Merge pull request #146 from HelgeGehring/update-toc

update toc, split maxwell docs

docs/_toc.yml

@@ -21,14 +21,16 @@ parts:
   - caption: Examples
     chapters:
     - file: photonics/examples/waveguide_modes.py
-    #- file: photonics/examples/leaky_waveguide.py
-    #- file: photonics/examples/bent_waveguide.py
-    - file: photonics/examples/vary_width.py
-    - file: photonics/examples/vary_wavelength.py
-    - file: photonics/examples/selecting_modes.py
-    - file: photonics/examples/calculate_GVD.py
-    - file: photonics/examples/fiber_overlap.py
-    - file: photonics/examples/crosstalk.py
+      sections:
+      #- file: photonics/examples/leaky_waveguide.py
+      #- file: photonics/examples/bent_waveguide.py
+      - file: photonics/examples/vary_width.py
+      - file: photonics/examples/vary_wavelength.py
+      - file: photonics/examples/selecting_modes.py
+      - file: photonics/examples/calculate_GVD.py
+      - file: photonics/examples/fiber_overlap.py
+      - file: photonics/examples/crosstalk.py
+      - file: photonics/examples/propagation_loss.py
     - file: photonics/examples/metal_heater_phase_shifter.py
     - file: photonics/examples/metal_heater_phase_shifter_transient.py
     - file: photonics/examples/si_heater_phase_shifter.py
@@ -40,7 +42,6 @@ parts:
     - file: photonics/examples/depletion_waveguide.py
     - file: photonics/examples/effective_area.py
     - file: photonics/examples/refinement.py
-    - file: photonics/examples/propagation_loss.py
     - file: electronics/examples/capacitor.py
     - file: electronics/examples/coax_cable.py
     - file: electronics/examples/coplanar_waveguide_vary_width.py

docs/math/maxwell.md

@@ -329,125 +329,6 @@ where $R$ is the radius of curvature in $x$-direction.
 
 See discussion on choice of R in {cite}`Masi:10`
 
-## TE/TM Polarization Fraction
-
-$$
-    \mathrm{TEfrac}
-    &=
-    \frac{
-        \int \left| E_{x_1} \right|^2 \mathrm{d}x\mathrm{d}y
-    }{
-        \int \left| E_{x_1} \right|^2 + \left| E_{x_2} \right|^2 \mathrm{d}x \mathrm{d}y
-    }
-
-    \mathrm{TMfrac}
-    &=
-    \frac{
-        \int \left| E_{x_2} \right|^2 \mathrm{d}x\mathrm{d}y
-    }{
-        \int \left| E_{x_1} \right|^2 + \left| E_{x_2} \right|^2 \mathrm{d}x \mathrm{d}y
-    }
-$$
-
-## Loss per meter [dB/m]
-
-$$
-    \text{Loss at }x_3\text{ [dB]}
-    &=-10 \log_{10} \frac{\left|E(x_3)\right|^2}{\left|E(x_3=0)\right|^2}
-    \\
-    &=-20 \log_{10} \frac{\left|E(x_3)\right|}{\left|E(x_3=0)\right|}
-    \\
-    &=-20 \log_{10} \mathrm{e}^{\Im\beta x_3}
-    \\
-    &=-20 \frac{\log_{\mathrm{e}} \mathrm{e}^{\Im\beta x_3}}{\ln 10}
-    \\
-    &=\frac{-20}{\ln 10} \Im\beta x_3
-    \\
-    \\
-    \text{Loss [dB/m]}
-    &=
-    \frac{-20}{\ln 10} \Im\beta \, 1\mathrm{m}
-$$
-
-## Effective Area
-
-As defined in {cite}`Agrawal2019`
-
-$$
-    A_{\text{eff}}
-    =
-    \frac{
-        \left( \int \left| \vec{\mathcal{E}} \right|^2 \mathrm{d}A \right)^2
-    }{
-        \int \left| \vec{\mathcal{E}} \right|^4 \mathrm{d}A
-    }
-$$
-
-## Confinement coefficient
-
-As defined in {cite}`Robinson2008`
-(and generalized for varying refractive indices in the active area)
-
-$$
-    \Gamma
-    =
-    \frac{
-        c \epsilon_0 \int n(\vec{x}) \left| \vec{\mathcal{E}} \right|^2 \mathrm{d}A
-    }{
-        \left( \int \vec{\mathcal{E}}^* \times \vec{\mathcal{H}}
-        +
-        \vec{\mathcal{E}} \times \vec{\mathcal{H}}^*
-        \mathrm{d}A \right) / 2
-    }
-$$
-
-## Overlap coefficient
-
-$$
-    c_{\nu\mu}
-    =
-    \frac{
-        \int \vec{\mathcal{E}}_\nu^* \times \vec{\mathcal{H}}_\mu
-        +
-        \vec{\mathcal{E}}_\nu \times \vec{\mathcal{H}}_\mu^* \mathrm{d}A
-    }{
-        \prod_{i=\{\mu,\nu\}}
-        \sqrt{
-            \int \vec{\mathcal{E}}_i^* \times \vec{\mathcal{H}}_i
-            +
-            \vec{\mathcal{E}}_i \times \vec{\mathcal{H}}_i^* \mathrm{d}A
-        }
-    }
-    =
-    c_{\mu\nu}^*
-$$
-
-## Characteristic impedance
-
-<https://ieeexplore.ieee.org/document/108320>
-
-Power and current:
-
-$$
-    P_k
-    =
-    \delta_{jk}
-    \int
-    \left(
-        \vec{\mathcal{E}}_j^* \times \vec{\mathcal{H}}_k
-    \right) \cdot \hat{x}_3
-
-    I_{zik} = \oint_{C_i} \mathcal{H} \ cdot
-$$
-
-Characteristic impedance:
-
-$$
-    P = I^T Z_c I
-
-    Z_c = [I^{-1}]^T P I^{-1}
-$$
-
 ## Calculating static potentials
 
