Air Force Research Laboratory Materials with Engineered Dispersion for the Enhancement of Light-Matter Interactions 10 January 2013 Ilya Vitebskiy, AFRL/RYDP Integrity Service Excellence
SUBTOPIC 1 Nonreciprocal effects in photonic structures with engineered dispersion Collaborators: A. Chabanov (University of Texas / AFRL): theory, fabrication, experiment T. Carroll (AFRL/RYDP): numerical simulations J. Bodyfelt (Ohio State University): numerical simulations I. Ternovskiy (AFRL/RYHE): time-domain simulations, experiment SUBTOPIC 2 Frozen light and giant transmission resonance in optical waveguides Collaborators: R. Reano & J. Burr (Ohio State University): experiment, fabrication, simulations M. de Sterke & N. Gutman (University of Sydney, Australia): theory, design 2
Nonreciprocal effects in photonic structures with engineered dispersion. Brief history of nonreciprocal effects in lossy structures. A standard optical isolator (optical diode) magnetic Faraday rotator placed between two polarizers Forward Incident wave 45º Faraday Polarizer 1 rotator Polarizer 2 Transmitted wave Forward propagating wave passes through, while backward propagating wave does not. The reasons why absorption undermines the performance of nonreciprocal component: (1) Energy loss. (2) Dichroism (ellipticity). (3) Weakness of light-matter interactions. Proposed solution at optical frequencies: Kottos, Vitebskiy, Kavanis, et al. Taming the Flow of Light via Active Magneto-Optical Impurities. OE (2012). Proposed solution at lower frequencies: 1. Figotin & Vitebskiy. "Absorption suppression in photonic crystals". Phys. Rev. B 77 (2008). 2. K. Smith, T. Carroll, J. Bodyfelt, I. Vitebskiy, and A. Chabanov. Enhanced Transmission and Giant Faraday Effect in Magnetic Metal-Dielectric Photonic Structures. Submitted to Phys. Rev. E (2013) 3
Selective enhancement of light-matter interactions in photonic structures with engineered dispersion Incorporation of magneto-optical material in photonic structures with engineered dispersion - Selective enhancement of desired light-matter interactions (such as: Faraday rotation, light emission, gain, acousto-optics, etc.) and selective suppression of undesired light-matter interactions (such as absorption, or anything else we don t want to get enhanced). - Increased bandwidth due to non-resonant character of field enhancement. - Development of qualitatively new features, such as: o One-way light propagation (electromagnetic unidirectionality) o Super-collimation (extreme directionality) o Strong bi-anisotropic and other multiferroic properties Recent Publications: - Smith & Chabanov. Enhanced Transmission and Nonreciprocal Properties of a Ferromagnetic Metal Layer, Ferroelectrics (2011) - Smith & Chabanov. Enhanced Microwave Transmission and Magneto-photonic Response, PIERS (2012) - K. Smith, T. Carroll, J. Bodyfelt, I. Vitebskiy, and A. Chabanov. Enhanced Transmission and Giant Faraday Effect in Magnetic Metal-Dielectric Photonic Structures. Submitted to PRE (2013) 4
Intuitive example: EM field distribution inside layered structure (HL) 3 H(HL) 3 H. Cobalt nano-layer will be placed at the electric field node H: alumina (ε=10), L: air, ε=1
Transmission (db) Forward and Backward transmission of (HL) 3 HC(HL) 3 H sandwiched between misaligned polarizers (normal incidence) 0-10 FW -20-30 BW -40-50 7.498 7.499 7.500 7.501 7.502 Frequency (GHz) 6
T Transmission and Faraday rotation of (HL) 3 HC(HL) 3 H 0.6 0.5 0.4 0.3 0.2 T + T - 0.1 0.0 90 (units of 1.5 1.0 0.5 60 30 o FR -10-5 0 5 10 f (MHz) 0 Co thickness: 180 nm, H i =0.1 koe 7
T Transmission and Faraday rotation of (HL) 3 HC(HL) 7 HC(HL) 3 H 1.0 0.8 0.6 0.4 T + T - 0.2 0.0 90 (units of 1.0 0.5 0.0 60 30 o FR -0.5-5 -4-3 -2-1 0 1 2 3 4 5 f (MHz) 0 Co thickness: 70 nm, H i =0.1 koe 8
A concept of nonreciprocal multilayer with one-way transmittance, wide (unlimited) aperture, and omnidirectional isolation Forward propagating waves can pass through, while backward propagating waves are reflected back to space regardless of the direction of incidence. The presence of a metallic (conducting) magnetic layers is essential! Forward propagating wave Backward propagating wave
