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@@ -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-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}
+<div class="amsmath math notranslate nohighlight" id="equation-876851f8-d50b-4d27-8131-767b434e7c6c">
+<span class="eqno">(2)<a class="headerlink" href="#equation-876851f8-d50b-4d27-8131-767b434e7c6c" 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>