1. Photonic bandgaps, omnidirectional confinement and active materials
Peter Bermel
November 5, 2004
Advisor: J.D. Joannopoulos

2. Motivation
Use omnidirectional reflectors to confine light in new ways (e.g., omniguides). Advantages:
Tight bends in waveguides
Core freedom (enables higher power)
Lower losses
More tractable fabrication
Combine PhCs and active materials for interesting physics

3. Outline Tuning resonance modes (in omnidirectional reflectors)
Channel drop filters
Coupling of dipoles to waveguide modes
Biochemical sensing
Omniguides in new geometries
Guiding light around silicon chips
Combining FDTD and 4 level atomic systems (in 3D!)
Optically pumped lasers

4. Tunable MEMS device
Design: two reflectors surround an adjustable air gap
Resonant modes are in the photonic band gap between the mirrors

5. Tunable MEMS device
Can adjust separation between two mirrors with electrostatic tuning
Resonant wavelength change goes as V2
Experimentally, 10V  shift of 60 nm in mode at mm
Tuning at mm and mm

6. Potential Telecom Applications
Tunable channel drop filter
Air gap modulation
Index modulation
Loss modulation
Free space optical comm modulator

7. Index modulation Response, dR/dn, high near sharp resonances
Can increase without bound under two conditions
Low absorption
Dielectric mirrors (negligible intrinsic loss)
With only 5 bilayers, the response around the resonance is increased by a factor of 660 (compared to Fabry-Perot oscillations)

8. Omniguides
An omnidirectional reflector, rolled into tube, offers several advantages over index-guided fibers
Gives rise to “core freedom”:
Active materials
Luminescent molecules (BioMEMS)
High power applications
Thermo-optical devices
Enables sharp bends (for miniaturization)
Allows for lower losses
Design improves coupling from fiber optics to this system compared to other PBG-based systems

9. Simulated system Fluorescent molecule at one end
Light is gathered at the other end
3 bilayers of tellurium (n=4.6) / polystyrene (n=1.6)
period a
core diameter 4a
waveguide length 50a

10. Results for source at center
High transmission, low loss in TM01 mode

11. Transmission spectrum
More than 100% transmission out the far end, compared to vacuum, just above the cutoff frequency
Known as the Purcell effect

12. Transmission for sources at r=1.2a
Coupling to modes different as orientation changes (TE vs. TM)
Strong transmission for all orientations

13. Transmission for sources at r=2a
Only r-orientation couples strongly to hollow-core modes
Other orientations couple to high index modes
comes from overlap of evanescent modes of source and propagating modes of cladding

14. Density of states Local density of states:
Predicts high emission near cutoff frequencies:
Observed in time-domain simulations

15. Source along z at r=2a

16. Transmission with low-index coating
Low-index coating like moving source toward center, except for minor corrections:
Cutoff frequency shifted by factor of neff
Dispersion increased by factor of neff
low-index coating

17. Transmission with low-index coating
Transmission just as high as for dipole in air at same position
Mode frequency shifted by 1/neff

18. Source along z at coating surface

19. On-chip omniguides
Do principles of omniguides hold when you change the geometry?
Several practical problems with cylindrical omniguides
Difficult to create a circular structure on a chip, and especially to have well-controlled bends and crosses; planar geometry easier
Challenging to fabricate one with a small core (due to process)

20. Design
Surround rectangular low-index core with omnidirectional reflectors on all sides
This arrangement gives rise to guided modes above the light line in the core, as in omniguides
Proper choice of materials, number of layers, and geometry allows one to minimize loss for a given core size (~ 4 mm)
(a)
(b)
square omniguide design with alternating layers of dielectric surrounding an oxide core.
(b) TEM cross-section of experimentally fabricated waveguide.

21. 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

22. Guiding along Straight Sections
We fabricated the straight waveguide and looked for a guided mode.
The bright spot observed experimentally suggests a guided mode.
black square outlines the core.
The loss for one of our guides was as low as dB / cm.

23. Guiding around Bends
Omnidirectional confinement mechanism works at all angles
leads to small losses for tight turns.
unlike fiber optics, which would have high losses for bends < 100 mm.
TEM cutaway view of our fabricated bending structure

24. Guiding around Bends
Transmission is pretty high throughout the range of omnidirectional reflectivity:
lower for slightly wider (but still tight) turns
especially after subtracting straight waveguide losses
paperclip bend
Transmission spectrum for 2 bends compared to a straight waveguide

25. Guiding around Bends
Simulation showing the efficient transmission of a light pulse around a sharp bend, at 3 different times:
Transmission peaks at 93%
Experimentally, losses are higher:
Transmission peaks at 32% (5-6 dB / bend)
Could be reduced if cracks in the structure were eliminated.

26. Simulating Active Materials & PhCs
Wrote a simulation which combines FDTD and 4-level atomic materials
No previous simulations of atomic materials in 2D or 3D photonic crystals have been done
Opens up possibilities for optimizing performance of real devices N4 N3
ħwpump
ħwfluoresce N2 N1
Energy level diagram used in simulation

27. Fluorescent Materials in 1D
Goal: optically pump fluorescent material in Fabry-Perot cavity
Technique: choose Bragg stack transparent at wpump, reflective at wfluoresce
Result: 99.86% or greater efficient conversion! w x w x
E(x,w) for empty cavity
E(x,w) for active cavity

28. Fluorescent Materials in 2D
Goal is to optically pump with a single pulse, as before
Introduce line of defects in middle of 2D PhC
In simulations, transmission at wfluoresce well above 100%; mark of gain material

