Alternative Bragg Fibers Peter Bermel, Yasha Yi, John Joannopoulos April 18, 2003

Introduction Motivation Designs Results Conclusion On-chip omniguide A & B Hybrid omniguide Results Conclusion

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

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)

Motivation Use flat omnidirectional reflectors [Fink et al., 1998]

Designs On-chip omniguide A On-chip omniguide B “Half” omniguide

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

Square waveguides Theory: TE modes: TM modes

On-chip omniguide A Surround cavity with mirrors Hard to make Quantum analogy: particle classically forbidden to escape Hard to make Putting mirrors together requires nano-lithography

On-chip omniguide A k=0 modes (E-field energy distrib). TE/TM12, w=0.191, Q=1000 TE/TM22, w=0.235 TE03, w=0.247 TE/TM13, w=0.258 TE/TM23, w=0.289

On-chip omniguide B Similar but easier to make Deposit layer-by-layer Omnidirectional reflection harder to achieve: Period different in different directions

On-chip omniguide B Increase core size Cuts down on tunnelling Decreases effect of corners Transmission for doubled core size

On-chip omniguide B k=0 modes TE/TM23, w=0.183 Q=4730

On-chip omniguide B k=0.2 modes TE01, w=0.207, Q=2490 TE/TM11, w=0.213, Q=3160 TE02, w=0.224, Q=2470

On-chip omniguide B Localized modes match theory in omnidirectional range here, w=0.17-0.25

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

Hybrid omniguide k=0 modes TM01, w=0.157, Q=9535 TE11, w=0.160

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

Local Density of States At (2.5a,2.5a) in 10a x 10a cell

Transmission losses For f=0.157, Q=105, vg=0.9c, l=1.5 mm, a=0.5 mm: Df Q=79 For f=0.157, Q=105, vg=0.9c, l=1.5 mm, a=0.5 mm: loss < 1 dB / cm!

Bending Losses

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 (n=1.46) core, Si3N4 (n=2)+ Si (n=3.5) cladding