Deploying to gh-pages from @ 4321ea3 🚀

_sources/pages/grating_couplers.ipynb

@@ -259,23 +259,25 @@
    "metadata": {},
    "source": [
     "### Grating period\n",
-    "The grating period (typically denoted by $\\Lambda$) is the parameter most likely to effect the efficiency of a grating coupler. It is the length of one period of the grating, and is measured in microns. The grating period is typically chosen to be near half the wavelength of the light being used. This is because the bragg grating period is related to the wavelength of light by the equation:\n",
+    "The grating period (typically denoted by $\\Lambda$) is the parameter most likely to effect the efficiency of a grating coupler. It is the length of one period of the grating, and is measured in microns. The grating period is related to the output angle of the light by the following equation, known as the Bragg condition:\n",
     "\n",
     "$\n",
-    "\\Lambda = \\frac{\\lambda}{2n_{eff}}\n",
+    "\\frac{\\lambda}{\\Lambda} = n_{eff} - \\sin(\\theta_{air})\n",
     "$\n",
     "\n",
+    "where $\\lambda$ is the free-space wavelength of the light, $n_{eff}$ is the effective index of the grating, and $\\theta_{air}$ is the angle of propogation of the light in the air compared to the surface normal. \n",
+    "\n",
     "\n",
     "```{warning}\n",
-    "If we were to choose this period to be exactly half the wavelength, the light would be diffracted at 90 degrees, which is problematic since a byproduct of this diffraction would be a large amount of light reflected back into the waveguide. This is known as the \"zeroth order\" diffraction. To avoid this, the grating period is typically chosen to be slightly less than half the wavelength of the light. This results in a diffraction angle slightly less than 90 degrees, which is ideal for coupling light into a fiber optic cable.\n",
+    "If we were choose the grating period such that the light would be diffracted at exactly 90 degrees, a byproduct of this diffraction would be a large amount of light reflected back into the waveguide. This is because there are different grating orders. The bragg equation above gives us the angle of the first order diffraction, but the second order will indcue twice the amount of change in direction. In the case of a waveguide, light would be reflected back along the waveguide. To avoid this, the grating period is typically chosen to result in a diffraction angle slightly less than 90 degrees, which is ideal for coupling light into a fiber optic cable.\n",
     "```\n",
     "\n",
     "\n",
     "### Grating etch depth\n",
-    "The grating etch depth is the depth of the grating teeth into the silicon waveguide. As the etch depth increases, the effective index of refraction of the etched area also decreases. The overall effective index of refraction of the grating coupler is a weighted average of the effective index of the etched and unetched areas...\n",
+    "The grating etch depth is the depth of the grating teeth into the silicon waveguide. As the etch depth increases, the effective index of refraction of the etched area also decreases. The overall effective index of refraction of the grating coupler is a weighted average of the effective index of the etched and unetched areas.\n",
     "\n",
     "### Grating fill factor\n",
-    "The grating fill factor is the ratio of the width of the grating teeth to the width of the grating period.\n",
+    "The grating fill factor is the ratio of the width of the grating teeth to the width of the grating period. The fill factor will affect the effective index of the grating.\n",
     " \n",
     "$\n",
     "ff = \\frac{w}{\\Lambda}\n",

_sources/pages/pdks.ipynb

@@ -6,9 +6,18 @@
    "source": [
     "# Process design kits\n",
     "\n",
-    "A {term}`process design kit` (PDK) is a system of software, models, and tools for modeling a fabrication process for use in designing integrated circuits (electronic or photonic). A PDK typically includes process flow information, a layer stack, process design rules, geometric device models, circuit models, and digital compact models for simulation."
+    "A {term}`process design kit` (PDK) is a system of software, models, and tools for modeling a fabrication process for use in designing integrated circuits (electronic or photonic). A PDK typically includes process flow information, a layer stack, process design rules, geometric device models, circuit models, and digital compact models for simulation.\n",
+    "\n",
+    "One such PDK is the [SiEPIC Ebeam PDK](https://github.com/SiEPIC/SiEPIC_EBeam_PDK) library. This library will be used for this class as it is required for the [OpenEBL](https://siepic.ca/openebl/) fabrication run. Conveniently, many of the tools we have learned to use have the SiEPIC PDK buit in, so it will be relatively easy to design and simulate our devices. GDS factory and Simphony have the PDK built in and ready to go, but KLayout requires the installation of a package. Go through parts 1, 2, and 3 of the [SiEPIC installation instructions](https://github.com/siepic/SiEPIC_EBeam_PDK/wiki/Installation-instructions). If you have already installed KLayout, skip to step 2.\n",
+    "\n",
+    "Installing the package will help you make sure your designs meet the design rules. For example, if you run the verification by clicking the \"Functional Verification\" button, you should see a text box saying there are no errors. However, if you open the \"Double-bus ring resonator sweep\" example, you will see a window open that shows all the errors. Before submitting to the OpenEBL run, make sure the verification runs without finding any errors. "
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": null,

