Office of Naval Research

MURI Quarterly Report for

Sept. 1–Nov. 30, 2002

For Dr. Kathryn Wahl and Dr. V. Browning on

GRANT NUMBER: N00014-01-1-0803

DOD/ONR MURI

Scalable and Reconfigurable Metamaterials

Principle Investigator: Xiang Zhang Co-PIs: G. Chen, T. Itoh, E. Yablonovitch, J. D. Joannopoulos, J. Pendry,

D. Smith, and S. Schultz

University of California in Los Angeles

Engineering IV, 420 Westwood Plaza

Los Angeles, CA 90095-1597

Summary Based on the feedbacks from annual review and the program roadmap, metamaterials such as plasmon wires, bubbles have been fabricated and characterized. Studies have been also continued on the super lenses using photonic crystals, metal films and multilayers metal films, and on metallic metamaterial structures. Some new theoretical and experimental results have been obtained. Significant interactions and collaborative efforts have been made between team members and with collaborators outside the team for the metamaterial simulations and characterizations. Work in Progress: Meta-material synthesis Metameterials synthesis: High-aspect Ratio Magnetic Metastructures: Zhang’s group continued on developing synthesis approaches for magnetic metamaterials for THz applications. By using Tagushi method, a set of Design-of-Experiments (DOE) is devised to investigate the dependence of device performances on process variables (gap G, length L, width W, and spacing S). The first set of samples (as shown in Fig. 1) is now being characterized using FTIR with help of UCSD group.

L :le

ngth G: gapS: space

W: w

idth

Fig. 1: The synthesis of THz magnetic metamaterials. Left: Design layout of split-ring structures with critical parameters. Right: Example of synthesized split-ring lattice (fmp ~ 1 THz). High aspect-ratio microstructure is essential for a pronounced magnetic response at high frequencies. To meet this critical requirement, Xiang Zhang’s group has been developing a microfabrication process named Photo-Proliferated Lithography (PPL), as sketched in Fig. 2. In the proposed PPL process, the initial thin layer of electroplated patterns on quartz wafer is exposed from backside and the defined features shadow the unexposed region. It is followed by electroplating the new layer of mold and the process can be iterated until desired aspect ratio is achieved. With this promising synthesis approach, we expect to produce split-ring structures with gap down to 2 micron and height up to 40 micron.

Lithography to define split rings (trenches in photoresist)

Electroplating Ni and self- aligned lithography to define new layer

Iterating electroplating and lithography to achieve high aspect ratio

Removal of Photoresist mold and conductive seed layer

Fig. 2: The proposed Photo-Proliferated Lithography for synthesizing of high aspect-ratio THz magnetic metamaterials. All Angle Negative Refraction Gang Chen’s group has fabricated the structure for All Angle Negative Refraction (AANR) as proposed by Joannapoulos’ group. The material used for the structure is Magnesium Calcium Titanate (MCT), obtained from Trans-tech Inc. The dielectric constant of the material measured at 6GHz is 38 and the loss tangent is 0.0003. The details of the structure are shown in the figure below. The sample was sent to Prof. Schultz at UCSD for characterization.

TOP VIEW:

CROSS SECTION:

quartz

Ni

TOP VIEW:

CROSS SECTION:

quartz

Ni

TOP VIEW:

CROSS SECTION:

Quartz

Resist

Resist layer 2

Ni

TOP VIEW:

CROSS SECTION:

quartz

Resist

Fig. 3: Schematic diagram of structures and parameters fabricated for All Angle Negative Refraction (AANR). Relatively Low Temperature Thermo Photovoltaic Cell Metamaterials: Follow the strategy of metamaterial concepts, Gang Chen’s group finds that the properties of the radiation energy transfer of blackbodies can be dramatically modified by a proper configuration of materials. They have analyzed the radiation energy transfer between layered, closely spaced media using Greens functions method. The analysis includes both near field and wave effects, which classical radiation transport ignores. Using the above approach, they have studied the radiation energy transfer between two half planes of SiC separated by a thin layer of vacuum. They further investigated a structure, which has potential use for relatively low temperature thermophotovolatic cell. The structure consists of a semi-infinite plane of SiC acting as the emitter, a thin vacuum gap (for example, 800 nm), an intermediary SiC thin film, and finally an active layer of photovoltaic cell materials. They have also noticed that the energy transmitted to the active layer increases steadily with the thickness of intermediary SiC film up to a value of 300nm and then steadily falls. This effect is because of the surface phonon polaritons resonance existing in the whole structure, and through which radiations from the emitter are enhanced due to tunneling at all wavelengths. Two other materials, Boron Nitride and Boron Carbide, support surface polariton modes at frequencies slightly above SiC and well matched with InSb as the active PV layer. Analysis shows that as temperature of the emitter falls to about 800K, the optimum bandgap for maximum photon-current conversion also falls to about 0.2 - 0.3eV. Photonic Bubble Arrays Theoretical simulation has been performed to demonstrate the feasibility of controlling an n x n bubble array by only 2n inputs through time-division multiplexing approach. Because the mechanism of heterogeneous bubble initiation/growth needs to be carefully understood to attain the time constants of bubble generation and annihilation processes and stable bubble size before the device design and fabrication., the thermostatic equilibrium conditions for the bubble growth initiation and bubble growth rate theory for inertia controlled and heat diffusion controlled regions are being under intensively investigation.

Metallic Nanowire Optics Gang Chen’s group is also exploring the unique optical properties of metal nanowires based on the feedback from Dr. Pazik. Theoretical investigations show that metal nanowire can function as optical waveguides without any diameter limitation due to cylindrical surface polariton effects. We are collaborating with the Dresslhaus group to deposit nanowire arrays, and using the cylindrical surface polariton effects to image or duplicate nanowire arrays. A Ti:sapphire laser-based experimental setup has been established and improved.

Metamaterials Physics Study Perfect Cylindrical Lenses During this period, Pendry’s group has continued their work on focusing with curved surfaces. As mentioned in the previous quarterly report, the original perfect lens consisting of a slab of negative refractive material cannot magnify the size of the image. To change the magnification the lens must use curved surfaces to break the translational symmetry and change the wave-vector. We had earlier reported that a metallic cylindrical annulus would work as a near-field lens in the extreme near field limit (kx → ∞). This focussing property for a cylindrical annulus is shown to result for the Maxwell’s equations as well, provided the values of the dielectric constant (ε) and the magnetic permeability (µ) become specified functions of the spatial co-ordinates.

As has been said before, only the use of curved surfaces can change the magnification of the image. It is possible to make a perfect magnifying glass that acts on both the radiative and near-field components by using a cylindrical annulus whose dielectric and magnetic permeability tensors are specified functions of the spatial coordinates.

Ward and Pendry have shown earlier [A.J. Ward and J.B. Pendry, J. Mod. Optics. 43, 773 (1996)] that changing the geometry using a co-ordinate transformation amounts to changing the ε and µ in the system. Make a co-ordinate transformation

q1(x,y,z), q2(x,y,z) , q3(x,y,z) . (1)

where (q1, q2, q3) are the new co-ordinates. Assuming the transformation to be diagonal for simplicity and rewriting the Maxwell’s equations in the new co-ordinate system,

∇× E = −µ’ µ0 (∂H/∂t), ∇× H = ε’ ε0 (∂E/∂t) (2)

We find that the form of the Maxwell’s equations do not change. But the ε and µ in the new co-ordinate frame are given by

εj’ = εj (Q1Q2Q3 / Qi2) , µj’ = µj (Q1Q2Q3 / Qi

2) , (3) where

2 2 22i

i i i

x y zQq q q

∂ ∂ ∂= + + ∂ ∂ ∂

(4)

Ej = Qj Ej , Hj = Qj Hj . (5)

To show that a cylindrical annulus can act as a perfect lens, we make a co-ordinate transformation from the Cartesian slab geometry into cylindrical co-ordinates as follows:

x = r0 exp(l/l0) cosφ, y = r0 exp(l/l0) sinφ , z = roZ. (6)

In this new frame the transformed values of the ε and µ for the perfect lens solution turn out to be

