A Survey of Various Photonic MetaStructures A journey to discover the governing principles of PMs

1
A Survey of VariousPhotonic Meta-Structures(A
journey to discover the governing principles of
PMs)

• Steve McDaniel
• MSEE, Reg. Patent Agent

2
Working Definitions

• Metamaterial (David Smith-Duke) Ordered
  composites that exhibit excep-tional properties
  not readily observed in nature and not
  observed in the constituent materials

Photonic Meta-structure (Presenter-UofU) An
ordered structure which gains its photonic
properties from its structural order rather than
its composition. May be found in nature.
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Travel Itinerary

• Waveguide Lenses
• Wire-grid Lenses
• Photonic Crystals

• Slow Light Metamaterials
• Resonant Antenna Lenses
• Negative Index Metamaterials

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Background Concepts

• Vg (group Velocity) Velocity of multi-frequency
  feature such as a pulse.
• Vp(Phase Velocity) Velocity of a feature of
  constant phase in a sinusoidal (single-frequency)
  waveform.

n c / vp

• Resonance affects Vg, Vp, Ke, n

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Background ConceptsWaveguide

• Vg 0 at Cutoff Freq.
• Vp Vg c2 (Air filled)
• Vp gt c (8 at Cutoff)
• neff c/Vp lt 1

                    ,
Source Allaboutcircuits.com, Microwaves101.com
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Waveguide Lens

• Bundle of Waveguides
• Vp gt c
• neff lt 1
• Converging Lens Is Concave

Metal Plate Lens Fresnel Type US Patent
4,194,209
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Waveguide Lens
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Slow Light Metamaterials

• Reduced Group Velocity (Vp ltlt C)
• Corresponds to Spectral Region of High Dispersion
  
• Material Dispersion
• Atomic or Molecular Resonance
• Waveguide or Form Dispersion
• Resonance Due to Geometry

Source Wikipedia- Dispersion (Optics)
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Slow Light Metamaterials
Figure 1 from Coupled Resonator Optical
Waveguides (CROWs), Proceedings of the SPIE-The
International Society for Optical Engineering, v
5735, n 1, 2005, p 52-9
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Slow Light Metamaterials

• CROW Strategies to Reduce Vg
• Reducing Coupling to Increase Resonator Tunneling
  Time
• Increase Resonator Perimeter without Increasing
  Intercavity Periodicity

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Resonant Antenna Lens

• Coupled Elements Such as Plates
• n Dependent On Element Spacing
• Similar Concepts to Some Metamaterials
• Predates Metamaterials

Figure from Hecht Section 5.2
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Resonant Antenna Lens

• Resonance Alters Phase Velocity
• Phase Velocity Corresponds to neff

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Wire Grid Lens
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Wire Grid Lens

• Minimal Lens Material
• Grid of Wires with Variable Spacing Between Grids
• Grid Spacing Changes Dielectric Constant?
• Similarities to Waveguide or Transmission Line

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Wire Grid Lens

• Luneburg Type Lens
• Graded Index (GRIN) Lens
• Circular Symmetry (Works With Multiple Sources)
• Broadband

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Photonic Crystals

• Periodic Structure
• Periodic Index Contrast Results in Photonic
  Bandgap
• Reflects External Radiation
• Inhibits Internal Spontaneous Emission
• Non-Absorbing
• 1D, 2D, or 3D

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Photonic Crystals
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Photonic Crystals
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Photonic Crystal Milestones

• 1887 - Lord Rayleigh
• "On the remarkable phenomenon of crystalline
  reflexion described by Prof. Stokes." Phil. Mag.
  26, pg. 256-265 (1888)

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Photonic Crystal Milestones

• 1912 William Lawrence Bragg
• Braggs Law of Reflection (2 d sin ? m ?).
• The Diffraction of Short Electromagnetic
• Waves by a Crystal, Proc. Cambridge
• Phil. Soc., 17, 43-57 (1913)

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Photonic Crystal Milestones

• 1946 E.M. Purcell
• Spontaneous Emission Probabilities at Radio
  Frequencies Phys. Rev. 69, 681 (1946)
• Enhancement
• Factor
• 3Q?3/4p2V

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Photonic Crystal Milestones

• 1987 E. Yablanovitch
• "Inhibited Spontaneous Emission in Solid-State
  Physics and Electronics", Phys. Rev. Lett., Vol.
  58, 2059 (1987)
• 1987 S. John
• "Strong Localization of Photons in Certain
  Disordered Dielectric Superlattices", Phys. Rev.
  Lett. 58, 2486 (1987)

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Photonic Crystal Milestones

• 1991 Yablonovitch, Gmitter, and Leung
• Fabrication of 3D photonic crystal
• Photonic band structure
• The face-centered-cubic case employing
  nonspherical atoms Phys. Rev. Lett. 67, 2295 -
  2298 (1991)

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Photonic Crystal Theory

• E. Yablanovitch
• Before the 1980s, spontaneous emission was
  often regarded as a natural and inescapable
  phenomenon, one over which no control was
  possible.
• Photonic Crystals JOURNAL OF MODERN OPTICS,
  1994, VOL. 41, NO. 2, 173-194

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Photonic Crystal Theory

• DENSITY OF STATES
• Photonic Crystals JOURNAL OF MODERN OPTICS,
  1994, VOL. 41, NO. 2, 173-194

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Photonic Crystal Theory

• DEFECTS
• Facilitate Controlled Transmission
• Figure 1 from Line-defect-waveguide laser
  integrated with a point defect in a
  two-dimensional photonic crystal slab (Applied
  Physics Letters, v 86, n 17, 25 April 2005, p
  171106-1-3).

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Negative Index Metamaterials

• Negative e and µ
• Obeys Snells Law
• Theorized by Victor Veselago in 1968
• Negative Phase Velocity Schuster 1904

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Negative Index Metamaterials Counterintuitive
Behaviors

• Light is Bent Beyond Surface Normal
• Left Handed
• Poynting Vector Anti-parallel to Phase Velocity

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Negative Index Metamaterials Counterintuitive
Behaviors
Figure 1 from Photorealistic images of objects
in effective negative-index materials by Dolling
et al. (Optics Express, Vol. 14, Issue 5, pp.
1842-1849).
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Negative Index MetamaterialsLC Circuit
Perspective
Figure 1 from Magnetic Response of Metamaterials
at 100 TerahertzS. Linden et al. (,Science 19
November 2004Vol. 306. no. 5700, pp. 1351 1353)
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Negative Index Metamaterials
.
Figures 1a and 5 from Negative index bulk
metamaterial at terahertz frequencies by Paul et
al. (Optics Express, Vol. 16, Issue 9, pp.
6736-6744, 28 April 2008).
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Travel Highlights

• Resonance Affects Group and Phase Velocity
• LC Circuit and Transmission Line Perspectives
  Useful
• Concepts Often Develop First In Microwave Region