pages/directional_couplers.html

@@ -564,8 +564,8 @@ <h3>Coupling length and the gap between waveguides<a class="headerlink" href="#c
 \]</div>
 <p>Because of this difference in propagation constants, the modes travel at different speeds down the waveguide and so the field intensity oscillates between the two waveguides. This is called beating. One beat is equivalent to the coupling length, or cross-over length, and it is the length it takes for all of the power from one waveguide to be coupled into the other. As the gap between the waveguides gets smaller, the beating gets faster since <span class="math notranslate nohighlight">\(\Delta n\)</span> gets larger, making the cross-over length shorter.</p>
 <p>This cross-over length <span class="math notranslate nohighlight">\(L\)</span>, that gives 100% power transfer is found with:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-4bdfdef2-0933-47d1-bde2-dfe5fc780a62">
-<span class="eqno">(2)<a class="headerlink" href="#equation-4bdfdef2-0933-47d1-bde2-dfe5fc780a62" title="Permalink to this equation">#</a></span>\[\begin{align}
+<div class="amsmath math notranslate nohighlight" id="equation-2c063316-513b-429f-a5da-483e312c9591">
+<span class="eqno">(2)<a class="headerlink" href="#equation-2c063316-513b-429f-a5da-483e312c9591" title="Permalink to this equation">#</a></span>\[\begin{align}
 L_{\text{cross-over}} = \frac {\lambda}{2\Delta n} \nonumber
 \end{align}\]</div>
 <p>This is found from determining what length when multiplied by the propagation constants makes the phase difference <span class="math notranslate nohighlight">\(\pi\)</span>:</p>

