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

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

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

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

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 1.582 mm Tuning at 1.402 mm and 1.582 mm

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

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)

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

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

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

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

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

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

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

Source along z at r=2a

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

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

Source along z at coating surface

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)

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.

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

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 6 dB / cm.

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

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

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.

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

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

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

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

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

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

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, 035316 (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).

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

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

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°

Potential applications: spatial light modulators Dn Phased array Superprism Tunable filters Fresnel lens

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

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

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.

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

Old detection technique Lots of radiation from point source escapes

Transmission spectrum Zoomed in near mode cutoff

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

Source along r at r=1.2a

Source along q at r=1.2a

Source along z at r=1.2a

Source along r at r=2a

Source along q at r=2a

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

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

[ 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

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

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

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

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

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).

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

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

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

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