2 202 20

1, 1, , ,

1, 1, ,

r r z z

r r z z

r r a r b

r r a r b

φ φ

φ φ

ε = µ = − ε = µ = − ε = µ = − < <

ε = µ = + ε = µ = + ε = µ = + > >

and the solution of the Maxwell’s equations is ( )0 expik

z z zH H r im ik z i t±φ= φ+ − ωl

where 2 2 2 2 2 2 2

0 0 0zk m r k r c−φ+ + = ωl

Thus, we have a perfect lens solution for a cylindrical geometry in the plane normal to the axis of the cylinders. We note that the ε and µ become functions of the spatial co-ordinates both inside and outside the annulus. However, if the electric field is everywhere perpendicular to the cylinder axis, εz is irrelevant and H is everywhere parallel to the cylinder axis. If, in addition, we neglect the magnetic field (electrostatic limit) µz is also irrelevant and therefore we retrieve our previous result obtained by conformal mapping of the slab geometry into the cylindrical geometry.

A

A

Fig. 4: Schematic for the magnification in the cylindrical annulus perfect lens

l

a

b

φ

+q

Fig.5: Schematic of the amplification of evanescent modes in the cylindrical lens

Simulation and Experimental Study on Optics of Plasmon and Superlens Imaging: Excitation of the rich degenerate states of surface plasmon on metamaterials offers the opportunity to access the deep sub-wavelength information using superlens. Following the work on the amplification of evanescent waves using superlens, Zhang’s group is devising a set of experiments in configuration and manipulation of plasmon optics and superlens imaging.

2 4 6 8 10 12 1410-2

10-1

100

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4

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Max(k

x /k0 )

Real(ε)

Real(εΜ)

-1.05 -1.01 -0.95

MTF

Spatial Resolution(1/λ)

Fig. 6. Preliminary simulation study predicts a resolution down to λ/6 achievable using thin Ag film by matching the plasmon resonance at interface.

Negative Metamaterials: In the previous quarter, UCSD had initiated an investigation into anisotropic negative index materials, termed indefinite media, which manifested interesting and unusual properties. In the coming quarter, UCSD will utilize their newly acquired prototyping capability to fabricate both isotropic negative index metamaterials and indefinite metamaterials to experimentally demonstrate the predicted properties. Photographs of a test split ring structure produced by the milling process are shown below. Such parameters as line widths and registration are on par with lithographically produced samples. Of particular utility is the ability to cut the circuit board material to allow assembly of the circuit board pieces into an egg-crate structure.

PR

Ag

Defect Engineering: Joannopoulos’ group has been continuing their studies of novel photonic crystal defect states as elements for building metamaterial structures at optical

Fig. 8 Snapshots of Magnetic and Electric field densities associated with a photonic crystal defect that possesses up to 98% oscillating magnetic multipole character. frequencies as described in the original proposal. In this regard they have calculated the magnetic and electric multipole contributions (vector spherical harmonics) to the radiation of a deliberately-designed defect state in a 3D photonic crystal that emulates the behavior of a single oscillating magnetic multipole even though there is no magnetic material involved with the structure. This defect state is shown in Fig. 8 and will eventually be investigated experimentally by the Schutz/Smith and Chen groups. They are also continuing our studies of negative refraction of electromagnetic waves in photonic crystal systems as interesting alternatives to the left handed materials that can

Fig. 9 A pulsed oscillating point-dipole on the top of a slab of 3D photonic crystal superlens passes through and is focused to an oscillating point image at the bottom. Top and bottom panels refer to two different cross sections are shown.

