Alternative Bragg Fibers

1
Alternative Bragg Fibers

• Peter Bermel, Yasha Yi, John Joannopoulos
• April 18, 2003

2
Introduction

• Motivation
• Designs
• On-chip omniguide A B
• Hybrid omniguide
• Results
• Conclusion

3
Motivation

• Want core freedom
• Active materials
• Luminescent molecules (BioMEMS)
• High power applications
• Thermo-optical devices
• Want compatibility with photonic devices
• Improve coupling from fiber optics to photonic
  crystals
• Want sharp bends for miniaturization

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Motivation

• Want something easy to make on chip
• Not 3-D photonic crystals
• Regular omniguide may be hard too
• Fortunately, only require 1 dB / cm loss
• (cf. optical fiber loss 0.1 dB / km)

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Motivation

• Use flat omnidirectional reflectors Fink et al.,
  1998

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Designs

• On-chip omniguide A
• On-chip omniguide B
• Half omniguide

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Related Work

• Spade waveguide
• Losses
• 2-5 dB / cm
• 0.4 dB for 90º bend of 40 mm

Fleming, Lin, Hadley, 2003
close-up of inner coating
Multi-mode propagation at visible wavelengths
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Square waveguides

• Theory
• TE modes
• TM modes

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On-chip omniguide A

• Surround cavity with mirrors
• Quantum analogy particle classically forbidden
  to escape
• Hard to make
• Putting mirrors together requires nano-lithography

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On-chip omniguide A

• k0 modes (E-field energy distrib).

TE/TM12, w0.191, Q1000
TE/TM22, w0.235
TE03, w0.247
TE/TM13, w0.258
TE/TM23, w0.289
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On-chip omniguide B

• Similar but easier to make
• Deposit layer-by-layer
• Omnidirectional reflection harder to achieve
• Period different in different directions

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On-chip omniguide B

• Increase core size
• Cuts down on tunnelling
• Decreases effect of corners
• Transmission for doubled core size

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On-chip omniguide B

• k0 modes

TE/TM23, w0.183 Q4730
TE/TM13, w0.163, Q2240
TE/TM22, w0.149, Q1360
TE/TM14, w0.207, Qgt5000
TE/TM33, w0.223, Q4400
TE/TM34, w0.248, Q4320
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On-chip omniguide B

• k0.2 modes

TE01, w0.207, Q2490
TE/TM11, w0.213, Q3160
TE02, w0.224, Q2470
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On-chip omniguide B

• Localized modes match theory in omnidirectional
  range
• here, w0.17-0.25

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Hybrid omniguide

• Eliminates losses at corners
• Flat substrate makes fabrication on chip feasible
• However, this structure is ideal and real
  structure will be made layer-by-layer

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Hybrid omniguide

• k0 modes

TM01, w0.157, Q9535
TM21? w0.235, Q530
TM11, w0.199, Qgt15000
TE11, w0.160
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Performance comparison

• On-chip omniguide B and hybrid omniguide compare
  favorably
• Modal areas
• On-chip omni. B - 100
• Hybrid omni. - 25.13
• Omniguide 14.44

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Local Density of States

• At (2.5a,2.5a) in 10a x 10a cell

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Transmission losses

• For f0.157, Q105, vg0.9c, l1.5 mm, a0.5 mm
• loss lt 1 dB / cm!

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Bending Losses
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Conclusions

• There are several viable alternatives to a
  cylindrical geometry for on-chip applications
• Fabrication target somewhere between on-chip
  omniguide B and hybrid omniguide structure (with
  SiO2 core)
• Could retain omnidirectional reflectivity with
  SiO2 (n1.46) core, Si3N4 (n2) Si (n3.5)
  cladding