Related Applications

This application is a continuation-in-part of application serial no. 255,107 filed October 7, 1988, a continuation-in-paπ of application serial no. 362,072 filed June 6, 1989, and a continuation-in-paπ of application serial no. 637,450 filed January 4, 1991.

Field of Invention

Generally this invention relates to methods of constructing lenses. More specifically, this invention relates to lenses comprising chiral materials.

Background of the Invention

It has been shown that, for time-harmonic electromagnetic fields with exp(-.ωt) excitation, a homogeneous, low loss, isotropic chiral (optically active) medium can be described electromagnetically by the following constitutive relations:

H = . ξ _c E + (l/μ) B

where E, B, D and H are electromagnetic field vectors and ε, μ, ς represent the dielectric- constant, permeability and chirality admittance of the chiral medium, respectively. A "chiral medium" comprises chiral objects of the same handedness, randomly oriented and uniformly distributed. A chiral object is a three-dimensional body that cannot be brought into congruence with its mirror image by translation and rotation. Therefore, all chiral objects can be classified in terms of their "handedness." The term "handedness," as known by those with skill in the an, refers to whether a chiral object is "right-handed" or "left-handed." That is, if a chiral object is right-handed (left-handed), its mirror image is left-handed (right-handed). Therefore, the minor image of a chiral object is its enantiomorph.

Chiral media exhibit electromagnetic chirality which embraces optical activity and circular dichroism. Optical activity refers to the rotation of the plane of polarization of optical waves by a medium while circular dichroism indicates a change in the polarization ellipticity of optical waves by a medium. There exists a variety of materials that exhibit optical activity. For example, for 0.63-μm wavelength, Teθ2 exhibits optical activity with a chirality admittance magnitude of 3.83 x 1Q ^~7 mho. This results in a rotation of the plane of polarization of 87° per mm. These phenomena, known since the mid nineteenth century, are due to the presence of the two unequal characteristic wavenumbers coπesponding to two circularly polarized eigenmodes with opposite handedness.

The fundamentals of electromagnetic chirality are known. See, e.g., J. A. Kong, Theory of Electromagnetic Waves, 1975; E. J. Post, Formal Structure of Electromagnetics, 1962. More recent work includes the macroscopic treatment of electromagnetic waves with chiral structures D. L. Jaggard et al. Applied Physics, 18, 211, 1979; the analysis of dyadic Green's functions and dipole radiation in chiral media, S. Bassiri et al. Aha Frequenza, 2, 83, 1986 and N. Engheta et al. IEEE Trans, on Ant. & Propag., 37, 4, 1989; the reflection and refraction of waves at a dielectric- chiral interface, S. Bassiri et al. /. Opt. Soc. Am. A5, 1450, 1988; and guided-wave structures comprising chiral materials, N. Engheta and P. Pelet, Opt. Lett., 14, 593, 1989. The following table compares the electromagnetic properties of chiral and nonchiral materials:

Prior lenses have been used to focus electromagnetic radiation in various systems. These prior homogeneous lenses exhibit a single focal point for the electromagnetic radiation and therefore require significant modifications and adjustments when used in systems requiring focusing over large ranges. There therefore exists a long-felt need in the an for lenses that are dynamic and which provide multiple focal points to improve systems performance.

Summary of the Invention

Chiral lenses provided in accordance with the present invention solve the aforementioned long-felt needs in the an for lenses which exhibit simplicity in design and are dynamically configurable to be used in any electromagnetic system intended to operate with a high degree of flexibility. Chiral lenses described herein are highly efficient for focusing electromagnetic radiation and due to their bifocalism, provide multichannel characteristics for electromagnetic energy, and especially optical and microwave rays using simple, homogeneous elements.

