A structured material is disclosed with magneto-gyrotropic characteristics including at least one continuous structurally-chiral material. The structured material has an electric permittivity and a magnetic permeability at least one of which varies within the structured material along a first direction in a repetitious fashion wherein a repetition unit includes a chiral component and is at least 25 nm in length. The structured material exhibits non-reciprocal electromagnetic wave propagation velocity characteristics along a second direction that includes a non-zero component along the first direction.

BACKGROUND

The invention relates to materials and devices for use with electromagnetic fields and relates in particular to materials and devices through which electromagnetic fields may propagate in unconventional ways. The ability of such devices to propagate electromagnetic fields in unconventional ways permits the materials to be used for a variety of known and yet unknown applications.

For example, U.S. Published Patent Application No. 2001/0038325 discloses a left-handed composite media for use at microwave frequencies in which negative effective electrical permittivity and negative effective magnetic permeability are simultaneously provided. Such materials with negative effective electrical and magnetic permeability are disclosed to be suitable for use as microwave lenses, beam steering elements, and prisms.

A negative index of refraction for incident radiation at the frequency of light has been demonstrated using photonic crystals inSuperprism Phenomena in Photonic Crystals, by H. Kosaka, T. Kawashime, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, PHYSICAL REVIEW B, vol. 58, No. 16 (October 1998). Such materials are disclosed to provide a propagation beam swing of ±90 degrees responsive to a ±12 degrees shift in the angle of incident radiation by modifying the group velocity of the incident radiation. A negative index of refraction has also been demonstrated in the vicinity of the photonic band gap inTheory of Light Propagation in Strongly Modulated Photonic Crystals: Refractionlike Behavior in the Vicinity of the Photonic Band Gap, by M. Notomi, PHYSICAL REVIEW B, vol. 62, No. 16 (October 2000). In particular, this article discloses that negative refraction is possible in regimes of negative group velocity and negative effective index above the first photonic band near the Brillouin zone center (Γ).

Other types of devices have been disclosed to be suitable for propagating light in one direction only. For example, U.S. Published Patent Application No. 2002/0162988 discloses a unidirectional gyrotropic photonic crystal that is disclosed to permit electromagnetic wave propagation of a certain frequency in one direction while impeding the electromagnetic wave propagation in the opposite direction.

Certain further materials are known to affect the circular polarization and amplitude of light. For example, U.S. Pat. No. 6,411,635 discloses a composite for use in selective single-mode lasing that includes a doped chiral medium. The selection is disclosed to be accomplished by producing an appropriate spatial gain distribution inside the chiral laser medium. U.S. Pat. No. 6,396,859 discloses a chiral structure that includes a defect in the form of a twist, and is disclosed to be used for filters, lasers and detectors. International PCT Publication WO 02/073247 discloses chiral substrate that is formed as a fiber to provide a fiber Bragg grating.

There continues to be a need however, for further materials and devices that provide unconventional electromagnetic field propagation characteristics, such as for example, slowing down light in one direction only, and that may provide directionality characteristics in two or three dimensions.

SUMMARY

The invention provides a structured material with magneto-gyrotropic characteristics including at least one continuous structurally-chiral material in accordance with an embodiment of the invention. The structured material has an electric permittivity and a magnetic permeability at least one of which varies within the structured material along a first direction in a repetitious fashion wherein a repetition unit includes a chiral component and is at least 25 nm in length. The structured material exhibits non-reciprocal electromagnetic wave propagation velocity characteristics along a second direction that includes a non-zero component along the first direction.

In accordance with another embodiment, the invention provides a photonic crystal having both magneto-optic activity and structural chirality. The photonic crystal has a refractive index that varies within the structured material along a first direction in a repetitious fashion wherein a repeat unit includes a continuous structurally chiral material. The photonic crystal exhibits non-reciprocal electromagnetic wave propagation velocity characteristics in a second set of directions that are not perpendicular to the first direction.

In accordance with another embodiment, the invention provides a waveguide having a central longitudinal axis, displaying both magneto-gyrotropic characteristics and structural chirality along the central longitudinal axis. The waveguide has an electric permittivity and a magnetic permeability at least one of which varies along the central longitudinal axis in a repetitious fashion, such that the waveguide displays non-reciprocal electromagnetic wave propagation characteristics along the central longitudinal axis.

