Metamaterials - Concept and Applications Dr Vesna Crnojević-Bengin Faculty of Technical Sciences University of Novi Sad March 2006

Overview Microwave passive circuits Metamaterials LH metamaterials Definition Examples LH metamaterials Idea Phenomena Realization LH microstrip structures Resonant and non-resonant structures Applications

Microwave Passive Circuits Rationale

Problem Dimensions  Performances End-coupled ms resonator: Antennas: narrow beam with only one source element? Classical theory: large source Metamaterials: ENZ substrate

Antenna on ENZ Substrate

Characteristics Definition Types Examples Metamaterials Characteristics Definition Types Examples

Material Characteristics Rel. permitivity εr Rel. permeability μr Rel. index of refraction Rel. characteristic impedance

Extreme values of εr and μr Metamaterials: EVL – Epsilon Very Large ENZ – Epsilon Near Zero MVL – Mu Very Large MNZ – Mu Near Zero MENZ – Mu and Epsilon Near Zero HIMP – High Impedance LIMP – Low Impedance HIND – High Index LIND – Low Index μr εr

Definition Metamaterials are artificial structures that exhibit extreme values of effective εr i μr.

Example – HIMP and LIMP

Metamaterials Do Not Exist Artificial materials Periodic structures Period much smaller then λ  Homogenization of the structure  Effective values of εr and μr

Examples of Metamaterials

First Ideas Development Realization Applications Left-Handed MM First Ideas Development Realization Applications

Other Quadrants? μr εr Single-negative MM: εr<0 or μr<0 evanescent mode (plasma,metals@THz) propagation mode (isotropic dielectrics) εr evanescent mode (ferrites)

? Veselago’s Intuition μr εr Double-negative MM: εr<0 and μr<0 ? evanescent mode (plasma,metals@THz) propagation mode (isotropic dielectrics) εr ? evanescent mode (ferrites)

Conditions of Existence No law of physics prevents the existence of DN MM Generalized entropy conditions for dispersive media must be satisfied ( )

Veselago’s Conclusions Propagation constant β is real & negative  Propagation mode exists  Antiparalel group and phase velocities  Backward propagation (Left-hand rule)  Negative index of refraction

Synonyms Double-Negative (DN) Left-Handed (LH) Negative Refraction Index (NRI) (Metamaterials)

Left-Handed Metamaterials Double-negative MM: εr<0 and μr<0 μr evanescent mode (plasma,metals@THz) propagation mode (isotropic dielectrics) εr propagation mode (Left-Handed MM) evanescent mode (ferrites)

Apparent Paradox Group velocity increases with frequency  superluminal propagation ?!? Explanation: LH MM is a dispersive media, where: Pulse can be superluminally propagated Group velocity does not bear a well defined physical meaning Velocity relevant to energy propagation is not group velocity but front velocity, always smaller then c

Consequences of LH MM Phenomena of classical physics are reversed : Doppler effect Vavilov-Čerenkov radiation Snell’s law Lensing effect Goss-Henchen’s effect

Snell’s Law !!!

Lenses Direct consequence of reversed Snell’s law

But Alas... Everything so far was “what if”... Can single- or double-negative materials really be made?

First SN MM – J. B. Pendry εr<0 - 1996. μr<0 - 1999.

Why is r negative? Plasmons – phenomena of excitation in metals Resonance of electron gas (plasma) Plasmon produces a dielectric function of the form: Typically, fp is in the UV-range Pendry: fp=8.2GHz

Why is μr negative?

Experimental Validation Smith, Shultz, et al. 2000.

Resonant and non-resonant structures Applications LH MS Structures Resonant and non-resonant structures Applications

Resonant LH Structures Split Ring Resonator (SRR)  Very narrow LH-range  Small attenuation Many applications, papers, patents Super-compact ultra-wideband (narrowband) band pass filters Ferran Martin, Univ. Autonoma de Barcelona

Wide Stopband Garcia-Garcia et al, IEEE Trans. MTT, juni 2005.

Complementary SRR Application of Babinet principle - 2004. CSRR gives ε‹0

LH BPF – CSRR / Gap November 2004. Gaps contribute to μ‹0 Low attenuation in the right stopband

BPF – CSRR / Stub August 2005. 90% BW Not LH!!!

Three “Elements” CSRR/Gap – steep left side CSRR/Stub – steep right side 2% BW

Multiple SRRs and Spirals Crnojević-Bengin et al, 2006.

Fractal SRRs Crnojević-Bengin et al, 2006.

