changes when the laser beam is circularly polarized?. Recapitulation of the Bloch equations for two-level systems 2. Optical Bloch equations and coherent effects. Martijn de Sterke School of Physics, University of Sydney, NSW 2006, Australia (Received 11 February 1999). electrons after optical excitation Graphene Bloch equations. Optical soliton propagation in fibres with resonant impurities and erbium-doped nonlinear systems are considered. The solutions of the Optical Bloch Equations are represented by a moving image of the Bloch vector as it evolves through time on the surface of the Bloch sphere. Viewed 595 times 1. Phase- and polarization-controlled two-photon rabi oscillation of the biexciton state in a semiconductor quantum dot In this paper, the optical Bloch equations describing the mechanism of cavity QED are investigated to obtain the transfer function of the Rabi oscillation with the. The linear and nonlinear properties of propagation of an electromagnetic field through a medium may be derived by the effective elimination of the medium from the coupled Maxwell-Bloch equations. Optical bloch equations and circular polarization. When i use the command to solve this 9 linear coupled differential equations with some initial conditions it is showing me no enough memory is available. We want to discuss formally the derivation Optical Bloch Equations, but usually when I teach you something, I have a general concept in mind and the concept right now here is, how can we get from unitary time evolution of a quantum system to rate equations anticipation. Maxwell-Bloch equations in the one-dimensional case: d2A' 1 d2A' - = - j'(w~)f(rn~)do~. Download books for free. for energy transfers, the form of the equations depends on that interpretation. Pauli Matrices (spin-1/2) Bx By Bz Simplest way to understand 2-level TDSE (after rotating frame). Puzzles such as Sudoku and Nonogrids. Application of the phase-modulated pulsed light for advance spectroscopic measurements is the area of growing interest. Classical Bloch equations and the limits of their applicability are derived from more general master equations. For weak laser fields (Ωp ≪ Γp i. Request PDF | Optical Bloch Equations | To set the stage, in Sect. propagation in optical fibers. of the Maxwell-Bloch equations. So it's easy to see that those 2 numbers will be 12 and 11. We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. equations, generation and recombination in semiconductors, semiconductor p-n heterojunctions. Eugene Demler3 and Immanuel Bloch1,2* Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. • Phenomenological – Exponential behavior is an approximation. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states. We build the differential equations based on a complete set of Bloch equations describing the all-optical atomic spin gyroscope, and obtain the transfer function through application of the Laplace transformation to these differential equations. termined by the mixing of the atomic states by the optical ﬁeld see Refs. 2 the important “dressed state” model is. In order to. Prove that the equations in (12. The optical properties of such systems are examined with the example of periodic sinusoidal gratings. Optical Communication Notes Pdf – OC Notes Pdf. 50, 1269 ( 1983)], it was found that the optical Bloch equations could not satisfactorily explain the signal that was observed for free-induction decay in the impurity ion cyrstal Pr3+:LaF3. CARL-Bloch Oscillations in a Self-Generated Optical Lattice Marina Samoylova1, 1Dipartimento di Fisica, Universit a degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy Recent attempts to improve gravimeters based on atom interferometry have achieved remarkable precision. Transform the Bloch equations into the rotating frame. When i use the command to solve this 9 linear coupled differential equations with some initial conditions it is showing me no enough memory is available. Hence, the microscopic founded Bloch equations can be used for the description of high intensity optical experiments on light harvesting complex of photosystem II (LHC II). We additionally offer variant types and with type of the books to. This physics course presents a general derivation of the master equation and the optical Bloch equations. Ideal Quantum Gases 90 6-1. The equation of motion is dR dt = t R, 2 where t FIG. The Darboux transformation formalism is adapted to this spectrally deformed system to construct its single and multi-soliton solutions. This Matlab code solves the Optical Bloch equations for light interacting with an ensemble of two-level atoms in the rotating wave approximation. Properties of the Light Emitted by the Atom. Maxwell–Bloch Equation Approach for Describing the Microscopic Dynamics of Quantum-Dot Surface-Emitting Structures. Finally, the use of the Bloch transformation in problems. Another equation is the reduced Maxwell-Bloch equation of quantum optics and the two others do not have physical