Silicon Photomultipler Investigation for Radiation Technologies

**Outline of Simulating Recovery** **Following the 2014 South Napa
Earthquake**

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**1. Abstract**

Ducting and Conversions of Whistler Waves in Varying Density Plasma With Boundary Conditions

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Nanophotonic Technology

Photonic ICs and Beyond

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In 1909, Arnold Sommerfeld published his proposed analytical proof of surface polarization waves [11] marking in our history of Photonics the cornerstone of the all nanophotonics is motivated. Sixty years following Sommerfeld’s publication, Chinese physicist Charles Kao published a solution for guiding Sommerfeld’s surface excitations using optical fiber [12] which in 2009 he would also receive a Nobel Prize. Today nanophotonic research is being conducted by many countries for many applications, yet their approach is surprising similar. The majority of resources and funding for nanophotonics is the development of better materials. This point will be further evident in following sections, but for now it should be mentioned that of those resources only a marginal portion is allocated in the direction of CMOS integration. Initially, this discovery was quiet shocking for two big reasons. First of all, in recent years Moore’s law’s famous exponential curve of computing performance and affordability over time has become less exponentially improving and we know one major cause of the bottleneck occurring in integrated circuits is interconnects. Illustrated in figure 1 is a comparison of the performance capability of optical fibers vs coaxial cables. In figure 2 is a relation of current nanophotonic waveguide capability compared to optical fiber which has strong implications for what is possible on chips and the potential need for an enhancing technology. Secondly, the CMOS business has been so profitable and so heavily investing in machinery that it seems logical to continue investing as a lot of the infrastructure exists. The answer to my initial shock is illustrated in figures 3. CMOS compatible nanophotonics occupies an extremely narrow space on a wide spectrum of possible use cases and therefore to expect so much of the resources to be allocated so narrowly this early in such a young immature science could greatly delay the achievable possibilities. The following sections, however, will discuss the results of the resources that were allocated for CMOS integrated nanophotonics and the modules that are in development to address Moore’s law.

Mie Scattering and the Onset of Sonoluminescence

Time between pulses of SL was found to be 3.069 × 10^{−5} ± 0.01 seconds, width of an SL pulse was found to be 1.925 ∗ 10^{−6} ± 0.04 seconds and Sonoluminescence was observed.

Diviner calibration

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Follow up questions-fibers

a) Overlap integral given by \[ \eta=\int_{-\infty}^{\infty} \Psi_{m^{'}} ^{output} \Psi_{m}^{input} dx\] The paper by tong et al, explains that they adjusted the overlap until the output is maximized. I think that for that occur then say the input was a gaussian *E* = *E*(0)*e*^{ax2} where *E*(0) would be a central maximum, then overlap adjusted until the output was *E*(0), making the overlap integral just integrating a gaussian.

b) Using the mode solver for this part. I wanted to see how modes would look after *L**P*_{01}, not single moded. So I went back to the paper and looked at the equation for the diameters that allow for single mode operation, $D< \frac{2.4 \lambda}{\pi \sqrt{n_0^2-n_1^2}}$, where *n*_{1} is 1 for air, and *n*_{0} is the index of refraction for the medium in use. From the tong paper, the second page of the paper, or pg.817 of the nature journal it was published in, index of refraction for Silica is said to be *n*_{0} = 1.46. This gives *N**A* = 1.063, using *λ* = 633*n**m*, the max diameter is then given to be 454.6 nm for single mode operation. So I will put diameters larger then this for non single modes. Using 600 nm for the diameter. The image generated looks just like two very sharp gaussians

c) I believe this is due to when the diameter of the wire is decreased below the wavelength its supposed to be guiding, more of the light is guiding outside the wire as a surface wave. So for 1550 nm , looking at the graph for loss, starting at wire diameters of 1200 nm we are already operating below the wavelength we want to guide so as the diameter decreases , more light is outside the wire leading to more loss. Compared to the 633 nm wavelength, you can see the increase in loss occurs when operating below 633 nm diameter wire but we are lower loss from 1200 nm until we get to 633 nm

d) To go along with this, the loss mechanism is from surface contamination. The silica wires are’t perfectly uniform. By virtue of that, when light is guided by surface waves it is more susceptible to the surface contaminations.

