From 1ea7bebbb26837558fcdb96c223ea60879d3f4b7 Mon Sep 17 00:00:00 2001 From: Helge Gehring <42973196+HelgeGehring@users.noreply.github.com> Date: Wed, 3 Apr 2024 09:03:15 -0700 Subject: [PATCH 1/2] update toc, split maxwell docs --- docs/_toc.yml | 19 ++--- docs/math/maxwell.md | 119 ------------------------------- docs/math/maxwell_quantities.md | 120 ++++++++++++++++++++++++++++++++ 3 files changed, 130 insertions(+), 128 deletions(-) create mode 100644 docs/math/maxwell_quantities.md diff --git a/docs/_toc.yml b/docs/_toc.yml index 515ada4f..684e7db9 100644 --- a/docs/_toc.yml +++ b/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 diff --git a/docs/math/maxwell.md b/docs/math/maxwell.md index 12b22897..baf45da2 100644 --- a/docs/math/maxwell.md +++ b/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 - - - -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 diff --git a/docs/math/maxwell_quantities.md b/docs/math/maxwell_quantities.md new file mode 100644 index 00000000..ee940a29 --- /dev/null +++ b/docs/math/maxwell_quantities.md @@ -0,0 +1,120 @@ +# 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 + + + +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: + +$$ + P = I^T Z_c I + + Z_c = [I^{-1}]^T P I^{-1} +$$ \ No newline at end of file From 5aedb84a26b880aec253bd2fcbf2fa6746be59f3 Mon Sep 17 00:00:00 2001 From: Helge Gehring <42973196+HelgeGehring@users.noreply.github.com> Date: Wed, 3 Apr 2024 09:07:27 -0700 Subject: [PATCH 2/2] add refs --- docs/math/maxwell_quantities.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/docs/math/maxwell_quantities.md b/docs/math/maxwell_quantities.md index ee940a29..dd0e2254 100644 --- a/docs/math/maxwell_quantities.md +++ b/docs/math/maxwell_quantities.md @@ -117,4 +117,9 @@ $$ P = I^T Z_c I Z_c = [I^{-1}]^T P I^{-1} -$$ \ No newline at end of file +$$ + +```{bibliography} +:style: unsrt +:filter: docname in docnames +``` \ No newline at end of file