applications yet. The Ideal Fermi Gas 91. Optical Bloch oscillations (BO) in waveguide arrays (WGAs) [1] is the optical analogue of the celebrated The remaining N 1 equations are to be satisfied by. And this is sort of the subject of master equation open system dynamics. OBE is defined as Optical Bloch Equations (physics) very frequently. ~ (3) for each k. It is the aim of this chapter to give an overview of the quantum mechanical foundations of the particle transport in semiconductors. Optical Bloch Equations for a Two‐Level Atom. Several theories have been proposed to explain this failure of the Bloch equations. Equation (1. Our model gives optical Bloch equations as a non-homogeneous system of ordinary linear differential equations. So it's easy to see that those 2 numbers will be 12 and 11. - The mode can be EH or HE depending upon which component contribute more to the axial direction. For weak laser fields (Ωp ≪ Γp i. In the approach proposed, the parameters entering the set of equations are expressed in terms of the geometry and the refractive index of the OWA. equations [2], [3] describe mode coupling in optical ﬁber as a ﬂow on the Poincaré sphere. equations of motion for tightly bound electron in one dimension to dx dt = 2 0a ~ sinka ~ dk dt = eE m ˝ dx dt: Take 0 = 1 eV, a = 2 A, E = 106V/cm, and ˝ = 10 14s. • Phenomenological – Exponential behavior is an approximation. It is shown that PTperiodic structures can exhibit unique characteristics stemming from the nonorthogonality of the associated Floquet-Bloch modes. The present invention generally relates to a single wavelength bi-directional optical transceiver including a transmitter and a receiver which have the same wavelength, and, more particularly, to a two-way single wavelength optical transceiver with a structure for avoidance or cut-off of an optical path to prevent optical signals from a transmitter from being introduced into a receiver in. Abstract:We present a theoretical investigation of the optical properties of an electrically pumped surface-emitting structure composed of quantum dot (QD) layers as active medium and Bragg reflectors. d 2 y d x 2 = 1 + d y d x + y + x d y d x. Optical bistability and multistability devices are widely used in the areas of optoelectronics such as optical memory, optical transistor, all-optical logic gate, and all-optical switching due to their ability of harnessing optical nonlinear characteristics [1-4]. ∗ e M )=−<ψ|(σ+M ∗+σ−M )|ψ>. electrons after optical excitation Graphene Bloch equations. equation 1 into equation 2, we are left with the optical °ow constraint equation: rI †v+It = 0 (3) Where rI = (Ix;Iy) is the spatial gradient, v = (u;v) = (¢x;¢y) is the optical °ow vector and It is the temporal gradient. 0 is simulated and the wake characteristics are compared to the single phase results at the same Reynolds. Abstract:We present a theoretical investigation of the optical properties of an electrically pumped surface-emitting structure composed of quantum dot (QD) layers as active medium and Bragg reflectors. The model is obtained from the equations of motion that result from the microscopic Hamiltonian by introducing at a certain stage an Ansatz that accounts for spontaneous emission and bath dephasing in a unitary manner. 12714 [gr-qc] View in: ADS Abstract Service. Continuing in this fashion, you can get the value of y ( 3) ( 0) and higher derivatives at x = 0, thus giving a solution to the original ODE. Several theories have been developed to explain the phenomenon. The Hyperbolic Bloch Equations of General Relativity. gradient constraint equation. 2 Feynman-Bloch Equations Assume deg = dge = d, the total Hamiltonian under the dipole approximation is: H = ~!0^¾ee ¡d^ ¢E = ~!0^¾ee ¡d¢E(^¾ge + ^¾eg) Using i~ O^_ = [O;H^]; the equations of motion in Heisenberg picture for ¾ij = h¾^iji are (note that the equations of motion for. We show that, in their unstable regime of operation, the "Maxwell-Bloch" equations that describe light-matter interactions and dynamics inside a bad-cavity-configured laser carry the same resonance properties as any externally driven mechanic or electric oscillator. It models the behavior of an electron–hole pair, which is an excitation process with two quasiparticles. The latter method is used to determine the time dependence of the mean momentum of a two-level atom subjected to monochromatic coherent light for general values of various. - The mode can be EH or HE depending upon which component contribute more to the axial direction. Semiconductor Bloch equations. Equation 1 can model many polarizable materials when combined with Maxwell’s equations in 1D, − B x = E ct +4 P ct, 2 E x =− B ct. How to calculate the new mfd of a lens when using an extension tube mathematics free full text computation analytical zoom locus padé approximation html cvx canvas™ : x01 optics google homework filter has step by math solver 9to5google. Rare-earth-doped crystals can be modelled as