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Nonlinear Bloch Waves In Resonantly Doped Photonic Crystals.

A. Kaso, S. John
Published 2006 · Medicine, Physics

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We demonstrate the existence of self-consistent Bloch modes in resonant nonlinear photonic crystals with a complex, intensity-dependent, and frequency-dependent dielectric function. Such a dielectric response may arise by "doping" the photonic crystal with resonant quantum dots, atomic impurities, or other two-level light emitters. These exact solutions of the nonlinear electromagnetic wave equation exhibit Bloch periodicity and describe fundamental eigenmodes of an active photonic crystal under incoherent pumping. In a simple model two-dimensional photonic crystal, doped with active two-level atoms, the optical field intensity of these waves shows a laserlike threshold behavior with pumping. This appears to be a universal property of active, nonlinear photonic crystals and photonic band gap materials, arising from multidirectional distributed feedback. We describe an iterative technique for computing the detailed properties of these exact, self-consistent nonlinear waves in strongly scattering photonic crystal architectures with regions of gain and loss.
This paper references
10.1364/OE.3.000012
Novel approach to photonic bands with frequency-dependent dielectric constants.
K. Sakoda (1998)
Phys. Rev. Lett
S John
10.1103/PhysRevA.58.4168
NON-MARKOVIAN QUANTUM FLUCTUATIONS AND SUPERRADIANCE NEAR A PHOTONIC BAND EDGE
Nipun Vats (1998)
10.1103/PHYSREVB.64.045116
Photonic bands of metallic systems. I. Principle of calculation and accuracy
K. Sakoda (2001)
10.1103/PHYSREVLETT.65.3152
Existence of a photonic gap in periodic dielectric structures.
Ho (1990)
J. Opt. Soc. Am. B
E Yablonovitch
Phys. Rev. Lett
S John
10.1070/PU1968V010N04ABEH003699
The Electrodynamics of Substances with Simultaneously Negative Values of ∊ and μ
V. Veselago (1968)
Phys. Rev. Lett
S John
10.1063/1.126944
Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes
P. Eliseev (2000)
10.1007/978-3-662-14324-7
Optical Properties of Photonic Crystals
K. Sakoda (2001)
Phys. Rev. B
C H Henry
10.1103/PHYSREVB.72.195110
Emission from an active photonic crystal
I. El-Kady (2005)
10.1021/AR970220Q
Lead salt quantum dots: the limit of strong quantum confinement.
F. Wise (2000)
Phys. Rev. B
V Kuzmiak
10.1103/PhysRevLett.96.127404
Self-tuned quantum dot gain in photonic crystal lasers.
S. Strauf (2006)
Acc. Chem. Res
F W Wise
Phys. Rev. A
D Vujic
10.1103/PHYSREVB.1.1628
Lifetimes of Bound Excitons in CdS
C. H. Henry (1970)
Appl. Phys. Lett
J I Fushman
10.1063/1.1941460
Accurate measurements of thermal radiation from a tungsten photonic lattice
C. H. Seager (2005)
10.1038/NMAT1530
Optical gain and stimulated emission in periodic nanopatterned crystalline silicon
Sylvain G. Cloutier (2005)
10.1038/417052a
All-metallic three-dimensional photonic crystals with a large infrared bandgap
J. Fleming (2002)
10.1103/PHYSREVB.53.7059
Green's-function theory for row and periodic defect arrays in photonic band structures.
McGurn (1996)
10.1103/PHYSREVLETT.53.2169
Electromagnetic absorption in a disordered medium near a photon mobility edge
S. John (1984)
10.1063/1.1584514
Direct measurement of polarization resolved transition dipole moment in InGaAs/GaAs quantum dots
K. Silverman (2003)
Phys. Rev. B
K Sakoda
10.1103/PHYSREVE.70.046605
Photonic band gap enhancement in frequency-dependent dielectrics.
O. Toader (2004)
10.1103/PHYSREVLETT.64.2418
Quantum electrodynamics near a photonic band gap: Photon bound states and dressed atoms.
John. (1990)
10.1103/PHYSREVLETT.58.2486
Strong localization of photons in certain disordered dielectric superlattices.
John (1987)
10.1103/PHYSREVB.48.17576
Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays.
McGurn (1993)
An introduction to theory and application of quantum mechanics / Amnon Yariv
A. Yariv (1982)
10.1126/SCIENCE.284.5421.1819
Two-dimensional photonic band-Gap defect mode laser
Painter (1999)
10.1103/PHYSREVB.43.12772
Quantum optics of localized light in a photonic band gap.
John. (1991)
Phys. Rev. A
N Vats
Phys. Rev. B
T Ito
J. Phys. Chem. B
V I Klimov
Optical Waves in Crystals
A. Yariv (1984)
Phys. Rev. Lett
T Quang
10.1364/OE.4.000481
Low-threshold laser oscillation due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals.
K. Sakoda (1999)
10.1103/PHYSREVLETT.78.1888
COLLECTIVE SWITCHING AND INVERSION WITHOUT FLUCTUATION OF TWO-LEVEL ATOMS IN CONFINED PHOTONIC SYSTEMS
S. John (1997)
Opt. Express
