In my post at the end of the summer, I talked a bit about what I actually did in that UROP. Upon rereading it, I have come to realize that it is a little jumbled and technical. I'd like to basically rephrase it in less technical terms, along with providing more context on what I did in the 2011 fall semester. Follow the jump to see more.
Many of you who have taken a high-school physics class may remember the laws governing refraction and reflection. When light, being an electromagnetic wave, is incident on a surface, it reflects at the same angle as that of its incidence relative to a line perpendicular to the surface off of which the light reflects. Light can also be transmitted through a material, but it gets bent in the process of refraction, and the amount of bending is given by the properties of the two materials the light passes through; specifically, it depends on a property known as the dielectric function, which essentially characterizes how a material responds to an applied electric field even if it doesn't have an overall electric charge. (Technically we should also be considering the magnetic permeability (not "diamagnetic function", which is something totally different) as well because light is composed of oscillating electric and magnetic fields, but the magnetic permeability of most materials considered here is very close to that of the vacuum, so they can be neglected.)
So then what is a photonic crystal? Put simply, it is an arrangement of different dielectric materials into units that repeat periodically in space. So why does this matter? I will leave out the technical details here, but essentially, the cool thing about light shone into an ideal photonic crystal is that depending on what the particular structure is like, certain ranges of wavelengths will be perfectly transmitted with no reflection (known as a photonic band), and certain ranges of wavelengths will be perfectly reflected with no transmission (known as a photonic band gap). This is similar to how electrons behave in semiconductors like those used in computer chips. In fact, the similarities between classical electromagnetic behavior and quantum electronic behavior go way deeper; I would strongly recommend reading the book Photonic Crystals by Joannopoulos et al to see how the similarities are fully fleshed out. Anyway, the study of photonic crystals is mostly a subset of the field of nanophotonics, in which light is manipulated through new structures in such a way that the behavior of light depends on the geometry of the structure much more than the material properties of the structure. This holds true for photonic crystals as well: the material properties like the dielectric function can be scaled along with the dimensions of the structure and the wavelengths allowed, so what matters most is the shape and configuration of one unit of the structure.
I have worked on two UROP projects regarding photonic crystals thus far. The first, from the 2011 fall semester, to the middle of the 2012 spring semester has been about photonic crystals and solar cells. The sun emits a spectrum of light that goes beyond what is visible to the human eye. Conventional solar cells are limited in how much light they can absorb and what wavelengths they can reasonably absorb. By contrast, once some additional factors are added in (because my previous discussion was about reflection and transmission, not absorption), it can be shown that certain photonic crystals can also do a really good job of absorbing light at certain frequencies. If a photonic crystal structure is placed on top of a solar cell substrate, it will be able to absorb a lot more wavelengths with more efficiency than a solar cell by itself. My work those semesters was in using computer simulations with the MEEP program to model the exact enhancement provided by the addition of photonic crystals, along with how that enhancement varies as a function of the angle of incidence; after all, the sun is not directly overhead in the sky all day, so these structures need to have justifiable performance at other times of the day as well.
The second project, since later in the 2012 spring semester to now, has been about photonic crystals and fluorescent dyes. Fluorescence is when electrons in atoms that gain energy somehow (through the absorption of light or through other means) release that energy in the form of light, and they do this in all directions out of phase. This is a form of spontaneous emission, to be contrasted with the stimulated emission that allows lasers to emit light in a very narrow beam in a single direction. Fluorescence is used to identify materials, make fluorescent lamps and white LEDs, and perform biology research. In this project, I have been modeling how photonic crystals can enhance the fluorescent emission of organic dyes. This will help with molecular imaging, as macromolecules like proteins have surfaces that look like photonic crystals, so these can be imaged better by pairing such surfaces with organic dye molecules. Maybe photonic crystals will be applied to other areas where fluorescent emission is important, like the things I mentioned earlier.
Where else are photonic crystals used? Well, butterflies that have incredibly bright-colored wings have molecular structures on their wing surfaces that look like photonic crystals; they reflect the wavelengths that are eventually seen much more efficiently than traditional pigments. The fact that photonic crystals can transmit light much better than conventional waveguides with minimal reflection means that they could be used in optical communication fibers and invisibility cloaks. In short, the range of possible uses for photonic crystals is already quite large and growing by the day!
