Photonic Crystal and its Application: A Basic Understanding

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Photonic Crystal and its Application A Basic
Understanding

• Cheung Chi Shing Stephen
• Lai Ho Fung

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Photonic Crystal Some History

• 1887 Lord Rayleighs study of Bragg Diffraction
  of 1-D PC
• - propose of 1-D photonic bandgap(stop band)

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Photonic Crystal Some History

• At 1987(100 years later!!!)
• -Eli Yablonovitch
• control of spontaneous emission of materials
  in PC
• -Sajeev John
• defected high-D PC give rise to strong
  localization of light

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Some daily examples - Butterflies
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Some daily examples shells
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Some daily examples

• A scan by SEM of the butterfly wing (blue)

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Photonic Crystals Definition

• Periodic structures with alternating refractive
  index (dielectric constant)

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Photonic Crystals Definition

• 1-D multi-layer membrane
• 2-D air columns in dielectric material
• 3-D stacking structure

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Photonic Crystals Definition

• Crucial property
• Photonic bandgap-
• Range of lights frequencies which the light
  cannot pass throught PCWHY?
• because
• BRAGG DIFFRACTION!

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Photonic Crystals Definition
Constructive interference 2d sin? n?. ( O(d)
O(?) )
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Photonic Crystals Definition

• eGaAs 13, eGaAlAs12, eAir1
• ??e?, range of photonic bandgap ?

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Computational method

• So, how do we know the PBG of a certain PC?
• EM waves travelling in PC are described by
  Maxwell Eqs.

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Computational method

• 1. Plane-wave expansion method
• Assume plane wave solutions, i.e.,

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Computational method

• The two curl equation can be rewritten as

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Computational method

• Where the first one is just like a
• Schrödinger equation with
• being the operator
• (?(k)/c)2 being the corresponding
  eigenvalue

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Computational method

• Hence given the boundary conditioins, i.e., the
  structure of the PC and e(r), H(r) and E(r) can
  be found
• Hk(r) ei(k.r) uk(r)

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Computational method

• An analogy to electronic bandgap in semiconductor

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Computational method

• 2. FDTD (Finite-difference time domain) method
• Consider again the two curl equations

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Computational method

• They can be expanded into

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Computational method
An electromagnetic wave interaction structure is
mapped into the space lattice by assigning
appropriate values of permittivity to each
electric field component, and permeability to
each magnetic field component.
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Physical Phenomena

• 1. Photonic bandgap(PBG)
• Bragg diffraction -gt destructive interference in
  PC -gt Photonic badgap
• 1-D PC only in one direction
• Because periodicity becomes different if the
  wave enters in a different direction

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Physical Phenomena

• 2-D PC 2-D PBG
• 3-D PC possibility of PBG in all direction

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Physical Phenomena

• 2. Strong localization of light
• If defects are introduced to the PC, light can
  be trapped within the defect.

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Physical Phenomena

• 3. wave guide

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Physical Phenomena

• 4. light spliter

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Applications

• Photonic crystal fiber ( PCF )
• Laser
• Future development

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Photonic crystal fiber ( PCF )

• Benefits
• high transmission speed
• not much interaction between photons
• ? low energy loss

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Photonic crystal fiber ( PCF )

• Air guiding PCF

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Photonic crystal fiber ( PCF )

• 1800 C
• 0.03mm

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Photonic crystal fiber ( PCF )

• Range of wavelength 440nm 2000nm
• Best reported loss
• 13dB/km over 100m _at_1.5µm
• wavelength

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Photonic crystal fiber ( PCF )

• Holey-assisted fiber
• Holey cladding
• (low refractive index)
• Core (high refractive
  index)

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Photonic crystal fiber ( PCF )

• As the refractive index of the central defect
  core is relative higher than the holey cladding
  materials
• ? wave is rather confined and transmits in the
  core

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Photonic crystal fiber ( PCF )

• Group dispersion is reduced to minimium
• Core area is 10 times greater than that of optic
  fiber
• Single mode maintains within a large range of
  wavelength

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Laser

• Pumping / Exciting
• Population inversion
• Spontaneous
  Stimulated
• emission
  emission
• Energy loss
  Resonator

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Laser

• Probability of an atom in excited state is given
  by

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Laser

• One may think increasing the temperature can
  increase the population of excited atoms
• ? Blackbody radiation

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Laser
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Laser

• However, blackbody radiation cannot produce
  intensive and monochromatic radiation
• One may try to reduce energy loss by using
  Photonic crystal as the resonator shielder

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Laser

• Relation between photonic band gap and
  semiconductor laser

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Laser
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Laser

• Spontaneous emission of excited electrons are
  inhibited
• Probability of electrons maintaining in the
  excited states ?
• Population inversion of laser ?
• Simulated emission ?
• Power loss ?

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Future development

• Size in micro- order devices
• Largely reduce the size of communication system
  to 1000 times

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Photonic crystal and its applications

• Q A