Negative Index Materials Reverse the Optical Doppler Effect

(Top L to R) Jiabi Chen, Yan Wang, Baohua Jia, Tao Geng; (Bottom L to R) Xiangping Li, Bingming Liang, Min Gu, and Songlin Zhuang

Authors: Jiabi Chen¹, Yan Wang^1,2, Baohua Jia³, Tao Geng¹, Xiangping Li³, Lie Feng¹, Wei Qian¹, Bingming Liang¹, Xuanxiong Zhang¹, Min Gu³, and Songlin Zhuang¹

Affiliation:
¹Shanghai Key Lab of Contemporary Optical System, Optical Electronic Information and Computer Engineering College, University of Shanghai for Science and Technology, China，
²College of physics and communication electronics, Jiangxi Normal University, China，
³Center for Micro-Photonics and CUDOS, Swinburne University of Technology, Australia

In the past couple of decades, we have witnessed a dramatic boost of the nanofabrication technology. As a result, man-made nanostructures and nanomaterials showing optical properties -- that have never been available naturally before -- came forth. Among these artificial materials, negative index materials have been intensively researched. The driving force for this is, on one hand, due to the potential fascinating applications of negative index materials in super-resolution perfect lens imaging, invisible cloaking and optical communications. On the other hand, it also originates from the curiosity to see the possibility to completely subvert the fundamental physics rules that we learned at school.

In the recent Nature Photonics paper published on March 7 [1], our team at University of Shanghai for Science and Technology in China together with collaborators from Swinburne University in Australia reported the first demonstration of the reversal of the well-known Doppler effect in the optical region with a negative index photonic crystal.

Fig. 1 (a) Normal Doppler effect in normal materials (n>0). (b) Inverse Doppler effect in negative index materials (n<0)

Our common knowledge of a Doppler effect comes from the increasing tone (frequency increase) of a whistling train approaching us and the falling tone (frequency decrease) when it recedes. The same thing happens to light waves. When a light source and an observer approach each other, blue-shifted (frequency increase) light will be observed, as illustrated in Fig.1a. The intriguing inverse Doppler effect is that red-shifted (frequency decrease) light is observed when the light source and an observer are approaching each other, as shown in Fig.1b, or vice versa. The Doppler effect is proportional to the refractive index of the medium that it passes. All naturally existing materials have a refractive index ≥ 1, therefore the normal Doppler effect is expected.

Fig 2: Measured transmission power as a function of the refraction angle θ for a normally incident beam respect to the first interface of the PC (the incident angle at the exit interface is 60°). Inset: Schematic diagram of the experimental setup.

We were able to reverse the Doppler effect for the first time in the optical region by constructing a two-dimensional silicon photonic crystal with a negative index property. In order to have the negative index property, the photonic crystal was tailored to have periodic pillars with nanometric sizes, in which a photonic bandgap can be generated. When shining a beam of CO₂ laser ( λ=10.6 μm corresponding to the 2nd band of the photonic crystal along the ΓM direction), the beam experiences a refraction with a negative index. The experimental result is presented in Fig. 2. At a refraction angle of approximately θ=-26º (incident angle is 60º as indicated in the inset of Fig. 2) high intensity signal could be measured clearly revealing that the photonic crystal prism is operating in the negative refraction region, with a measured n_p=-0.5062.

We employed a highly sensitive two-channel heterodyne interferometric experimental setup to measure the inverse Doppler effect, and at the same time used a positive-index ZnSe prism (n_p=2.403) to conduct the controlled experiment. The results shown in Fig. 3a clearly indicates the measured beat frequency Δf < f^'₂ - f₀k (where f₀ is the original frequency of the CO₂ laser, f^’₂ the reference Doppler frequency shift at the detector surface and k is defined as

Note that the Doppler shift can and can only be positive, i.e. , which indicates that the Doppler frequency is blue-shifted and larger than the original frequency of the CO₂ laser when the optical path becomes larger in the negative index materials.