In accordance with a further embodiment, the invention provides a system for achieving non-reciprocal electromagnetic wave propagation characteristics. The system includes a structured material exhibiting both magneto-gyrotropy and structural chirality. The structured material has an electric permittivity and magnetic permeability at least one of which varies in a repetitious fashion along at least a first direction, wherein the repetition unit includes a continuous structurally chiral material. The electromagnetic wave propagation characteristics are manifested in any second direction that is not perpendicular to the first direction.

The drawings are show for illustrative purposes only and are not to scale.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

The invention relates to the design of a photonic crystal that provides extraordinary properties arising from the general design of constituent materials. Such properties may include an effective negative refractive index and the ability to significantly reduce the propagation speed of light at multiple frequencies (both externally tunable and switchable) in various embodiments of the invention, as well as the ability to effectively stop light inside the structure at a particular strength of the external stimuli (and release it when the external stimulus is adjusted). This special interaction with electromagnetic waves may be produced at any optical (visible, infrared) or microwave (radar) frequencies, allowing the disclosed matter to a have a potentially significant impact in various scientific and technological areas that will be enabled by these exceptional properties.

An important characteristic of a photonic crystal formed in accordance with an embodiment of the invention is the presence of both magneto-gyrotropy and structural chirality (or handedness) in the underlying material structure. Due to the interplay of these material symmetry elements, electromagnetic waves are restricted to propagate in only a few special ways. As mentioned above, certain properties arise that are not observed in conventional materials. First, light propagates differently in opposite directions through such materials, as the dependence of light frequency, ω, on the wavevector {right arrow over (k)} becomes non-reciprocal ω({right arrow over (k)})≠ω(−{right arrow over (k)}). Second, external fields (magnetic, mechanical, etc.) may tune the position of two frequency intervals where light is allowed to propagate along one direction with a certain velocity while in the opposite direction is restricted to only one electromagnetic mode that has drastically smaller group velocity. Using such fields may lead to the latter velocity to be completely reduced to zero, thus leading to a state of light localization (e.g., frozen light). At this frequency, both the first and second-derivatives of ω with respect to {right arrow over (k)} become zero at a particular value of {right arrow over (k)}, which corresponds to an electromagnetic wave with zero group velocity and infinite mass of the photon. Further, for other frequency intervals (which can be placed by design in any desired spectral region), light propagates through the material experiencing an effective negative refractive index, which is a concept of significant scientific and technological interest at present. The disclosed material design is also valuable because it allows fabrication of optically, infra-red and microwave active devices in certain embodiments.

Photonic materials of various embodiments of the invention rely on the presence of magneto-gyrotropy in structurally chiral (or handed) materials. Magneto-gyrotropy comprises the phenomena related to electromagnetic wave propagation in materials where the permittivity (ε) and/or permeability (μ) tensors have at least a pair of non-zero complex conjugate off-diagonal elements in the principal material coordinate system (εi,j≠i≠0) causing well known gyrotropic effects (Faraday and Kerr wave polarization rotation, circular birefringence, etc.). For magneto-gyrotropic materials, the constitutive tensors are not symmetric (εij≠εjiand/or μij≠μji), but they in fact become Hermitian (εij=ε*jiand/or μij=μ*ji, where the star (*) denotes complex conjugate). Such materials are common, most of them containing well known magnetic atoms, and are generally classified into two groups. The first group comprises pure metals and metallic alloys, and the second group contains dielectric and semimagnetic compounds. See for example,Modern Magnetooptics and Magnetooptical Materials, A. K. Zvezdin, and V. A. Kotov, Institute of Physics Publishing, Bristol and Philadelphia (1997).

A description of structural chirality in certain embodiments includes the representation of a spiral, which may display either a right-hand or left-hand chirality. This handedness may arise in each of 1, 2 and 3 dimensions. Structural chirality is common in materials, and it can be the result of an intrinsic material organization tendency, or can be produced by directed organization in man-made fabrication processes. For embodiments desired to be active at microwave frequencies (gigahertz, millimeter wavelengths) the fabrication becomes trivial due to the macroscopic nature of the constitutive elements.