 As in the static case

docs/math/maxwell_quantities.md

@@ -0,0 +1,125 @@
+# Quantities of optical modes
+
+## TE/TM Polarization Fraction
+
+$$
+    \mathrm{TEfrac}
+    &=
+    \frac{
+        \int \left| E_{x_1} \right|^2 \mathrm{d}x\mathrm{d}y
+    }{
+        \int \left| E_{x_1} \right|^2 + \left| E_{x_2} \right|^2 \mathrm{d}x \mathrm{d}y
+    }
+
+    \mathrm{TMfrac}
+    &=
+    \frac{
+        \int \left| E_{x_2} \right|^2 \mathrm{d}x\mathrm{d}y
+    }{
+        \int \left| E_{x_1} \right|^2 + \left| E_{x_2} \right|^2 \mathrm{d}x \mathrm{d}y
+    }
+$$
+
+## Loss per meter [dB/m]
+
+$$
+    \text{Loss at }x_3\text{ [dB]}
+    &=-10 \log_{10} \frac{\left|E(x_3)\right|^2}{\left|E(x_3=0)\right|^2}
+    \\
+    &=-20 \log_{10} \frac{\left|E(x_3)\right|}{\left|E(x_3=0)\right|}
+    \\
+    &=-20 \log_{10} \mathrm{e}^{\Im\beta x_3}
+    \\
+    &=-20 \frac{\log_{\mathrm{e}} \mathrm{e}^{\Im\beta x_3}}{\ln 10}
+    \\
+    &=\frac{-20}{\ln 10} \Im\beta x_3
+    \\
+    \\
+    \text{Loss [dB/m]}
+    &=
+    \frac{-20}{\ln 10} \Im\beta \, 1\mathrm{m}
+$$
+
+## Effective Area
+
+As defined in {cite}`Agrawal2019`
+
+$$
+    A_{\text{eff}}
+    =
+    \frac{
+        \left( \int \left| \vec{\mathcal{E}} \right|^2 \mathrm{d}A \right)^2
+    }{
+        \int \left| \vec{\mathcal{E}} \right|^4 \mathrm{d}A
+    }
+$$
+
+## Confinement coefficient
+
+As defined in {cite}`Robinson2008`
+(and generalized for varying refractive indices in the active area)
+
+$$
+    \Gamma
+    =
+    \frac{
+        c \epsilon_0 \int n(\vec{x}) \left| \vec{\mathcal{E}} \right|^2 \mathrm{d}A
+    }{
+        \left( \int \vec{\mathcal{E}}^* \times \vec{\mathcal{H}}
+        +
+        \vec{\mathcal{E}} \times \vec{\mathcal{H}}^*
+        \mathrm{d}A \right) / 2
+    }
+$$
+
+## Overlap coefficient
+
+$$
+    c_{\nu\mu}
+    =
+    \frac{
+        \int \vec{\mathcal{E}}_\nu^* \times \vec{\mathcal{H}}_\mu
+        +
+        \vec{\mathcal{E}}_\nu \times \vec{\mathcal{H}}_\mu^* \mathrm{d}A
+    }{
+        \prod_{i=\{\mu,\nu\}}
+        \sqrt{
+            \int \vec{\mathcal{E}}_i^* \times \vec{\mathcal{H}}_i
+            +
+            \vec{\mathcal{E}}_i \times \vec{\mathcal{H}}_i^* \mathrm{d}A
+        }
+    }
+    =
+    c_{\mu\nu}^*
+$$
+
+## Characteristic impedance
+
+<https://ieeexplore.ieee.org/document/108320>
+
+Power and current:
+
+$$
+    P_k
+    =
+    \delta_{jk}
+    \int
+    \left(
+        \vec{\mathcal{E}}_j^* \times \vec{\mathcal{H}}_k
+    \right) \cdot \hat{x}_3
+
+    I_{zik} = \oint_{C_i} \mathcal{H} \ cdot
+$$
+
+Characteristic impedance:
+
+$$
+    P = I^T Z_c I
+
+    Z_c = [I^{-1}]^T P I^{-1}
+$$
+
+```{bibliography}
+:style: unsrt
+:filter: docname in docnames
+```