In contrast the measured frequency differences Δf for four velocities are all less than f^'₂ - f₀k as shown in Fig. 3b (note that here f^'₂ - f₀k < 0), which clearly demonstrates that the Doppler effect measured in the ZnSe prism is normal.

Fig. 3 (a) Measured frequency shifts ∆f in the NIM PC prism compared with the value of f^'₂ - f₀k. (b) Measured frequency shifts ∆f in the positive index ZnSe prism compared with the value of f^'₂ - f₀k.

Our results indicate that reversed Doppler effect at the optical frequency has been observed for the first time by refracting the beam in a negative index photonic crystal. The fascinating negative index materials will lead to more counterintuitive phenomena such as the perfect lens imaging and invisible cloaking.

Reference:
[1] Jiabi Chen, Yan Wang, Baohua Jia, Tao Geng, Xiangping Li, Lie Feng, Wei Qian, Bingming Liang, Xuanxiong Zhang, Min Gu and Songlin Zhuang, “Observation of the inverse Doppler effect in negative-index materials at optical frequencies,” Nat. Photonics 2011 IN PRESS; Published online March 6th 2011; doi: 10.1038/nphoton.2011.17. Abstract.

Controlling Quantum Pathways for Raman Scattering in Graphene

Feng Wang beside a diagram showing how lowering the Fermi energy eliminates quantum pathways in graphene (lower left). The upper plot reveals that when destructively interfering quantum pathways are blocked, Raman scattering intensity is strongly enhanced (pale blue vertical, labeled G). At the same scattering, and at specific values of the Fermi energy, the plot reveals “hot electron luminescence” (labeled H.L.). (Click on image for best resolution.)


Scientists at the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) and the University of California at Berkeley have learned to control the quantum pathways determining how light scatters in graphene. Controlled scattering provides a new tool for the study of this unique material – graphene is a single sheet of carbon just one atom thick – and may point to practical applications for controlling light and electronic states in graphene nanodevices.

The research team, led by Feng Wang of Berkeley Lab’s Materials Sciences Division, made the first direct observation, in graphene, of so-called quantum interference in Raman scattering. Raman scattering is a form of “inelastic” light scattering. Unlike elastic scattering, in which the scattered light has the same color (the same energy) as the incident light, inelastically scattered light either loses energy or gains it.

Raman scattering occurs in graphene and other crystals when an incoming photon, a particle of light, excites an electron, which in turn generates a phonon together with a lower-energy photon. Phonons are vibrations of the crystal lattice, which are also treated as particles by quantum mechanics.

Quantum particles are as much waves as particles, so they can interfere with one another and even with themselves. The researchers showed that light emission can be controlled by controlling these interference pathways. They present their results in a forthcoming issue of the journal Nature [1].

Fig.1: The quantum pathways in Raman scattering are optically stimulated electronic excitations only possible if the initial electronic state is filled and the final state is empty (top). As pathways are removed by doping the graphene and lowering the Fermi energy (bottom), light from scattering may increase or decrease, depending on whether the removed pathways interfere constructively or destructively with the remaining pathways.

Manipulating quantum interference, in life and in the lab

“A familiar example of quantum interference in everyday life is antireflective coating on eyeglasses,” says Wang, who is also an assistant professor of physics at UC Berkeley. “A photon can follow two pathways, scattering from the coating or from the glass. Because of its quantum nature it actually follows both, and the coating is designed so that the two pathways interfere with each other and cancel light that would otherwise cause reflection.”

Wang adds, “The hallmark of quantum mechanics is that if different paths are nondistinguishable, they must always interfere with each other. We can manipulate the interference among the quantum pathways that are responsible for Raman scattering in graphene because of graphene’s peculiar electronic structure.”

In Raman scattering, the quantum pathways are electronic excitations, which are optically stimulated by the incoming photons. These excitations can only happen when the initial electronic state is filled (by a charged particle such as an electron), and the final electronic state is empty.

Quantum mechanics describes electrons filling a material’s available electronic states much as water fills the space in a glass: the “water surface” is called the Fermi level. All the electronic states below it are filled and all the states above it are empty. The filled states can be reduced by “doping” the material in order to shift the Fermi energy lower. As the Fermi energy is lowered, the electronic states just above it are removed, and the excitation pathways originating from these states are also removed.

