Ultra-Slow Light Propagation in Room Temperature Solids Robert W. Boyd The Institute of Optics and Department of Physics and Astronomy University of Rochester, Rochester, NY USA http://www.optics.rochester.edu Presented at Laser Optics 2003, St. Petersburg, Russia, July 3, 2003.
Interest in Slow Light Fundamentals of optical physics Intrigue: Can (group) refractive index really be 10 6? Optical delay lines, optical storage, optical memories Implications for quantum information
Slow Light group velocity phase velocity
Slow Light in Atomic Media Slow light propagation in atomic media (vapors and BEC), facilitated by quantum coherence effects, has been successfully observed by many groups.
Challenge/Goal Slow light in room-temperature solid-state material. Slow light in room temperature ruby (facilitated by a novel quantum coherence effect) Slow light in a structured waveguide
Slow Light in Ruby Need a large dn/dw. (How?) Kramers-Kronig relations: Want a very narrow absorption line. Well-known (to the few people how know it well) how to do so: Make use of spectral holes due to population oscillations. Hole-burning in a homogeneously broadened line; requires T 2 << T 1. 1/T 2 1/T 1 inhomogeneously broadened medium homogeneously broadened medium (or inhomogeneously broadened) PRL 90,113903(2003); see also news story in Nature.
Spectral Holes Due to Population Oscillations b b Γ bc 2γ ba = 2 T 2 Γ ba = 1 T 1 ω c a a Γ ca E 3, ω + δ E 1, ω atomic medium ω + δ measure absorption Population inversion: ( ρ ρ ) = ( 0) ( δ) i δ t ( δ) iδt wt () w + w e + w e bb aa w population oscillation terms important only for δ 1/ T1 Probe-beam response: ρ ( ω + δ) = ba µ h ba 1 ω ω + i/ T ba 2 [ ( 0) ( δ ) Ew + Ew ] 3 1 Probe-beam absorption: ( 0) αω ( + δ) w 2 Ω T 2 T1 δ 1 2 2 + β linewidth 2 β = ( 1/ T1 )( 1+Ω T 1 T 2 )
Spectral Holes in Homogeneously Broadened Materials Occurs only in collisionally broadened media (T 2 << T 1 ) Boyd, Raymer, Narum and Harter, Phys. Rev. A24, 411, 1981.
Experimental Setup Used to Observe Slow Light in Ruby Digital Oscilloscope Function Generator Argon Ion Laser Reference Detector Ruby Diffuser EO modulator f = 40 cm f = 7.5 cm 7.25 cm ruby laser rod (pink ruby)
Measurement of Delay Time for Harmonic Modulation 1.4 1.2 P = 0.25 W 1.0 Delay (ms) 0.8 0.6 0.4 0.2 P = 0.1 W solid lines are theoretical predictions 0 0 200 400 600 800 1000 Modulation Frequency (Hz) For 1.2 ms delay, v = 60 m/s and ng = 5 x 10 6
Gaussian Pulse Propagation Through Ruby 1.2 512 µs 1.0 Normalized Intensity 0.8 0.6 0.4 0.2 Input Pulse Output Pulse v = 140 m/s ng = 2 x 10 6 0-20 -10 0 10 20 30 Time (ms) No pulse distortion!
