Improve knowledge baseHEADmaster

1 files changed, 14 insertions, 10 deletions

diff --git a/source/know/concept/fabry-perot-cavity/index.md b/source/know/concept/fabry-perot-cavity/index.md
index d5ea0ea..c648549 100644
--- a/source/know/concept/fabry-perot-cavity/index.md
+++ b/source/know/concept/fabry-perot-cavity/index.md
@@ -10,11 +10,13 @@ layout: "concept"
 ---
 
 In its simplest form, a **Fabry-Pérot cavity**
-is a region of light-transmitting medium surrounded by two mirrors,
-which may transmit some of the incoming light.
-Such a setup can be used as e.g. an interferometer or a laser cavity.
+is a region of light-transmitting medium surrounded by two parallel mirrors,
+which may let some of the light escape.
+Such a setup can be used as e.g. a laser cavity or an interferometer.
+Below, we treat this simple system as an exercise
+for calculating *quasinormal modes* in 1D,
+i.e. modes with complex resonances.
 
-Below, we calculate its quasinormal modes in 1D.
 We divide the $$x$$-axis into three domains: left $$L$$, center $$C$$, and right $$R$$.
 The cavity $$C$$ has length $$\ell$$ and is centered on $$x = 0$$.
 Let $$n_L$$, $$n_C$$ and $$n_R$$ be the respective domains' refractive indices:
@@ -95,8 +97,8 @@ $$\begin{aligned}
     \end{bmatrix}
 \end{aligned}$$
 
-We do not want to simply satisfy this equation
-by setting $$A_1$$, $$A_2$$, $$A_3$$ and $$A_4$$,
+We do not want to satisfy this equation
+by simply setting $$A_1$$, $$A_2$$, $$A_3$$ and $$A_4$$,
 so we demand that the system matrix is not invertible,
 i.e. its determinant is zero:
 
@@ -116,7 +118,9 @@ $$\begin{aligned}
     - 2 n_C (n_L + n_R) \cos(k_m n_C \ell)
 \end{aligned}$$
 
-Finally, some further rearranging gives a convenient transcendental equation:
+Finally, some further rearranging gives a convenient transcendental equation,
+keeping in mind that $$k_m$$ and the indices $$n_L$$, $$n_C$$ and $$n_R$$
+are generally complex numbers:
 
 $$\begin{aligned}
     \boxed{
@@ -223,9 +227,9 @@ $$\begin{aligned}
     &= (1 - r_R) A_3 e^{i k_m (n_C - n_R) \ell/2}
 \end{aligned}$$
 
-Note that we have not demanded continuity of the electric field.
-This is because the mirrors are infinitely thin "magic" planes;
-had we instead included the full microscopic mirror structure,
+Note that we have not demanded continuity of the electric field,
+because the mirrors are infinitely thin "magic" planes in this case.
+If we had instead included the full microscopic mirror structure,
 then we would have demanded continuity as before.