1. Photonic Crystals: A New Frontier in Modern Optics
MARIAN FLORESCU
NASA Jet Propulsion Laboratory
California Institute of Technology

2. “ If only were possible to make materials in which electromagnetically waves cannot propagate at certain frequencies, all kinds of almost-magical things would happen”
Sir John Maddox, Nature (1990)
I would like to begin my talk with a quote of the Nature magazine editor, published few few years after the theoretical prediction of photonic crystals, as a part of a rather pessimistic paper regarding the possibility of creating such crystals. Fortunately, over the past 15 years, this pessimism has been proven wrong, and in this talk I will like present some of the almost-magical word of photonic crystals.

3. Photonic Crystals Photonic crystals: periodic dielectric structures.
interact resonantly with radiation with wavelengths comparable to the periodicity length of the dielectric lattice.
dispersion relation strongly depends on frequency and propagation direction
may present complete band gaps  Photonic Band Gap (PBG) materials.
Two Fundamental Optical Principles
Localization of Light
S. John, Phys. Rev. Lett. 58,2486 (1987)
Inhibition of Spontaneous Emission
E. Yablonovitch, Phys. Rev. Lett (1987)
Photonic crystals are periodic dielectric structures. Their interact resonantly with radiation with wavelengths comparable to the periodicity length of the dielectric lattice. The dispersion relation of the light propagating through PC is strongly depending on the frequency and propagation direction. If there band gaps are present in the photonic band structure, then they are simply called PBG materials.
The simplest example is a Bragg stack of dielectric planes, which presents spectral range over which the transmission of light is strongly suppressed. In quantum optics we are mostly interested in the density of states of the photonic reservoir associated with the PC, which is presented here, with the gap characterized by the absence of elmgn modes, and the band edge frequencies. We note the fast variations with the frequency of the PDOS in the spectral range surrounding the band edge freq. (in this low-dimensional system, the PDOS is actually divergent at the BEFs, a square root divergence).
A whole new research field was created with the invention of photonic crystals. These are artificial periodic structures that have the ability of inhibiting the linear propagation of light in all directions.
Photonic crystals were originally proposed as means to realize two fundamental optical principles:the localization and trapping of light in a bulk material and the complete inhibition of spontaneous emission over a broad frequency range.
Photonic crystals not only have the ability to guide and confine light but also provide a novel environment for quantum mechanical light-matter interaction , which make make them suitable for a series of revolutionazing applications.
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Guide and confine light without losses
Novel environment for quantum mechanical light-matter interaction
A rich variety of micro- and nano-photonics devices

4. Photonic Crystals History
1987: Prediction of photonic crystals
S. John, Phys. Rev. Lett. 58,2486 (1987), “Strong localization of photons
in certain dielectric superlattices”
E. Yablonovitch, Phys. Rev. Lett (1987), “Inhibited spontaneous
emission in solid state physics and electronics”
1990: Computational demonstration of photonic crystal
K. M. Ho, C. T Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990)
1991: Experimental demonstration of microwave photonic crystals
E. Yablonovitch, T. J. Mitter, K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991)
1995: ”Large” scale 2D photonic crystals in Visible
U. Gruning, V. Lehman, C.M. Englehardt, Appl. Phys. Lett. 66 (1995)
1998: ”Small” scale photonic crystals in near Visible; “Large” scale
inverted opals
1999: First photonic crystal based optical devices (lasers, waveguides)
Photonic crystals were introduced independently and simultaneously in 1987 by two researchers, each following different paths. Sajeev john was formulating an answer to the question whether andreson localization of electrons in a disordered solid can be extended to photons in a strongly scattering medium, and predicted that localized stated of the electromagnetic field can be created in a periodic dielectric medium. At the same time, yablo was trying to address the possibility of suppressing the unwanted spontaneous emission affecting the semiconductor lasers, and predicted that a 3d periodic dielectric can produce a forbidden gap in the electromagnetic spectrum where.
As a consequence of the unique properties of photonic crystals, they attracted wordwide attention of physicist, chemists or engineers such that the field of photonic crydtal is in continue expansion, with the number of publishe papars doublig every two years.

5. Photonic Crystals- Semiconductors of Light
Periodic array of atoms
Atomic length scales
Natural structures
Control electron flow
1950’s electronic revolution
Photonic Crystals
Periodic variation of dielectric
constant
Length scale ~ 
Artificial structures
Control e.m. wave propagation
New frontier in modern optics
Photonic crystals may be regarded as semicondutors of light. Rather than a periodic array of atoms which scatter and modify the energy-momentum of electrons, PC consinsists of a periodic dielectric structure having spatially periodic constant, with a periodicity of the order of the wavelength of light. They are artificial structures that control the flow of light, and are expected to lead to a new photonic era, similar to the electronic revolution produced by the semicondutors.

