# 物理代写|电动力学代写electromagnetism代考|Absorption, Emission and Scattering – the Basic Processes

## 物理代写|电动力学代写electromagnetism代考|Absorption, Emission and Scattering – the Basic Processes

This section is devoted to an outline of the evaluation of the basic diagrams, Figures 10.1-10.3 using the Coulomb gauge Hamiltonian for a charged particle interacting with the quantised electromagnetic field; after that, the extension to the physically interesting cases involving many charges (atoms, molecules, condensed matter, plasmas etc.) will be seen to be quite straightforward. The matrix elements required are given in Appendix $\mathrm{F}$.

Figure 10.1 shows the primitive absorption and emission vertices that correspond to first-order perturbation theory; there is no denominator to evaluate. Consider the absorption vertex; according to Eq. (F.1.5), the perturbation operator is
$$\mathrm{K}a^1=-\sum{\mathbf{q}, \sigma} \mathbf{f}e(\mathbf{q}) \cdot \hat{\boldsymbol{\varepsilon}}(\mathbf{q})\sigma \mathrm{C}{\mathbf{q}, \sigma}$$ If the initial and final states for the absorption of a photon by a free charge are $\Phi_n^0=$ $\left|\varphi{\mathbf{P}}, \mu\left[n_{\mathbf{Q}}\right]\right\rangle$ and $\Phi_k^0=\left|\varphi_{\mathbf{P}^{\prime}}, \mu\left[n_{\mathbf{Q}}-1\right]\right\rangle$, respectively, the matrix element is (cf. (F.1.8))
$$\left\langle\Phi_k^0\left|\mathrm{~K}a^1\right| \Phi_n^0\right\rangle=-\frac{e}{m} \sqrt{\frac{\hbar^2}{2 \varepsilon_0 \Omega \mathcal{E}{\mathbf{Q}}}} \mathbf{P} \cdot \hat{\boldsymbol{\varepsilon}}(\mathbf{Q})_\mu \delta^3\left(\mathbf{P}+\hbar \mathbf{Q}-\mathbf{P}^{\prime}\right) .$$
The emission vertex has the same form, with $\mathbf{Q} \rightarrow-\mathbf{Q}$.
We have to recognise that a free charge cannot absorb or emit a (real) photon because energy cannot be conserved in such a transition. To see this, consider a charge initially at rest and an incident photon with wave vector $\mathbf{Q}$. After absorbing the photon, the particle must have momentum $\hbar \mathbf{Q}$. Thus, we have
$$\begin{array}{ll} E_n^0=\hbar Q c, & \mathbf{P}_n^0=\hbar \mathbf{Q}, \ E_k^0=\frac{\hbar^2 Q^2}{2 m}, & \mathbf{P}_k^0=\hbar \mathbf{Q}, \end{array}$$
for the initial and final energy and momentum of the (charge + photon) system. But since the final speed of the particle is $v_k=\hbar Q / m$, conservation of energy would require $v_k=2 c$ which is impossible. ${ }^{12}$ Photons are absorbed and emitted by free charges in virtual transitions to which energy conservation does not apply.

## 物理代写|电动力学代写electromagnetism代考|Birefringence

The light scattered by a molecule in a uniform static field (either electric or magnetic), when this field makes an angle to the propagation direction of the light beam, is in general elliptically polarised. The Kerr and Cotton-Mouton effects correspond to the electric and magnetic field cases, respectively [60]. The rotation of the plane of polarisation in the absence of any external fields (‘optical activity’) is the characteristic property of chiral substances; the same effect can be induced in any fluid substance by an external magnetic field applied along the direction of the light (the Faraday effect). Analogous birefringence phenomena in the absence of applied external fields may be induced by the intense optical fields of powerful lasers.

