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New Era of Discreteness and Periodicity in OpticsGeorge Stegeman, KFUPM Chair ProfessorProfessor EmeritusCollege of Optics and Photonics/CREOLUniversity of Central Florida, USA11887

1-DPeriodic in 1D Bragg gratingWhat Is Meant By Discreteness and Periodicity?Collection of similar, discrete optical structures, materials, devices etc. which as anensemble create new phenomena, functionalities or applications.Frequently periodicities are involved in discreteness, i.e. the structure arrangement is (quasi-) periodic in space.

Periodic in 2D Photonic crystal fiberPeriodic in 1D Waveguide array1990sWhite Light IncidenceClassic example of periodicity involving interference dielectric mirror (frequency filter)n1n2n1Single large (many optical wavelengths in size) block of material (e.g. glass) Essentially nothing happensMulti-layer structure- different refractive indices (optical impedances) in each layer, layer thicknesses /2 n1n2- Periodicities of order a few wavelengths Analogy to solid state physics, but now with complete control over band structure Multiple bands for propagation, i.e. Floquet-Bloch analysis of modes and dispersion Guiding of radiation requires introducing defects into regular structures Fabrication tolerances can be very demanding but technology available For an excellent discussion, see http://ab-initio.mit.edu/photons/3Where Did Awareness of New Optics From Discreteness Start?Pioneering paper: E. Yablanovitch, Inhibited Spontaneous Emission in Solid-State Physics and Electronics, Phys. Rev. Lett., 58, 2059 (1987) Atom in infinite medium radiates in alldirections at at when electron in an excitedstate (lifetime gm) drops to ground state viaspontaneous emission (fundamental process)Inside a cavity, only radiation incavity modes cav=md/2 is allowedn=1, 2, 3, i.e. standing wavesd-

|g>|m>4Discreteness New Scienceatcav=md/2atcavLifetime of excited state altered Fundamental process inhibited!atcav-

|g>|m>-|g>|m>Length Scales of Periodicity and Consequences1.Optical Wavelength- periodically modulated (in space) dispersion relations- prime examples are photonic crystals and waveguide arrays- many new wavevectors available for wavevector-conserving interactions- control of anomalous diffraction (space) and dispersion (time) possible- many new solitons- basic concepts closely related to solid state physics

2.Sub-optical Wavelength- modified optical properties when averaged over a wavelength- prime example is meta-materials unique optical properties- negative refractive index- novel dispersion relations and propagation properties- etc.- effective medium theories importantPhotonic CrystalsPhotonic CrystalFibersWaveguide ArraysNegative Index1 D Photonic Crystal n1n2White Light Incidence Constructive interference on reflection at gap!band gapk0/airreducible Brillouin zoned

FrequencyGapd=/2

w

718871987

1-D2-D3-DPeriodic in 1D Bragg gratingPeriodic in two dimensionsPeriodic in three dimensions

3D Photonic Crystal: MITSuper-prism Effect LasersNegative Refraction

I.II.ULGXWK0.20.40.60.8021% gap

L'LK'GWU'XU''UW'Kz9Prisms: Bulk OpticsSnells Law: n1sin(1)=n2sin(2)n1n212

Refractive Index Dispersion in Visible

Angular Dispersion

10

Super Prism: Photonic CrystalBulkG X gap

PhotonicCrystalAngular Dispersion

L'LK'GWU'XU''UW'KzSuper Prism Effect: Control Both Magnitude and Sign of Angular Dispersion

Input GuidesOutput GuidesPCSOI Planar Photonic Lattice

Near -K direction0.4o/nmNear -M direction1.3o/nm(100x normal glass prism)A. Lupu, E. Cassan, S. Laval, et. al., Opt. Expr. 12, 5690 (2004)122D Optical Circuits in Quasi-3D Photonic Crystals Note: This 2D circuit must be imbedded in a 3D photonic crystalto avoid radiation loss along the z-axis!

yxzGuided Wave Planar Device ConceptLight Channels introduced by eliminating one row and/or column13 2D Optical Circuits in Quasi-3D Photonic Crystals zkzIf height z is finite,we must couple toout-of-plane wavevectors

Make it as tall as possible!!

14Reducing Bending Losses: Technical University of Denmark

Two Bend Loss/Loss of Straight Guide Optimized

Un-optimized

OptimizedL.H. Frandsen, A. Harpth, P.I. Borel, M. Kristensen, J.S. Jensenand O. Sigmund, Opt. Expr., 12, 5916 (2004)15Photonic Crystal Fibres: Cylindrical 1D Photonic Crystals

Defect Necessary for Guiding geometry, shape and filling material can be varied fabrication improved to loss of 0.58dB/km at 1550nm exquisite control of dispersion in effective index - zero group velocity dispersion (GVD) wavelength - multiple zero GVD wavelengths - phase-matching of nonlinear interactions photonic band gaps fibers

wavelength size modal areas enhanced NLO

Courtesy of Phillip Russell, Bath Universitywavelength (mm)0.50.60.70.80.91.0- 300-- 2001000100200300( /n.kpsmm)anomalousnormalbulk silicasilica strand(computed)silica webs reduceGVD in PCFGVD (ps/nm-km)Wavelength (m)Group Velocity Dispersion (GVD) Control: Bath UniversityFiber Transmission LineTemporal Pulse

17wavelength (m)dispersion (ps/nm.km)202468101.61.41.21normalanomalousd = 0.57 m = 2.47 md = 0.58 m = 2.59 mControl of dimensions to better than 1% requiredPCF With Ultra-Flat and Ultra-Small Dispersion (GVD): Bath

d = hole size= hole separation11 periods18

Supercontinuum Generation: Opt. Expr. May 2006, Bath Fiberpump=1550nm

100fs pulsesA nonlinear optics feast of effects!!Self- and cross-phase modulationMulti-wave mixingStimulated Raman, Anti-stokes RamanRaman Self-Frequency ShiftThird Harmonic GenerationEtc.