Chiral lenses will be particularly useful in optical and microwave systems and subsystems, integrated optical and photonic devices, monolithic microwave integrated circuit, and electronic and photonic surveillance systems. Furthermore, chiral lenses provided in accordance with the present invention will be adaptable for varied uses in remote sensing and radar imagery applications, optical and telecommunication systems, "smart skins" for aerospace applications and missile guidance systems. Lenses in accordance with the present invention comprise chiral materials.

Brief Description of the Drawing

Figure 1 depicts a helix which is a prefened embodiment of a chiral structure used in the practice of the present invention.

Figure 2 illustrates a homogeneous chiral sphere which is an idealized chiral lens in accordance with the present invention wherein the source is a dipole element.

Figure 3 is a graph of the location of the two focal points of the chiral lens shown in Figure

2 as a function of the normalized chirality admittance Ω, where Ω = ξ^ jε _c , ε = ε _c , and μ/μ _c =

0.7.

Figure 4 illustrates a hemispherical chiral lens provided in accordance with the present invention.

Figures 5A-5C illustrate a thin chiral lens fabricated over a dielectric substrate.

Figure 6 illustrates a thin chiral lens in accordance with the present invention.

Detailed Description of Preferred Embodiments

An exceedingly wide variety of chiral structures are amenable to the practice of this invention, so long as such structures exhibit an effective capacity to conduct electric cunent and have the same handedness. Furthermore, the full range of the electromagnetic spectrum will exhibit bifocalism in accordance with the present invention depending upon the size of the chiral constituents in the chiral medium, the physical size of the lens, and the particular frequency under investigation. Chiral structures employable in the practice of this invention can be naturally- occurring or man-made. A prefened chiral structure is the single-turn wire helix given in Figure 1, having total stem length 21, loop radius a, and thickness t as noted therein.

Prefened materials for constructing helices include copper, gold, silver, iron, and aluminum. As will be appreciated by those skilled in the art, chiral structures can be produced, for example, by molding, extruding or otherwise shaping a suitable metal, alloy, polymer or other conducting structure. These chiral structures are embedded in a suitable host material which is generally constituted so as to contain the chiral moieties and to cause them to adhere to or form articles or coatings upon articles. Polymerizable materials such as acrylics, epoxies and the like are exemplary host materials. Other solidifiable materials may be used as well. Suitable host media comprise liquids, polymeric, polymerizable or otherwise solidifiable materials, and certain solids with varying degrees of loss. The chiral material may be homogeneous or may comprise chiral structures of varying size, shape, and constitution to provide broadband characteristics. Materials which can be either naturally occurring or man-made may be employed. Chiral molecular species are also suitable in accordance with certain embodiments of the invention. Thus, natural or synthetic molecules or molecules having chirality introduced by electromagnetic forces may be used.

Chiral materials used in connection with the invention described and claimed herein can be described in accordance with the following examples:

Examples

Example 1 - Construction of Helices

Elemental copper having conductivity of about 5.0 x 10 mhos is drawn into cylindrically shaped wire having diameter (t) of about 0.1 millimeters. The wire is then shaped into single-turn helices having stem half-length ( ) and loop radius (a) of about 3.0 millimeters, as shown in Figure 1.

Example 2 - Incorporation of Helices into a Lossy or Low-Loss Host Medium

The components of an ECCOSORB (Emerson and Cuming) lossy or low-loss material preparation are mixed in an open-top, cardboard box having known internal volume. Before the preparation solidifies, an appropriate number of the copper helices constructed in Example 1 is uniformly added to reach the desired concentration (N) helices per square centimeter. The matrix is stined well and allowed to fully solidify.

Derivation of the Separate Focal Length Expressions for Lenses Comprising

Chiral Materials

As discussed above, the electromagnetic properties of a homogeneous isotropic chiral medium may be described by the constitutive relations: D = ε _c E + iξ _c B and H = iξ _c E + B/μ _c .

