| | My favorite character in Atlas Shrugged is John Galt. One of the crucial traits of this character is his extraordinary technical ability. I can adore a fictional character, and part of the reason I adore this one is his possession of that trait.
Adoration is one thing, admiration is another. Galt’s technical genius is admirable only in the derivative sense that I would admire that trait in a real person. I cannot admire a fictional character. I can admire the character’s creator as creator, but not the character.
Fortunately, there are in our time many individuals whose mathematical and scientific accomplishments are at the high level of the fictional character John Galt. They are not well known to the general public. I want to tell you about one such man.
Eli Yablonovitch invented the concept of a photonic band gap. He arrived at this concept in 1987 while doing research on making telecommunication lasers more efficient. Another physicist Sajeev John arrived at the concept independently that same year. John came to the concept in the course of pure research attempting to create light localization.
Four years later, Yablonovitch was the first to create a successful photonic band-gap crystal. He used a variant of the crystal structure of diamond, a variant now called yablonovite. The structure was formed by drilling three intersecting arrays of holes, 400 nanometers in diameter, into a block of ceramic material. This structure, at this scale, was able to eliminate the propagation of electromagnetic radiation in the microwave range. Photonic band-gap crystals are yielding a new generation of optical fibers capable of carrying much more information, and they are contributing to the realization of nanoscopic lasers and photonic integrated circuits.
The name photonic crystalsounds like a crystal made of light. That is incorrect. A photonic crystal is an artificial crystal (or quasicrystal) made usually of solids such as dielectrics or semiconductors. The electrical properties of a semiconductor are intermediate between a dielectric (an insulator) and a conductor.
In a dielectric material, the valence electrons of the atoms are tightly bound to them. They are confined to energy levels within the band of levels called the valence band. Above that band of levels is a broad band of energies inaccessible to the electrons under the laws of quantum mechanics. That forbidden band is called the band gap. Above the band gap is a band in which electrons could move freely in the material if only enough energy were applied to them to raise them to that band of energy levels. This band is called the conduction band.
In a semiconductor, the valence electrons are less tightly bound to atoms than they are in a dielectric. The band gap is smaller. A smaller boost of energy is needed to induce the flow of electrons, a current. The degree of electrical conductivity of a semiconductor can be precisely controlled by doping one semiconductor chemical element with small amounts of another.
When an electron is promoted across the band gap, an effective positive charge called a hole is created in the valence levels below the gap. The holes, like the electrons, can be entrained into currents. By controlling the supply of electrons and holes above and below the band gap, carefully designed semiconductors are able to perform electronic switching, modulating, and logic functions. They can also be contrived to serve as media for photo detectors, solid-state lasers, light-emitting diodes, thermistors, and solar cells.
The properties of an electronic band gap depend on the type of atoms and their crystal structure in the solid semiconductor. To comprehend and manipulate the electronic properties of matter, electrons and their alterations must be treated not only in their character as particles, but in their character as quantum-mechanical waves. The interatomic spacing of the atoms in matter is right for wave-interference effects among electrons. This circumstance yields the electronic band gaps in semiconductors as well as the conductive ability of conductors.
A photonic band gap is a range of energies of electromagnetic waves for which their propagation through the crystal is forbidden in every direction. The interatomic spacing in semiconductors are on the order of a few tenths of a nanometer, and that is too small for effecting photonic band gaps in the visible, infrared, microwave, or radio ranges of the spectrum. Creation of photonic band gaps for these very useful wavelengths requires spatial organizations in matter at scales on the order of a few hundred nanometers and above.
In the 70’s and 80’s, researchers had been forming, in semiconductors, structures called superlattices. These were periodic variations in semiconductor composition in which repetitions were at scales a few times larger than the repetitions in the atomic lattice. The variations could consist of alternating layers of two types of semiconductors or in cyclic variations in the amount of selected impurities in a single type of semiconductor. These artificial lattices allowed designers, guided by the quantum theory of solids, to create new types of electronic band gaps and new opticoelectronic properties in semiconductors.
Photonic crystals are superlattices in which the repeating variation is a variation in the refractive index of the medium. It is by refractions and internal partial reflections that photonic band gaps are created. The array of holes that Yablonovitch and his associates drilled for the first photonic crystal formed a superlattice of air in the surrounding dielectric solid. Additional workable forms of photonic-crystal superlattice have been demonstrated since that first one. Costas Soukoulis and colleagues created a crystal of crisscrossed rods, and it has yielded photonic band gaps in the infrared part of the spectrum. Photonic crystals have been created mostly in dielectric or semiconductor media, but Shawn Yu Lin and associates have created them in tungsten. These may prove useful in telecommunications and in the conversion of infrared radiation into electricity.
In 2001 Eli Yablonovitch co-founded the company Luxtera, which is now a leading commercial developer of silicon photonic products.
Photonic crystals, manipulators of light, they are alive. They are alive “because they are the physical shape of the action of a living power—of the mind that had been able to grasp the whole of this complexity, to set its purpose, to give it form.” –AR 1957
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