inhomogeneously broadened two-level atoms. it isa assp. It is the aim of this chapter to give an overview of the quantum mechanical foundations of the particle transport in semiconductors. Then, the classical degrees of freedom can be described by the Fokker–Planck equation, or equivalently, the Langevin equation. This means that the laser induces a forced oscillation of the system (the system accompanies the laser oscillation with a phase shift and an amplitude which. In the shaded ~light or dark! area, the perturbation mode has negative excitation energy; in the dark shaded area, the mode grows or decays exponentially in time. (2012) Variational iteration method for solving the time-fractional diffusion equations in porous medium. In physics and chemistry, specifically in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and electron spin resonance (ESR), the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = (Mx, My, Mz) as a function of time when relaxation times T1 and T2 are present. You will learn about various solutions of the optical Bloch equations, and you will discuss the quantum Monte Carlo wavefunction approach. Hi, I'm trying to derive the optical bloch equations for this system: But I'm not sure how to write down the original equation of motion of the … Press J to jump to the feed. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. Bloch Oscillations in an Array of Curved Optical Waveguides G. 45) with E(t) · 2E0 cos(!t) = E0 ¡ ei!t +e¡i!t ¢ (1. How to solve time dependent Optical Bloch Equations for a three level system? 0. In comparison with the optical Bloch equations, these equations contain six additional parameters: the zero-point values D, and D 2 for the polarization variables, the coupling coefficients s, Yi, "/2 and the asymmetric dephasing rate (y 'l - 3' i ) / 2. Bloch (born August 28, 1961) is a software engineer and a technology author, formerly employed at Sun Microsystems and Google. 25 Optical Illusions That Prove Your Brain Sucks. Lecture 24 - Motion in perpendicular electric and magnetic fields. The solutions of the Optical Bloch Equations are represented by a moving image of the Bloch vector as it evolves through time on the surface of the Bloch sphere. See a jet stream speeding through Jupiter's atmosphere in this new view taken by NASA's Juno spacecraft. , [6, 5]), an adaptation of our code to higher dimensions is very likely. renormalization. And this is sort of the subject of master equation open system dynamics. 12 - 11 = 1. We additionally offer variant types and with type of the books to. 2 the important “dressed state” model is. Bloch equations, transverse spin relaxation time. The marginal ray is an on-axis ray which travels from the center of an object to the edge of the stop and to the center of the image. 08 Lens Equations. Density Matrix Equations of Motion for a Two-Level Atom 6. They consist of three first-order equations for the electric field in a single longitudinal cavity mode, which became nonlinear because the system oscillates between at least two discrete energy levels. See a jet stream speeding through Jupiter's atmosphere in this new view taken by NASA's Juno spacecraft. and by developing multiple scaling approach to the Maxwell-Bloch-Heisenberg equation up to the third-order in terms of expansion parameter, the complex mKdV equation was derived [42,43]. Coherent Regime: Optical Bloch Equations 77 5-4. 422 Atomic and Optical Physics II, Spring 2013 View the complete course: http://ocw. 2 the important "dressed state" model is. in optical lattices by chapter 4 introduces the discrete nonlinear Schr˜odinger equation 2. It is a Bloch plane wave with slowly varying amplitude a(t,x). y ( x) = 1 + x + 3 2 x 2 + y ( 3) ( 0) 6 x 3 + …. 4392 Laird, Budimir, and Skinner: Derivation of the Bloch equations namics has subsided. Coupled system of differential equations on Hartree-Fock level Electron-electron interaction. [9, 11, 21] and the references given therein. This physics course presents a general derivation of the master equation and the optical Bloch equations. needs to be modelled by extending Bloch equations beyond the Hartree-Fock approximation (Boltzmann equation) Anisotropic carrier distribution. Lecture 24 - Motion in perpendicular electric and magnetic fields. 47) or H = µ "1 ¡„E(t) ¡„E() " ¶ „ (‰ = ¡ [@ ‰ ‰ ‰ ‰ A = ¡ „ " ¡"()() " ¡"(). for energy transfers, the form of the equations depends on that interpretation. Such equations, analogous to the Maxwell-Bloch or optical Bloch equations, lack one of the beautiful and most useful features of the Bloch equations. — The split-step method can be used to solve this equation. rdot() functions and is a bit more sophisticated and a bit. The slow time (spatial) scale refers to a duration (distance) that is much longer than the optical time period (lattice constant of the photonic crystal). Rabi frequency (excitons!) as well as to. CARL-Bloch Oscillations in a Self-Generated Optical Lattice Marina Samoylova1, 1Dipartimento di Fisica, Universit a degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy Recent attempts to improve gravimeters based on atom interferometry have achieved remarkable precision. Using a matrix formulation the three effects can be collectively described by the form M1 = A*M+B, where A is a 3x3 matrix and B is a 3x1 vector. edu/8-422S13 Instructor: Wolfgang Ketterle In this lecture, the. How to solve time dependent Optical Bloch Equations for a three level system? 