Negative Refraction in a Semiconductor Metamaterial in the Mid-Infrared Anthony J. Hoffman, Leonid Alekseyev, Evgenii E. Narimanov, and Claire Gmachl Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA

Deborah L. Sivco Lucent Technologies, Murray Hill, NJ 07974, USA

Abstract: We fabricate a semiconductor metamaterial using an anisotropic n+-GaInAs/i-AlInAs heterostructure that supports negative index modes in the mid-infrared. We demonstrate a negative index over a wide range of incidence angles and for λ~13.3–15µm wavelengths. ©2006 Optical Society of America OCIS codes: (160.4670) Optical materials; (160.6000) Semiconductors

1. Introduction The potential for subwavelength resolution [1] and aberration-free imaging shown by novel planar systems based on materials with a negative refractive index (NIMs) [2] has recently attracted considerable attention [3-6]. The usual approach to NIMs is based on simultaneously negative values of the dielectric permittivity and magnetic permeability. While this approach was successful in the microwave spectral range [3], extending it to infrared (IR) and optical frequencies proved to be very challenging as resonant structures that provide negative electric and magnetic response have to be scaled down to nanometer size. While single layers of such resonators were recently fabricated the task of building the corresponding 3-dimensional material has yet to be accomplished [4,5]. Furthermore, the intrinsically resonant nature of the magnetic response in these metamaterials implies high losses [4], which make them unsuitable for applications such as imaging and waveguiding [6]. On the other hand, NIMs based on dielectric photonic crystals, which have low loss, are also severely limited in their utility for imaging applications as their resolution is bound by the characteristic length scales of the photonic crystal, which is on the order of the wavelength. To address these issues, an alternative approach has recently been proposed [7] which obviates the need for a negative magnetic permeability and does not require the periodic patterning of a photonic crystal. This method, based on the anisotropy of the dielectric response, circumvents major manufacturing obstacles to achieving NIM behavior at IR or optical frequencies and allows for imaging and waveguiding applications. Here, we present an experimental study of the first such NIM in the mid-IR, based on an n+-GaInAs/i-AlInAs heterostructure. 2. Material design As shown in our theoretical work, a strongly anisotropic dielectric material with opposite signs of permittivity in two directions (ε|| > 0, ε⊥ < 0), supports transverse magnetic (TM) guided modes with the refractive index (1) n = ε ⊥ν ⋅ Sign (ν ) , where ν = 1 - k2/(κ2ε||), with k and κ being the wavevector and mode parameter, respectively [7]; n evidently can be negative depending on the combination of ε||, ε⊥ , and the wavelength. The required anisotropy can be achieved in a metamaterial formed by alternating layers with positive and negative dielectric constants. The dielectric function for such a sample based on an n+-GaInAs / i-AlInAs heterostructure is shown in Fig. 1(a). For this material, the

Fig. 1(a) In-plane (blue line, ε|) and transverse (red curve, ε⊥) components of the dielectric function of a n+-GaInAs / i-AlInAs heterostructure (lower inset). The top insets show the calculated beam refraction patterns below and above the critical wavelength λ0 ≈ 13.3um (dashed line). (b) TM Reflection coefficient (in gray scale) vs. incidence angle and wavelength off the semi-infinite metamaterial calculated for TM (b) and TE (c) polarized incident waves.

refraction of an incident TM wave is positive below the critical wavelength λ0 ≈ 13.3 µm and negative for all angles in the interval 13.3 µm < λ < 18µm, as shown in the insets of Fig. 1(a). The transition from negative to positive refraction at the critical wavelength of λ0 clearly manifests itself thereby in the simulated (TM) reflectivity of the metamaterial, as shown in Fig. 1(b), through a discontinuity of the Brewster angle (marked by zero reflectance) and an increase in reflectance (which is dampened by some loss in the material). As expected, no such sharp transition features are seen in the equivalent reflectance of the transverse electric (TE) mode (Fig. 1(c)), as the refraction of the ordinary (TE) wave is always positive. 3. Sample composition and characterization A sample consisting of 80 nm layers of nominally undoped Al0.48In0.52As interleaved with 80 nm layers of In0.53Ga0.47As doped ≥ 1019 cm-3 was grown on InP substrate by molecular beam epitaxy; the total thickness of the epitaxial layer is ~ 8 µm. The material was characterized by transmission and reflection measurements performed as a function of wavelength, incidence angle, and polarization. To minimize the effects of experimental and environmental fluctuations, the ratio of the TM over TE polarization data are used and analyzed. Fig. 2(a) shows the measured reflectance (TM/TE) in a gray-scale plot versus incidence angle and wavelength. The data are directly compared with the corresponding theoretical calculation shown in Fig. 2(b). The fringes, seen in both graphs, are due to interference effects in the epitaxial layer of the sample. Despite the fringe structure complicating the observed pattern (c.f. Fig. 1(b, c) corresponding to reflection from the half-infinite metamaterial), the data clearly show the expected transition from positive to negative refraction with a sharp boundary at λ0 ≈ 13um, in an excellent agreement with the theoretical prediction. Note, there are no free parameters in the model. All the material properties are known to a sufficient degree and the carrier density is independently extracted from the experimental minimum in the amplitude of the interference fringes at ~6 µm which corresponds to the spectral regime where the index of refraction of the epitaxial layer is equal to that of the InP substrate.

Fig. 2: TM/TE-reflectance in a gray-scale versus incidence angle and wavelength for a ~ 8 µm thick slab of mid-IR InGaAs/AlInAs metamaterial. (a) experimental data, (b) theoretical model.

4. Conclusion We have demonstrated an n+-i-n+ semiconductor metamaterial with negative refraction in the mid-IR. To the best of our knowledge, these are the first results of a 3-dimensional non-magnetic left-handed metamaterial in this wavelength range. Being based solely on epitaxial III-V semiconductor growth, this material has great potential for applications. Acknowledgement This work was in part supported by the Princeton Institute for the Science and Technology of Materials (PRISM). References [1] J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000) [2] V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of sigma and mu,” Sov. Phys. Usp. 10, 509 (1968). [3] R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001). [4] V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005) [5] S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negativeindex metamaterials,” PRL 95, 137404 (2005). [6] VA Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Optics Letters 30, 75-77 (2005) [7] V. A Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101(R) (2005).