“We were able to control the excitation pathways in graphene by electrostatically doping it – applying voltage to drive down the Fermi energy and eliminate selected states,” Wang says. “An amazing thing about graphene is that its Fermi energy can be shifted by orders of magnitude larger than conventional materials. This is ultimately due to graphene’s two-dimensionality and its unusual electronic bands.”

The Fermi energy of undoped graphene is located at a single point, where its electronically filled bands, graphically represented as an upward-pointing cone, meet its electronically empty bands, represented as a downward-pointing cone. To move the Fermi energy appreciably requires a strong electric field.

Fig.2: A flake of graphene was grown on copper and transferred onto an insulating substrate of silicon dioxide. The Fermi energy in the graphene was adjusted by varying the gate voltage on the overlying ion gel, which confines a strongly conducting liquid in a polymer matrix.

Team member Rachel Segalman, an associate professor of chemical engineering at UC Berkeley and a faculty scientist in Berkeley Lab’s Materials Sciences Division, provided the ion gel that was key to the experimental device. An ion gel confines a strongly conducting liquid in a polymer matrix. The gel was laid over a flake of graphene, grown on copper and transferred onto an insulating substrate. The charge in the graphene was adjusted by the gate voltage on the ion gel.

“So by cranking up the voltage we lowered the graphene’s Fermi energy, sequentially getting rid of the higher energy electrons,” says Wang. Eliminating electrons, from the highest energies on down, effectively eliminated the pathways that, when impinged upon by incoming photons, could absorb them and then emit Raman-scattered photons.

What comes of interference, constructive and destructive

“People have always known that quantum interference is important in Raman scattering, but it’s been hard to see,” says Wang. “Here it’s really easy to see the contribution of each state.”

Removing quantum pathways one by one alters the ways they can interfere. The changes are visible in the Raman-scattering intensity emitted by the experimental device when it was illuminated by a beam of near-infrared laser light. Although the glow from scattering is much fainter than the near-infrared excitation, changes in its brightness can be measured precisely.

“In classical physics, you’d expect to see the scattered light get dimmer as you remove excitation pathways,” says Wang, but the results of the experimenter came as a surprise to everyone. “Instead the signal got stronger!”

The scattered light grew brighter as the excitation pathways were reduced – what Wang calls “a canonical signature of destructive quantum interference.”

Why “destructively?” Because phonons and scattered photons can be excited by many different, nondistinguishable pathways that interfere with one another, blocking one path can either decrease or increase the light from scattering, depending on whether that pathway was interfering constructively or destructively with the others. In graphene, the lower and higher-energy pathways interfered destructively. Removing one of them thus increased the brightness of the emission.

“What we’ve demonstrated is the quantum-interference nature of Raman scattering,” Wang says. “It was always there, but it was so hard to see that it was often overlooked.”

In a second observation, the researchers found yet another unexpected example of inelastic light scattering. This one, “hot electron luminescence,” didn’t result from blocked quantum pathways, however.

When a strong voltage is applied and the graphene’s Fermi energy is lowered, higher-energy electron states are emptied from the filled band. Electrons that are highly excited by incoming photons, enough to jump to the unfilled band, thus find additional chances to fall back to the now-vacant states in what was the filled band. But these “hot” electrons can only fall back if they emit a photon of the right frequency. The hot electron luminescence observed by the researchers has an integrated intensity a hundred times stronger than the Raman scattering.

The road taken

The poet Robert Frost wrote of coming upon two roads that diverged in a wood, and was sorry he could not travel both. Not only can quantum processes take both roads at once, they can interfere with themselves in doing so.

The research team, working at UC Berkeley and at Berkeley Lab’s Advanced Light Source, has shown that inelastic light scattering can be controlled by controlling interference between the intermediate states between photon absorption and emission. Manipulating that interference has enabled new kinds of quantum control of chemical reactions, as well as of “spintronic” states, in which not charge but the quantum spins of electrons are affected. Strongly enhanced Raman scattering can be a boon to nanoscale materials research. Hot luminescence is potentially attractive for optoelectronics and biological research, in which near-infrared tags – even weak ones – could be very useful.