6. Natural Photonic Crystals:
Structural Colours through Photonic Crystals
Natural opals
In recent years, scientists have discovered that the iridescence of various colorful creatures, from beetles to birds to butterflies, is often due to microscopic structures known as photonic crystals. Unlike pigments, which absorb or reflect certain frequencies of light as a result of their chemical composition, the way that photonic crystals reflect light is a function of their physical structure. That is, a material containing a periodic array of holes or bumps of a certain size may reflect blue light, for example, and absorb other colors even though the crystal material itself is entirely colorless. Because a crystal array looks slightly different from different angles (unlike pigments, which are the same from any angle), photonic crystals can lead to shifting shades of iridescent color that may help some animals attract mates or establish territories.
Periodic structure  striking colour effect even in the absence of pigments

7. Artificial Photonic Crystals
Requirement: overlapping of frequency gaps along different directions
High ratio of dielectric indices
Same average optical path in different media
Dielectric networks should be connected
Woodpile structure
Inverted Opals
On the experimental front, an extremely large number of methods create 3D photonic crystal structures have been investigated. From micro-lithography to self assembly of artificial opals and laser lattices that provide the seed on which the periodic structure will grow. I present here some of the earliest structures produced with the periodicity on the micrometer length scale.
The current experimental effort is directed at decreasing the disorder present in the structures, increasing their scalability and, in the mean time, there is a continuous search for designing new structures with more robust band gaps.
S. Lin et al., Nature (1998)
J. Wijnhoven & W. Vos, Science (1998)

8. Photonic Crystals: Opportunities
complex dielectric environment that controls the flow of radiation
designer vacuum for the emission and absorption of radiation
Passive devices
dielectric mirrors for antennas
micro-resonators and waveguides
Active devices
low-threshold nonlinear devices
microlasers and amplifiers
efficient thermal sources of light
Integrated optics
controlled miniaturisation
pulse sculpturing
A whole new research field was created with the invention of photonic crystals. These are artificial periodic structures that have the ability of inhibiting the linear propagation of light in all directions.
Photonic crystals were originally proposed as means to realize two fundamental optical principles:the localization and trapping of light in a bulk material and the complete inhibition of spontaneous emission over a broad frequency range.
Photonic crystals not only have the ability to guide and confine light but also provide a novel environment for quantum mechanical light-matter interaction , which make make them suitable for a series of revolutionazing applications.
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9. Defect-Mode Photonic Crystal Microlaser
Photonic Crystal Cavity formed by a point defect
O. Painter et. al., Science (1999)

10. Photonic Crystals Based Light Bulbs
C. Cornelius, J. Dowling, PRA 59, 4736 (1999)
“Modification of Planck blackbody radiation by photonic band-gap structures”
3D Complete Photonic Band Gap
Suppress blackbody radiation in the infrared and redirect and enhance thermal energy into visible
Solid Tungsten Filament
3D Tungsten Photonic Crystal Filament
Another technological application of pc is based on their ability to modify
Experimental results showed that a large photonic band gap for wavelengths from 8 to 20 microns proved ideally suited for suppressing broadband blackbody radiation in the infrared and has the potential to redirect thermal excitation energy into the visible spectrum
This would raise the efficiency of an incandescent electric bulb from 5 percent to greater than 60 percent.
Researchers at Sandia National Laboratories (SN have shown that filaments fabricated of tungsten lattices emit remarkably more energy than solid tungsten filaments in certain bands of near-infrared wavelengths when heated. Because near-infrared is the wavelength region closest to visible light, the day may not be too distant when tungsten lattice emissions realized at visible wavelengths provide a foundation for more efficient lighting—the first significant change in Edison's light bulb since its invention.
S. Y. Lin et al., Appl. Phys. Lett. (2003)
Light bulb efficiency may raise from 5 percent to 60 percent

11. Solar Cell Applications
Funneling of thermal radiation of larger wavelength (orange area) to thermal radiation of shorter wavelength (grey area).
Spectral and angular control over the thermal radiation.