The quantities ε _c , μ _c , and ξ _c are, respectively, the permittivity, permeability, and chirality admittance of the medium. The additional chirality admittance parameter is introduced to account for the new characteristics resulting from the medium's handed constituents. From Maxwell's equations and these constitutive relations, it can be seen that chiral media possess a polarization birefringence with circularly polarized eigenmodes. These eigenmodes propagate with

9 9 9 9 1 /9 wavenumbers k ₊ = ± ωμ _c ξ _c + [ω μ _c ξ _c + ω μ _c ε _c ] , where k conesponds to the right-circularly polarized (RCP) mode and k_ to the left-circularly polarized (LCP) mode.

Referring now to the drawings wherein like reference numerals refer to like elements, the properties of the chiral lens are derived by placing an electric dipole source at the exterior of a spherical lens as shown in Figure 2. However, if instead the dipole were located inside the lens, die results and analysis would have been similar to what follows. Since it is known by those with skill in the art that a focal point of any lens is the point where parallel rays converge, it is possible to look at this phenomenon in a "reverse" order and place a radiator at a focal point and find the parallel beams. As shown in Fig. 2, the geometry under consideration consists of a homogeneous sphere 10 of radius a made from an optically active that is a chiral material in accordance with the present invention. The sphere is characterized by the electrical parameters ε _c , μ _c , and ξ _c and is embedded in a simple dielectric with permittivity ε and permeability μ. Thus, the interior of the sphere supports both k ₊ and k_, while its exterior supports only k = ω" εμ. In a preferred embodiment, the radiator or source 20 is a dipole element radiating in the optical or microwave regime. The source 20 is directed along the x-axis and is located at a distance b > a from the origin. Its excitation is

with the spherical coordinates (r,θ,φ) and related unit vectors also depicted m Fig. 2. It should be noted that the unprimed coordinates denote the observation point, whereas the primed ones represent the location of the source.

Using the dyadic Green's function _r _ιol (r,r') for a homogeneous chiral sphere, the electric field outside the sphere is expressed as

E(r) = iωμ j r ⁽ ^r,r')« J(r') dV (2)

where, for all observation points with r > b, r _tol (r,r') is given by

_r ^(I1 V _{r =} _____ _α _ _{δ )} (2n+l) (n-m)i = ^tot 4ick ^_ - ^{1 m} ° n(n+l) (n+m)!

{ [ (k) ₊ c;w? ) ₊ ² v _mn( k)]v- _πn( k)

(3)

The spherical vector wave function V _c-nn (k) and _c-nn (k) are simply related to the usual M _c-nn (k) and Nc _mn (k), where δ _m0 is the Kronecker delta. This dyadic Green's function was derived, for example, in commonly owned application serial no. 637,450, filed on January 4, 1991, the teachings of which are specifically incorporated herein by reference. Written explicitly,

m 1 d

Ve , _m m _n n(k) = P osθ) ^fraφ) fj _n (kr)e _G + ^[rj _π (kr)]e ₀ 2 sinθ

^^ _Ϊ ^)^!^^^-^^

+ n(n+l) P osθ) ^(mφ) ^e, (4)

and Wc _mn (k) is obtained from Vc _mn (k) by exchanging 1/kr with -1/kr. The superscript (1) in Eqn. (3) indicates that the spherical Bessel functions j _n (kr) are replaced by the spherical Hankel functions h" ^J (kr). The coefficients e , e™, f ^* and f ^* are

^e _f | = k ² {j ₊ aj_[(/± i) ² ajh + ( ₊ i) ² jah] +aj _[(/± i) ² ajh + (/ ₊ i) ² jdh] n J

- 4 [j _dβh + 9j ₊ ajjh] } /2D (5a)

= ζ = - k ₁ .2/(r ,2 - 1 )Q ₊ 3j_ + 3j JQdh - 3jh) / 2D (5b)