Non-Resonant LH Structures June 2002. Eleftheriades Caloz & Itoh Oliner Transmission Line (TL) approach Novel characteristics: Wide LH-range Decreased losses

Conventional (RH) TL Microstrip

LH TL Dual structure

!!! = A Very Simple Proof Materials: LH TL: Analogy between solutions of the Maxwell’s equations for homogenous media and waves propagating on an LH TL Materials: LH TL: = !!!

Microstrip Implementation Unit cell

Dispersion Diagrams RH TL LH TL

Is This Structure Purely LH? Unit cell

CRLH TL Real case – RH contribution always exists

LH TL Characteristics Wide LH-range Caloz, Itoh, IEEE AP-S i USNC/URSI Meeting, juni 2002.

2-D LH Metamaterials

Applications of LH MM Guided wave applications Filters Radiated wave applications Antennas Refracted wave applications Lenses

Guided Wave Applications Dual-band and enhanced-bandwidth components Couplers, phase shifters, power dividers, mixers) Arbitrary coupling-level impedance/phase couplers Multilayer super-compact structures Zeroth-order resonators with constant field distribution Lai, Caloz, Itoh, IEEE Microwave Magazin, sept. 2004.

Dual-Band CRLH Devices Second operating frequency: Odd-harmonic - conventional dual-band devices Arbitrary - dual-band systems Phase-response curve of the CRLH TL : DC offset – additional degree of freedom  Arbitrary pair of frequencies for dual-band operation Applications: Phase shifters, matching networks, baluns, etc.

Dual-Band BLC Lin, Caloz, Itoh, IMS’03. Conventional BLC operates at f and 3f RH TL replaced by CRLH TL  arbitrary second passband

CµS/CRLH DC Caloz, Itoh, MWCL, 2004. Conventional DC:  broad bandwidth (>25%)  loose coupling levels (<-10dB) CRLH DC:  53% bandwidth  coupling level −0.7dB

ZOR Sanada, Caloz, Itoh, APMC 2003. Operates at β=0 Resonance independent of the length Q-factor independent of the number of unit cells

SSSR Crnojević-Bengin, 2005. LZOR=λ/5 LSSSR=λ/16 Easier fabrication More robust to small changes of dimensions

Radiated Wave Applications 1-D i 2-D LW antennas and reflectors ZOR antenna, 2004. - reduced dimensions Backfire-to-Endfire LW Antenna Electronically controlled LW antenna CRLH antenna feeding network

Backfire-to-Endfire LW Antena Operates at its fundamental mode Less complex and more-efficient feeding structure Continuous scanning from backward (backfire) to forward (endfire) angles Able to radiate broadside Liu, Caloz, Itoh, Electron. Lett., 2000.

Electronically Controlled LW Antenna Frequency-independent LW antenna Capable of continuous scanning and beamwidth control Unit cell: CRLH with varactor diode β depends on diode voltage

Antenna Feeding Network Itoh et al, EuMC 2005.

Refracted Wave Applications Most promising Not much investigated - 2-D, 3-D Negative focusing at an RH–LH interface Anisotropic metasurfaces Parabolic refractors...

Current Research... Subwavelength focusing: Grbic, Eleftheriades, 2003, (Pendry 2000): NRI lense with εr=−1 and µr=−1 achieves focusing at an area smaller then λ2 Anisotropic CRLH metamaterials: Caloz, Itoh, 2003. PRI in one direction, NRI in the orthogonal Polarization selective antennas/reflectors

Future Applications Miniaturized devices based ZOR MM beam-forming structures Nonlinear MM devices for generation of ultrashort pulses for UWB systems Active MM - dual-band matching networks for PA, high-gain bandwidth distributed PA, distributed mixers Refracted-wave structures – compact flat lenses, near-field high-resolution imaging, exotic waveguides SN MM – ultrathin waveguides, flexible single-mode thick fibers, very thin cavity resonators Terahertz MMs – medical applications Natural LH MM – currently not known to exist SF MM - chemists, physicists, biologists, and engineers tailor materials missing in nature

Main Challenges Wideband 3-D isotropic LH meta-structure

Main Challenges Development of fabrication technologies (LTCC, MMIC, nanotechnologies) Development of nonmetallic LH structures for applications at optical frequencies Miniaturization of the unit cell Development of efficient numerical tools

“LH materials … one of the top ten scientific breakthroughs of 2003.” Conclusion “LH materials … one of the top ten scientific breakthroughs of 2003.” Science, vol.302, no.5653, 2004. “MMs have a huge potential and may represent one of the leading edges of tomorrow’s technology in high-frequency electronics.” Proc. of the IEEE, vol.93, no.10, Oct.2005.