E

H

side side

top top

small medium large

Oscillating magnetic dipole Point defect in finite crystal

work both at microwave and optical frequencies. In a collaborative effort with Pendry, they have recently shown that single-beam negative refraction in photonic crystals is possible for all incoming angles in a regime of positive effective index of refraction. The frequency range is chosen so that for all incident angles, one obtains a single negative-refracted beam. They call this effect All-Angle Negative Refraction (AANR) and have determined the set of sufficient criteria for its observation. Moreover, we succeeded in designing and numerically simulating a photonic crystal micro-superlens in 2D. More recently, we have extended these ideas to 3D photonic crystal systems. To realize AANR in 3D, sufficient criteria are: 1. the frequency range be near a negative “photonic-mass” region; 2. the frequency range be below the diffraction threshhold; 3. the photonic-crystal constant-frequency contour be all-convex and larger than that of air; and 4. the symmetry of the photonic modes allow good coupling with incident wave. Clearly, this is only possible in the first few bands. A rough rule for determining the optimal geometric lattice for AANR is just to maximize the number N of nearest-neighbor reciprocal-lattice sites to a critical wavevector C. If AANR is to be realized in the fundamental (i.e. the first two) bands, then C is a corner of the first Brillouin zone. In this case, a simple-cubic (SC) reciprocal lattice with N = 8 should be used, resulting in a SC photonic crystal with (111) surface termination. If AANR is to be realized in the next higher bands, then C is a corner of the second Brillouin zone, which in most lattices is just G after translation by a reciprocal-lattice vector. This is the usual effective negative-index situation, and the Face-Centered Cubic (FCC) reciprocal lattice which has N = 12 should be chosen, giving a Body-Centered Cubic (BCC) structure in real space. To illustrate this phenomenon, we succeeded in designing and numerically simulating a BCC photonic crystal micro-superlens in 3D. The results are shown in Figure 8 for two different polarizations of the oscillating point dipole. We note that for the polarization on the right panels of Figure 8 a point image is formed on the other side of the lens while for the polarization on the left panels the image is reflected with essentially no transmission. Joannopoulos’ group is currently working with the Chen and Schultz/Smith groups to eventually fabricate this photonic crystal superlens and experimentally demonstrate its performance. Metallic Metamaterials Yablonovitch group’s primary research interest has been the conception and design of near-field optical structures that take advantage of surface plasmon excitation. The dispersion curve for a thin film of silver on a sapphire substrate is illustrated in Fig. 9 below as a function of film thickness. The dispersion curve clearly indicates that plasmons at ultraviolet frequencies (E ~ 3 eV) possess wavelengths corresponding to free x-rays (p ~ 100 eV/c). Surface plasmons are thus excitations that can be used to resolve features below the far-field limit of optical radiation; it is the resonance of surface plasmons in thin films that the perfect lens for the near-field utilizes. We expect that other lens structures with greater functionality can take advantage of the very short wavelength of surface plasmons, and we are working towards the design of such structures.

Fig.10 – Dispersion relation for the symmetric surface plasmon supported by a thin silver film coating of a sapphire substrate. The film thickness determines the coupling of plasmons on opposite surfaces, thus influencing the symmetric plasmon dispersion. Their collaborative effort has focused on discussions of a theoretical nature with Prof. Pendry. A product of this discourse was the notion that surface plasmon dispersion can be tuned through precise control of the metal film thickness supporting the plasmon modes. Further discussions have elucidated other factors that must be considered in thin film structure design, in particular heat dissipation and film thickness tolerances are of critical import. Metamaterials Characterization: UCSD has now acquired (via a separate ONR grant) a milling machine capable of producing prototype ring/wire based metamaterials that are being utilized as negative refractive index materials. The numerically controlled precision milling machine (LPKF, Oregon), shown in the photographs below, can produce small quantities of circuit-board based metamaterials, suitable for testing in our 2-D apparatus.

UCSD (Schultz, Smith and Dimitri Basov) and UCLA continued on collaboration in designing and characterizing higher frequency (THz) metamaterial structures. Metamaterials Devices Itoh’s group has developed a considerable number of novel components, antennas and structures bases on the transmission line approach of LH materials. A few of them are described below.

A. Coupled-Line Coupler with Arbitrary Coupling

Combining a LH-TL with a conventional RH-TL into a coupled-line coupler has lead to a backward coupler operating as an (enhanced) forward coupler (coupling increasing with the electrical length le). This coupler is capable of virtually any loose/tight coupling level, as illustrated in Fig. 1, where 0-dB coupling is achieved over more than 35% bandwidth. Coupling rapidly increases to reach 0-dB as frequency is decreased below f0 because le increases when ω decreases (le= l/λ ∝ 1/ω) in the LH range. A symmetric (quadrature) LH/LH coupler, providing similar performances was also investigated, and observed to be based on both magnetic and electric coupling phenomena, very different from those occurring conventional couplers.