From 3000 nm!19

an is field at n-th channel center is propagation constant of single isolated channel E(x) is the transverse channel waveguide field. c is coupling constant due to field overlap

n n+1Waveguide Arrays: Coupling Between Waveguidesan+1nn+1

E(x)an

20Arrays of Weakly Coupled Waveguides: Discrete Diffraction

Discrete diffraction Light spreads (diffracts) through array by discrete diffraction, via coupling c 1D or 2D lattices of waveguides feature dimensions of order of the wavelength of light periodicity multiple (Floquet-Bloch) bands for propagation- negative refraction- normal, zero or anomalous diffraction- discrete Talbot effect- photonic Bloch oscillations Many novel discrete spatial solitons- solitons with fields in-phase or out-of-phase in adjacent channels- interface solitons at edges, corners and between dissimilar arrays

DistanceWaveguide Number

20-20211D Diffraction in Waveguide Arrays

kz

kxd-

Normal diffraction

Anomalous diffractionZero diffractionD < 0 normal diffraction D > 0 anomalous diffractionkx Bloch wavevector (momentum)Homogeneous Medium

Normal diffraction

1-3 degrees22

Finite Beam Excitation

DistanceWaveguide Number

020-20W

zDiffraction in Bulk Media

23Length Scales of Periodicity and Consequences2.Sub-optical Wavelength- modified optical properties when averaged over a wavelength- prime example is meta-materials unique optical properties- negative refractive index- novel dispersion relations and propagation properties- etc.

- effective medium theories important- basic concepts closely related to solid state physicsNegative Index Materials: Problem in Materials Science

Negative Dielectric Constant Found in nature (metals) due to electron plasma resonancesNegative Magnetic Permiability Not found in nature

Composite Materials with MetalsFor metallic (sub-wavelength) inclusions Plasmon (collective electron) resonances with resonant frequencies depending on shape and size both electric and magnetic properties changedPioneer: V. G. Veselago, Soviet Physics USPEKI 10, 509 (1968).Negative Index Materials in the Near Infrared

Al2O3Au=2000nm

Shuang Zhang, Wenjun Fan, N. C. Panoiu,K. J. Malloy, R. M. Osgood and S. R. J. Brueck, Phys. Rev. Lett., 95, 137404 (2005)26Examples of Repercussions and Possible Applications:Contra-directional Energy and Phase Velocity

Wave vectorsPoynting vectors(energy flow)Maxwells Equation predict:Courtesy of Allan Boardman, Salford University

Wave vectorsPoynting vectors(energy flow)

27CloakingJ. B. Pendry, D. Schurig, D. R. Smith, Science, 312, 1780 (2006)

Quote: it is now conceivable that a material can be constructed whose permittivity and permeability values may be designed to vary independently and arbitrarily throughout a material, taking positive or negative values as desired.Each of the rays intersecting the large sphere is required to follow a curved, and therefore longer, trajectory than it would have done in free space, and yet we are requiring the ray to arrive on the far side of the sphere with the same phase. Works over a narrow spectral bandwidthSummaryDiscreteness with periodicity introduces new paradigms into optics

Fundamental wave properties, namely refractive index, dispersion, scattering and interference, and diffraction can be controlled and/or eliminated

3. New physical phenomena are introduced and well-known effects are changed.

New ultra-compact optical devices possible

And much, much more.. 29

Negative Index Materials: Martin Wegeners GroupOptics Letters, 31, 1800, (2006)

= 1500nmdGXMirreducible Brillouin zone

2-D Photonic Crystals - Array of Pillars: MITfrequency w (2c/d) = d / lGXMG00.20.40.60.81TM Photonic Band GapTM bandsn2/n1=3.5EH

EHTMTEOrthogonal Field DistributionsEz

(+ 90 rotated version)

Ez+32Electrically Pumped, Semiconductor Photonic Crystal Laser:Park et. al. Science Sept 3, 2004

2007 100A and 0.9V threshold330.30.20.10.01020304050607080fibre length (cm)relative coupled powerPcoupled energy 5.6 Jpulse duration 6 nsec SAS0.0000.0100.020Highly Efficient Raman Shifter: Bath Un. Science 2002

Stokes(683 nm)

anti-Stokes(435 nm)

hydrogenfilledpump(532 nm)

34

kz (1/m)=kxd (units of )Band 1:Band 2:Band 3:Band 4:Floquet-Bloch Bands

35GXM

(k not conserved)

2D Photonic Crystal Cavity Modes: MITGXMGfrequency (c/a)Bulk Crystal Band Diagram00.20.40.6Photonic Band Gap

A point defectcan push upa single modefrom the band edge

High Q cavities36Endlessly Single Mode FibresNormal fibers: single mode for

2a

endlessly single-mode

The smaller the , the smaller the influence of the air holes the larger the effective ncl the smaller with proper design V