“Likewise the phenomenon of hot electron luminescence, because it immediately follows excitation by a probe laser, could become a valuable research tool,” says Wang, “particularly for studying ultrafast electron dynamics, one of the chief unusual characteristics of graphene.”

Reference
[1] Chi-Fan Chen, Cheol-Hwan Park, Bryan W. Boudouris, Jason Horng, Baisong Geng, Caglar Girit, Alex Zettl, Michael F. Crommie, Rachel A. Segalman, Steven G. Louie, and Feng Wang, “Controlling Inelastic Light Scattering Quantum Pathways in Graphene,” Nature, (Published online March 16, 2011). Abstract.

[The report is written by Paul Preuss of Lawrence Berkeley National Laboratory]

First Demonstration of Spin-Orbit Coupling in Ultracold Atomic Gases

Ian Spielman (photo courtesy: Joint Quantum Institute, USA)

Physicists at the Joint Quantum Institute (JQI), a collaboration of the National Institute of Standards and Technology (NIST) and the University of Maryland-College Park, have for the first time caused a gas of atoms to exhibit an important quantum phenomenon known as spin-orbit coupling. Their technique opens new possibilities for studying and better understanding fundamental physics and has potential applications to quantum computing, next-generation "spintronics" devices and even "atomtronic" devices built from ultracold atoms.

In the researchers' demonstration of spin-orbit coupling, two lasers allow an atom's motion to flip it between a pair of energy states. The new work, published in Nature*, demonstrates this effect for the first time in bosons, which make up one of the two major classes of particles. The same technique could be applied to fermions, the other major class of particles, according to the researchers. The special properties of fermions would make them ideal for studying new kinds of interactions between two particles—for example those leading to novel "p-wave" superconductivity, which may enable a long-sought form of quantum computing known as topological quantum computation.

In an unexpected development, the team also discovered that the lasers modified how the atoms interacted with each other and caused atoms in one energy state to separate in space from atoms in the other energy state.

Fig 1. [image courtesy: Ian Spielman, JQI] : In an ultracold gas of nearly 200,000 rubidium-87 atoms (shown as the large humps) the atoms can occupy one of two energy levels (represented as red and blue); lasers then link together these levels as a function of the atoms’ motion. At first atoms in the red and blue energy states occupy the same region (Phase Mixed), then at higher laser strengths, they separate into different regions (Phase Separated). Also, see related phase diagrams in Fig.3 .

One of the most important phenomena in quantum physics, spin-orbit coupling describes the interplay that can occur between a particle’s internal properties and its external properties. In atoms, it usually describes interactions that only occur within an atom: how an electron’s orbit around an atom’s core (nucleus) affects the orientation of the electron’s internal bar-magnet-like “spin.” In semiconductor materials such as gallium arsenide, spin-orbit coupling is an interaction between an electron’s spin and its linear motion in a material.

“Spin-orbit coupling is often a bad thing,” said JQI’s Ian Spielman, senior author of the paper. “Researchers make ‘spintronic’ devices out of gallium arsenide, and if you’ve prepared a spin in some desired orientation, the last thing you’d want it to do is to flip to some other spin when it’s moving.”

“But from the point of view of fundamental physics, spin-orbit coupling is really interesting,” he said. “It’s what drives these new kinds of materials called ‘topological insulators.’”

One of the hottest topics in physics right now, topological insulators are special materials in which location is everything: the ability of electrons to flow depends on where they are located within the material. Most regions of such a material are insulating, and electric current does not flow freely. But in a flat, two-dimensional topological insulator, current can flow freely along the edge in one direction for one type of spin, and the opposite direction for the opposite kind of spin. In 3-D topological insulators, electrons would flow freely on the surface but be inhibited inside the material. While researchers have been making higher and higher quality versions of this special class of material in solids, spin-orbit coupling in trapped ultracold gases of atoms could help realize topological insulators in their purest, most pristine form, as gases are free of impurity atoms and the other complexities of solid materials.

