diff --git a/book/pages/scattering_parameters.ipynb b/book/pages/scattering_parameters.ipynb
index 45877a7..7ae9760 100644
--- a/book/pages/scattering_parameters.ipynb
+++ b/book/pages/scattering_parameters.ipynb
@@ -15,9 +15,15 @@
    "source": [
     "## What are scattering parameters?\n",
     "\n",
-    "Scattering parameters (S-parameters) are values that represent linear characteristics of devices that operate at radio frequencies or higher and are used in both RF electronics and in photonics. For a given photonic device, while knowing the actual shape of the device is useful, what we really care about is how light propagates through it. S-Parameters give us this necessary information by telling us how much light will exit a given port based on how much light was inserted and where. \n",
+    "For a given photonic device, while knowing the actual shape of the device is useful, what we really care about is how light propagates through it. Scattering parameters (S-parameters) are complex numbers that represent the magnitude and phase multiplier acting on the light between every port in a device. S-parameters are collected into an s-matrix which then represents the complete 1st order (linear) input-output response of the device.\n",
     "\n",
-    "For a device with N ports, there will be N<sup>2</sup> s-parameters, which are normally organized in an NxN matrix, ofen called the Scatter Matrix. Each S-parameter is a complex number that gives the magnitude and phase of the wave exiting the exit port given the wave entering the input port. The notation for S-Parameters is S<sub>(output port)(input port)</sub>. So, S<sub>13</sub> will be for the light entering port 3 and exiting port 1\n",
+    "For a device with N ports, there will be N<sup>2</sup> parameters. The notation for S-Matrices is S<sub>(output port)(input port)</sub>, so S<sub>13</sub> will be for the light entering port 3 and exiting port 1. Parameters with the input and output port represent reflections from the device back into the same port, while different output and input ports represent the transmission from the input port into the output ports.\n",
+    "\n",
+    "It is easiest to represent s-parameters in polar coordinate form.\n",
+    "\n",
+    "#### Example\n",
+    "\n",
+    "A device has the s-parameter $S_{21} = 0.98 e^{j\\frac{\\pi}{2}}$. This means the light accumulates $90^\\circ$ of phase, and its intensity/power will be 96% ($0.98^2 = 0.9604$) of the input when we measure the output on port 2 and put input light in port 1.\n",
     "\n",
     "\n"
    ]
@@ -27,11 +33,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## TODO: Why are S-Parameters useful?\n",
+    "## Why are S-Parameters useful?\n",
     "\n",
-    "Scattering parameters allow us to characterize the bechavior of photonic circuits in a comprehensive way. They describe the relationship between a photonic circuit's input signals and its output signals in terms of power, phase, and impedance. They allow us to understand how various elements within a photonic circuit interact. \n",
+    "* S-parameters allow us to represent a potentially complex photonic component as a matrix, which is much simpler to store and use in computation than other options (e.g. nonlinear functions, FDTD simulations, etc.).\n",
+    "* It allows us to connect the device arbitrarily to other components and simulate its behavior in any photonic circuit.\n",
+    "* Wavelength dependence (dispersion) can be represented simply by adding an extra dimension to the s-matrix.\n",
     "\n",
-    "When we know the scattering parameters of elements within a photonic circuit, we can use simulation software and modelling tools to design, simulate, and test circuits according to desired performance metrics. These tools enable us to optimize circuit designs before the fabrication process, and validate the fabrication process after they've been manufactured. "
+    "S-Parameters are used in circuit-level simulation software, e.g. simphony, sax, Lumerical Interconnect, etc."
    ]
   },
   {