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	<id>http://gisaxs.com/index.php?action=history&amp;feed=atom&amp;title=Reflectivity_oscillations_below_critical_angle</id>
	<title>Reflectivity oscillations below critical angle - Revision history</title>
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	<updated>2026-04-08T19:27:43Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.31.7</generator>
	<entry>
		<id>http://gisaxs.com/index.php?title=Reflectivity_oscillations_below_critical_angle&amp;diff=4458&amp;oldid=prev</id>
		<title>KevinYager at 19:56, 15 October 2014</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Reflectivity_oscillations_below_critical_angle&amp;diff=4458&amp;oldid=prev"/>
		<updated>2014-10-15T19:56:55Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 19:56, 15 October 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In [[reflectivity]] experiments, when the angle of incidence is below the [[critical angle]], the beam experiences [[total external reflection]]. Thus, the reflectivity goes to 100% (&amp;lt;math&amp;gt;\scriptstyle R =1 &amp;lt;/math&amp;gt;) for any &amp;lt;math&amp;gt;\scriptstyle \theta &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\lt &lt;/del&gt;\theta_c&amp;lt;/math&amp;gt;, or for &amp;lt;math&amp;gt;\scriptstyle q &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\lt &lt;/del&gt;q_c&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In [[reflectivity]] experiments, when the angle of incidence is below the [[critical angle]], the beam experiences [[total external reflection]]. Thus, the reflectivity goes to 100% (&amp;lt;math&amp;gt;\scriptstyle R =1 &amp;lt;/math&amp;gt;) for any &amp;lt;math&amp;gt;\scriptstyle \theta &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt; &lt;/ins&gt;\theta_c&amp;lt;/math&amp;gt;, or for &amp;lt;math&amp;gt;\scriptstyle q &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt; &lt;/ins&gt;q_c&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;However, one sometimes sees oscillations of the reflectivity even below this angle (especially in [[x-ray]] reflectivity, though it is also possible in neutron reflectivity). These oscillations can be thought of as [[waveguide]] modes appearing while the reflectivity angle is in between the critical angle of the substrate, and the critical angle of the film. Notably, these variations are only visible (in reflectivity) due to the non-zero absorption of the film. However, even a very small absorption can be measured, because the waveguide modes inherently travel through the film many times.&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;However, one sometimes sees oscillations of the reflectivity even below this angle (especially in [[x-ray]] reflectivity, though it is also possible in neutron reflectivity). These oscillations can be thought of as [[waveguide]] modes appearing while the reflectivity angle is in between the critical angle of the substrate, and the critical angle of the film. Notably, these variations are only visible (in reflectivity) due to the non-zero absorption of the film. However, even a very small absorption can be measured, because the waveguide modes inherently travel through the film many times.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Reflectivity_oscillations_below_critical_angle&amp;diff=4457&amp;oldid=prev</id>
		<title>KevinYager at 19:56, 15 October 2014</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Reflectivity_oscillations_below_critical_angle&amp;diff=4457&amp;oldid=prev"/>
		<updated>2014-10-15T19:56:35Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 19:56, 15 October 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In [[reflectivity]] experiments, when the angle of incidence is below the [[critical angle]], the beam experiences [[total external reflection]].&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In [[reflectivity]] experiments, when the angle of incidence is below the [[critical angle]], the beam experiences [[total external reflection]]&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. Thus, the reflectivity goes to 100% (&amp;lt;math&amp;gt;\scriptstyle R =1 &amp;lt;/math&amp;gt;) for any &amp;lt;math&amp;gt;\scriptstyle \theta \lt \theta_c&amp;lt;/math&amp;gt;, or for &amp;lt;math&amp;gt;\scriptstyle q \lt q_c&amp;lt;/math&amp;gt;.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;However, one sometimes sees oscillations of the reflectivity even below this angle (especially in [[x-ray]] reflectivity, though it is also possible in neutron reflectivity). These oscillations can be thought of as [[waveguide]] modes appearing while the reflectivity angle is in between the critical angle of the substrate, and the critical angle of the film. Notably, these variations are only visible (in reflectivity) due to the non-zero absorption of the film. However, even a very small absorption can be measured, because the waveguide modes inherently travel through the film many times&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Reflectivity example-real density.png|thumb|center|400px|Reflectivity calculation in a film with purely-real density (no absorption).]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Reflectivity example-real density.png|thumb|center|400px|Reflectivity calculation in a film with purely-real density (no absorption).]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Reflectivity example-complex density.png|thumb|center|400px|Reflectivity calculation in a film with a complex density (finite value of the imaginary part of the complex potential; corresponds to film absorption).]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Reflectivity example-complex density.png|thumb|center|400px|Reflectivity calculation in a film with a complex density (finite value of the imaginary part of the complex potential; corresponds to film absorption).]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Reflectivity_oscillations_below_critical_angle&amp;diff=4455&amp;oldid=prev</id>
		<title>KevinYager: Created page with &quot;In reflectivity experiments, when the angle of incidence is below the critical angle, the beam experiences total external reflection.  Image:Reflectivity example...&quot;</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Reflectivity_oscillations_below_critical_angle&amp;diff=4455&amp;oldid=prev"/>
		<updated>2014-10-15T19:52:32Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;In &lt;a href=&quot;/index.php/Reflectivity&quot; title=&quot;Reflectivity&quot;&gt;reflectivity&lt;/a&gt; experiments, when the angle of incidence is below the &lt;a href=&quot;/index.php/Critical_angle&quot; title=&quot;Critical angle&quot;&gt;critical angle&lt;/a&gt;, the beam experiences &lt;a href=&quot;/index.php/Total_external_reflection&quot; class=&quot;mw-redirect&quot; title=&quot;Total external reflection&quot;&gt;total external reflection&lt;/a&gt;.  Image:Reflectivity example...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;In [[reflectivity]] experiments, when the angle of incidence is below the [[critical angle]], the beam experiences [[total external reflection]].&lt;br /&gt;
&lt;br /&gt;
[[Image:Reflectivity example-real density.png|thumb|center|400px|Reflectivity calculation in a film with purely-real density (no absorption).]]&lt;br /&gt;
[[Image:Reflectivity example-complex density.png|thumb|center|400px|Reflectivity calculation in a film with a complex density (finite value of the imaginary part of the complex potential; corresponds to film absorption).]]&lt;/div&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
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