Usually, atoms do not exhibit the same kind of spin-orbit coupling as electrons exhibit in gallium-arsenide crystals. While each individual atom has its own spin-orbit coupling going on between its internal components (electrons and nucleus), the atom’s overall motion generally is not affected by its internal energy state.

But the researchers were able to change that. In their experiment, researchers trapped and cooled a gas of about 200,000 rubidium-87 atoms down to 100 nanokelvins, 3 billion times colder than room temperature. The researchers selected a pair of energy states, analogous to the “spin-up” and “spin-down” states in an electron, from the available atomic energy levels. An atom could occupy either of these “pseudospin” states. Then researchers shined a pair of lasers on the atoms so as to change the relationship between the atom’s energy and its momentum (its mass times velocity), and therefore its motion. This created spin-orbit coupling in the atom: the moving atom flipped between its two “spin” states at a rate that depended upon its velocity.

Fig 2. [image courtesy: Ian Spielman, JQI]: Construction of spin-orbit coupling. a, the red and blue lines denote the two laser-coupled atomic levels and the solid black lines denote the laser coupling. b, computed eigen-energies (dispersion relation) for an atom coupled under this laser-coupling. c, measurement of the quasi-momentum where the dispersion has its minima or minimum. d, representative data used to construct c.

“This demonstrates that the idea of using laser light to create spin-orbit coupling in atoms works. This is all we expected to see,” Spielman said. “But something else really neat happened.”

They turned up the intensity of their lasers, and atoms of one spin state began to repel the atoms in the other spin state, causing them to separate.

“We changed fundamentally how these atoms interacted with one another,” Spielman said. “We hadn’t anticipated that and got lucky.”

Fig 3. [image courtesy: Ian Spielman, JQI; click on the image to see a larger version]: Phase diagrams. a, computed phase diagram of the spin-orbit coupled system taking into account only single-particle energies (ignoring interactions). b, phase diagram including interactions, showing the appearance of a phase mixed (hashed) to phase separated (bold line) transition. d, data at fixed total spin (magnetization) showing the transition from phase mixed the phase separated.

The rubidium atoms in the researchers’ experiment were bosons, sociable particles that can all crowd into the same space even if they possess identical values in their properties including spin. But Spielman’s calculations show that they could also create this same effect in ultracold gases of fermions. Fermions, the more antisocial type of atoms, cannot occupy the same space when they are in an identical state. And compared to other methods for creating new interactions between fermions, the spin states would be easier to control and longer lived.

A spin-orbit-coupled Fermi gas could interact with itself because the lasers effectively split each atom into two distinct components, each with its own spin state, and two such atoms with different velocities could then interact and pair up with one other. This kind of pairing opens up possibilities, Spielman said, for studying novel forms of superconductivity, particularly “p-wave” superconductivity, in which two paired atoms have a quantum-mechanical phase that depends on their relative orientation. Such p-wave superconductors may enable a form of quantum computing known as topological quantum computation.

Reference
[1] Y.-J. Lin, K. Jiménez-García and I.B. Spielman, "Spin-orbit-coupled Bose-Einstein condensates", Nature, Nature, 471, 83–86 (03 March 2011). Abstract.

[We thank National Institute of Standard and Technology for materials used in this report]

Extremely High Refractive Index Terahertz Metamaterial

(From L to R) Bumki Min, Muhan Choi and Seung Hoon Lee

Author: Bumki Min

Affiliation: Department of Mechanical Engineering and KAIST Institute for Optical Science and Technology, Korea Advanced Institute of Science and Technology, South Korea

For the past ten years, researchers in the field of metamaterials have been focusing on the demonstration of negative refractive index, as the negative side of the index could not be reached with naturally existing materials. Partly due to this overwhelming enthusiasm over the negative refractive index, the positive side of the index spectra has not been seriously explored, though the range of positive index in natural materials was still very limited.

