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TECHNICAL NOTEBOOK I back to basics

BACK TO BASICS: History of photonic and

Costas M. SOUKOULIS 1,2 We will review the history of photonic crystals and overview 1 Ames Laboratory and Department of Physics, Iowa State University, of the theoretical and experimental efforts in obtaining a Ames, Iowa, USA photonic bandgap, a frequency band in three-dimensional 2 Institute of Electronic Structure structures in which electromagnetic (EM) waves & Laser (IESL), FORTH, are forbidden, is presented. Many experimental groups Heraklion, Crete, Greece [email protected] all over the world still employ this woodpile structure to fabricate PCs at optical , , enhance nanocavities, and produce nanolasers with a low threshold limit. We have been focused on a new class of materials, the so-called metamaterials (MMs) or negative-index materials, which exhibit highly unusual electromagnetic properties and hold promise for new device applications. Metamaterials can be designed to exhibit both electric and magnetic resonances that can be separately tuned to occur in frequency bands from megahertz to terahertz frequencies, and hope-fully to the visible region of the EM spectrum.

ovel artificial materials (pho- However, many serious obstacles must at the same time, are easier to fabri- tonic crystals (PCs), MMs, be overcome before the impressive pos- cate (see Fig. 1). We thus modified the Nnonlinear optical MMs, op- sibilities of MMs, especially in the op- tical MMs containing gain media, tical regime, become real applications. , chiral optical MMs and plasmonics) enable the realization of innovative electromagnetic (EM) properties unattainable in naturally History of photonic existing materials. These materials, crystals: from characterized here as MMs, have been to woodpile structures in the foreground of scientific interest Shortly after the introduction of the in the last ten years. There has been a concept of photonic band-gap (PBG) truly amazing amount of innovation materials [1,2], our group at Iowa during the last few years and more is State/Ames Lab discovered the first yet to come. Clearly, the field of PCs diamond PBG structure that can exhi- and MMs can develop breaking tech- bit a complete 3D photonic gap [1,2]. nologies for a plethora of applications, Complete gaps were found in the two where control over is a prominent diamond structures. However, this dia- ingredient – among them telecommu- mond dielectric structure is not easy Figure 1. A “ball and the stick” model of the diamond structure, viewed from an nications, solar energy harvesting, bio- to fabricate, especially at the micron angle such that the channels along a [110] logical and THz imaging and sensing, and submicron length for or direction are observable. Shrinking the size optical isolators, nanolasers, quantum optical devices. Therefore, it is impor- of the “balls”, while keeping the “sticks” emitters, wave sensors, switching and tant to find new periodic structures and “3-cylinder” diamond structure with “air-cylinder”. , and medical diagnostics. that possess full photonic gaps, but,

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bandgaps. Many experimental groups around the world still use the woodpile structure to fabricate photonic crystals at optical wavelengths. These designs have been instrumental in bringing forward the revolutionary fields of pho- tonic crystals [1-2], negative , and metamaterials [4-5], extending the  Figure 3. Short rods in the diamond realm of electromagnetics while ope- structure are replaced by an equivalent ning exciting new applications. large horizontal rod, which is a layer-by- layer structure or woodpile structure [1].  Figure 2. Rod connected diamond History of metamaterials: structure with rods colored along the from microwaves vertical direction. to structures diamond structure to obtain other infrared wavelengths. Structures made Microwave metamaterials photonic structures easier to by advanced processing [3] and fabricate—hence, the introduction wafer fusion techniques operate at Our group at Armes Lab demonstrated of a layer-by-layer (or woodpile) ver- near-infrared wavelengths. It also was negative properly designed sion of diamond. Figure 2 shows the fabricated by direct laser writing to ope- PCs in the microwave regime and rod-connected diamond structure rate at infrared and near-infrared wave- also demonstrated sub- with rods colored along the [100] ver- lengths. Inverse woodpile PCs made resolution of λ/3. We fabricated a tical direction. Figure 3 presents the from silicon by CMOS-compatible left-handed material (LHM) with the woodpile design – short rods in the deep reactive-ion etching were the first highest negative-index transmission diamond structure are replaced by an nanostructures to reveal spontaneous peak corresponding to a loss of only equivalent large horizontal rod. emission inhibition. In another ap- 0.3 dB/cm at 4 GHz frequencies. We The layer-by-layer (woodpile) struc- proach, “3-cylinder” photonic crystals established that split-ring resonators ture was first fabricated in the mi- were fabricated by a deep X- litho- (SRR) also have a resonant electric res- crowave regime by stacking alumina graphy technique in polymers (see Fig. ponse, in addition to their magnetic cylinders that demonstrated a full 5) and the transmission spectra show a response. The SRR electric response is 3D photonic bandgap at 12-14 GHz. 3D photonic bandgap centered at 125 cut-wire like and can be demonstrated We fabricated this woodpile structure µm (2.4 THz) in good agreement with by closing the gaps of the SRRs, thus and demonstrated a full 3D photonic theoretical calculations. destroying the magnetic response. We bandgap at 100 and 500 GHz. The These photonic crystal designs (dia- studied both theoretically and experi- woodpile structure was then fabri- mond lattice [1,2] and the woodpile mentally the transmission properties cated by microelectronic fabrication structure [3], respectively) provided of a lattice of SRRs for different inci- technology (see Fig. 4) and operated at the largest completed 3D photonic dent polarizations.

