Metal-Free Flat Lens Using Negative Refraction by Nonlinear Four-Wave Mixing

Abstract

A perfect lens with unlimited resolution has always posed a challenge to both theoretical and experimental physicists. Recent developments in optical meta-materials promise an attractive approach towards perfect lenses using negative refraction to overcome the diffraction limit, improving resolution. However, those artificially engineered meta-materials usually company by high losses from metals and are extremely difficult to fabricate. An alternative proposal using negative refraction by four-wave mixing has attracted much interests recently, though most of existing experiments still require metals and none of them has been implemented for an optical lens. Here we experimentally demonstrate a metal-free flat lens for the first time using negative refraction by degenerate four-wave mixing with a thin glass slide. We realize optical lensing effect utilizing a nonlinear refraction law, which may have potential applications in microscopy.Flat lenses using negative refraction create a new avenue for novel optical imaging applications, attracting intense interests from optics, microwave and even acoustic communities [1][2][3][4][5][6][7]. Unlike traditional optical lenses, a flat lens which can bend incoming waves at negative angles opposed to those within normal refraction regime [1][2][3] can form an image much more sharply thanks to its ability to negatively refract waves at all-angle including the evanescent ones, making itself a "perfect lens" to overcome the diffraction limit [2,6]. Such lenses have been realized in many formats ranging from optics, microwave to acoustic, including photonic crystals [7], metal thin film [6], meta-material [5, 9-12], etc. However, most of them suffer from high losses in association with metallic materials, which are the key elements bringing in negative permittivity and artificial permeability. Secondly, fabrications of such nano/micro structures raise additional obstacle for their practical applications. In nonlinear optics, alternative approaches to achieve negative refraction have been proposed including phase conjugation, time reversal and four wave mixing (4WM) [3,13,14]. In contrast to those artificially engineered methods i.e. meta-materials and photonic crystals, which create spatial dispersion for negative refraction using linear composition of different materials, nonlinear optics explores nonlinear wave mixings with angle matching schemes to fulfill the requirements for negative refraction. Principally, only a thin flat nonlinear slab is required. Up to now, such negative refractions using wave mixing have been realized in some thin films with high nonlinearity such as metal and graphite thin film [15][16][17]. However, in these experiments due to their low nonlinear conversion efficiencies or materials' optical transparency, none of them has been implemented for imaging purpose.In this letter, we experimentally demonstrate a metal-free flat lens using negative refraction by degenerate four-wave mixing with a simple thin glass slide. Within glass slides containing thi...

Phase-controlled two-wave mixing in a moving grating

“…A 1;2 0 are the initial amplitudes of the two waves. Equations 3and (4) indicate that the two waves exchange energy along the propagation axis z. This process is affected by two factors:…”

“…Nonlinear wave mixing is of great importance to optical science and technology. It can bridge several optical channels, allowing information exchange and energy transfer in applications such as optical signal processing, holographic information, and imaging science [1][2][3][4][5]. Its simplest form is the mixing between two waves, which conventionally occurs in a nonlinear medium where the index of refraction nonlinearly responds to the incident beams.…”

“…Similar phase problems arise in other physical systems; for example, in photorefractive media, the relative phase between the index variation and the intensity interference pattern spontaneously rising from the spatial drift of photoexcited electrons can be controlled externally through direct current (DC) electric fields [1,21]; in quantum wells, an external DC field must be introduced to vary the near-degenerated TWM in a moving grating [22,23]. Hence, the relative phase here plays an important role in determining the TWM's gain strength and directionality, similar to the phase-controlled nonlinear process [4,5]. It would be better to isolate the generation of grating and control the phase independently in order to lower the high-intensity demand for TWM and precisely regulate TWM through phase, so that TWM can be more easily accessible and controllable in applications such as all-optical near-degenerated wavelength conversion, optical isolation, and optical switching even at low photon levels.…”

Dielectric Optical-Controllable Magnifying Lens by Nonlinear Negative Refraction

“…To address this problem, alternative approaches have been proposed in nonlinear optics to achieve the nonlinear version of negative refraction using phase conjugation, time reversal and four wave mixing (4 WM) 17 18 19 , where negative refractions can be attained by exploring nonlinear wave mixings with right angle matching schemes. In contrast to those artificially engineered methods, i.e., meta-materials and photonic crystals in linear optics, ideally only a thin flat nonlinear slab is required to enable this nonlinear negative refraction 20 21 22 23 24 25 . Such negative refractions using nonlinear wave mixing have been demonstrated in some thin films with high nonlinearity such as the metal and graphite thin films 20 21 .…”

“…Such negative refractions using nonlinear wave mixing have been demonstrated in some thin films with high nonlinearity such as the metal and graphite thin films 20 21 . Moreover, a flat lens utilizing negative refraction of nonlinear mixing waves has successfully shown its 1D and 2D imaging ability 25 . However, this lens still lacks the magnification capability, which is crucial for imaging applications.…”