12. Foundations of Future CI
Cavity all-optical transistor
Photonic crystal all-optical transistor
Iin
Iout IH
Pump Laser
H.M. Gibbs et. al, PRL 36, 1135 (1976)
Probe Laser
Fundamental Limitations
switching time • switching intensity = constant
Incoherent character of the switching  dissipated power
All-optical transistor: On the practical side, my research has been done in the context of all-optical transistor action.
An all-optical transistor is analogous to an electronic transistor, where the electric currents are replaced by laser pulses, and presents general and fundamental limitations. It is these limitations, especially the fundamental limitations, that I addressed in thesis research work.
Principle: Small optically induced changes in the index of refraction of the nonlinear medium can determine important changes in the output signal. For example, let’s assume that the device is initially tuned slightly off resonance. With increasing input power, the intensity inside the resonator increases, thereby changing the index of refraction of the cavity, and pulling it towards the resonant condition. This, in turn, increases the intensity inside the cavity and, implicitly, gives yet further change in the index of refraction and so on.
Major Disadvantages:
There is a fundamental trade-off between the switching time and and the switching intensity. Assume we start with a given system (size and strength of the nonlinearity). Then the switching time is determined by the build-up time of the cavity and the cavity response time (related to the cavity bandwidth). If we want to decrease the response time of the cavity, we have to increase the cavity width, which , in turn, increases the decay rate and the dissipated power in the cavity. Implicitly, this determines a larger switching threshold intensity.
Alternatively, the strength of the nonlinearity determines a strong connection between the switching time and the size of the device. Starting with a given strength of the filling medium nonlinearity, it is possible to increase the length of the device in order to decrease the switching power (the path length determines the nonlinear phase acquired by the signal field). However, this requires a longer round-trip cavity time, and determines a strong increase in the switching time.
M. Florescu and S. John, PRA 69, (2004).
Operating Parameters
Holding power: nW
Switching power: pW
Switching time: < 1 ps
Size: m
Operating Parameters
Holding power: mW
Switching power: 3 µW
Switching time: ns
Size: m

13. Single Atom Switching Effect
Photonic Crystals versus Ordinary Vacuum
Positive population inversion
Switching behaviour of the atomic inversion
M. Florescu and S. John, PRA 64, (2001)

14. Quantum Optics in Photonic Crystals
Long temporal separation between incident laser photons
Fast frequency variations of the photonic DOS
Band-edge enhancement of the Lamb shift
Vacuum Rabi splitting
T. Yoshie et al. , Nature, 2004.

15. Foundations for Future CI: Single Photon Sources
Enabling Linear Optical Quantum Computing and Quantum Cryptography
fully deterministic pumping mechanism
very fast triggering mechanism
accelerated spontaneous emission
PBG architecture design to achieve
prescribed DOS at the ion position
M. Florescu et al., EPL 69, 945 (2005)

16. CI Enabled Photonic Crystal Design (I)
Photo-resist layer exposed to multiple laser beam interference that produce a periodic intensity pattern
Recently, holographic lithography has emerged as a promising technique for inexpensive fabrication of photonic crystals.
In this case, a photo-resist layer is exposed to a multiple laser beam interference that produce a periodic intensity pattern which is transferred to the photo-resist, to produce the periodic dielectric structure.
10 m

Four laser beams interfere to form a
3D periodic intensity pattern
3D photonic crystals fabricated
using holographic lithography
O. Toader, et al., PRL 92, (2004)
M. Campell et al. Nature, 404, 53 (2000)

17. CI Enabled Photonic Crystal Design (II)
O. Toader & S. John, Science (2001)
In recent years, there has been a concerted effort to realize 3D PBG’s in which light propagation is prohibited in all directions for a certain spectral range, defined by the overlapping of the band gaps along different k space directions.
I present here one of the latest proposal for such a 3D PBG material, which consists in a ordered array of interleaving square spiral posts on a tetragonal lattice. By optimizing and inverting the structure it is possible to obtain a very large band gap (between the x and the y bands), and the resulting PDOS presents very important variations with the frequency in the band edges region. The largest gap for the inverted structure is almost 24%, one of the largest one that has been predicted.

18. CI Enabled Photonic Crystal Design (III)
S. Kennedy et al., Nano Letters (2002)
On the experimental front, an extremely large number of methods create 3D photonic crystal structures have been investigated. From micro-lithography to self assembly of artificial opals and laser lattices that provide the seed on which the periodic structure will grow. I present here some of the earliest structures produced with the periodicity on the micrometer length scale.
The current experimental effort is directed at decreasing the disorder present in the structures, increasing their scalability and, in the mean time, there is a continuous search for designing new structures with more robust band gaps.

19. Multi-Physics Problem: Photonic Crystal Radiant Energy Transfer
Photonic Crystals
Optical Properties
Rethermalization
Processes:
Photons
Electrons
Phonons
Transport
Properties:
Photons
Electrons
Phonons
Metallic (Dielectric)
Backbone
Electronic
Characterization

20. Summary Photonic Crystals: Photonic analogues of semiconductors that
control the flow of light
PBG materials: Integrated optical micro-circuits
with complete light localization
Designer Vacuum:
Frequency selective control of
spontaneous and thermal emission
enables novel active devices
Potential to Enable Future CI:
Single photon source for LOQC
All-optical micro-transistors
CI Enabled Photonic Crystal Research and Technology:
Photonic “materials by design”
Multiphysics and multiscale analysis