Transmission (db) TE wave transmission of (HL) 3 HCA(LH) 3 (oblique incidence) 0-20 -40-60 -80-100 7.5 8.0 8.5 9.0 Frequency (GHz) A: ε xx =ε yy =10, ε zz =2.5; µ xx =µ yy =1, µ zz =4 10
Transmission (db) TM wave transmission of (HL) 3 HCA(LH) 3 (oblique incidence) 0-20 -40-60 -80-100 7.5 8.0 8.5 9.0 Frequency (GHz) 11
Transmission (db) Backward TE transmission (isolation) of (HL) 3 HCA(HL) 3 H sandwiched between misaligned polarizers (oblique incidence) 0-20 -40-60 -80-100 7.5 8.0 8.5 9.0 Frequency (GHz) 12
Transmission (db) Backward TM transmission (isolation) of (HL) 3 HCA(HL) 3 H sandwiched between misaligned polarizers (oblique incidence) 0-20 -40-60 -80-100 7.5 8.0 8.5 9.0 Frequency (GHz) 13
Transmission (db) Backward TE-wave transmission of (HL) 3 HFA(HL) 3 H sandwiched between misaligned polarizers (oblique incidence). The absence of metallic layers results in isolation failure at oblique incidence! 0-20 -40-60 -80-100 7.5 8.0 8.5 9.0 Frequency (GHz) F: ε=12, σ=0 14
Transmission (db) Backward TM-wave transmission of (HL) 3 HFA(HL) 3 H sandwiched between misaligned polarizers (oblique incidence). The absence of metallic layers results in isolation failure at oblique incidence! 0-20 -40-60 -80-100 7.5 8.0 8.5 9.0 F: ε=12, σ=0 Frequency (GHz) 15
Frozen light and giant transmission resonance in optical waveguides Collaborators: R. Reano & J. Burr (Ohio State University) M. de Sterke & N. Gutman (University of Sydney, Australia) 16
EM waves with vanishing group velocity vg 0, at s ks. k 1. Dramatic increase in density of modes. 2. Qualitative changes in the eigenmode structure (can lead to the frozen mode regime). Examples of stationary points: - Regular band edge (RBE): - Stationary inflection point (SIP): - Degenerate band edge (DBE): k k, v k k 2 1/ 2 g g g g g k k v k k 3 2 2/3,. 0 0 g 0 0 k k v k k 4 3 3/ 4,. d d g d d. a) b) c) frequency RBE frequency SIP frequency DBE g 0 d wavenumber k wavenumber k wavenumber k Each stationary point is associated with slow light, but there are some fundamental differences between these three cases. 17
Frozen mode regime in a semi-infinite photonic crystal Semi-infinite photonic crystal Incident wave of frequency s Transmitted slow mode Reflected wave - What happens if the incident wave frequency is equal to that of slow mode with v g = 0? - Will the incident wave be converted into the slow mode inside the photonic crystal, or will it be reflected back to space? Let us see what happens if the slow mode is related to (1) RBE, (2) SIP, (3) DBE. 18
Summary of the case of a plane wave incident on a semi-infinite photonic crystal with slow mode. - The case of a Regular Band Edge: incident wave is reflected back to space without producing slow mode. - The case of a Stationary Inflection Point: incident wave is converted into the slow mode with huge diverging amplitude. - The case of a Degenerate Band Edge: incident wave is reflected back to space, but not before creating the frozen mode with huge diverging amplitude and vanishing energy flux. S I S R 19 Semi-infinite photonic crystal ST ω g ω 0 ω d k k k Regular Band Edge Stationary Inflection Point Degenerate Band Edge 19
The simplest periodic layered structure displaying a SIP (Figotin & Vitebskiy, Phys. Rev. B 67, 2003) In a unit cell L, there are three layers, one of which is magnetic. A 1 A 2 F A 1 A 2 F A 1 A 2 F A 1 A 2 F A 1 A 2 F X Z L L Y Anisotropic layers with misaligned in-plane anisotropy A 1 A 2 Y X 20
Can the frozen mode regime be realized in optics, where layered structures are not practical? - 2D and 3D photonic structures (Hui Cao and co-authors) - Periodic arrays of coupled optical resonators. - Periodic optical waveguides. This is, by far, the most attractive approach! It was pioneered by Martjin de Sterke, Nadav Gutman, and co-authors (University of Sydney, Australia). First experimental realization of the DBE structure has been done by Ronald Reano and Justin Burr (Ohio State University). Experimental results are yet to be finalized.