9 9 where D = 2/[h dj ₊ dj_ + dh j j - hθh(/ + l)G ₊ dj_+j_dj ₊ ) and the following notation has been used:

j = j _n ( ^ka ) and

^ ^B E5W

j± = J _n ^(k ± ^a) and dj± = £^ gf i ^r J _n ⁽ ± ^r) 1 L

h = h ⁽ a) and »-E [*»)

1/9 9 1/9

In Eqns. (5a) and (5b), / = (εμ) /[^ + (βjμ _c )] is the ratio of the intrinsic impedance inside the sphere to that outside. Noting that

and performing the integration in Eqn. (3), we obtain the complete expression for the electric field in the region r > b:

^E(r> ""SI ^ { ^V -' >( ^] ά | ^[r» '» ^] l _b - W-» ^Γ)]

+ Wl(k,(-[e ]h';>(kb)-k ² j„(kb))} (6)

The focal points can now be found by simplifying Eqn. (6) with the help of the following asymptotic expansions, which are valid for p » n » 1:

h ) - i e ^il P> " *<" ⁺ rø, j _(p) . J- [ _e i[Y„(P) - Kn+rø _{+ c} . _c .] ₍₇₎

P 2p

where

These expansions have previously been used to examine nonchiral spherical lenses. Following this approach, the focal points of a chiral sphere may be obtained. Limiting attention to the e _χ -e _z plane, i.e. φ -= 0, and to geometries and frequencies for which (7) can be used to replace all of the Bessel and Hankel functions in Eqn. (6). Furthermore, the approximation that there are no reflections at the interface between lens and the surrounding dielectric and, thus, set / - 1 is made. Under these conditions, the electric field in the far zone may be expressed in the form:

E(r) = E ₊ (r) + E_(r) (9)

with RCP and LCP components given by

_E+(r) . « . _{( ±} , , _ Ggl { _e HY _n ⁽ k 0 -Vkb ^)] fi→ ₊ 9P____Λ ± ' lόbkr ^ ^{δ φ} ^ ₁ n(n+D 1 I sinθ 3Θ* J

+ ₍ _ _{1 e} Uγ _n (kr)-2γ _n (ka) ₊ γ _rι (kb) ₊ 2γ _n (k _± a)] ( Pfcosθ) ₊ ^ __! £_-!?__1

(. sinθ ae ¹ β

(10)

It should be noted that only amplitude terms that decay as 1/r have been retained in this expression. Ideally, in the geometrical optics limit, when the dipole source is at the focal point, the field on the opposite side of the lens should approach that of a plane wave. Restricting this case to θ = π, for which Eqn. (10) simplifies to

E _± (r) = - ^(- _{β ±} i e ⁱ M<--« ⁺ » ^{+ 2} > S _± (11)

with ⁰ f . 4

∑ ⁰ i ■q 2 / I 2 1 2 \ * __. /-J _ _ _ ₊ _ _ ₊ - -.

^ ^« (H - E ⁺ kB ⁺ ς_) 24 (kr) ³ (ka) ³ (kb) ³ (k+a) ³

(12)

2 where q = n + 1/2. It is preferably desired to retain terms with order q in the exponential, since all higher order terms are negligible. Furthermore, for most points of observation with r » a and r » b, the r dependence in S_ may be ignored. The exception occurs as b approaches one of the two focal points, denoted by F ₊ and F_. There, It is anticipated the r dependence will prevail as the field begins to resemble a paraxial plane wave. Hence, the focal points must occur when the exponent is dominated by 1/kr, that is when - 2/ka + 1/kF- _j . + 2/k+a = 0 or

At these points, the sum in Eqn. (12) may be approximated y the integral

S _± - J e ^iq2/2kr q dq = ikr{ 1 - e ^iα(kr) } (14)

where α(kr) is introduced as an undeterminable phase term. Substituting (14) into (11), the form of the electric field on the opposite side of the lens is obtained:

E _± (r> ~ -^ <e ₀ ± ie _φ ) - ⁱ « ^r - ^: « ⁺ > ^{+ 2 ]} < ₁₅₎

Thus, by placing the source at either F ₊ or F_, a plane wave for one of the chiral eigenmodes is approximately achieved.