Matt Bigelow and Nick Lepeshkin in the Lab
Alexandrite Displays both Saturable and Inverse-Saturable Absorption Mirror Sites: 4 T 2 or 4 T 1 s 2,m rapid Al, Cr s 1,m rapid 2 E T 1,m = 260 ms 4 A 2 O Inversion Sites: Be 4 T 2 or 4 T 1 rapid 2 E a s 1,i T 1,i ~ 50 ms 4 A 2 b
Inverse-Saturable Absorption Produces Superluminal Propagation in Alexandrite At 476 nm, alexandrite is an inverse saturable absorber Negative time delay of 50 ms correponds to a veleocity of -800 m/s M. Bigelow, N. Lepeshkin, and RWB, accepted for publication in Science, 2003
Slow and Fast Light --What Next? Longer fractional delay (saturate deeper; propagate farther) Find material with faster response (technique works with shorter pulses)
Artificial Materials for Nonlinear Optics Artifical materials can produce Large nonlinear optical response Large dispersive effects Examples Fiber/waveguide Bragg gratings PBG materials CROW devices (Yariv et al.) SCISSOR devices
NLO of SCISSOR Devices (Side-Coupled Integrated Spaced Sequence of Resonators) Shows slow-light, tailored dispersion, and enhanced nonlinearity Optical solitons described by nonlinear Schrodinger equation Weak pulses spread because of dispersion intensity 0 50 20 40 60 80 100 100 120 150 t (ps) z (resonator #) 0 But intense pulses form solitons through balance of dispersion and nonlinearity. intensity 0 50 20 40 60 80 100 100 120 150 t (ps) z (resonator #) 0
Slow Light and SCISSOR Structures E 3 E 4 R group index keff k0 build-up 2 π F 0 2π L 2 π Fn n E 1 E 2 L c FnR c FnR slope = Fn c c nr c FnR slope = Fn c c FnR frequency, ω
Microdisk Resonator Design All dimensions in microns 10 10 0.25 0.45 2.0 trench trench linear taper 25 20 d = 10.5 0.5 linear taper 25 2.0 gap s1 = 0.08 s2 = 0.10 s3 = 0.12 s4 = 0.20 GaAs Al x Ga 1-x As (x = 0.4) J. E. Heebner and R. W. Boyd
Photonic Device Fabrication Procedure (1) MBE growth (2) Deposit oxide AlGaAs-GaAs structure Oxide (SiO2) AlGaAs-GaAs structure (3) Spin-coat e-beam resist (4) Pattern inverse with e-beam & develop (5) RIE etch oxide PMMA Oxide (SiO2) AlGaAs-GaAs structure (6) Remove PMMA Oxide (SiO2) AlGaAs-GaAs structure (7) CAIBE etch AlGaAs-GaAs Oxide (SiO2) AlGaAs-GaAs structure PMMA Oxide (SiO2) AlGaAs-GaAs structure PMMA Oxide (SiO2) AlGaAs-GaAs structure (8) Strip oxide AlGaAs-GaAs structure
Disk Resonator and Optical Waveguide in PMMA Resist AFM
All-Pass Racetrack Microresonator 100 nanometer gap 10 micron diameter 2.5 micron height 500 nanometer guide width Thanks to P.T. Ho and R. Grover, U. Maryland, for help with final etch.
Five-Cell SCISSOR with Tap Channel 5 microns 100 nanometer gaps 500 nanometer guides 2.5 micron height
Resonator-Enhanced Mach-Zehnder Interferometers 10 microns ~100 nanometer gaps 500 nanometer guides 2.5 micron height
Laboratory Characterization of Photonic Structures Characterization of fiber ring-resonator devices (Proof of principle studies) Characterization of nanofabricated devices
Fiber-Resonator Optical Delay Line Fiber optical delay line: 2.5 27 ns (delay) First study one element of optical delay line: intensity (arb. units) 2.0 1.5 1.0 0.5 non-resonant 51 ns (FWHM) resonant variable wavelength pulse 0.0 0 50 100 150 time (ns)
Transmission Characteristics of Fiber Ring Resonator circumference = 31 cm variable coupling Measure transmission vs. l for various values of the finesse undercoupled critically coupled transmission transmission transmission F = 51 F = 40 F = 30 transmission transmission transmission F = 12 F = 7.3 F = 6.8 overcoupled transmission F = 17 transmission F = 4.4 0 5 10 15 20 25 D wavelength (pm) 0 5 10 15 20 25 D wavelength (pm)
Laboratory Characterization of Photonic Structures Characterization of fiber ring-resonator devices (Proof of principle studies) Characterization of nanofabricated devices
Microresonator-Based Add-Drop Filter output for on-resonance input variable wavelength input output for off-resonance input 1.0 transmission 0.5 0.0 1.54 1.55 wavelength 1.56 1.57 (micrometers)
Phase Characteristics of Micro-Ring Resonator In Out normalied linear transmission 1.0 0.5 0.0 transmission 1.54 1.55 1.56 1.57 wavelength (microns) effective phase shift 4p 3p 2p p 0 induced phase shift 1.57 1.56 1.55 1.54 wavelength (microns)
All-Optical Switching in a Microresonator- Enhanced Mach-Zehnder Interferometer output 2 input output 1 output intensity (arb. units) increasing pulse energy output port #1 output port #2 increasing pulse energy ( ~1 nj) output position (x)
Summary Demonstration of slow light propagation in ruby and superluminal light propagation in alexandrite Argue that artificial materials hold great promise for applications in photonics because of large controllable nonlinear response large dispersion controllable in magnitude and sign
Thank you for your attention.
Comparison of University of Rochester and University of Arizona Bob and Ruby Hyatt and Galina
Photonic Structures --What Next?
Performance of SCISSOR as Optical Delay Line power (mw) power (mw) power (mw) 06 6 0 6 0 Input (duty factor = 1/3) Output --delayed one time slot by six resonators in linear limit Output --delayed four time slots by 26 resonators in linear limit power (mw) 6 0 0 50 100 time (ps) Output --delayed four time slots by 26 resonators in nonlinear limit
Frequency Dependence of GVD and SPM Coefficients 1.0 0.5 0.0 (GVD) k'' eff (2FT/p) 2 /L soliton condition (SPM) g eff g (2F/p) 2 (2pR/L) -0.5-4p -2p 0 p F F 3F normalized detuning, f 0 2p F 4p F
Soliton Propagation 5 µm diameter resonators with a finesse of 30 SCISSOR may be constructed from 100 resonators spaced by 10 µm for a total length of 1 mm power (µw) 0.3 0.2 0.1 0 0 20 Weak Pulse 40 60 80 z (resonator #) 100 50 100 150 200 250 t (ps) pulse disperses 0 soliton may be excited via a 10 ps, 125mW pulse simulation assumes a chalcogenide/gaaslike nonlinearity power (W) 0.3 0.2 0.1 0 0 20 Fundamental Soliton 40 60 80 z (resonator #) 100 50 100 150 200 250 pulse preserved t (ps) 0
Dark Solitons SCISSOR system also supports the propagation of dark solitons. power (mw) 20 0 20 60 z (resonator #) 100 300 t (ps) 100 0
SCISSOR Dispersion Relations Single-Guide SCISSOR No bandgap Large intensity buildup Double-Guide SCISSOR Bandgaps occur Reduced intensity buildup 1.498 separation = 1.5 p R wavelength (mm) 1.522 1.546 1.571 Bragg + resonator gap resonator gap 1.597 20 0 intensity build-up - p L - p p 2L 2L Bloch vector (k eff ) L p Bragg gap 20 0 - L p - p p 2L 0 2L intensity build-up Bloch vector (k eff ) L p
Phase Characteristics of Fiber Ring Resonator Place ring resonator inside Mach-Zhender interferometer and measure transmission versus wavelength. In variable coupler undercoupled critically coupled Out transmission transmission transmission F = 51 F = 40 F = 30 transmission transmission transmission F = 12 F = 7.3 F = 6.8 overcoupled transmission F = 17 transmission F = 4.4 0 10 20 30 40 D wavelength (pm) 0 10 20 30 40 D wavelength (pm)
Phase Characteristics of Fiber Ring Resonator Extracted phase strcuture In variable coupler undercoupled critically coupled Out phase phase phase F = 51 F = 40 F = 30 phase phase phase F =12 F =7.3 F =6.8 overcoupled F= 17 F =4.4 phase phase 40 30 20 10 wavelength detuning (pm) 0 40 30 20 10 wavelength detuning (pm) 0
"Fast" (Superluminal) Light in SCISSOR Structures Requires loss in resonator structure keff -k0 2p L overcoupled critically coupled undercoupled overcoupled - 8 dw 0.5 0 power (arb. units)1.0 (time-advanced) propagation through undercoupled SCISSOR -120 0 8 dw frequency detuning, w-w R -80-40 delay (ps) 0 propagation through vacuum 40