FIGS. 1A and 1Bshow two examples of one-dimensional (1D) structures that are suitable for visible and infra-red operation.FIG. 1Acontains a diagrammatic representation of a 1D periodic cholesteric liquid crystal composite10that includes rod-like liquid crystal molecules12periodically twisting along a helix axis upon doping with a chiral molecule). The composite10also includes a plurality of magnetizable particles14that may be randomly distributed about the molecules12. These particles may be smaller than the wavelength of interest to avoid scattering losses (e.g., smaller than 1/10 of the wavelength), and should coact to create a relatively strong and uniform magnetic field around the molecules12in the presence of an externally applied magnetic field. In other embodiments, the material that forms a helix or other chiral structure may itself be either externally magnetizable or may be formed of a permanent magnet. The period of a full revolution of the helix may be, for example, at least as long as a wavelength of the electromagnetic field of interest, such as 100 nm. In particular, the wavelength of interest may be the wavelength for which the non-reciprocal electromagnetic field propagation properties are achieved.

FIG. 1Bshows a 1D periodic cholesteric liquid crystal composite16that can be viewed as being made of a plurality of layers18of oriented elements20. Each molecular layer is slightly rotated with respect to a previous layer such that the stack of layers18provides a continuous helical structure. The composite16may also include a plurality of magnetizable elements22as discussed above with reference toFIG. 1A. In further embodiments, it may be possible to use this approach to have a non-zero net magnetic activity even in the absence of the external magnetic field, for example by using rod-like particles, orienting them globally, then polymerizing the whole mixture, thereby freezing in the cholesteric (helical) structure with vertically oriented rods that have mangetooptic activity. This design may be suitable for visible and near-infra-red wavelengths since periodicity of the structure could be on the order of the wavelength, and cholesteric liquid crystals are known to have a pitch length from few hundreds of nanometers to microns. For longer wavelength radiation (e.g., microwave frequencies), it may be possible to stack thin foils that are optically uniaxial, making certain that each foil is slightly rotated from the previous one.

FIGS. 2A and 2Bshow a two-dimensional (2D) composite in which a slab24includes plurality of holes26, each of which receives a cholesteric liquid crystal28having a plurality of layers30of aligned elements32that are rotated with respect to each other as discussed above with reference toFIG. 1B. The elements32may be molecules having a size of about 1/100 of the diameter of the cylinder, or possibly about 1 nm. Magnetogyrotropic properties are provided for example, by using a magnetic material matrix, or by magnetizing the chiral liquid crystal with magnetizable particles inside the cylinders shown for clarity. The plurality of liquid crystal units28provide a plurality of parallel chirality axes (each aligned in the vertical direction as shown at A). Again, such a composite may be used for visible, near-infra-red or microwave operation. In further embodiments, other possible structures include those having multiple chirality axes resulting from packing of double twist cylinders on a simple cubic lattice (P4232 symmetry), as seen in cholesteric blue phases II as disclosed for example, inLasing in a Three-Dimensional Photonic Crystal of the Liquid Crystal Blue Phase II, W. Cao, A. Munoz, P. Palffy-Muhoray, and B. Taheri, Nature Materials, v.1, p. 111 (2002).

FIGS. 3A and 3Bshow a three-dimensional (3D) composite40in which spiral elements42having chirality axes along a z direction are provided in an x by y array as shown inFIG. 3B. The spiral elements42may be formed of a magnetic material, or in further embodiments, the composite40may include magnetizable elements as discussed above. The composite ofFIG. 3Bmay be formed by glancing angle deposition techniques in which the chiral axis is perpendicular to substrate. See for example,Fabrication of Tetragonal Square Spiral Photonic Crystals, S. R. Kennedy, M. J. Brett, O. Toader and S. John, Nano Letters v.2, no. 1, p. 59 (2002). Other multidimensional chiral structures (e.g., single gyroid phase, I4132 symmetry) could be produced by self-assembly, or by directed fabrication processes (e.g. interference lithography with elliptically polarized light) such as disclosed inFabrication of Photonic Crystals for the Visible Spectrum by Holographic Lithography, M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, A. J. Turberfield, Nature, v.404, no. 6773, p. 53 (2000). In addition, post-processing may be used to enhance the optical properties while preserving the structural chirality of the material, such as filling the air spaces between the spiraling columns with magneto-gyrotropic media, or with a desired refractive index material needed (if the columns themselves are made of a magneto-gyrotropic medium).

