Photonic crystal

  Photonic crystals are periodic optical (nano)structures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons. Photonic crystals occur in nature and in various forms have been studied by science for the last 100 years.

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Introduction

Photonic crystals are composed of periodic dielectric or metallo-dielectric (nano)structures that affect the propagation of electromagnetic waves (EM) in the same way as the periodic potential in a semiconductor crystal affects the electron motion by defining allowed and forbidden electronic energy bands. Essentially, photonic crystals contain regularly repeating internal regions of high and low dielectric constant. Photons (behaving as waves) propagate through this structure - or not - depending on their wavelength. Wavelengths of light (stream of photons) that are allowed to travel are known as "modes". Disallowed bands of wavelengths are called photonic band gaps. This gives rise to distinct optical phenomena such as inhibition of spontaneous emission, high-reflecting omni-directional mirrors and low-loss-waveguiding, amongst others.

Since the basic physical phenomenon is based on diffraction, the periodicity of the photonic crystal structure has to be of the same length-scale as half the wavelength of the EM waves i.e. ~200 (blue) to 350 (red) nm for photonic crystals operating in the visible part of the spectrum - the repeating regions of high and low dielectric constants have to be of this dimension. This makes the fabrication of optical photonic crystals cumbersome and complex.

Naturally Occurring Photonic Crystals

A prominent example of a photonic crystal is the naturally occurring gemstone opal. Its play of colours is essentially a photonic crystal phenomenon based on Bragg diffraction of light on the crystal's lattice planes. Another well-known photonic crystal is found on the wings of some butterflies such as those of genus Morpho ^[1].

History of Photonic Crystals

The simplest form of a photonic crystal is a one-dimensional periodic structure, such as a multilayer film (a Bragg mirror); electromagnetic wave propagation in such systems was first studied by Lord Rayleigh in 1887 ^[2], who showed that any such one-dimensional system has a band gap. One dimensional periodic systems continued to be studied extensively, and appeared in applications from reflective coatings where the reflection band corresponds to the photonic band gap and to distributed feedback (DFB) diode lasers where a crystallographic defect is inserted in the photonic band gap to define the laser wavelength. Two dimensional periodic optical structures, without band gaps, received limited study in the 1970s and 1980s. The possibility of two- and three-dimensionally periodic crystals with corresponding two- and three-dimensional band gaps was not suggested until 100 years after Rayleigh, by Eli Yablonovitch and Sajeev John in 1987 ^{[3] [4]}, and such structures have since seen growing interest by a number of research groups around the world, with potential applications including LEDs, optical fiber, nanoscopic lasers, ultrawhite pigment, radio frequency antennas and reflectors, and photonic integrated circuits. Many research groups explore controlling the pace of light emission using 3D photonic crystals^[5]. have verified the 17-year old prediction of American physicist Eli Yablonovitch that ignited a world-wide rush to build tiny "chips" that control light beams. Researchers say it has many potential uses, not only as a tool for controlling quantum optical systems, but also in efficient miniature lasers for displays and telecommunications, in solar cells, and even in future quantum computers.

Fabrication Challenges

The major challenge for higher dimensional photonic crystals is in fabrication of these structures, with sufficient precision to prevent scattering losses blurring the crystal properties and with processes that can be robustly mass produced. One promising method of fabrication for two-dimensionally periodic photonic crystals is a photonic-crystal fiber, such as a "holey fiber". Using fiber draw techniques developed for communications fiber it meets these two requirements. For three dimensional photonic crystals various techniques ^[6] have been used including photolithography and etching techniques similar to those used for integrated circuits. Some of these techniques are already commercially available like Nanoscribe's Direct Laser Writing system^[7]. To circumvent nanotechnological methods with their complex machinery, alternate approaches have been followed to grow photonic crystals as self-assembled structures from colloidal crystals.

Computing Photonic Band Structure

The photonic band gap (PBG) is essentially the gap between the air-line and the dielectric-line in the ω − k relation of the PBG system. To design photonic crystal systems, it is essential to engineer the location and size of the bandgap; this is done by computational modeling using any of the following methods.

1. Plane wave expansion method.
2. Finite Difference Time Domain method
3. Order-N spectral method
4. KKR method

Essentially these methods solve for the frequencies (normal models) of the photonic crystal for each value of the propagation direction given by the wave vector, or vice-versa. The various lines in the band structure, correspond to the different cases of n, the band index.

The plane wave expansion method, can be used to calculate the band structure using an eigen formulation of the Maxwell's equations, and thus solving for the eigen frequencies for each of the propagation directions, of the wave vectors. It directly solves for the dispersion diagram. Electric field strength values can also be calculated over the spatial domain of the problem using the eigen vectors of the same problem. For the picture shown to the right, corresponds to the band-structure of a 1D DBR with air-core interleaved with a dielectric material of relative permittivity 12.25, and a lattice period to air-core thickenss ratio (d/a) of 0.8, is solved using 101 planewaves over the first irreducible Brillouin zone.

Applications

Photonic crystals are attractive optical materials for controlling and manipulating the flow of light. One dimensional photonic crystals are already in widespread use in the form of thin-film optics with applications ranging from low and high reflection coatings on lenses and mirrors to colour changing paints and inks. Higher dimensional photonic crystals are of great interest for both fundamental and applied research, and the two dimensional ones are beginning to find commercial applications. The first commercial products involving two-dimensionally periodic photonic crystals are already available in the form of photonic-crystal fibers, which use a nanoscale structure to confine light with radically different characteristics compared to conventional optical fiber for applications in nonlinear devices and guiding exotic wavelengths. The three-dimensional counterparts are still far from commercialization but offer additional features possibly leading to new device concepts (e.g. optical computers), when some technological aspects such as manufacturability and principal difficulties such as disorder are under control.

See also

• Photonic-crystal fiber
• Thin-film optics
• Superprism

References

1. ^ S. Kinoshita, S. Yoshioka and K. Kawagoe “Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale” Proc. R. Soc. Lond. B 269, 1417-1421 (2002) http://lib.store.yahoo.net/lib/buginabox/kinoshita.pdf
2. ^ J. W. S. Rayleigh, "On the remarkable phenomenon of crystalline reflexion described by Prof. Stokes." Phil. Mag. 26, 256-265. (1888)
3. ^ E. Yablonovitch "Inhibited Spontaneous Emission in Solid-State Physics and Electronics", Phys. Rev. Lett., Vol. 58, 2059 (1987) http://www.ee.ucla.edu/faculty/papers/eliy1987PhysRevLett.pdf
4. ^ S. John, "Strong Localization of Photons in Certain Disordered Dielectric Superlattices", Phys. Rev. Lett. 58, 2486 (1987) http://www.physics.utoronto.ca/~john/john/p2486_1.pdf
5. ^ The research group of prof. W.L. Vos in the Netherlands P. Lodahl, A.F. van Driel, I.S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W.L. Vos "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals" Nature 430, 654 - 657 (2004) http://cops.tnw.utwente.nl/pdf/04/nature02772.pdf
6. ^ Review: S.Johnson (MIT) Lecture 3: Fabrication technologies for 3d photonic crystals, a survey http://ab-initio.mit.edu/photons/tutorial/L3-fab.pdf
7. ^ Homepage of Nanoscribe - a spin-off enterprise of the Karlsruhe Institute of Technology http://www.nanoscribe.de