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

2. Introduction Motivation Designs Results Conclusion
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

4. 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)

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

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

7. 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

8. Square waveguides
Theory:
TE modes:
TM modes

9. 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

10. 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

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

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

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

14. 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

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

16. 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

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

18. Performance comparison
On-chip omniguide B and hybrid omniguide compare favorably
Modal areas:
On-chip omni. B - 100
Hybrid omni
Omniguide – 14.44

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

20. 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!

21. Bending Losses

22. 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