29. Fluorescent Materials in Omniguides
Want to duplicate success with a 3D structure – hollow omniguide fiber
Transmission ends up being orders of magnitude above original signal
Efficiency 82.8% for parameters used; could be improved with tweaking
Final resonant state created by active material in core

30. Conclusion
Found several applications for omnidirectional reflectors & omniguides
Channel add/drop filters
Biochemical sensors
Guiding light around Si chips
Started looking at behavior of atomic materials in PhCs:
Can create efficient lasers in 1D, 2D or 3D systems

31. Future plans Physics of active materials in PhCs
Looking at other systems using atomistic FDTD simulation
Coupling of fluorescence from single atoms/molecules
Slow light, combining ideas from EIT and photonic bands
Role of disorder & spontaneous emission

32. References (http://jdj.mit.edu/~bermel/)
Peter Bermel, John D. Joannopoulos, "Simulations of four-level atomic materials", Phys. Rev. B (to be submitted).
Peter Bermel, Yasha Yi, John D. Joannopoulos, Lionel C. Kimerling, "Bending in on-chip waveguide structures", Opt. Lett. (submitted).
Yasha Yi, Shoji Akiyama, Peter Bermel, Xiaoman Duan, and Lionel C. Kimerling, "On-chip Si-based waveguide with 1D photonic crystal cladding," Opt. Express 12, 4775 (2004).
Peter Bermel, John D. Joannopoulos, Yoel Fink, Paul A. Lane, Charles Tapalian, "Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides," Phys. Rev. B 69, (2004).
Yasha Yi, Peter Bermel, Kazumi Wada, Xiaoman Duan, John. D. Joannopoulos, and Lionel. C. Kimerling, "Tunable multichannel optical filter based on silicon photonic band gap materials actuation", Appl. Phys. Lett. 81, 4112 (2002).
Yasha Yi, Peter Bermel, Kazumi Wada, Xiaoman Duan, John. D. Joannopoulos, and Lionel. C. Kimerling, "Low Voltage Tunable One Dimensional Photonic Crystal With Large Air Defects", Proceedings of Material Research Society, vol. 722, L3.3 (2002).

34. Omnidirectional Reflectors
Special type of 1-D PhC
Reflect all incident light
all angles
all polarizations

35. Using omniguides for chemical-biological sensing
John Joannopoulos, Peter Bermel
MIT
Charles Tapalian, Paul Lane
Draper Labs

36. Improving modulation response
Two types of response:
phase modulation
resonance modulation
Response of fringes limited
Max phase change goes as k·x
Response goes as derivative of phase change
Result: Response is no more than 4pd/l
Df=29°

37. Potential applications: spatial light modulatorsDn
Phased array
Superprism
Tunable filters
Fresnel lens

38. Optical spatial light modulators
Optical phased array – gradually change phase of elements to control angle of outgoing light
Superprism – slight change in prism index leads to substantial tilt in outgoing beam Dn
Optical phased array
Superprism

39. What contrast is needed?
For resonances with Q of 1000, only need Dn=0.002
For superprism, incident Dq of 1.4°  exiting Dq=20°
For WDM applications
400 GHz bandwidth requires Dn=0.008
50 GHz bandwidth requires Dn=0.001

40. Old detection technique
Put fluorescent molecules on optical fiber But that’s inefficient!
Optical fibers rely on total internal reflection
However, fluorescent molecules radiate in a pattern in which much of the light won’t be internally reflected.

41. Old detection technique
Simulation: point source in silica fiber (n=1.6) with air cladding

42. Old detection technique
Lots of radiation from point source escapes

43. Transmission spectrum
Zoomed in near mode cutoff

44. Density of states Density of states given by
Large even within omnidirectionally-reflecting range
Need to ensure no coupling to the propagating modes in high-dielectric medium

45. Source along r at r=1.2a

46. Source along q at r=1.2a

47. Source along z at r=1.2a

48. Source along r at r=2a

49. Source along q at r=2a

50. Conclusion Omniguides can capture light radiated by pointlike sources
Can choose parameters to ensure low losses
Coupling into cladding problem for dipoles on surface
Can introduce coating on inner surface to enhance performance

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

52. [ figs courtesy Y. Fink et al., MIT ]
A drawn omniguide
[ figs courtesy Y. Fink et al., MIT ]
Photonic crystal structural uniformity, adhesion, physical durability through large temperature excursions
white/grey
= chalco/polymer

53. Materials choice Can achieve similar effects with different materials
Easier to make titania/silica experimentally
Faster to simulate higher-contrast tellurium/polystyrene system
Losses decrease exponentially with # layers

54. Number of bilayers
For all modes, losses decrease exponentially with number of layers
Calculated for core of size 10a, material Te/PS

55. Core size For TE01 mode, losses decrease as 1/R3
For TM modes, losses decrease as 1/R
Calculated for 4 bilayers of Te/PS

56. On-chip photonic waveguides with low bending losses
Peter Bermel, Yasha Yi, Xiaoman Duan, John Joannopoulos, Lionel Kimerling
Massachusetts Institute of Technology

57. Overview
Photonics provides an alternative to fiber optics which offers:
tighter bends
higher power transmission
We have successfully fabricated a device with a CMOS-compatible process.
Experimental losses:
6 dB / cm for straight sections.
5-6 dB / turn for sharp bends (turning radius of 1 wavelength).

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

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

60. 4 level atoms in photonic crystals
Peter Bermel, Elefterios Lidorikis, John D. Joannopoulos

61. Photonic Crystals
Dielectric media with periodicity in one or more directions
Acts like mirror for a range of frequencies