Many of you who have taken a high-school physics class may remember the laws governing refraction and reflection. When light, being an electromagnetic wave, is incident on a surface, it reflects at the same angle as that of its incidence relative to a line perpendicular to the surface off of which the light reflects. Light can also be transmitted through a material, but it gets bent in the process of refraction, and the amount of bending is given by the properties of the two materials the light passes through; specifically, it depends on a property known as the dielectric function, which essentially characterizes how a material responds to an applied electric field even if it doesn't have an overall electric charge. (Technically we should also be considering the magnetic permeability (not "diamagnetic function", which is something totally different) as well because light is composed of oscillating electric and magnetic fields, but the magnetic permeability of most materials considered here is very close to that of the vacuum, so they can be neglected.)
So then what is a photonic crystal? Put simply, it is an arrangement of different dielectric materials into units that repeat periodically in space. So why does this matter? I will leave out the technical details here, but essentially, the cool thing about light shone into an ideal photonic crystal is that depending on what the particular structure is like, certain ranges of wavelengths will be perfectly transmitted with no reflection (known as a photonic band), and certain ranges of wavelengths will be perfectly reflected with no transmission (known as a photonic band gap). This is similar to how electrons behave in semiconductors like those used in computer chips. In fact, the similarities between classical electromagnetic behavior and quantum electronic behavior go way deeper; I would strongly recommend reading the book Photonic Crystals by Joannopoulos et al to see how the similarities are fully fleshed out. Anyway, the study of photonic crystals is mostly a subset of the field of nanophotonics, in which light is manipulated through new structures in such a way that the behavior of light depends on the geometry of the structure much more than the material properties of the structure. This holds true for photonic crystals as well: the material properties like the dielectric function can be scaled along with the dimensions of the structure and the wavelengths allowed, so what matters most is the shape and configuration of one unit of the structure.
I have worked on two UROP projects regarding photonic crystals thus far. The first, from the 2011 fall semester, to the middle of the 2012 spring semester has been about photonic crystals and solar cells. The sun emits a spectrum of light that goes beyond what is visible to the human eye. Conventional solar cells are limited in how much light they can absorb and what wavelengths they can reasonably absorb. By contrast, once some additional factors are added in (because my previous discussion was about reflection and transmission, not absorption), it can be shown that certain photonic crystals can also do a really good job of absorbing light at certain frequencies. If a photonic crystal structure is placed on top of a solar cell substrate, it will be able to absorb a lot more wavelengths with more efficiency than a solar cell by itself. My work those semesters was in using computer simulations with the MEEP program to model the exact enhancement provided by the addition of photonic crystals, along with how that enhancement varies as a function of the angle of incidence; after all, the sun is not directly overhead in the sky all day, so these structures need to have justifiable performance at other times of the day as well.
The second project, since later in the 2012 spring semester to now, has been about photonic crystals and fluorescent dyes. Fluorescence is when electrons in atoms that gain energy somehow (through the absorption of light or through other means) release that energy in the form of light, and they do this in all directions out of phase. This is a form of spontaneous emission, to be contrasted with the stimulated emission that allows lasers to emit light in a very narrow beam in a single direction. Fluorescence is used to identify materials, make fluorescent lamps and white LEDs, and perform biology research. In this project, I have been modeling how photonic crystals can enhance the fluorescent emission of organic dyes. This will help with molecular imaging, as macromolecules like proteins have surfaces that look like photonic crystals, so these can be imaged better by pairing such surfaces with organic dye molecules. Maybe photonic crystals will be applied to other areas where fluorescent emission is important, like the things I mentioned earlier.
Where else are photonic crystals used? Well, butterflies that have incredibly bright-colored wings have molecular structures on their wing surfaces that look like photonic crystals; they reflect the wavelengths that are eventually seen much more efficiently than traditional pigments. The fact that photonic crystals can transmit light much better than conventional waveguides with minimal reflection means that they could be used in optical communication fibers and invisibility cloaks. In short, the range of possible uses for photonic crystals is already quite large and growing by the day!
