Properties of radiating sources in omnidirectionally reflecting Bragg fibers

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Properties of radiating sources in
omnidirectionally reflecting Bragg fibers

• John D. Joannopoulos, Yoel Fink, Peter Bermel
• MIT
• Charles Tapalian, Paul A. Lane
• Draper Labs

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Omnidirectional Reflectors

• 1-D periodic photonic crystal
• Brewster angle outside light line of air leads to
  reflection at
• all angles, and
• all polarizations, for
• frequencies in omnidirectional band gap

Projected bandstructure for omnidirectional
reflector
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Omnidirectionally reflectingBragg fibers

• A cylindrically symmetric omnidirectional
  reflector encloses a hollow region (Yeh Yariv,
  1978)
• Bandstructure like omnidirectional reflector plus
  1D defect modes

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A drawn omniguide
figs courtesy Y. Fink et al., MIT

• Photonic crystal structural uniformity, adhesion,
  physical durability through large temperature
  excursions

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Uses for Bragg fibers

• Long-distance light propagation
• Core freedom
• Biological sensors
• Active materials
• High power applications
• Thermo-optical devices
• Compatible with photonic devices
• Improve coupling from fiber optics to photonic
  crystals
• Want sharp bends for miniaturization

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Biological sensing

• Put fluorescent molecules on optical fiber
• But thats inefficient!
• Optical fibers rely on total internal reflection
• However, fluorescent molecules radiate in a
  pattern in which much of the light wont be
  internally reflected.

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Biological sensing

• Simulation point source in silica fiber (n1.6)
  with air cladding

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Biological sensing

• Lots of radiation from point source escapes

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Biological sensing

• Use omnidirectionally reflecting Bragg fibers
  instead!
• Mostly transparent at excitation frequency
• Highly reflective at fluorescent frequency
• Predict very high efficiencies can test
  computationally

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Simulation Technique

• Finite difference time domain (Yee, 1966)
• Yee lattice which has different components at
  different points
• Leapfrog integration of Maxwells equations

Yee lattice for 3D Cartesian coordinates
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Simulated system

• Molecule at one point near end
• modeled by electric dipole
• Light is gathered at the other end
• 3 bilayers of tellurium (n4.6) / polystyrene
  (n1.6)

period a
core diameter 4a
waveguide length 50a
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Results for source at center

• High transmission, low loss in TM01 mode

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Transmission spectrum

• Flux measured as a function of frequency by
• More than 100 transmission above cutoff
  frequency
• Purcell effect
• Physically reasonable

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Transmission spectrum

• Zoomed in near mode cutoff
• Peak enhancement is about a factor of 20

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Density of States

• Definition
• Calculation method (Gilat Raubenheimer, 1966)
• Calculate w and vg for each point on a lattice in
  Brillouin zone
• Calculate density of states with isofrequency
  surface inside cell, defined by

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Density of states

• DOS for Bragg fiber is large even within
  omnidirectionally-reflecting range
• Need to avoid coupling to propagating modes in
  high-dielectric medium

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Density of states

• Local density of states
• 1D Van Hove singularities ? high emission near
  cutoff frequencies
• Observed in time-domain simulations

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Transmission for sources at r1.2a

• Coupling to modes different as orientation
  changes (TE vs. TM)
• Strong transmission for all orientations

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Source along r at r1.2a
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Source along q at r1.2a
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Source along z at r1.2a
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Transmission for sources at r2a

• Only r-orientation couples strongly to
  hollow-core modes
• Other orientations couple to high index modes
• comes from overlap of evanescent modes of source
  and propagating modes of cladding

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Source along r at r2a
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Source along q at r2a
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Source along z at r2a
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Transmission with low-index coating

• Low-index coating like moving source toward
  center, except for minor corrections
• Cutoff frequency shifted by factor of neff
• Dispersion increased by factor of neff

low-index coating
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Transmission with low-index coating

• Transmission just as high as for dipole in air at
  same position
• Mode frequency shifted by 1/neff

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Source along z at coating surface
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New detection technique

• Place fluorescent molecules away from waveguide
  surface (using coating, if necessary)
• Collection rate can be higher than total emission
  in vacuum!
• Implication much higher sensitivities

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Conclusions

• Omnidirectionally reflecting Bragg fibers can
  capture light radiated by molecules much more
  efficiently than fiber optics
• Enhances emission in unique way associated with
  1D periodicity
• Dipole moment orientation affects efficiency
• Molecules on inner surface couple to cladding
  modes until low-index coating is introduced
• Can apply these results to create sensitive
  chemical detection systems

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Future Directions

• Theoretical modelling of fluorescent emission
  process
• Observation of dynamics
• Exploration of parameter space
• Experimental testing of Purcell enhancement

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Active material model

• Optical pumping and lasing take place at two
  separate frequencies
• Must compete with non-radiative decay processes

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New detection technique

• Steps to create fluorescence
• Send in excitation frequency at w0.4
• Excite pulse at w0.19
• Can reproduce physics of energy transfer between
  fields and atoms with semiclassical model

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Photonic Crystals

• Dielectric media with periodicity in one or more
  directions
• Behave like semiconductors, but for photons
• Photonic bandgap ? reflections
• Defects ? localized states

Diamond lattice photonic bandstructure
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Materials choice

• Can achieve similar effects with different
  materials
• Easier to make titania/silica experimentally
• Faster to simulate higher-contrast
  tellurium/polystyrene system
• Losses decrease exponentially with layers

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Number of bilayers

• For all modes, losses decrease exponentially with
  number of layers
• Calculated for core of size 10a, material Te/PS

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Core size

• For TE01 mode, losses decrease as 1/R3
• For TM modes, losses decrease as 1/R
• Calculated for 4 bilayers of Te/PS