The location of the two points is plotted as a function of ^ for k ₊ > k_ > k in Fig. 3. It is seen that the separation between F ₊ and F_ increases with chirality. Furthermore, when k_ = k, the LCP focal point moves to infinity indicating no focusing of that mode. As the chirality is increased even further, the region k ₊ > k > k_ (not shown), where the LCP wave is defocused but

RCP wave remains focused is reached. Hence, the chiral lens can serve simultaneously as a concave and a convex lens. This is startlingly unexpected result and evinces the solution to a long- felt need in the art for dynamic lenses which are adaptable for use in multichannel modes.

Thus by employing a wave-oriented approach based on dyadic Green's functions it is seen that a spherical chiral lens possesses two distinct focal points for two eigenmodes of propagation. It is worth noting that these focal points could have been obtained directly from geometrical optics. However, unlike the ray optics approach, the above analysis can also be used to explain the behavior of electromagnetic fields when the dipole source is not situated at one of the focal points. This result can be generalized to an arbitrarily shaped lens made from chiral media and also to other frequency ranges such as infrared, microwave and millimeter wave regimes.

These chiral lenses could be used in a variety of new applications, including: couplers for waveguides, polarization filters and new antennas for remote sensing. A possible arrangement for

this last application could consist of a single chiral lens with two antennas; a transmitter radiating a circularly-polarized wave with one handedness at one focal point and a receiver detecting the return signal of a circularly polarized wave with the opposite handedness at die other.

Referring now to Figure 4, a spherical chiral lens 30 in accordance with the present invention is illustrated. It will be recognized by those with skill in the art that while a hemispherical chiral lens 30 is illustrated, the chiral lens could be spherical or take on any arbitrary shape depending on the particular application. The lens 30 comprises a chiral material 40 having the material parameters illustrated. The outside environment 50 has standard permittivity and permeability and surrounds the chiral lens. Applying a similar analysis as described above, hemispherical chiral lens 30 will exhibit two focal points.

Figures 5A-5C illustrate a thin spherical chiral lens 60 fabricated on a dielectric substrate 70. The dielectric substrate 70 exhibits a separate permittivity and permeability (εj,μ _j ) while the outside medium exhibits the standard dielectric permittivity and permeability (ε,μ). Thin spherical chiral lens 60 comprises chiral material 40 with chirality parameters heretofore discussed. Similarly, the thin spherical chiral lens 60 exhibits two focal points and can act as both a convex and concave lens in accordance with the present invention.

Referring to Figure 6, a thin chiral lens 80 comprises a chiral material 40 having chiral parameters. The dielectric 50 surrounds the thin chiral lens 80 and has standard non-chiral permittivity and permeability. As discussed above and similar to the embodiments found in Figures 4 and 5A-5C, chiral lens 80 exhibits two focal points due to the two circularly polarized eigenmodes of propagation having two different wave numbers present in the lens when incident with electromagnetic radiation.

Chiral lenses described herein are thus particularly useful since they exhibit bifocalism due to the propagation of electromagnetic radiation therethrough in two circularly polarized eigenmodes with two different, unequal wave numbers. Since two circularly polarized eigenmodes with unequal wave numbers are present in the chiral medium, the lenses described and claimed herein can focus one of the modes while defocusing the other mode if desired in preferred embodiments. The chiral lenses are particularly useful as couplers for waveguides, polarization filters, and new antennas for remote sensing. Furthermore, all electromagnetic lens applications are improved through the use of chiral lenses provided in accordance with the present invention.

There have thus been described certain preferred embodiments of chiral lenses provided in accordance with the present invention. While preferred embodiments have been described and disclosed, it will be recognized by those with skill in the art that modifications are within the spirit and scope of the invention. The appended claims are intended to cover all such modifications.