In further embodiments, structures including two or three non-parallel chirality axes may be provided. For example, such further non-parallel chirality axes may be mutually orthogonal to one another. Since the exact theoretical prediction of the optical properties of such material structures may be difficult, especially when the constituents interact with light in complex ways, one may predict the optical properties expected from the interplay of magneto-gyrotropy and structural chirality by analyzing a one-dimensional material system, when the structure has only one chirality axis. Thus, the propagation of light in helical media (similar to that shown inFIG. 1Aor1B) in the presence of magneto-gyrotropy is examined as a representative problem. This may be referred to as representative because a wave propagating along the helical axis when the magneto-gyrotropic vector is also oriented along the same direction, should experience the maximum effects of this combination of optical property elements. In fact, the same qualitative effects may be found for electromagnetic waves that propagate along a direction on which both the magneto-gyrotropic vector and the helical axis have a non-zero projection (thus not necessarily strictly parallel).

Some of the special properties of the disclosed hybrid material become evident by examining certain operational diagrams that show dispersion relations ω({right arrow over (k)}), {right arrow over (k)}={circumflex over (z)}kzmatching the angular frequency ω to the corresponding spatial frequencies, kz(Bloch wavevector) of electromagnetic waves that are allowed to propagate along the {circumflex over (z)}-axis. The material is taken as the representative helical medium with uniform rotation (e.g., a uniform, perfectly circular spiraling) with its helical axis also along {circumflex over (z)}-axis. The parameter γ is a measure of the strength of the magneto-gyrotropy along the same {circumflex over (z)}-axis, and its sign may be changed by reversing the direction of an external magnetic field. For any given frequency therefore, when γ≠0, the forward (+{circumflex over (z)}) or backward (−{circumflex over (z)}) propagating waves have a different kzand a different group velocity (the slope of the  curve at kz), which show that light will be transmitted differently along opposite paths through this material.

In particular,FIG. 4shows dispersion relations for axial propagation of electromagnetic waves in a uniform helical medium in the absence of magneto-gyrotropy (γ=0) as shown at50aand50b, and in the presence of magneto-gyrotropy where γ>0 as shown at52aand52b. The values50aand52aare for left-hand circularly polarized light, and the values50band52bare for right-hand circularly polarized light. Similar dispersion relations for axial propagation of electromagnetic waves in a uniform helical medium in the presence of magneto-gyrotropy where γ<0 may be shown by inverting (flipping) the relation for γ>0 along the 0.0 wavevector (vertical line in graph). By examining, for example, the allowed modes at a reduced frequency of 0.6 when γ≠0, it may be seen that only two light modes may propagate, and while they are either both on the positive side or both on the negative side of the diagram (thus same sign of phase velocity, {right arrow over (v)}p=ω/{right arrow over (k)}), their slopes (i.e., group velocity, {right arrow over (v)}=∂ω/∂{right arrow over (k)}) have opposite signs. Propagating waves for which vp·vg<0 are characteristic of negative refractive index materials, first postulated in 1968. See, for example,The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ, V. G. Veselago, Soviet Physics Usp., vol.10, no. 4, p.509 (1968);Negative Refraction Makes a Perfect Lens, J. B. Pendry, Physical Review Letters, v.85, no.18, p. 3966 (200); andExperimental Verification of a Negative Index of Refraction, R. A. Shelby, D. R. Smith, S. Schultz, Science, no.292, p.77 (2001). Uses of such materials may include a wide range of applications from nanotechnology and nano-imaging to radar technology and focusing much larger wavelength waves. While progress is continuously made towards understanding the negative refractive index properties and potential applications, there have been only few designs of actual negative refractive index materials, virtually all of them operating at the millimeter wavelength (microwave) scale for which the structured optical materials involves macroscopic metal wires, plates, etc.

