Artificial meta-materials with periodically modulated dielectric constant (periodicity in optical properties, lattice constant light

wavelength)

“Periodic electromagnetic media”

PHOTONIC CRYSTALS

http://www.nanoscribe.de/

Novotny §11

Artificial meta-materials with periodically modulated dielectric constant (periodicity in optical properties, lattice constant light

wavelength)

“Periodic electromagnetic media”with photonic bandgap: optical insulators

Photonic crystals are kind of “oven mitts” for holding and manipulating light!

(e.g., light can be guided along curved paths, tight corners etc.)

PHOTONIC CRYSTALS

Three-dimensional Si photonic crystal

Y. A. Vlasov et al., Nature 414, 289 (2001) S.-Y. Lin et al., Nature 394, 251 (1998)

PHOTONIC CRYSTALS

Two-dimensional arrays of high refractive index structures can be fabricated using a combination of e-beam lithography for pattern definition and electrochemical deposition for structure formation. The potential of this method is demonstrated for CdSe, where (a) mushrooms, (b) nanopillars, (c) walls, and (d) crosses are prepared. Such arrays have potential in optical device applications such as photonic crystals and waveguides. [Advanced Materials, 15, 49 (2003)]

PHOTONIC CRYSTALS

Summary of general theory for band calculation(Schrödinger-like equation)

See a simplified 1-D exerciseIn Novotny-Hecht §11

c

Mode profiles, dispersion and photonic bangap

Higher frequency mode is localized in the medium with lower dielectric constant (e.g., air)and vice versa.

Relevance of theratio between the 2dielectric constants

1-D

2-D System

Applications1. Limit/Enhance spontaneous emission in new-generation

LASER devices

2. Light guiding around tight corners (ultra compact optics, invisible cloak)

3. High Q resonators (optical filtering, switching, sensor, antennas)

4. Refractive optics (negative refraction index, superlenses)

5. Time delay, dispersion control (control of the signal speed)

6. Optical PC fibers

7. Light circuits (optical-logic devices)Dielectric metameterial + Plasmonic coverJ. C. Soric et al (corr. auth. Andrea Alù) (Texas Univ.)New Journal of Physics 15, (2013) 033037

PHOTONIC CRYSTALS

2D Silicon photonic crystal waveguide bend

Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)

Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)

2D Silicon photonic crystal waveguide bend

Silicon-on-insulator (SOI)

Si

SiO2

Si neff 1.7

n 1.5

SiSiO2

Photonic waveguides

PHOTONIC CRYSTALSA brief overview

Lenk et al., Physics Rep. 517, 107 (2011)

Electromagnetic waves in a medium with index of refraction n: at n 500 THz, speed v=c/n108 m/s l=v/n 10-4 m (e.g. 200nm, nanoparticles: Photonics) at n 1 GHz, speed v=c/n108 m/s l=v/n 0.1 m (usually a few cm, macroscopic world…)

e.m. waves and nanotechnology meet at extremely high frequencies (visible light)but definitely not at ordinary computer clock frequencies.

Is there any physical entity which meets nanotechnology at computer clock frequencies?Yes: SPIN WAVES.Why?Because their propagation velocity ( km/s) is extremely lower than the speed of light.In this way, SPIN WAVES have wavelengths comparable with nanometric sizes of nanoelements,and can be manipulated by Bragg diffraction, for example, across a lattice of nanomagnets.

What are SPIN WAVES?They are coherent collective spin oscillations due to the joint precession of magnetic moments,under the action of some magnetic field.Hence, they represent collective excitations of MAGNETIC SYSTEMS.

CONSIDERATIONS

FERROMAGNETISM: ORIGINS1. Fe, Co, Ni, Gd: FM originates from free electrons deriving from

3d, 5d internal shells, only partially occupied by electrons

2. Narrow energy bands (low atomic interaction: ); (a: lattice const)

3. Indistinguishability among electrons of a same band: the low-energy (spontaneous) spin configuration occurs at maximum spin multiplicity (kind of an extension of the atomic Hund rule);

4. “Exchange” interactions: introduced to account for the intrinsic, quantum statistical tendency of spins to align; short-range interaction, and order;

5. “Macrospin” formation, regions where spin (and magnetic moments) are fully aligned, size (Ms satur. magn., A exchange stiffness constant: material-dependent parameters);

6. Dipolar (demagnetizing) interactions : long-range interaction, tendency of magnetic moments to be antiparallel (favoring a long-range magnetic disorder);

7. Thermal energy: typically favors disorder (at any distance range).

5.1R2/a

3d

20

2

sex M

A

l

H

M

Hysteresis loop

Hcoerc

Magnetic domains and hysteresis loops

Domain wall rotations and shifts until saturation

Hext = 0

Hext

Mresudual

saturation: Ms

1. Loop areaenergy2. soft/hard3. memories

Magnetization M is thevolume density of

magnetic momentswith an orientation

Bloch domain wall

Neél domain wall

Domain walls

Experimental techniques

Magnetic forcemicroscope

Kerr effect Spectroscopy:

Light polarizationdirection is shifted by reflection against a magnetic surface

”Kerr loops” are a measurement of the hysteresis loops

Spin waves

Coherent collective spin oscillations due to the joint precession of magnetic moments1. Formerly, only background noise in reading/writing MRAM processes.2. Up to date: “Information carriers” in magnonic crystal devices acting as waveguides.

SWs do not involve charge motion, hence energy (Ohm) losses are extremely low:Magnonic crystals are hence ideal candidates for dissipation-less device technology

Landau-Lifshits equation describing a damped precession motionHeff=H0+Hdip+Hex+Hanis

Magnonic Crystals•Magnonic Crystals (MCs) are a new class of metamaterials with periodically modulated magnetic properties. They are promising candidates for waveguides and memories.•In MCs, the information carriers are spin waves, (SWs). Being these waves within the GHz frequency regime, their wavelengths are comparable to the (submicrometric) dimensions of MC constituents.• Spin wave dispersion and nonzero bandwidth is determined by inter-dot interaction, which is mainly dipolar. The dispersion and bandwidth of the modes is influenced by the underlying magnetic configuration.•Slight changes of an applied magnetic field can modify magnon bandwidth and propagation properties (tunable magnetic filters); •E.g., in the same device the information carrier speed can be slowed down to zero, turning a waveguide into a memory.

0 100 200 300 400 500 6006

8

10

12

Freq

uenc

y (G

Hz)

Separation (nm)

EM

1-DE

F

1-BA

array of anti-dotsarray of dots

Group velocity:vg=dw/dk

Magnonic Spin-Logic Devices

Simple 1-D waveguide

Complex 4-input gate

Magnonic Spin-Logic DevicesYIG waveguide

Magnonic Spin-Logic Devices

– Theory

• Measurements

1st Brillouin zone.

In hexagonal 2D structures

equivalent modes in equivalent scattering

geometries give different dispersion

relations!

Frequency pass-band and propagation speed are tunable by a magnetic fieldApplications: tunable filters, versatile devices like waveguides turning into memories etc.