Introduction 22 Alternative platform: fiber based multimode waveguides N. Gutman et al., Slow and frozen light in optical waveguides with multiple gratings: DBEs and SIPs, PR A 85, 033804 (2012). Issues: (1) Non-planar and multimode; (2) analysis by coupled mode theory
Design 23 Silicon waveguide core, silicon dioxide waveguide cladding, 450 nm x 250 nm cross section
(norm.) (norm.) Transmission properties of finite structure 24 Finite structure - Periods: 65, gap: 50 nm, offset: 120 nm. Excitation is at both ports 1 and 3. Red lines correspond to condition 1, the excitation condition for maximum transmission. (α 2 = 0.5588, 2 = 0.4413, and = 89.46 o ) Blue lines correspond to condition 2, maximum reflection. (α 2 = 0.4413, 2 = 0.5588, and = 269.1 o ) (a) 1 (b) 1 cond. 1 cond. 2 0.5 cond. 1 cond. 2 0.5 0 1.508 1.51 1.512 l (mm) 0 1.508 1.51 1.512 l (mm) (a) Sum of the powers at ports 1 and 3; (b) Sum of the powers at ports 2 and 4. Near unit transmission at first resonance.
This work 25 We present a full three-dimensional design and analysis of coupled periodic dielectric optical waveguides that can exhibit a giant slow light resonance associated with a DBE. We show that coupled periodic dielectric waveguides can be designed to exhibit a DBE at optical telecommunications wavelengths in the silicon-on-insulator (SOI) material system. Analysis in SOI is chosen with a view towards implementation in silicon photonics. We show that the separation distance between the coupled waveguides is a critical design parameter to exploit the unique resonance properties of the DBE structure. The coupling of the resonance mode with the input light can be controlled continuously by varying the input power ratio between the two input arms and their relative phase difference. This allows to achieve a nearly perfect transmission efficiency of the slow wave structure and fully exploit the advantages of DBE-related resonance.
Transmission properties of finite structure 26 (a) (b) (c) (d) Finite structure - Periods: 65, gap: 50 nm, offset: 120 nm. Power input at port 1 denoted α 2 ; power input to port 3 is β 2 = 1-α 2 ; relative phase difference between ports 1 and 3 denoted with Φ; (a) Power at port 1; (b) Power at port 2; (c) Power at port 3; (d) Power at port 4.
Conclusions 27 We presented a full 3D design and analysis of coupled periodic dielectric optical waveguides Giant DBE-related transmission resonances at optical telecommunications wavelengths Material system is silicon-on-insulator material system Design enables continuous control of coupling between input light and resonance mode Transmission from zero to near unity by adjusting input power ratio and phase The proposed design can be implemented in silicon photonics J. Burr, N. Gutman, C. M. de Sterke, I. Vitebskiy, R. Reano, "Degenerate band edge resonances in coupled periodic silicon optical waveguides," Optics Express, in preparation.