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magnetic-dipole resonance via the magnetic field of the light and via the . The latter can be ac- complished under normal incidence of light with respect to the substrate – which was much easier for these ear- ly experiments. We varied the lattice constant, opened and closed the slit and thereby unambiguously showed the presence of the predicted magnetic resonance at around 100 THz frequen- Figure 4. -microscope cies, equivalent to 3 µm wavelength [4]. image of a “woodpile” photonic crystal made by silicon with a Figure 5. The “three-cylinder” photonic crystal We published our experimental re- complete at 12 µm [1]. made from negative tone resist [1]. sults on miniaturized gold SRR arrays, which showed a magnetic resonance at We showed that as one decreases the and can be easily measured for perpen- twice the frequency, i.e., at around 200 size of the SRR, the scaling breaks down dicular propagation. A simple unifying THz, equivalent to 1.5 µm wavelength and the operation frequency saturates at circuit approach offered clear intuitive [4]. By experiments performed under some value. We will come back to this as well as quantitative guidance for the oblique incidence of light, again loosely important point below. We suggested design and optimization of negative-in- speaking, we not only coupled to the a new 3D left-handed material design dex optical metamaterials SRR via the electric field of light, but that gives an isotropic negative index of also via its magnetic field. Only this refraction. This design has not been fa- Optical metamaterials coupling can be mapped onto an effec- bricated yet. We introduced new designs tively negative magnetic permeability. that were fabricated and tested at GHz In the optical transmission expe- We reached the limit of size scaling frequencies. These new designs were very riments on very small samples, we by further miniaturized SRRs (see useful in fabricating negative-index ma- took advantage of the fact that, loo- Fig. 6). Thus, the LC frequency should terials at THz and optical wavelengths sely speaking, one can couple to the also scale inversely proportional to size.

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Figure 6. The operation frequency of magnetic metamaterials increased rapidly. The structures operating at 1, 6 and 100 THz frequency, respectively, were fabricated in 2004, and the one at 200 THz in 2005.

It does not though. At frequencies hi- bringing one close to the edge of vali- gher than the damping rate, the elec- dity of describing these structures by trons in the metal develop a 90-degrees using effective material parameters. phase lag with respect to the driving elec- Nevertheless, our optical experiments tric field of the light. Our work showed and the retrieval of effective parameters that this limit is reached at around 900 suggested the possibility of obtaining a nm eigenwavelength – unfortunately negative magnetic permeability – even just outside of the visible regime. under normal incidence of light with Despite of this saturation, reducing respect to the substrate (see Fig. 7). the capacitance of the SRR can further We also investigated the optical increase the frequency. In this fashion, properties of these double-fishnet one gets a continuous transition optical metamaterials under oblique between a traditional SRR and a pair of incidence of light and for different cut wires [4,5]. Of course, this frequency polarizations. We found an angular increase at fixed SRR side length comes , which can be interpreted with a price: It also means that the ratio in terms of spatial dispersion due to of operation wavelength and size of the interaction among the different unit resonating object decreases significantly, cells (see Fig. 8).

Figure 7. Fabrication progress of negative index materials vs year. This figure is taken from the article in Nature 5, 523 (2011) written by Soukoulis and Wegener [4].

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These structures operating at around 1.5 µm wavelength were based on gold as metal. Soon thereafter, we could reproduce the same effects at comparable wavelength at much lower damping by using instead of gold.

