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物理代写|光学作业代写Optics代考|The Interference Filter

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• 几何光学 Geometrical optics

• 波动光学

• 量子光学

物理代写|光学作业代写Optics代考|coherence length

Experimental configurations for two-photon quantum beats, e.g. [2226], employ interference filters in order to control the “coherence length of the photon”.

The extent of the correlation fringes is determined by the coherence length of the photons, which can be shaped by an interference filter, apparently operating on the output spectral distribution $\Phi\left(\omega_{1}, \omega_{2}\right)$ of the ensemble of photons generated by an active source over a long time, such as the spontaneous parametric down-conversion mechanism [16-17].

However, from a physical perspective, a Fourier transform – or a superposition of spectral components – necessitates the simultaneous presence of the entire range of spectral components. But this is not the case when only one photon, at any given time, crosses an interference filter. A single monochromatic photon propagating through a Fabry-Perot type filter, or a Bragg refractive index grating in a waveguide, will be delayed randomly by repeated internal reflections and will acquire an integer multiple of a bias phase or time-delay. The higher the internal reflectivity of the cavity, the longer some photons may bounce back and forth inside the cavity resulting in a “longer photon” output, which is interpreted as a longer coherence length. Such optical signals are best described by means of the mixed time-frequency (or Wigner-type) spectrum, e.g. [19] with the frequency amplitude itself being a function of time $S(\omega, t)$ specifying, in other words, a time-varying number of monochromatic photons being carried by different photonic wavefronts. The time-stretching of the photonic group will be equivalent to pulse expansion for a narrower Fourier spectrum.

物理代写|光学作业代写OPTICS代考|group of photons entering

Thus, a group of photons entering, simultaneously, a resonant cavity of an interference filter, will exit at different times as the higher the internal reflectivity, the longer the time that some photons will bounce back and forth inside the cavity. This process will cause the initially bunched photons to spread out in time and give rise to a longer coherence length for photon coincidence counting (Halder et al. [27]). The wavefunction describing this output would take the form:
$$\left|\Phi_{\text {out }}(\boldsymbol{r}, t)\right\rangle=\Sigma_{m} c_{\mathrm{n}}(\boldsymbol{r}, t) f_{\mathrm{n}}(\boldsymbol{r}) \delta\left(t-t_{m}\right)\left|\Psi_{\mathrm{n}}(\omega, t)\right\rangle$$
where the times $t_{m}$ specify the existence of a group of $\mathrm{n}$ photons at location $\boldsymbol{r}$. The pure state of a photonic wavefront is monochromatic and timedependent as detailed in Chapter 3 , whereas the overall mixed state of the ensemble is multi-chromatic and time-independent (e.g. the bi-photon wavefunction [25-26]).

The temporal profile of the optical field carried by a photon or any instantaneous photonic wavefront should be determined from a pure quantum state wavefunction because it should be unaffected by the spectral distribution of an ensemble of measurements. However, for interference to take place, at least two coefficients $c_{\mathrm{n}}(\mathrm{n}>0)$ have to be non-zero in eq. $(5.24)$.

物理代写|光学作业代写OPTICS代考|GROUP OF PHOTONS ENTERING

|披出去 (r,吨)⟩=Σ米Cn(r,吨)Fn(r)d(吨−吨米)|Ψn(ω,吨)⟩

Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。