Presentation on theme: "Interaction of Electromagnetic Radiation with Matter"— Presentation transcript:
1Interaction of Electromagnetic Radiation with Matter
2Dielectric Constant and Atomic Polarizability Under the action of the electric field, the positive and negative charges inside each atom are displaced from their equilibrium positions.The induced dipole moment isp = αEWhere α is atomic polarizability.
3Dielectric Constant and Atomic Polarizability The dielectric constant of a medium will depend on the manner in which the atoms are assembled. Let N be the number of atoms per unit volume. The polarization can be written approximately asP=Np=NαE=ε0ΧEWhere Χ is susceptibility.
4Dielectric Constant and Atomic Polarizability The dielectric constant ε of the medium isIf the medium is nonmagnetic (i.e., μ=μ0), the index of refraction is given by
5Classical Electron Model In classical physics, we assume that the electrons are fastened elastically to the atoms and obey the following equation of motionThe electric field of the optical wave in the atom can be written as
6Classical Electron Model The equation has the following steady-state solutionThe induced dipole moment isThe atomic polarizability is
7Classical Electron Model If there are N atoms per unit volume, the index of refraction of such a medium isIf the second term in this equation is small compared to 1, the index of refraction can be written as
8Dispersion and Complex Refractive Index From the equationWe can get that the index of refraction is higher for the waves with larger ω.The phenomenon that the refractive index depends on frequency is called the phenomenon of dispersion.
9Dispersion and Complex Refractive Index The imaginary term iϒω in the equationaccounts for the damping of electron motion and gives rise to the phenomenon of optical absorption.
10Dispersion and Complex Refractive Index The complex refractive index can be written as
11Dispersion and Complex Refractive Index For a wave written asIn whichUsing the complex refractive index, the wave number K becomes
12Dispersion and Complex Refractive Index The electric field of the wave becomes
13Optical Pulse and Group Velocity In the pulsed mode, the pump energy can be concentrated into extremely short time durations, thereby increasing the peak power.The propagation of a pulse due to dispersion can be described by representing the pulse as a sum of many plane-wave solutions of Maxwell’s equations.
14Optical Pulse and Group Velocity The scalar amplitude ψ(z,t) can be thought of as one of the components of electromagnetic field vectors. If A(k) denotes the amplitude of the plane-wave component with wave number k, the pulse ψ(z,t) can be written as
15Optical Pulse and Group Velocity A laser pulse is usually characterized by its center frequency ω0 or wave number k0 and the frequency spread Δ ω or spread in wave number Δk. In other words, A(k) is sharply peaked around k0. We expand ω(k) around the value k0 in terms of a Taylor series:
16Optical Pulse and Group Velocity The ψ(z,t) becomesThe integral in above equation is a function of the composite variable [z – (dω/dk)0t] only and is called the envelope function
17Optical Pulse and Group Velocity The amplitude of the pulse can be written asThis shows that, apart from an overall phase, the laser pulse travels along undistorted in shape
18Optical Pulse and Group Velocity The group velocity of the pulse isThe group velocity represents the transport of energy.后面的几个公式纯粹就是微分推导，可在黑板上推，或带过。