Optical metamaterials containing gain media Our experimental efforts to bring gain Figure 8. 3D Photonic-Metamaterials Structures. This figure is taken from the article in media into close proximity of SRR ar- Nature Photonics 5, 523 (2011) written by Soukoulis and Wegener [4]. rays operating around 1.5 µm wavelen- gth to compensate for these losses were perpendicular to the plane of the me- (negative, unexpected, and/or posi- motivated by our own early theoretical tamaterial layer. Three different gain tive). Our approach verified that the work suggesting this approach might pumping schemes were applied in coupling between the work. However, our efforts over several the simulations and the efficiencies resonance and the gain medium is years based on using thin semiconduc- of their corresponding loss compen- dominated by near-field interactions. tor films as gain media in the near field sations were studied by investigating Our model can be used to design new of the SRR were not successful. The the line width of the resonant current. pump-probe experiments to compen- experiments did show some loss re- We have also studied the effect of the sate for the losses of metamaterials. duction, with line shapes in agreement background dielectric of gain. with theory, but the beneficial effects We have introduced an approach Graphene for THz were not large enough at the end of for pump-probe simulations of me- applications the day. Thus, we eventually gave up tallic metamaterials coupled to gain working in this direction. materials. We study the coupling Graphene – a one-atom-thick conti- Nevertheless, we studied loss com- between the U-shaped SRRs and the nuous sheet of carbon atoms – has pensation of SRR structures with a gain material described by a four-level special properties (e.g., electric and gain layer underneath in quite some gain model. Using pump-probe simu- chemical tunability, high kinetic induc- detail theoretically. Numerical re- lations, we find a distinct behavior for tivity allowing for strongly confined sults showed that the gain layer could the differential transmittance ∆T�/T� plasmons, large THz optical conduc- compensate the losses of the SRR, of the probe pulse with and without tivity) that make it a desirable mate- for light propagating parallel and SRRs in both magnitude and sign rial for manipulating terahertz waves.

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Experiments and theory were in good agreement.

Conclusion 3D printing benefits from metamate- rials and vice versa. By this combina- tion, printing of thousands of different effective material properties may beco- me accessible by using only a few ingre- dient material cartridges – in analogy to printing thousands of different from just three cartridges in to- day’s 2D graphical printers. Today, many fundamental metama- terial effects have been demonstrated experimentally in microwaves, optics, thermodynamics, mechanics, and transport. Most scientifically fascina- ting to the authors are sign reversals of Figure 9. 3D Chiral Metamaterials. This figure is taken from the article inNature Photonics 5, effective material parameters and the 523 (2011) written by Soukoulis and Wegener [4]. possibility of cloaking in all of these areas. Sign reversal has been shown for THz applications operate at frequencies Chiral optical the magnetic permeability, refractive between microwave and far infrared. metamaterials index, dynamic mass density, diffe- Some metamaterials could benefit by rential mechanical stiffness, thermal replacing the metals currently used in At this point we reminded ourselves length-expansion coefficient, and the fabrication with graphene. Graphene that optical activity and circular di- Hall coefficient. also offers the advantage of a potential chroism can be explained by using enhancement of terahertz wave confine- magnetic-dipole resonances excited ment [6] and smaller, more sub-wavelen- by the electric-field of the light and Acknowledgements gth metamaterial resonators made from vice versa. This fact is related to bi-ani- The work at Ames Laboratory graphene rather than metals. However, sotropy (see Fig. 9). was partially supported by the US as we pointed out in our analysis of pu- Our early work in this direction Department of Energy (Basic Energy blished experimental measurements of used SRR or variations thereof ar- Science, Division of Materials Sciences the THz optical conductivity of graphe- ranged into single or different layers. and Engineering) under Contract ne, the experimental data have shown These samples were fabricated by No. DE-AC02-07CH11358 Work significantly higher electrical losses at using electron-beam lithography of at FORTH was supported by the THz frequencies than have been esti- several aligned layers. This led to very European Research Council under mated by theoretical work or have been large circular birefringence effects the ERC Advanced Grant No. 320081 assumed in mostly very optimistic nu- at negligible linear birefringence. (PHOTOMETA). n merical simulations, showing that more research needs to be done to make meta- FURTHER READING material devices from graphene. We also [1] J.P. Markos and C.M. Soukoulis, Wave Propagation: From to Photonic Crystals and Left- published an analysis and comparison Handed Materials (Princeton, New Jersey, 2008) of gold- and graphene-based resonator [2] C.M. Soukoulis, Bending Back Light: The Science of Negative Index Materials. Opt. and Phot. nanostructures for THz metamaterials News, June 2006, 16 (2006) and an ultrathin graphene-based mo- [3] C.M. Soukoulis, M. Kafesaki and E.N. Economou, Negative index materials: New frontiers in dulator. Metamaterial resonators and optics. Adv. Mater. 18, 1941 (2006) plasmonic applications have different [4] C.M. Soukoulis and M. Wegener, Past Achievements and future challenges in the develop- requirements for what can be conside- ment of 3D photonic metamaterials. Nature Photon. 5, 523 (2011) red a good conductor. We published [5] P. Tassin, T. Koschny, M. Kafesaki and C.M. Soukoulis, A comparison of graphene, superconduc- a systematic comparison of graphene, tors and metals as conductors for metamaterials and plasmonics. Nature Photon. 6, 259 (2012) superconductors, and metals as conduc- [6] P. Tassin, T. Koschny and C.M. Soukoulis, Graphene for terahertz applications. Science 341, ting elements in either metamaterials or 620 (2013) plasmonics [6].

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