0. Event: Workshop "The Gross-Pitaevskii equation and its application for BEC in optical lattices" (2008). needs to be modelled by extending Bloch equations beyond the Hartree-Fock approximation (Boltzmann equation) Anisotropic carrier distribution. The Anharmonic Oscillator Picture for the Optical Polarization 765 Xl3) with a Realistic Population-Relaxation Matrix 767 Homogeneous, Inhomogeneous, and Intermediate Dephasing 769 Examples of Single-Frequency Techniques 775 Appendix 6A: Reduced Equations of Motion for the Density Operator 776 Appendix 6B: The Optical Bloch Equations 181 7. The model is obtained from the equations of motion that result from the microscopic Hamiltonian by introducing at a certain stage an Ansatz that accounts for spontaneous emission and bath dephasing in a unitary manner. In fact, OBO and OZT are the. Quantum coherence, correlation and decoherence in semiconductor nanostructures | Toshihide Takagahara | download | Z-Library. So it's easy to see that those 2 numbers will be 12 and 11. Its component in the equatorial plane depends on phase, but may be chosen to be along the x axis without loss of generality. Application of the phase-modulated pulsed light for advance spectroscopic measurements is the area of growing interest. As only the mentioned three levels are involved, we have n1 + n2 + n3 = 1. Lecture 23 - Semiclassical equations of motion, Bloch oscillations, effective mass, holes. 1 produces the usual polariton dispersion relation 6. Xll CONTENTS 6. The Bethe–Salpeter equation (BSE), derived from the many-body perturbation theory (MBPT), is a widely used method for describing the optical absorption process in molecules and solids[32;33;36;24;1;25;7]. equations, generation and recombination in semiconductors, semiconductor p-n heterojunctions. Could you show me the Eq. optical matrix element Carrier dynamics. Topics to be covered include: translational symmetry and Bloch's theorem, rotational symmetry and group representation, electron-electron interaction and Hartree-Fock equations, APW, OPW, pseudopotential and LCAO schemes of energy band calculations, Boltzmann equation and thermoelectric phenomena, optical properties of semiconductors. For in- stance, the solutions of associated linear systems obey. Several theories have been developed to explain the phenomenon. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. Then,the optical Bloch equations for the density operators are solved under the external pump-fields, in terms of which the nonlinear polarization is evaluated. They are analogous to (but not at all equivalent to) the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. The Darboux transformation formalism is adapted to this spectrally deformed system to construct its single and multi-soliton solutions. (The parameters nj can also be interpreted as excitation densities with units of m −3; only in rate equation systems containing nonlinear terms, e. Circularly polarized few-cycle optical solitons were found which are valid for long pulses. 31 for optical bloch equations? Thanks very much. We numerically solve Maxwell's equations by using the FFT-finite difference beam propagation method and the Bloch equations by using the finite difference method. A transfer function is the basis for further control system design. Those numbers will be 2 results. The Bloch equations as originally applied to nuclear magnetic. In particular,. Optical Bloch Equations 293 6. 68) is repre- sented by p= p++ p−= −M ∗σ+−M σ−. 2) for and Δ = 0. Theories of radiation pressure based on rate equations and on the optical Bloch equations are developed within a common framework that allows comparison of the two. It is shown that the presence of nonreciprocity in the system allows for a complete normal-mode dephasing in one of the propagation directions, resulting in a unidirectional breakdown in Bloch oscillations. O^_ = [O;H^]; the equations of motion in Heisenberg picture for¾ij=h¾^ijiare (note that the equations of motion for operators ^¾ij. This means that the laser induces a forced oscillation of the system (the system accompanies the laser oscillation with a phase shift and an amplitude which. Physical Discussion‐Differences with Other Evolution Equations. The homogeneously broadened single-mode laser equations are described as follows, dE dt = [(1 + i )E(t) + AP(t)] (1) dP dt = (1 i )P(t) E(t. The equation of motion is dR dt = t R, 2 where t FIG. The Bloch equations as originally applied to nuclear magnetic. The