pages/grating_couplers.html

@@ -487,22 +487,23 @@ <h1>Essential parameters<a class="headerlink" href="#essential-parameters" title
 <p><img alt="gif" src="https://github.com/BYUCamachoLab/Photonics-Bootcamp/blob/main/book/images/Notebook_Images/gc_parameters.png?raw=true"/></p>
 </div><section id="grating-period">
 <h2>Grating period<a class="headerlink" href="#grating-period" title="Permalink to this heading">#</a></h2>
-<p>The grating period (typically denoted by <span class="math notranslate nohighlight">\(\Lambda\)</span>) is the parameter most likely to effect the efficiency of a grating coupler. It is the length of one period of the grating, and is measured in microns. The grating period is typically chosen to be near half the wavelength of the light being used. This is because the bragg grating period is related to the wavelength of light by the equation:</p>
+<p>The grating period (typically denoted by <span class="math notranslate nohighlight">\(\Lambda\)</span>) is the parameter most likely to effect the efficiency of a grating coupler. It is the length of one period of the grating, and is measured in microns. The grating period is related to the output angle of the light by the following equation, known as the Bragg condition:</p>
 <p><span class="math notranslate nohighlight">\(
-\Lambda = \frac{\lambda}{2n_{eff}}
+\frac{\lambda}{\Lambda} = n_{eff} - \sin(\theta_{air})
 \)</span></p>
+<p>where <span class="math notranslate nohighlight">\(\lambda\)</span> is the free-space wavelength of the light, <span class="math notranslate nohighlight">\(n_{eff}\)</span> is the effective index of the grating, and <span class="math notranslate nohighlight">\(\theta_{air}\)</span> is the angle of propogation of the light in the air compared to the surface normal.</p>
 <div class="admonition warning">
 <p class="admonition-title">Warning</p>
-<p>If we were to choose this period to be exactly half the wavelength, the light would be diffracted at 90 degrees, which is problematic since a byproduct of this diffraction would be a large amount of light reflected back into the waveguide. This is known as the “zeroth order” diffraction. To avoid this, the grating period is typically chosen to be slightly less than half the wavelength of the light. This results in a diffraction angle slightly less than 90 degrees, which is ideal for coupling light into a fiber optic cable.</p>
+<p>If we were choose the grating period such that the light would be diffracted at exactly 90 degrees, a byproduct of this diffraction would be a large amount of light reflected back into the waveguide. This is because there are different grating orders. The bragg equation above gives us the angle of the first order diffraction, but the second order will indcue twice the amount of change in direction. In the case of a waveguide, light would be reflected back along the waveguide. To avoid this, the grating period is typically chosen to result in a diffraction angle slightly less than 90 degrees, which is ideal for coupling light into a fiber optic cable.</p>
 </div>
 </section>
 <section id="grating-etch-depth">
 <h2>Grating etch depth<a class="headerlink" href="#grating-etch-depth" title="Permalink to this heading">#</a></h2>
-<p>The grating etch depth is the depth of the grating teeth into the silicon waveguide. As the etch depth increases, the effective index of refraction of the etched area also decreases. The overall effective index of refraction of the grating coupler is a weighted average of the effective index of the etched and unetched areas…</p>
+<p>The grating etch depth is the depth of the grating teeth into the silicon waveguide. As the etch depth increases, the effective index of refraction of the etched area also decreases. The overall effective index of refraction of the grating coupler is a weighted average of the effective index of the etched and unetched areas.</p>
 </section>
 <section id="grating-fill-factor">
 <h2>Grating fill factor<a class="headerlink" href="#grating-fill-factor" title="Permalink to this heading">#</a></h2>
-<p>The grating fill factor is the ratio of the width of the grating teeth to the width of the grating period.</p>
+<p>The grating fill factor is the ratio of the width of the grating teeth to the width of the grating period. The fill factor will affect the effective index of the grating.</p>
 <p><span class="math notranslate nohighlight">\(
 ff = \frac{w}{\Lambda}
 \)</span></p>

pages/pdks.html

@@ -306,6 +306,8 @@ <h1>Process design kits</h1>
 <section class="tex2jax_ignore mathjax_ignore" id="process-design-kits">
 <h1>Process design kits<a class="headerlink" href="#process-design-kits" title="Permalink to this heading">#</a></h1>
 <p>A <a class="reference internal" href="glossary.html#term-process-design-kit"><span class="xref std std-term">process design kit</span></a> (PDK) is a system of software, models, and tools for modeling a fabrication process for use in designing integrated circuits (electronic or photonic). A PDK typically includes process flow information, a layer stack, process design rules, geometric device models, circuit models, and digital compact models for simulation.</p>
+<p>One such PDK is the <a class="reference external" href="https://github.com/SiEPIC/SiEPIC_EBeam_PDK">SiEPIC Ebeam PDK</a> library. This library will be used for this class as it is required for the <a class="reference external" href="https://siepic.ca/openebl/">OpenEBL</a> fabrication run. Conveniently, many of the tools we have learned to use have the SiEPIC PDK buit in, so it will be relatively easy to design and simulate our devices. GDS factory and Simphony have the PDK built in and ready to go, but KLayout requires the installation of a package. Go through parts 1, 2, and 3 of the <a class="reference external" href="https://github.com/siepic/SiEPIC_EBeam_PDK/wiki/Installation-instructions">SiEPIC installation instructions</a>. If you have already installed KLayout, skip to step 2.</p>
+<p>Installing the package will help you make sure your designs meet the design rules. For example, if you run the verification by clicking the “Functional Verification” button, you should see a text box saying there are no errors. However, if you open the “Double-bus ring resonator sweep” example, you will see a window open that shows all the errors. Before submitting to the OpenEBL run, make sure the verification runs without finding any errors.</p>
 </section>
 <script type="text/x-thebe-config">
     {