Garcia et al. Reply: In their Comment [1] Bogdanov and Rossler (BR) make essentially two criticisms of our work [2]. We cannot agree with them and show that they are wrong. BR claim that practically always "multidomain structures are stabilized by the demagnetizing influence of surfaces" [3]. However, surprisingly in a recent paper [4] BR claim that when the magnetization vector lies in the xoy plane it does not create a demagnetizing field on the surface. This is what we did, in considering the case of thin magnetic films [2] in which the magnetization vector lies in the film plane (xoy) and the magnetic structures are sequence Néel domain walls. Moreover, BR note the following at the end of their Comment: "Irregular domain patterns occur in thin magnetic layers when ordering effects due to dipolar forces are weakened and are overcome by crystal and magnetic imperfections." This is what we considered. Indeed, it is well known [3] that the Neél wall is a linear dipole and its demagnetizing factor N d͑͞d 1 L͒ ø 1 when the film thickness d ø L, L is the wall width. Dipole-dipole interaction between Neél walls can be described by a field H i 2p 2 M s dL 2 ͑2R͒ 23 where R is the distance between the walls (see, e.g., [5]). Therefore we can neglect the magnetostatic interaction between the walls when B . ͑p͞Q͒ ͑d͞L͒ ͑L͞2R ͒ 3 where B is the amplitude of variations of anisotropy K or exchange interaction A and Q K͞2pM 2 s , Q 0.1 0.3 for Co. L ¿ d and R ¿ L for stable chaotic patterns presented in Fig. 3 of [2] and so their stability is determined by variations of K or A even when B ø 1.BR emphasize the difference between Eq.(2) of [2] and the equation for nonlinear oscillations with periodical variable parameters: "The former is initial value or Cauchy problems, the latter are boundary value problems." At the same time formal analogy between equations of the type of Eq. (2) and dynamic system equations widely used for the study of stationary states in different processes, including pattern formation (see [6] and numerous references therein). In particular, this approach was used to analyze solutions of Eq. (2) in the form of different domain walls [5]. We used this analogy only to prove that Eq. (2) has chaotic solutions in principle. Obviously, we can place the film boundaries at some points a and b where, for example, du͞dx 0, and establish in that way a chaotic solution satisfied by these neutral boundary conditions in a film whose size is equal the distance between a and b. We emphasize in [2] that extremely small variations of the boundary conditions result in radical changes of the solutions of Eq. (2). This is the main property of chaotic patterns and so it is generally known that studying chaotic solutions as a boundary value problem has no mathematical meaning.

We theoretically discuss the possibility of having materials with zero effective permittivity that would create band gaps in a wide range of frequencies up to the visible. The physical realization of these materials is also discussed in terms of embedding metallic nanoparticles and nanowires in a dielectric medium. In the limit of long wavelengths, these composites will behave like a homogeneous medium with zero permittivity that will completely reflect electromagnetic waves. We present transmittivity calculations by using finite-difference time domain for periodic structures that proves the concept and shows the validity of the long wavelength approximation. The striking result is that the cutoff frequency ωc is determined by the lattice parameter of the composite. By properly choosing the lattice constant of the composite and permittivity of metal and dielectric constituents, we can have full band gaps at any frequency range but especially in the visible.

Abstract.Two types of optical metamaterials operating at near-IR and mid-IR frequencies, respectively, have been designed, fabricated by nanoimprint lithography (NIL), and characterized by laser spectroscopic ellipsometry. The structure for the near-IR range was a metal/dielectric/metal stack "fishnet" structure that demonstrated negative permittivity and permeability in the same frequency region and hence exhibited a negative refractive index at a wavelength near 1.7 µm. In the mid-IR range, the metamaterial was an ordered array of four-fold symmetric L-shaped resonators (LSRs) that showed both a dipole plasmon resonance resulting in negative permittivity and a magnetic resonance with negative permeability near wavelengths of 3.7 µm and 5.25 µm, respectively. The optical properties of both metamaterials are in agreement with theoretical predictions. This work demonstrates the feasibility of designing various optical negative-index metamaterials and fabricating them using the nanoimprint lithography as a lowcost, high-throughput fabrication approach.

We show by pump-probe spectroscopy that the optical response of a fishnet metamaterial can be modulated on the femtosecond time scale. The modulation dynamics is dominated by pump-induced changes in the constituting dielectric medium, but the strength of modulation is dramatically enhanced through the plasmon resonance. The pump-induced spectral responses of the metamaterial provide understanding on how the resonance is modified by pump excitation. Our study suggests that metamaterials can be used as high-speed amplitude/phase modulators with terahertz-bandwidth.

Acoustic crystal devices, with dimensions on the order of several wavelengths, are studied by using the finite-difference time domain method in the moderately long wavelength propagation regime. From the focusing and imaging process performed by a square shaped lens, it is shown that diffractive effects dominate over those due to refraction. The major role of the device edge diffraction is shown by means of the well known Babinet principle. The first examples of imaging with a sonic plane lens, both with crystal structure and massive, and with an acoustic prism able to change the propagation direction of a plane wave, are presented.