Metamaterial and Invisibility Cloaks ```Name: Josh Status: student Grade: 9-12 Location: IL Country: USA Date: Winter 2009-2010 ``` Question: I am interested in metatmaterials. Specifically, how do materials with a negative index of refraction work? I have tried to understand some articles on invisibility cloak research from Lawrence Berkeley Laboratory, but it is a bit beyond my high school physics course. Would you please help me? Replies: Here is a response to this question from a friend of mine, Daniel Roberts, who is an expert in the field of metamaterials: Snell's law describes the refraction of light as it passes from one material to another (n1*sin(x1) = n2*sin(x2) ), where the n's are the indices of refraction and the x's are the angles as measured from the normal. Traditionally, this is taught for n1 and n2 > 0 (in fact, usually they are taken to be > 1). Additionally, the angles are measured from opposite sides of the normal. However, Snell's law also holds for one (or both) n's negative. Since (- sin x) = sin (-x), this means that the ray will refract on the same side of the normal. You can find a diagram and more information here (http://people.ee.duke.edu/~drsmith/negative_index_about.htm). Your question about how these material's work is a bit more complicated. Metamaterials are not found in nature; they are engineered to have structures with specific properties. These structures are usually smaller than the wavelength of light. The light can only "see" things over the course of a wavelength, and thus if things change at a scale smaller than the wavelength, the light sees it as "one" material. These structures can be engineered so that over a small frequency range, the phase velocity (the speed at which the peaks and troughs move as determined by the refraction formula v = c/n) can be opposite to the energy velocity (the speed and direction in which the wave's power moves). That is the signature of negative refraction (since if you plug a negative value of n into v = c/n, you will see that the phase velocity for negative index materials must be negative - where as the direction of the wave's energy will be positive). Here is a bit more on metamaterials (http://people.ee.duke.edu/~drsmith/about_metamaterials.html). Douglas Stanford Hi Josh I appreciate your extra-curricular interest in physics. Generally, I can go query the Internet for questions like this. You could not do that 5 or 10 years ago because the information was just not there. But that is different these days because there is a lot of professional tutorial information available to us online. (That lets me portray myself as a know-it-all, as long as I can read) So I went to http://www.google.com and searched for "negative index of refraction invisibility" And I hit gold. Wikipedia is an on-line encyclopedia that permits people (who want to add to an issue) to submit edits. And what you often find are first line researchers in the field publishing their results in a tutorial fashion in real-time. It is not like anyone can visit the site and change the text. Potential editors have to submit their inputs to the Wikipedia staff who have a barn full of subject matter experts who review the validity of the inputs and actually modify the Wiki content. So whenever Wikipedia comes up on my searches, I look at that first. But if that does not work there are always other results from your search and you might find something that is easier to understand, that might give you step up to understand the other more complex stuff. Some of the stuff though really is just trash and not really worth your time. Sometimes you just find companies trying to get you to buy their smoke and mirrors. So, Negative Refraction: Rather than send you an e-mail that rivals the size of the epistles of St Paul (as if I could write such an article on negative refraction), please refer to this URL: http://en.wikipedia.org/wiki/Metamaterial This explained it pretty well for me and it just loaded with other links explaining terms that you might not understand, so follow through with it until you understand this stuff. Here is another URL that I found coherent: http://www.physorg.com/news93882787.html Here is another: http://berkeley.edu/news/media/releases/2008/08/11_light.shtml Notice this 2nd one is from Berkeley. That should be a tip off that these guys know what they are doing. (YOU REALLY CANNOT BELIEVE EVERYTHING YOU READ ON THE INTERNET THESE DAYS) If you find a word you are not familiar with, http://dictionary.reference.com is helpful in that regard. And I learn all this stuff too by answering questions like these. So thanks, keep going, and good luck in your career. Sincere regards, Mike Stewart Here is a response to this question from a friend of mine, Daniel Roberts, who is an expert in the field of metamaterials: Snell's law describes the refraction of light as it passes from one material to another (n1*sin(x1) = n2*sin(x2) ), where the n's are the indices of refraction and the x's are the angles as measured from the normal. Traditionally, this is taught for n1 and n2 > 0 (in fact, usually they are taken to be > 1). Additionally, the angles are measured from opposite sides of the normal. However, Snell's law also holds for one (or both) n's negative. Since (- sin x) = sin (-x), this means that the ray will refract on the same side of the normal. You can find a diagram and more information here ( http://people.ee.duke.edu/~drsmith/negative_index_about.htm). Your question about how these material's work is a bit more complicated. Metamaterials are not found in nature; they are engineered to have structures with specific properties. These structures are usually smaller than the wavelength of light. The light can only "see" things over the course of a wavelength, and thus if things change at a scale smaller than the wavelength, the light sees it as "one" material. These structures can be engineered so that over a small frequency range, the phase velocity (the speed at which the peaks and troughs move as determined by the refraction formula v = c/n) can be opposite to the energy velocity (the speed and direction in which the wave's power moves). That is the signature of negative refraction (since if you plug a negative value of n into v = c/n, you will see that the phase velocity for negative index materials must be negative - where as the direction of the wave's energy will be positive). Here is a bit more on metamaterials ( http://people.ee.duke.edu/~drsmith/about_metamaterials.html). Douglas Stanford Go to http://www.msnbc.msn.com/id/12961080/ for a layman's article from MSNBC. 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