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7frequency (GHz)

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eter

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CRLH-TL

RH-TLSSβ

β

( )0

0

3.9e

f GHzf

== ∞l

e Cλ= ↑l le Cλ= ↑l lLH RH

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7frequency (GHz)

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CRLH-TL

RH-TLSSβ

β

( )0

0

3.9e

f GHzf

== ∞l

e Cλ= ↑l le Cλ= ↑l lLH RH

Fig. 12 Measured performances of the RH-LH quasi-0-dB coupled-line backward coupler with spacing s=0.3mm (s/h=0.19). The transition frequency is f0=3.9 GHz. β and S represent the propagation constant and the Poynting vector, respectively, in each of the two lines. The same s/h provides less then -10-dB coupling in the conventional case.

B. Dual-Band Non-harmonic Branch-Line Coupler The conventional branch-line coupler is characterized by the periodic repetition of its

spectrum at odd harmonics of the design frequency. Replacing the branches-lines by CRLH-TLs, as shown in the prototype of Fig. 13 increases the versatility of the component by making two arbitrary operating frequencies available. The underlying principle can be understood from the additional degree of freedom provided by the DC-offset due to the LH contribution allows an arbitrary pair of frequencies (at 90º and 270º) to be intercepted by the phase curve of the CRLH-TL. The performances of the fabricated component are shown in Fig. 13.

0.6 0.8 1 1.2 1.4 1.6 1.8 2frequency (GHz)

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eter

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LE-LHTLs

0Z 0Z0

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0.6 0.8 1 1.2 1.4 1.6 1.8 2frequency (GHz)

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eter

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LE-LHTLs

0Z 0Z0

2Z

0

2Z

LE-LHTLs

0Z 0Z0

2Z

0

2Z

Fig. 13 Measured performances of the dual-band inharmonic branch-line coupler. The design frequencies are 920 MHz and 1740 MHz, respectively.

C. Negative “Reflective/Refractive” Phase-Conjugating Antenna Array Meta-Interface The concept of “meta-interface”, concentrating RH/LH interface effects within a thin

interface and thereby avoiding losses and dispersion inherent to an artificial LH-MM, is approached in the negative “reflection/refraction” structure described in Fig. 14. The incident (RF) wave is reflected (IF) backward to the source after phase-conjugation (phase inversion of incoming RF with LO-freq = 2× RF-freq at each element) realized by Schottky diode mixers, which may be interpreted as negative reflection. More interestingly, half of the IF signal is re-radiated on the other side of the substrate with a negative-refractive-like angle due to the use of bidirectional slot antenna elements. These effects are illustrated in Fig. 14 for the case of a 30º incoming angle. Near-field focusing effects were also observed.

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rθ

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tθRF-in

5.2 GHz

IF-out 15.22 GHz

IF-out 25.22 GHz

LO=10.42 GHz

r iθ θ=tθ

sindϕ β θ−

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ϕϕ−

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rθ

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IF-out 15.22 GHz

IF-out 25.22 GHz

LO=10.42 GHz

r iθ θ=tθ

sindϕ β θ−

sindϕ β θ+

ϕϕ−

sindϕ β θ− +

sindϕ β θ− −

Fig. 14 Working principle and measured far-field patterns of the negative reflection/refraction phase-conjugating meta-interface

Work Planned for Next Quarter Metamaterial Synthesis o Continue on metallization and molding development o Continue on optimizing microstereolithography system o Continue developing nanofabrication for metamaterials: near-field based lithography

and two photon nano-fabrication o Developing NSOM (near field scanning optical microscopy) for optical diagnostics of

local density of state (LDOS) of metamaterials o Demonstrate working tunable plasmonic filters in 1-2 THz o Chen’s group will collaborate with UCSD on analysis and characterization the

fabricated AANR samples. o The materials issues concerning InSb and the other materials being proposed will be

looked into. Also Chen’s group will look into suppressing some of the radiation at the unwanted wavelengths in order to increase the efficiency of the photovolatic cell.