optical Bloch equations are known in the literature in two very general limits in relation with the relaxation processes. The real-valued Maxwell-Bloch equations on R 3 are investigated as a Hamiltonian dynamical system obtained by applying an S 1 reduction to an invariant subsystem of a dynamical system on C 3. If time permits, we discuss experiments in which we confine the matter wave sample to a one-dimensional geometry and study Bloch osciallations and transport in a one-dimensional gas. 50, 1269 ( 1983)], it was found that the optical Bloch equations could not satisfactorily explain the signal that was observed for free-induction decay in the impurity ion cyrstal Pr3+:LaF3. The resulting electric polarization density of the medium Lecture 12 1. where the rate equations for electrons and holes are written separately. Modified optical Bloch equations for solids. Starting from Maxwell equations:. - Helical EH and HE modes contain both axial electric and magnetic fields. 0 is simulated and the wake characteristics are compared to the single phase results at the same Reynolds. 44 The recent visualizations of optical Bloch wave packet motion in these structures14 ,15 17 19 have considered the case of a constant transverse index gradient, which simulates the effect of a dc ﬁeld in the corresponding quantum-mechanical problem, with single-band excitation at the input plane. 12 - 11 = 1. dot() and hamiltonian. Maxwell’s equations with purely real frequency within the optical pass band emerge. Talanina and C. Simply discussing what modifications make sense provides a strong plausibility argument for the optical Bloch equations. NASA Image and Video Library. Other example is the description of a cold atoms motion in an optical lattice with mathematical model based on the Gross-Pitaevskii equation [1]. Kannari, F & Obara, M 1990, ' Multilevel maxwell-bloch-equation description of ultrashort laser pulse amplification in inhomogeneously broadened XeCl media ', Journal of the Optical Society of America B: Optical Physics, vol. 2 Hamiltonian and Equations of Motion 13 2. It is the aim of this chapter to give an overview of the quantum mechanical foundations of the particle transport in semiconductors. Bloch Floquet state. 6 Partially Polarized and Unpolarized Light 22 1. higher-order terms in the Taylor series. it isa assp. For weak laser fields (Ωp ≪ Γp i. Several theories have been developed to explain the phenomenon. It is supposed. The Maxwell–Bloch equations, also called the optical Bloch equations describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. - EH and HE Modes. Its component in the equatorial plane depends on phase, but may be chosen to be along the x axis without loss of generality. Now, we will make the deduction of Bloch's optical equations by examining the temporal dependence of the elements of the density operator matrix. This Course will start on April 12, 2017. equations of motion for tightly bound electron in one dimension to dx dt = 2 0a ~ sinka ~ dk dt = eE m ˝ dx dt: Take 0 = 1 eV, a = 2 A, E = 106V/cm, and ˝ = 10 14s. edu/8-422S13 Instructor: Wolfgang Ketterle In this lecture, the. – Numerical solutions for all cases. Equation (1. Based on the Kubo-Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. (3) More precisely, the above equation is equivalent to the system (1), if we impose the constraint Tr(g. The optical properties of silicon quantum dots specially the EL is affected by different factors such as the preparation methods and conditions (laser ablation, deposition. Optical fiber wave guides- Introduction, Ray theory transmission, Total Internal Reflection, Acceptance angle, Numerical Aperture, Skew rays. Precession and T2-relaxation are linear effects, but T1-relaxation is non-linear. Raimond Atoms and photons September 12, 2016 2 / 112. In the approach proposed, the parameters entering the set of equations are expressed in terms of the geometry and the refractive index of the OWA. The soliton and breather solutions in the. Deriving the optical Bloch equations from the von Neumann equations. (The parameters nj can also be interpreted as excitation densities with units of m −3; only in rate equation systems containing nonlinear terms, e. ρ= 1 2 (I+Xcosφsinθ+Ysinφsinθ+Zcosθ) = 1 2 (I+~rρ· ~σ) whereIis the identity matrix,~σis the 3-element ‘vector’ of Pauli Matrices (X,Y,Z), and~rρis the unit Bloch vector. They are analogous to the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. Equation 1 can model many polarizable materials when combined with Maxwell’s equations in 1D, − B x = E ct +4 P ct, 2 E x =− B ct. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. EL is an optical property which depends on the nature of the material. The results may have potential applications in optical splitting and waveguiding devices and shed light on the coherent phenomena in optical lattices. equations, generation and recombination in semiconductors, semiconductor p-n heterojunctions.