Systems in accordance with various embodiments of the invention may utilize conventional fabrication techniques, and even self-assembling routes, thus allowing straightforward fabrication of structures working at much smaller wavelengths, such as the highly desirable visible and infra-red regimes, other than the relatively macroscopic microwave spectral region (used in radar technology).

It has further been discovered that structurally chiral materials exhibit another significant property in addition to the negative refractive index behavior. When the structural chirality exhibits ellipticity (instead of a uniform, perfectly rotating, circular helix, e.g. imagine a non-uniform one, deformed perpendicular to the helix axis, with an elliptical cross-section), the variation of the strength of the magnetogyrotropy (γ) results in very large changes of the group velocity (rate at which power is carried by the wave) in two frequency regions along a given propagation direction.

For example, the distribution of the elements of a helix may be changed from being uniformly distributed (as shown at60inFIG. 5A), to be biased along an x direction (as shown at62inFIG. 5B) or biased along a y direction as shown at64inFIG. 5C). This may be achieved by a variety of techniques, including mechanically deforming the helix in either the x or y direction to form an eliptical shaped helix in cross-section. In further embodiments, the helix may be designed to stretch when subjected to an electric or electromagnetic field, and in further embodiments, the electric permittivity and/or magnetic permeability may be changed (without mechanically acting on the helix) when subjected to an external magnetic or electromagnetic field.

As shown inFIG. 6, the rotation angle distribution φ(z) may not be a linear function of z. In particular, while a uniformly distributed helix (as shown at60inFIG. 5A) may provide a substantially linear relation70, an x-axis biased helix (as shown at62inFIG. 5B) may provide a non-linear relation72, and a y-axis biased helix (as shown at64inFIG. 5C) may provide another non-linear relation74.

As shown inFIG. 7, the variation of the strength of the magneto-gyrotropy (γ) results in very large changes of the group velocity (rate at which power is carried by the wave) in two frequency regions along a given direction (e.g., the z azis). In particular,FIG. 7shows the effect of the strength of magneto-gyrotropy (γ) on the dispersion curves ω(k) for a non-uniform hybrid medium where γ=0.00 (as shown at80), γ=0.05 (as shown at82), γ=0.10 (as shown at84), and γ=0.15 (as shown at86).

While changing the velocity of light in a material by applying an external stimulus by itself has important practical applications in the design of various electromagnetic wave devices, there are further possibilities. In the above design, the application of an external stimulus changing the value of γ can result in slowing down the wave beyond usual limits, as at one particular value of γ the group velocity at frequency ω* becomes zero and the effective mass of the photon becomes infinite, as shown at84inFIG. 7. In particular, the relation at84inFIG. 7shows dispersion curves for a non-uniform helical medium with magneto-gyrotropy, when at ω=ω* one of the two allowed modes (with k*) has a zero group velocity and infinite photon effective mass.

The same qualitative situation depicted inFIG. 7may be obtained by structurally perturbing the material (e.g., mechanical deformation) while keeping the magneto-gyrotropic strength constant. For example, as shown inFIGS. 8A–8C, a uniformly distributed helix as shown at90inFIG. 8A, may be slightly deformed along an x-direction as shown at92inFIG. 8B, or further deformed along an x-direction as shown at94inFIG. 8C. The resulting frequency response relations for the helixes90,92and94are shown at96,98and100respectively inFIG. 9.

As shown inFIG. 10, a structured material102of the invention may be used with a biasing unit104to change the frequency on interest ω* may be tuned. Thus, the disclosed material design allows multiple pathways for tunability of its optical properties, such that at a frequency ω* the only two allowed light waves can propagate either in the forward (+{circumflex over (z)}) or in the backward (−{circumflex over (z)}) direction, with one of them bearing a very special feature. In accordance with an embodiment, therefore, only a backward wave may have a finite group velocity (slope ≠0), as the forward wave has a nearly zero velocity (inflection point at ω*(k*), slope→0). In addition, at ω*(k*) the curvature may also become zero, a situation that physically corresponds to wave with an infinite effective photon mass.