The key idea behind the realization of high refractive index is quite simple [1-3]. From a perspective on artificial atoms (or molecules), we need to increase the dipole moment of an artificial atom, that can be induced by incident light. Though simple in its structure, I-shaped metallic patches proposed in this work possess all the requirements for the high refractive index. By periodically arranging I-shaped metallic patches with narrow gaps in-between, we can increase the capacitance of the constituting subwavelength-scale capacitors (I-shaped metallic patches). As the gap closes, the capacitance diverges rapidly and this leads to the huge accumulation of charges at the end of the I-shaped metallic patches. This huge accumulation of charges, in turn, results in extreme polarization density, and therefore the huge effective permittivity.

However, there is another problem to solve. We have to minimize the diamagnetic effect that gives rise to the decrease in effective permeability. This can be achieved simply by thinning the metallic structure and by decreasing the metallic volume fraction.

Figure 1: (left) Unit cell structure of the high-index metamaterial made of a thin I-shaped metallic patch symmetrically embedded in a dielectric material. (middle) Optical micrographs of the fabricated single, double, and triple layer metamaterials. (right) Photograph of a flexibility test for the fabricated metamaterials.

To confirm the theoretical prediction, the measurement of complex refractive index of the proposed high index metamaterials was performed with terahertz time-domain spectroscopy (THz-TDS). The experimentally-obtained refractive indices (real parts) of metamaterials having different gap width (from 80 nm to 30 μm) are plotted in Fig.1. For the sample with the smallest gap width, we obtained the peak refractive index of 38.64 and the quasi-static limiting value greater than 20.

So far, we couldn’t test metamaterials with smaller gap-width than this, but it will be interesting to see what will happen to the refractive index -- once the gap width becomes smaller than the thickness of metallic patches. If the gap width becomes smaller than the thickness of metallic patch, the increase of refractive index with respect to the reduction in gap will be more pronounced, since the subwavelength capacitor enters into the regime of parallel plate capacitor.

In addition, it is worthwhile to note that the overall refractive index is proportional to the refractive index of the substrate. For the present work, we have used a relatively low refractive index dielectric (polyimide whose real index is around 1.8) as a substrate. We expect that higher refractive index will be achieved with the use of higher index natural materials as substrates.

Figure 2: Frequency dependent effective refractive indices of single layer metamaterials with varying gap widths. Inset shows the scanning electron micrographs of a nanogap (~80 nm) high-index metamaterial.

While the proposed I-shaped metallic patch structure has shown the proof of concept, it exhibits polarization dependency owing to the structural anisotropy of the unit cell. In order to access the feasibility of isotropic high index metamaterials, we have fabricated two different types of 2D isotropic high index metamaterials and conducted additional experiments and analyses to verify the polarization independency (See Fig.3). Although the structures are different, the underlying physics is the same: Maintain small gap width for large capacitance and thin metallic patch for negligible diamagnetism.

Figure 3: (left) Polarization-angle-resolved effective refractive index for a single layer hexagonal high index metamaterial. Here, the gap width is 1.5 μm and the thickness is 1.82 μm. (right) Polarization-angle-resolved effective refractive index for a single layer window-type high index metamaterial. Here, the gap width is 1.5 μm and the thickness is 1.82 μm.

High refractive index metamaterials might provide a new way of achieving subwavelength resolution in an imaging system. Subwavelength imaging is being investigated through the utilization of negative index metamaterials (or singly negative materials). In contrast to this “perfect (or super) lens” concept, it might be possible to build a huge NA (numerical aperture) lens that provides the subwavelength-scale resolving power. In the design of high refractive index lens, spatially-varying gradient index can be obtained simply by controlling the gap between unit cells, thereby making it possible to fabricate a very thin flat metamaterial lens. However, among its limitations are the short focal length of high index lens and the working distance, which should be investigated more carefully in near future.

References:
[1] J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction”, Phys. Rev. Lett. 94, 197401 (2005). Abstract.
[2] J. Shin, J. T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth”, Phys. Rev. Lett. 102, 093903 (2009). Abstract.
[3] M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index”, Nature 470, 369 (2011). Abstract.