o After examining the heterogeneous bubble initiation/growth theory, Chen’s group

plans to move on with the device design and fabrication. The basic experimental set up for the thermal bubble generation and observation is expected to be finished during this period.

o Chen’s group will carry out the fundamental experiment on nanowire waveguides to

find out the optimal conditions for coupling the laser light into metal nanowires. Metamaterial Physics and Characterization: o UCSD has now acquired (via a separate ONR grant) a milling machine capable of

producing prototype ring/wire based metamaterials that are being utilized as negative refractive index materials. The numerically controlled precision milling machine (LPKF, Oregon), shown in the photographs below, can produce small quantities of circuit-board based metamaterials, suitable for testing in our 2-D apparatus.

o MIT Joannopoulos’ group will continue working with the Chen and Schultz/Smith

groups to eventually fabricate this photonic crystal superlens and experimentally demonstrate its performance.

o Eli Yablonovitch group at UCLA expects that other lens structures with greater

functionality can take advantage of the very short wavelength of surface plasmons, and they will work towards the design of such structures.

Metamaterial Devices The current efforts will be pursued and a number of new potential directions will be explored in the coming months. These are mainly divided into three categories o Components: backward coupled-line couplers, broad-band multi-band hybrids, broad-

band baluns, predistorters for filters and active devices, pulse compressors for radar applications, combination of LHs and ferrites for slow-wave structures

o Antennas: fundamental mode leaky-wave antenna, passive and active, single-element

reflectodirective LH antenna o Structures: passive impedance surfaces exhibiting LH behaviors with possible

implementation in LTCC technology, development of negative reflection/refraction concept and application, exploration of novel effects in 2D TL structures

Synergy and Interactions: UCSD has continued and expanded its collaboration with the UCLA group on terahertz structures, providing characterization of various wire and split ring lithographic structures fabricated by UCLA. As part of this collaboration, graduate students and postdocs from UCLA have made numerous trips to work at the UCSD facilities, sometimes staying for several days. UCSD has also continued work with MIT, providing assistance in designing an all-angle negative refraction PBG sample for characterization in the UCSD 2-D scattering chamber. A PBG sample has now been produced by MIT and received at UCSD, and will be measured in the upcoming quarter. Chen’s student, Arvind Narayanaswamy, is working with Joannapoulos’ student on all angle negative refraction. Mr. Narayanaswamy is also co-supervised by Joannapoulos. The Chen group is also working with the Dresselhaus group at MIT on plasmonic effects in nanowire arrays.

Eli’s collaborative effort has focused on discussions of a theoretical nature with Prof. Pendry. A product of this discourse was the notion that surface plasmon dispersion can be tuned through precise control of the metal film thickness supporting the plasmon modes. Further discussions have elucidated other factors that must be considered in thin film structure design, in particular heat dissipation and film thickness tolerances are of critical import.

John Pendry has been collaborating with the MIT group on two problems. In the first, the problem of sub-wavelength imaging using the negative refractive effect with photonic crystals was examined. It was noted that the existence of photonic states bound to the lens surface was the key to the amplification of the evanescent waves and negative refractive index is not essential to the perfect lens problem. The photonic crystal imposes a natural

cut-off to the maximum transverse wave vector for which there is amplification and this is when the transverse wave vector becomes comparable to the underlying Bragg vector due to the periodicity of the crystal. In the second, the possibility of designing synthetic magnetic media that emit radiation with a purely magnetic character has been explored. By identifying point defect modes in a 3D photonic crystal whose local field pattern resembles an oscillating magnetic moment, it is shown that modes can be designed with a primarily magnetic multipole character in the far field: over 98% of the emitted power goes into magnetic multipole radiation. It should be noted that these photonic crystals that exhibit magnetic properties have completely non-magnetic constituents and can be designed to operate without losses even at optical frequencies unlike natural paramagnetic and ferromagnetic media. Further, John Pendry will be visiting the UCSD group in March and April 2003 for collaborative studies. Zhang’s group presenting synthesis of Metamaterials on ASME IMECE 2002 conference, nanotechnology track