Certain kinds of processes cannot be described using the simple interaction (10.176); for example, it cannot describe chirality (a change in the polarisation state of the beam) in isotropic media since the optical rotation angle far from resonance depends purely on the imaginary part of the T-matrix. Since $d$ is a real operator, (10.176) leads to a real T-matrix element; the generalised diamagnetic susceptibility (9.136) is also purely real and so cannot contribute to optical activity. For such a case one must introduce the magnetic dipole interaction involving the magnetic induction vector $\mathbf{B}$; the magnetic dipole operator is pure imaginary. This means giving up the assumption that the electric field is approximately uniform, and for consistency one must also include the electric quadrupole term that couples to the electric field gradient; thus, in the next multipolar approximation one has $$V^1=-\mathbf{d} \cdot \mathbf{E}^{\perp}-\mathbf{m} \cdot \mathbf{B}-\mathbf{Q}: \nabla \mathbf{E}^{\perp}$$
It should also be mentioned that recent work has shown that (laser) light can be engineered to possess a twisting or helical phase structure that can be characterised by assigning orbital angular momentum to photons. The plane wave description of the field variables $\left(\mathbf{A}, \mathbf{B}, \mathbf{E}^{\perp}\right)$ cannot describe such properties, and a different formulation is required. Given the requisite field variable expansions (e.g. (7.246)), the perturbation theory of light scattering summarised here, based on the Kramers-Heisenberg dispersion formula, can be reworked and novel phenomena identified. A detailed study can be found in [61]; a striking prediction is of novel chiroptical birefringence effects in which the molecular quadrupole operator plays an essential role.

The quantum mechanical approach to the optical birefringence of a rarefied medium considers a beam of photons being scattered by a molecule. For such a system, the initial state can be represented by a molecule in a given initial state and photons linearly polarised along one direction of polarisation and in a single specified mode $\mathbf{k}$ of the field. In the distant future, the final state of the system has the molecule in its original state but recognises that there is a non-zero probability that photons have transferred from one polarisation direction $\lambda$ to the other $\lambda^{\prime}$, without a change of momentum. Thus, although this is a case of forward scattering, a transition (the ‘polarisation flip’) has occurred and the scattering theory based on the T-matrix is still appropriate for the calculation of this probability. The observations that one makes on the incident and emergent light beams in a birefringence experiment are their intensities and the characteristics of the polarisation ellipse of each expressed through the azimuth and ellipticity angles; these observables are summarised elegantly by the Stokes parameter formalism (Chapter 7 ).

# 电动力学代考

## 物理代写|电动力学代写electromagnetism代考|Absorption, Emission and Scattering – the Basic Processes

$$\mathrm{K} a^1=-\sum \mathbf{q}, \sigma \mathbf{f} e(\mathbf{q}) \cdot \hat{\boldsymbol{\varepsilon}}(\mathbf{q}) \sigma \mathrm{C} \mathbf{q}, \sigma$$

$\Phi_k^0=\left|\varphi_{\mathbf{P}^{\prime}}, \mu\left[n_{\mathbf{Q}}-1\right]\right\rangle$, 矩阵元素分别为 (cf. (F.1.8))
$$\left\langle\Phi_k^0\left|\mathrm{~K} a^1\right| \Phi_n^0\right\rangle=-\frac{e}{m} \sqrt{\frac{\hbar^2}{2 \varepsilon_0 \Omega \mathcal{E} \mathbf{Q}}} \mathbf{P} \cdot \hat{\varepsilon}(\mathbf{Q})_\mu \delta^3\left(\mathbf{P}+\hbar \mathbf{Q}-\mathbf{P}^{\prime}\right) .$$

$$E_n^0=\hbar Q c, \quad \mathbf{P}_n^0=\hbar \mathbf{Q}, \quad E_k^0=\frac{\hbar^2 Q^2}{2 m}, \quad \mathbf{P}_k^0=\hbar \mathbf{Q}$$

## 物理代写|电动力学代写electromagnetism代考|Birefringence

$$V^1=-\mathbf{d} \cdot \mathbf{E}^{\perp}-\mathbf{m} \cdot \mathbf{B}-\mathbf{Q}: \nabla \mathbf{E}^{\perp}$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: