Photonic Crystals: Properties, Modeling, and Applications
Photonic Crystals: Properties, Modeling, and Applications
Wolfgang Freude Jan-Michael Brosi, Christian Koos,* Juerg Leuthold
Institute of Photonics and Quantum Electronics (IPQ), University of Karlsruhe, Germany * Now with Carl Zeiss AG, Corporate Research and Technology, 73447 Oberkochen, Germany
Universität Karlsruhe (TH) Institut für Photonik und Quantenelektronik (IPQ) http://www.ipq.uni-karlsruhe.de This work was supported by DFG in the Priority Program SP 1113 “Photonic Crystals”, by the DFG Center for Functional Nanostructures (CFN) within Projects A3.1 and A4.4, by the Initiative of Excellence of the Karlsruhe Institute of Technology (KIT), and by the Deutsche Telekom Stiftung. We acknowledge technological support by the European Network of Excellence ePIXnet (silicon photonics platform) and by ASML Netherlands B.V.
Schottky-Seminar, Walter-Schottky-Institut (WSI), Technische Universität January 27, 2009, München
Shapes of Photonic Crystals — 1D Photonic Crystals
Joannopoulis, J. D.; Johnson, S. G.; Winn, J. W.; Meade, R. D.: Photonic crystals Molding the flow of light, 2. Ed. Princeton: University Press 2008
J. S. Foresi, P. R. Ville- neuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, E. P. Ippen: Photo- nic-bandgap microcavities a z in optical waveguides. Nature 390 (1997) 143145
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 1 2D Photonic Crystals
Joannopoulis, J. D.; Johnson, S. G.; Winn, J. W.; Meade, R. D.: Photonic crystals Molding the flow of light, 2. Ed. Princeton: University Press 2008
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 2 3D Photonic Crystals — Opals and Woodpile
http://www.sandia.gov/media/photonic.htm
Lin, S. Y.; Fleming, J. G.; Hetherington, D. L.; Smith, B. K.; Biswas, R.; Ho, K. M.; Sigalas, M. M.;. Zubrzycki, W.; Kurtz, S. R.; Bur, J.: A three-dimensional photonic crystal operating at infrared wavelengths. Nature 394 (1998) 251253 Lin, S. Y.; Fleming, J. G.: A three-dimensional optical photonic crystal. J. Lightw. Technol. 17 (1999) 19441947
Noda, S.; Tomoda, K.; Yamamoto, N.; Chutinan, A.: SotomayorTorres, C. M.; Romanov, S. G.: Opal- and polymer-based photonic crystals. Heraeus Full three-dimensional photonic bandgap crystals at Summer School on Photonic Crystals, Wittenberg, July 1425, 2002. near-infrared wavelengths. Science 289 (2000) 604 http://www.photonische-kristalle.de/summerschool 606
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 3
3D Photonic Crystals — Direct Laser Writing
Prof. Dr. Martin Wegener´s group at the Institute of Applied Physics, University of Karlsruhe http://www.aph.uni-karlsruhe.de/... …wegener/en/research/photonic-crystals
http://www.sandia.gov/media/photonic.htm
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 4 Metamaterials vs. Photonic Crystals
Martin Wegener´s group at the Institute of Applied Physics, University of Karls- ruhe http://www.aph.uni-karlsruhe.de/wegener/en/research/photonic-crystals
Gießen, H.: Öffentliche Vorlesung über Tarnkappen im Mercedes Museum am 22.7.2008. http://www.pi4.uni-stuttgart.de/ Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 5
Metamaterials in the Microwave Range — Cloaking
Schurig, D.; Mock, J. J.; Justice, B. J.; Cummer, S. A.; Pendry, J. B.; Starr, A. F.; Smith, D. R.: Metamaterial electromagnetic cloak at microwave frequencies. Sciencexpress http://www.sciencexpress.org 19 Oct 2006 10.1126/science.1133628
Liu, R.; Ji, C.; Mock, J. J.; chin, J. Y.; Cui, T. J.; Smith, D. R.: Broadband ground-plane cloak. Science 323 (2008) 366369 Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 6 Metamaterials in the Optical Range — Towards an Ideal Lens?
Linden, S.; Enkrich, C.; Wegener, M.; Zhou, J.; Koschny, T.; Soukoulis, C. M.: Magnetic Response of Metamaterials at 100 Terahertz. Science 306 (2004) 13511353 Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 7
Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals
• Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 8 Maxwell’s Equations and the Scaling Law
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 9 Microwave Experiments
Enlargement of structure by = 20,000 (400 nm 8 mm) Decrease of frequency by 20,000 (200 THz 10 GHz) Advantages: • Highly precise fabrication (CNC), equivalent accuracy 0.5 nm • Highly accurate measurement equipment with large bandwidth • Flexible and modular setup
Material:
Ceramic-reinforced PTFE (Teflon) Refractive index at 10 GHz similar as for silicon at 200 THz
Accurate real-time check of numerical simulations (“analogue computer”) Influence of fabrication imperfections may be investigated Result: Simulations with finite-integration technique (FIT) and guided- mode expansion (GME) method well suited for design Brosi et. al., J. Lightw. Technol., vol. 25, no. 9, pp. 2502-2510, Sept. 2007 Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 10 Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals
• Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 11 2D Photonic Crystal Bandstructure — Infinitely High Air Cylinders
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 12 2D Photonic Crystal Bandstructure — Infinitely High Air Cylinders
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 13 2D Photonic Crystal Bandstructure — Eigenvalues
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 14 1D Photonic Crystal Bandstructure — Computation Example (1)
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 15 1D Photonic Crystal Bandstructure — Computation Example (3)
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 17 1D Photonic Crystal Bandstructure — Insertion Loss
L
a z GHz
0 –15 insertion–30 l oss i ndB dB –60
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 18
1D Photonic Crystal Bands — GaAs / GaAlAs Multilayer Film
Joannopoulis, J. D.; Johnson, S. G.; Winn, J. W.; Meade, R. D.: Photonic crystals Molding the flow of light, 2. Ed. Princeton: University Press 2008 (Sect. 4 Fig. 2 p. 46) Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 19
1D Photonic Crystal Bands — Group Delay at Band Edges
a
meas. phase ---- linear part meas. group delay d( f ) tfg() dt
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 20 2D Photonic Crystal with Air Cylinders — Complete Bandstructure
z TE f / GH f / GHz f / GHz TM
15 15 f / GHz
10 10
5 5 > > - - -- - k ---> - k ---> y k x y yy x z k k kz k k 0 0 0 0 0 0
TE TM
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 22 Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 23 High-Bitrate Optical Transmission and Signal Processing
modu- line amplifier dispersion line lator compensator laser receiver
• Laser: Optical carrier at = 1.55 µm • Modulator: Transfers signals on optical carrier (10 Gbit/s …100 Gbit/s) • Line: Attenuation and positive dispersion dispersion (= frequency-dependent group velocity) impulse broadening • Amplifier • Dispersion compensator (DC): Negative dispersion impulse shortening • Optical cross-connect (OCX): Aggregation & grooming (requires delay), switching
Goals:
Modulator, DC, delay with high functionality and low price Silicon chips fabricated with CMOS technology Possible combination of optics and electronics
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 24
In this Scenario: Applications for Photonic Crystals
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 25 2D Photonic Crystals with Defects
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 26 Vision of Photonic Crystals: Guide, Filter, Delay, NL Processing
Joannopoulis, J. D.; Johnson, S. G.; Winn, J. W.; Meade, R. D.: Photonic crystals Molding the flow of light, 2. Ed. Princeton: University Press 2008
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 27
Photonic Crystals and Silicon Photonics
Silicon-on-insulator (SOI) systems promise: • Full integration of electronic and optical components • Low-cost CMOS-based technology • Fabrication of ultra-compact and ultra-fast optical devices • Electronically powered light sources so far only in hybrid integration • Fabrication of active and passive optical components. Wafer-Bonded III-V Laser CMOS Drivers
Photodetector with Built-in Filter
Input High-Speed Signal Electro-optical Modulator
Output Silicon-Wire- Signal Waveguide Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 28 Silicon-Organic Hybrid Systems: Improvements over SOI
Silicon-organic hybrid (SOH) systems promise in addition: • Wide choice of low-index materials (backend processing) • Large (2)-nonlinearity (strained silicon not fit for standard CMOS) • Large (3)-nonlinearity • No impairment by TPA-induced FCA large intensities • Emphasis in this talk on tunable dispersion and SOH modulators Wafer-Bonded III-V Laser CMOS Drivers
Photodetector with Built-in Filter
Input High-Speed Signal Electro-optical Modulator
Output Silicon-Wire- Signal Waveguide Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 29 Photonic Crystals in SOI
Dielectric transparent material (silicon) with periodic structure
Bragg reflexion, if e / 2 a No light propagation for certain frequencies
photonic bandgap
Introducing defects (impurities, doping) Light propagation along defects
Slow group velocity vg (slow light) and large dispersion vg( f)
Designing vg(f) by structural changes
Applications for tailored dispersion: • Large negative chromatic dispersion, e.g., for dispersion compensation • Slow light for optical delay, e.g., for aggregation in OXC • Slow light for increased light-matter interaction, e.g., for modulation
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 30 Fabrication Technologies
Structure roughness: Main source of losses
• Losses increase for small group velocities vg
• Losses limit the lowest usable vg
Numerical investigations of roughness loss
• Air hole positions regular
• Radii with normal distribution, r = 5 nm
Design goal: Minimum loss
Comparison of different structures: Broadband slow light with vg / c = 4 %
gailrass silicon glass
symmetric in air symmetric in glass unsymmetric membrane structure buried structure silicon-on-insulator (SOI) Variation of defect (WG) width, mode number and height of silicon layer (220 nm)
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 31
Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 32 Slow Light in Photonic a Crystal (1)
Parameter h Waveguide height ~ 220 nm r Radii of air holes ~ 120 nm
Ex a Lattice constant of PC ~ 400 nm
TE polarisation: Dominant electric field Ex
0.35 c Lichtlinie / f a Without crystal defects:
0.30 Photonic bandgap
Frequenz Frequenz c Vacuum speed of light 0.25 k Propagation constant in z-direction 0.00.20.40.60.81.0 Ausbreitungskonstante k a /
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 33 Slow Light in Photonic a Crystal (2)
Parameter h Waveguide height ~ 220 nm r Radii of air holes ~ 120 nm a Lattice constant of PC ~ 400 nm
0.35
c Lichtlinie f a / With crystal defects: Waveguiding in
0.30 photonic bandgap
Frequenz Light propagation exp(jt –jkz) 0.25 c Vacuum speed of light 0.0 0.2 0.4 0.6 0.8 1.0 k Propagation constant in z-direction Ausbreitungskonstante k a /
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 34 Slow Light in Photonic a Crystal (3)
Parameter h Waveguide height ~ 220 nm r Radii of air holes ~ 120 nm a Lattice constant of PC ~ 400 nm
0.35
c Lichtlinie f a / With crystal defects: Waveguiding in
0.30 photonic bandgap
Frequenz Light line: Describes propagation in 0.25 homogeneous cladding (here: air) 0.0 0.2 0.4 0.6 0.8 1.0 • Below LL: Guiding of modes in silicon layer Ausbreitungskonstante k a / • Above LL: Radiation (leaky waves)
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 35 Slow Light in Photonic a Crystal (4)
Parameter h Waveguide height ~ 220 nm r Radii of air holes ~ 120 nm a Lattice constant of PC ~ 400 nm
0.35 d f v Group velocity c v 2 g Lichtlinie g d k f a /
tLv / tg Group delay 0.30 gg
f 22d k C Frequenz C Chromatic dispersion 2c d f 2 0.25 f 2 d t 0.0 0.2 0.4 0.6 0.8 1.0 g Ausbreitungskonstante k a / Lcd f C = 1ps/(mm nm): Impulse with bandwidth 1 nm (125 GHz) widens during propagation over a distance of 1 mm by 1 ps.
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 36 Slow Light in Photonic a Crystal (5)
Parameter h Waveguide height ~ 220 nm r Radii of air holes ~ 120 nm a Lattice constant of PC ~ 400 nm
Dispersion 15 0.35 c / g c v 0.2 Lichtlinie 10 f a / C [ps/(mm nm)] [ps/(mm
0.30 0.1 5 Frequenz 0.25 Gruppengeschw. 0.0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.27 0.28 0.29 Ausbreitungskonstante k a / Frequenz f a / c
vg approaches zero at Brillouin zone boundary at k = / a
C very large because vg changes strongly with f
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 37
Broadband Slow Light in a Photonic Crystal
Optimizing dispersion properties: Systematic variation of structural parameters
• Hole radii not too small ( r > 100 nm) • Wall thickness between holes not too small ( > 100 nm)
Dispersion 8 c 0.2
Lichtlinie / g c v 6
/ 0.28 f a C
4 nm)] [ps/(mm 0.1
0.27 2 Frequenz
Gruppengeschw. 0.0 0 0.6 0.8 1.0 0.270 0.275 0.280 Ausbreitungskonstante k a / Frequenz f a / c Group velocity only 3.9 % of vacuum speed of light in a bandwidth of 1.9 THz
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 38 Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 39 Negative Chromatic Dispersion
Optimizing dispersion properties: Systematic variation of structural parameters
• Hole radii not too small ( r > 100 nm) • Wall thickness between holes not too small ( > 100 nm)
Dispersion 0.2 15 c
Lichtline / g c v
/ 0.28 10 f a
0.1 C [ps/(mmnm)]
5
0.27 0.0 0 Frequenz Frequenz
Gruppengeschw. -5 0.6 0.8 1.0 0.270 0.275 0.280 Ausbreitungskonstante k a / Frequenz f a / c Negative chromatic dispersion of 4.5 ps / (mm nm) and regions with linear dispersion
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 40 Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 41 Improved Coupling with Taper (1)
slow-light waveguide strip waveguide
Taper: Slight continuous structural change
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 42 Improved Coupling with Taper (2)
0
Mit Ohne Taper Taper -5
Ex
Transmission [dB] -10
190 195 200 Frequenz f [THz] Loss < 0.5 dB / transition
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 43 Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 44 Tunable Dispersion Compensator (1)
Idea: Linear falling and linear rising L
dispersion C(f ) in series
C C (f )L 2 2 0 Cges Lges = C1(f ) L1 + C2(f ) L2
C (f ) L 1 1 Flattened total dispersion Cges Lges C L ges ges Dispersion
Tuning of section 1 (e. g., by cooling or f carrier injection): f 0 Refractive index change n Frequenz f
Shift by f
Total dispersion Cges Lges changes
Section 1: C1, L1 Section 2: C2, L2
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 45 Tunable Dispersion Compensator (2)
Idea: Linear falling and linear rising L
dispersion C(f ) in series C L C ges ges 0 Cges Lges = C1(f ) L1 + C2(f ) L2
Flattened total dispersion Cges Lges
Dispersion
Tuning of section 1 (e. g., by cooling or f carrier injection): f0 Refractive index change n Frequenz f
Shift by f
Total dispersion Cges Lges changes
Section 1: C1, L1 Section 2: C2, L2
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 46 Tunable Dispersion Compensator (3)
Idea: Linear falling and linear rising L
dispersion C(f ) in series C L C ges ges 0 Cges Lges = C1(f ) L1 + C2(f ) L2
Flattened total dispersion Cges Lges
Dispersion
Tuning of section 1 (e. g., by cooling or f carrier injection): f0 Refractive index change n Frequenz f
Shift by f Entwurf
Total dispersion Cges Lges changes 50 nm] / [ps L x
Design: Based on waveguide with negative C dispersion minimum 0 Tuning range (19 … +7) ps / (mm nm) in an optical bandwidth of 125 GHz. Dispersion 193 194 195 Frequenz f [THz]
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 47 Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 48 Tunable Delay Line (1)
g
Idea: Linear falling and linear rising group t
delay tg(f ) in series t (f ) tg, ges = tg1(f ) + tg2(f ) g, ges
Constant total group delay tg, ges t (f ) g2 t (f ) C < 0 g1 2 Gruppenlaufzeit Gruppenlaufzeit Linear tg -depencence by constant positive C1 > 0 f or negative dispersion C: f0 Frequenz f C − d tg /df
Tuning of section 1
Section 1: tg1 Section 2: tg2
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 49 Tunable Delay Line (2)
g
Idea: Linear falling and linear rising group t t (f ) delay tg(f ) in series g, ges
tg, ges = tg1(f ) + tg2(f )
Constant total group delay tg, ges
Gruppenlaufzeit Gruppenlaufzeit Linear tg -depencence by constant positive f or negative dispersion C: f0 Frequenz f C − d tg /df
Tuning of section 1
Sektion 1: tg1 Sektion 2: tg2
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 50 Tunable Delay Line (3)
g
Idea: Linear falling and linear rising group t t (f ) delay tg(f ) in series g, ges
tg, ges = tg1(f ) + tg2(f )
Constant total group delay tg, ges
Gruppenlaufzeit Gruppenlaufzeit Linear tg -depencence by constant positive f or negative dispersion C: f0 Frequenz f C − dtg /df
L /
c Entwurf
Tuning of section 1
g t Total group delay tg, tot changes. 50
Design: Tuning range 42 ps (1.7 bit at 40 Gbit/s) in an optical bandwidth of 125 GHz 0 for a length of 1 mm. Gruppenlaufzeit 192 193 194 195 Frequenz f [THz] Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 51 Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 52 Silicon-on-Insulator and Silicon-Organic Hybrid Systems Silicon-on-insulator (SOI) offers: • Mature silicon technology, with 35 nm and higher-resolution lithography • Compatibility with CMOS electronics
• Foundry service low cost
• Ultra-compactness due to high confinement of optical modes
Silicon-on-insulator issues: Silicon-organic hybrid systems (SOH) combine the best of two worlds: • No naturalStrong electro-optic effect effect in silicon Kerr-effect without TPA
Mateorial Strainedλ [nm] siliconEO coefficientbreaks up inversionMate symmetryrial λ [nm] n [m2/W] FOM 2 TPA • Free-carrier absorption measures needed to remove carriers-17 DAST 1535 r11 = 50 pm/V DDMEBT 1500 2 x 10 est. > 5 (3) • in silicon is reasonably large, yet impaired by TPA-induced-1 6FCA EO polymers 1300 r33 = 90 – 133 pm/V PTS (PDA) 1600 2.2 x 10 > 27 LiNbO 1500 r ≈ r = 30 pm/V -18 3 33 42 Si 1500 4.5 x 10 0.3
Mutter et al., Cleo Europe 2007, paper CE-1449 Koos, C.; Jacome, L.; Poulton, C.; Leuthold, J.; Freude, W.: Non- linear silicon-on-insulator waveguides for all-optical signal proces- Chen et al., Appl. Phys. Lett. 70, 1997, 3335-3337 sing. Opt. Express 15 (2007) 5976–5990, May 2007
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 57 SOH MZ-Modulator with Slow-Light Photonic Crystal Slot WG
J.-M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, W. Freude: High- speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide, Opt. Express, vol. 16, pp. 41774191, March 2008 Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 58
SOH PM with Slow-Light Slotted Photonic Crystal WG
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 59 SOH MZ-Modulator: Expected Data
Structure r2 / a fo (THz) vg,opt/c Г L (m) f3dB (GHz) 0.3 196.4 2.4% 4.8 36 103 W1.4 196.6 3.4% 3.2 54 97 dispersion 196.9 4.8% 2.2 80 90 large 196.2 6.4% 1.5 113 83 197.7 8.2% 1.1 155 76 0.38 197.5 3.2% 3.1 57 87 W1.25 0.36 196.5 4.0% 2.2 80 78 dispersion 0.34 195.8 5.2% 1.6 111 71 flattened 0.32 195.2 6.6% 1.1 158 61 0.30 194.6 7.9% 0.8 215 53
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 60 Taper for Broadband Low Dispersion Slow Light PC Slot-WG
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 61 Fabrication of SOH Phase (and MZ) Modulator with PC Taper
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 62 Rib-to-Slot Transition
a b c d
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 63 Two Slow-Light Photonic Crystal Families
varying radii identical radii, shifted position
J.-M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, W. J. Li, T. P. White, L. O`Faolain, A. Gomez-Iglesias, T. F. Krauss: Freude: High-speed low-voltage electro-optic modulator with a polymer- Systematic design of flat and slow light in photonic crystal waveguide. infiltrated silicon photonic crystal waveguide, Opt. Express, vol. 16, Opt. Express, vol. 16, pp. 62276232, April 2008 pp. 41774191, March 2008
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 64
Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 67 Broadband Slow Light PC WG with Low Dispersion
Brosi, J.-M.; Koos, C.; Andreani, L. C.: Dumon, P.; Baets, R.; Leuthold, J.; Freude, W.: '100 Gbit/s / 1 V optical modulator with slotted slow-light polymer- infiltrated silicon photonic crystal', OSA Topical Meeting on Slow and Fast Light (SL'08), Boston (MA), USA, 13–16 July 2008. Paper SWC3 Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 68
Outline
• Fundamentals of photonic crystals Maxwell’s equations and the scaling law Bandstructure of photonic crystals • Applications and technology
Optical communications and silicon photonics Slowing down light Designing chromatic dispersion Coupling to photonic crystals
• Photonic crystal devices Tunable dispersion compensator Tunable delay line Electro-optic modulator Measurements
• Summary
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 69 Photonic Crystals: Properties, Modeling, and Applications
• PC could find applications whenever dispersion properties need tailoring
• Slow-light devices have increased losses,
but may be designed for wide bandwidth
• PC especially useful in hybrid combination
with nonlinear organic materials for tunable dispersion ( 19…+7) ps / (mm nm) for tunable delay 01.7 bit / mm @ 40 Gbit/s for electro-optic modulation 100 Gbit/s / 1 V
• A few experiments demonstrated
the use of microwave models the present status of our EO modulator
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 70 Further Reading (1/2)
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 71 Further Reading (2/2)
Tue, Jan 27, 2009 Institut für Photonik und Quantenelektronik (IPQ), Universität Karlsruhe 72