<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 14 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:Helvetica;
panose-1:2 11 6 4 2 2 2 2 2 4;}
@font-face
{font-family:Helvetica;
panose-1:2 11 6 4 2 2 2 2 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
h1
{mso-style-priority:9;
mso-style-link:"Heading 1 Char";
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:24.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:36.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
span.Heading1Char
{mso-style-name:"Heading 1 Char";
mso-style-priority:9;
mso-style-link:"Heading 1";
font-family:"Cambria","serif";
color:#365F91;
font-weight:bold;}
span.EmailStyle18
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:72.0pt 72.0pt 72.0pt 72.0pt;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:2025983157;
mso-list-type:hybrid;
mso-list-template-ids:930488156 67698705 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
@list l0:level1
{mso-level-text:"%1\)";
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level2
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level3
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level4
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level5
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level6
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level7
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level8
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level9
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
ol
{margin-bottom:0cm;}
ul
{margin-bottom:0cm;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-US" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">David and all,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Just for the record, there are three kinds of velocity for electromagnetic waves:<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo1"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><span style="mso-list:Ignore">1)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The phase velocity, it governs refraction and as you may guess, the refractive index, n, is the material property related to it. May have any velocity,
+/- infinity. <o:p></o:p></span></p>
<p class="MsoListParagraph"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">v_phase = omega/k<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo1"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><span style="mso-list:Ignore">2)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The group velocity, this how fast a pulse of light moves and it is always slower than c.
<o:p></o:p></span></p>
<p class="MsoListParagraph"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">v_group = domega/dk<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo1"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><span style="mso-list:Ignore">3)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The energy transport velocity, relevant for resonant structures, always slower than c<o:p></o:p></span></p>
<p class="MsoListParagraph"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">v_energy = see Amsterdam effect and the book by Brillouin on propagation<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Then (as indicated in the first point), on top of this there is the possibility of negative epsilon and mu leading to negative refractive index. This may happen
at a resonance (small bandwidth, limited response time), and is associated with so-called perfect lenses and optical cloaks. Can be made as a meta material. It amplifies the near-field (longitudinal component).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I hope this helps some.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Cheers, Martin<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<div>
<p class="MsoNormal"><span lang="DE" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Dr. Martin B. van der Mark</span><span lang="DE" style="color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Principal Scientist, Minimally Invasive Healthcare</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Philips Research Europe - Eindhoven</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">High Tech Campus, Building 34 (WB2.025)</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Prof. Holstlaan 4</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">5656 AE Eindhoven, The Netherlands</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Tel: +31 40 2747548</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<div>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> General [mailto:general-bounces+martin.van.der.mark=philips.com@lists.natureoflightandparticles.org]
<b>On Behalf Of </b>davidmathes8@yahoo.com<br>
<b>Sent:</b> dinsdag 20 oktober 2015 1:26<br>
<b>To:</b> Nature of Light and Particles - General Discussion; Richard Gauthier; Chip Akins<br>
<b>Subject:</b> [General] To Infinity and Beyond: zero phase index?<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<h1 style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:15.0pt;margin-left:0cm;background:white">
<span style="font-size:12.0pt;font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal">Rich, Chip, John W, Martin et al</span><span style="font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal"><o:p></o:p></span></h1>
<h1 style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:15.0pt;margin-left:0cm;background:white" id="yui_3_16_0_1_1445294444662_15279">
<span style="font-size:12.0pt;font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal">I've wondered if the photon or quanta within the confines of an electron could really travel at FTL velocities. </span><span style="font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal"><o:p></o:p></span></h1>
<h1 style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:15.0pt;margin-left:0cm;background:white" id="yui_3_16_0_1_1445294444662_15279">
<span style="font-size:12.0pt;font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal">Indeed, one of the parametric models Richard has proposed does fit known experiments to date. </span><span style="font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal"><o:p></o:p></span></h1>
<div id="yui_3_16_0_1_1445294444662_15900">
<p class="MsoNormal" style="background:white"><span style="font-family:"Helvetica","sans-serif";color:black"><o:p> </o:p></span></p>
</div>
<div id="yui_3_16_0_1_1445294444662_15899">
<p class="MsoNormal" style="background:white"><span style="font-family:"Helvetica","sans-serif";color:black">So here is an interesting tool for experimentalists: an o</span><span style="font-size:13.5pt;font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt">n-chip
zero-index metamaterial.</span><span style="font-family:"Helvetica","sans-serif";color:black"><o:p></o:p></span></p>
</div>
<h1 style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:15.0pt;margin-left:0cm;background:white" id="yui_3_16_0_1_1445294444662_15279">
<span style="font-size:12.0pt;font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal"> </span><span style="font-family:"Helvetica","sans-serif";color:#222222;letter-spacing:-.4pt;font-weight:normal"><a href="http://www.nature.com/nphoton/journal/vaop/ncurrent/full/nphoton.2015.198.html" id="yui_3_16_0_1_1445294444662_15318"><span style="font-size:12.0pt">http://www.nature.com/nphoton/journal/vaop/ncurrent/full/nphoton.2015.198.html</span></a><o:p></o:p></span></h1>
<div id="yui_3_16_0_1_1445294444662_15317">
<p class="MsoNormal" style="background:white"><span style="font-family:"Helvetica","sans-serif";color:#333333">"This novel on-chip metamaterial platform opens the door to exploring the physics of zero index and its applications in integrated optics."</span><span style="font-family:"Helvetica","sans-serif";color:black"><o:p></o:p></span></p>
</div>
<div id="yui_3_16_0_1_1445294444662_15317">
<p class="MsoNormal" style="background:white"><span style="font-family:"Helvetica","sans-serif";color:black"><o:p> </o:p></span></p>
</div>
<div id="yui_3_16_0_1_1445294444662_15317">
<p class="MsoNormal" style="background:white"><span style="font-family:"Helvetica","sans-serif";color:black">Best<o:p></o:p></span></p>
</div>
<div id="yui_3_16_0_1_1445294444662_15317">
<p class="MsoNormal" style="background:white"><span style="font-family:"Helvetica","sans-serif";color:black"><o:p> </o:p></span></p>
</div>
<div id="yui_3_16_0_1_1445294444662_15317">
<p class="MsoNormal" style="background:white"><span style="font-family:"Helvetica","sans-serif";color:black">David<o:p></o:p></span></p>
</div>
</div>
</div>
<br>
<hr>
<font face="Arial" color="Gray" size="1">The information contained in this message may be confidential and legally protected under applicable law. The message is intended solely for the addressee(s). If you are not the intended recipient, you are hereby notified
that any use, forwarding, dissemination, or reproduction of this message is strictly prohibited and may be unlawful. If you are not the intended recipient, please contact the sender by return e-mail and destroy all copies of the original message.<br>
</font>
</body>
</html>