K Sakoda
Phys. Rev. Lett
K M Ho
Appl. Phys. Lett
M Kim (1911)
10.1364/OL.28.001909
Three-dimensional photonic-crystal emission through thermal excitation.
Shawn-Yu Lin (2003)
J. Chem. Phys
M Shib
J. Phys. B
S M Barnett
10.1063/1.479988
Permanent dipole moment and charges in colloidal semiconductor quantum dots
Moonsub Shim (1999)
10.1103/PHYSREVB.50.16835
Photonic band structures of two-dimensional systems containing metallic components.
Kuzmiak (1994)
10.1070/QE1975V004N07ABEH009654
Spontaneous emission from a medium with a band spectrum
V. Bykov (1975)
Opt. Lett
S Y Lin (1909)
Opt. Express
S Nakamura
10.1063/1.2138792
Coupling of PbS quantum dots to photonic crystal cavities at room temperature
I. Fushman (2005)
Phys. Rev. E
K Busch
Phys. Rev. B
I El-Kady (1951)
Phys. Usp
V G Veselago
10.1063/1.1661499
Coupled‐Wave Theory of Distributed Feedback Lasers
H. Kogelnik (1972)
10.1103/PHYSREVB.55.7427
Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation
V. Kuzmiak (1997)
10.1103/PHYSREVA.64.033801
Single-atom switching in photonic crystals
Marian Florescu (2001)
Phys. Rev. E
O Toader
J. Appl. Phys
H Kogelnik
Appl. Phys. Lett
A M Yacomotti
Appl. Phys. Lett
C H Seager
Phys. Rev. B
A R Mcgurn
10.1021/JP9944132
Optical Nonlinearities and Ultrafast Carrier Dynamics in Semiconductor Nanocrystals
V. Klimov (2000)
10.1103/PHYSREVB.64.045117
Photonic bands of metallic systems. II. Features of surface plasmon polaritons
T. Ito (2001)
Electron. Lett
K Kounoike
Phys. Rev. B
A R Mcgurn
10.1126/SCIENCE.1100968
Electrically Driven Single-Cell Photonic Crystal Laser
H. Park (2004)
10.1063/1.2207842
All-optical bistable band-edge Bloch modes in a two-dimensional photonic crystal
A. Yacomotti (2006)
Appl. Phys. Lett
P G Eliseev
10.1364/OPEX.12.006606
Ultra-fast photonic crystal/quantum dot all-optical switch for future photonic networks
H. Nakamura (2006)
10.1063/1.1592614
Three-dimensional photonic-crystal emitter for thermal photovoltaic power generation
S. Lin (2003)
10.1126/SCIENCE.1061738
Polarization Mode Control of Two-Dimensional Photonic Crystal Laser by Unit Cell Structure Design
S. Noda (2001)
10.1103/PHYSREVA.56.4273
Resonance fluorescence near a photonic band edge: Dressed-state Monte Carlo wave-function approach
T. Quảng (1997)
10.1103/PHYSREVE.58.3896
PHOTONIC BAND GAP FORMATION IN CERTAIN SELF-ORGANIZING SYSTEMS
K. Busch (1998)
10.1049/EL:20053011
Investigation of spontaneous emission from quantum dots embedded in two-dimensional photonic-crystal slab
K. Kounoike (2005)
Phys. Rev. B
V Kuzmiak
10.1088/0953-4075/29/16/019
Decay of excited atoms in absorbing dielectrics
S. Barnett (1996)
10.1103/PhysRevLett.95.203901
Magnetic metamaterials at telecommunication and visible frequencies.
C. Enkrich (2005)
10.1364/OL.23.001707
Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals.
V. Kopp (1998)
10.1038/nature03009
Current-induced resonance and mass determination of a single magnetic domain wall
E. Saitoh (2004)
10.1103/PHYSREVB.58.7230
DISTRIBUTION OF ELECTROMAGNETIC FIELD AND GROUP VELOCITIES IN TWO-DIMENSIONAL PERIODIC SYSTEMS WITH DISSIPATIVE METALLIC COMPONENTS
V. Kuzmiak (1998)
Opt. Express
K Sakoda
Phys. Rev. E
N Aközbek
10.1109/50.65882
Erbium-doped glasses for fiber amplifiers at 1500 nm
W. Miniscalco (1991)
An Introduction to Theory and Applications of Quantum Mechanics
A. Yariv (1982)
10.1038/nature03119
Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity
T. Yoshi'e (2004)
10.1103/PHYSREVA.50.1764
Spontaneous emission near the edge of a photonic band gap.
John. (1994)
10.1103/PHYSREVLETT.76.2484
Resonant nonlinear dielectric response in a photonic band gap material.
John. (1996)
Nat. Mater
S G Cloutier
Z. Genack, Opt. Lett
V I Kopp
Phys. Rev. A
S John
Appl. Phys. Lett
K L Silverman
10.1038/nature02772
Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals
P. Lodahl (2004)
Sov. J. Quantum Electron
V P Bykov
Phys. Rev. Lett
S Strauf
Phys. Rev. A
M Florescu
Appl. Phys. Lett
S Y Lin
10.1063/1.2203234
Surface-emitting photonic-crystal distributed-feedback laser for the midinfrared
M. Kim (2006)
Phys. Rev. B
S John
10.1126/SCIENCE.1096796
Metamaterials and Negative Refractive Index
D. Smith (2004)
10.1103/PHYSREVA.72.013807
Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching
D. Vujic (2005)
10.1103/PHYSREVLETT.58.2059
Inhibited spontaneous emission in solid-state physics and electronics.
Yablonovitch (1987)
10.1103/PHYSREVE.58.3876
SELF-INDUCED TRANSPARENCY SOLITARY WAVES IN A DOPED NONLINEAR PHOTONIC BAND GAP MATERIAL
N. Akozbek (1998)



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