This material may thus not only act as an optical isolator (unidirectional propagation of light), but it may either trap light or just allow it to propagate at previously unseen reduced velocities in normal dielectric materials. This hybrid material design allows tuning the properties of the structure to properly match a material's ω* to the desired application frequency. Finally, electromagnetic waves with frequencies very close to ω* may propagate with such small velocities, that it is clear that the disclosed hybrid material opens avenues towards radically new, solid state based devices. Examples include optical buffering or memory (optical routers in telecom employ miles long optical fibers to introduce time delays), low threshold lasing, and a general enhancement of most other nonlinear optical phenomena which can be introduced by further adding active centers in the overall magneto-gyrotropic structurally chiral material as disclosed, for example inFrozen Light, S. John, Nature, no. 390, p.661 (1997). In general, a number of possible embodiments can be envisioned where practical devices take advantage of these special materials (either as the only, or as one of multiple components), all with the common feature of manipulating electromagnetic waves at optical, infrared, microwaves and other frequencies.

A material design therefore is provided that features a unique set of properties. These include the ability to propagate electromagnetic waves with an effectively negative refractive index, and the ability to dramatically slow down the waves inside the material to such an extent that the wave would effectively stop, that is, to exhibit a zero group velocity and infinite photon mass. Moreover, these properties are widely tunable by external stimuli such as magnetic field direction and intensity, mechanical deformation, etc.

In still further embodiments, a system may include a structured material106within a waveguide108that is coupled to a bias source110and an excitation source112. The system may provide for light amplification by stimulated emission of radiation (lasing) by having the excitation source pump the cavity within the waveguide108that includes the structured material. If, for example, the output waver is slowed within the cavity, more efficient excitation and stimulated emission of photons may be achieved. The wavelength of the output wave may optionally be tuned by the biasing source110.

In further embodiments, the invention may provide negative refractive index materials and the ability to reduce the speed of light to record low values. Since these may be exhibited at the same time and in the same material, another set of applications is enabled, where the combination is needed (as opposed to e.g., using the material simply as a negative refractive medium). Thus, many sets of applications are enabled by material design of certain embodiments of the invention that include various combinations of particular material structures, compositions (specific desirable hybrids from polymers, glasses, nanoparticles, etc.), and device architectures.

Various embodiments of the invention, therefore, provide for the use of negative refractive index materials for designing optical devices that are able to reversibly slow down and even stop and store light inside a material by applying an external stimulus (localization of light). Many further known and unknown potential uses may exist for materials of various embodiments of the invention.

In further embodiments, a structured material may be used as an optical waveguide or fiber optic device as shown inFIG. 12. In particular, the core120may include a chiral material122and the cladding124may have magneto-gyrotropic characteristics provided by magnetic elements126. The cladding may also include chiral material128that, for example, is wrapped closely around but outside of the chiral material122of the core as shown in accordance with an embodiment. The core material may provide that light of a particular wavelength of interest may move in one direction at a speed that is much slower than the conventional speed of the light. Such a system may be suitable for use in coupling fiber optic communication systems with electronic devices that conventionally operate at much slower speeds than the speed of fiber optic communication.

In still further embodiments a waveguide or fiber optic device130may include a core132with structural chirality and a cladding134as shown inFIGS. 13 and 14. In this embodiment, the core132has a cross section that is symmetric upon a 180 degree in-plane rotation, and may be produced from a twisted pair of equal diameter fibers which are partially fused to form the structurally chiral core132as shown inFIGS. 13 and 14.

In accordance with a further embodiment, the core may be formed such that its cross section is symmetric only upon a 360 degree rotation. In this embodiment, a core may be produced from a twisted pair of different diameter fibers136aand136b, which may be further partially fused to produce a structurally chiral core with an asymmetric cross section. This core may further include a cladding138as shown inFIG. 15. Again, at least one of the core material and the cladding material adjacent to the core has to display magneto-gyrotropic properties.

Those skilled in the art will appreciate that numerous variations, modifications and improvements may be made to the above disclosed embodiments without departing from the spirit and scope of the invention.