Follow Up Questions To Presentation on Codirectional Coupling

Revisting the initial value problem of \[ \begin{bmatrix} \tilde{A}(z)\\
\tilde{B}(z)\\
\end{bmatrix} = F(z;z_0)
\begin{bmatrix}
\tilde{A}(z_0)\\
\tilde{B}(z_0) \\
\end{bmatrix}\] The question is to solve this subject to the initial condition of when power is launched only into the mode a at *z*_{0} = 0. This means $\tilde{B}(0)=0$ and $\tilde{A}(0)\neq 0$. \[ F(z;z_0)=
\begin{bmatrix}
\frac{\beta_c cos \beta_c(z-z_0)-i\delta sin \beta_c(z-z_0)}{\beta_c}e^{i \delta (z+z_0)} & \frac{i \kappa_{ab}}{\beta_c}sin\beta_c(z-z_0)e^{i \delta (z+z_0)}\\
\frac{i \kappa_{ba}}{\beta_c}sin\beta_c(z-z_0)e^{-i \delta (z+z_0)} &\frac{\beta_c cos \beta_c(z-z_0)+i\delta sin \beta_c(z-z_0)}{\beta_c}e^{-i \delta (z+z_0)} \\
\end{bmatrix} \] Subject to our initial conditions then \[\begin{bmatrix} \tilde{A}(z)\\
\tilde{B}(z)\\
\end{bmatrix} = F(z;0)
\begin{bmatrix}
\tilde{A}(0)\\
0 \\
\end{bmatrix}\] Carrying the matrix multiplication step by step \[\begin{bmatrix} \tilde{A}(z)\\
\tilde{B}(z)\\
\end{bmatrix}=\begin{bmatrix}
\frac{\beta_c cos \beta_c(z)-i\delta sin \beta_c(z)}{\beta_c}e^{i \delta (z)} & \frac{i \kappa_{ab}}{\beta_c}sin\beta_c(z)e^{i \delta (z)}\\
\frac{i \kappa_{ba}}{\beta_c}sin\beta_c(z)e^{-i \delta (z)} &\frac{\beta_c cos \beta_c(z)+i\delta sin \beta_c(z)}{\beta_c}e^{-i \delta (z)} \\
\end{bmatrix}
\begin{bmatrix}
\tilde{A}(0)\\
0 \\
\end{bmatrix}\] \[\begin{bmatrix} \tilde{A}(z)\\
\tilde{B}(z)\\
\end{bmatrix}=\begin{bmatrix}
\frac{\tilde{A}(0) \beta_c cos \beta_c(z)-i\delta sin \beta_c(z)}{\beta_c}e^{i \delta (z)} & 0\\
\tilde{A}(0) \frac{i \kappa_{ba}}{\beta_c}sin\beta_c(z)e^{-i \delta (z)} & 0\\
\end{bmatrix} \] This leaves us then with \[\tilde{A}(z)=\tilde{A}(0)\left( cos \beta_c z -\frac{i \delta}{\beta_c} sin \beta_c z \right) e^{i \delta z} \] \[\tilde{B}(z)=\tilde{A}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} \] Looking back at my slides I wrote that $\tilde{B}(z)=\tilde{B}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} $, which given my initial conditions would be wrong since $\tilde{B}(0)=0$. Thankfully, this error doesn’t propagate through the rest of the presentation as that error only shows up on slide 8 and the rest of the figures I made are still accurate. I want to point out another error I made in the paper in regards to figure 1 here. The error is that in the figure in the paper, I wrote the same error for the power, corresponding to the blue line in figure one. I wrote $\frac{P_a(z)}{P_b(o)}$, when in fact it should be $\frac{P_a(z)}{P_a(o)}$, It was corrected for the presentation and here.