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Chapter 2:
Optical Hyperspace: Negative Refractive Index and Subwavelength Imaging
The art and science of optics is centered upon our ability to control the refractive index of materials, thereby directing the flow of light. From the stained-glass windows of Gothic cathedrals to modern LCD projectors, from Galileo's telescope to terabit optical communication systems, devices made possible by skillful manipulation of the refractive index have resulted in countless technological and cultural breakthroughs. For centuries, the refractive index has been regarded as a strictly positive quantity — such was the universal experience. Recent advances in fabrication and processing techniques, however, have enabled the creation of materials with a negative refractive index. This development opens many new chapters in the fields of optical physics and device engineering. Negative index greatly expands the parameter space accessible for manipulating light, opening the way for devices with unprecedented capabilities — for example, imaging systems with subwavelength resolution and ultrasmall waveguides. The novel systems made possible by negative index materials (NIMs) may bring about revolutionary technological changes. In the present chapter we describe a method to achieve negative refraction via materials with a hyperbolic dispersion relation. Both natural materials and metamaterials can exhibit this property. We show that in addition to providing a simple path to nonmagnetic negative refraction, the hyperbolic dispersion relation enables novel devices for waveguiding and subwavelength imaging. The present-day interest in NIMs started in the early 2000s. The origins of the subject, however, date back many decades. Indeed, as a general wave propagation phenomenon, negative refraction has been known since the early 20th century. It was noted, in particular, that negative refraction naturally occurs at the interface with a medium characterized by negative phase velocity. No such materials were known in the electromagnetic domain, and so the early discussions involved only mechanical oscillations. The first detailed treatment of negative refraction in electromagnetism was provided by Veselago in 1968. He showed that to attain negative phase velocity for electromagnetic (EM) waves, the material response must be of the form ϵ < 0, μ < 0. When this condition is satisfied, the E, H, and k vectors form a left-handed triplet. As a result, the wave vector k and the Poynting vector S are oriented in opposite directions; the system has negative phase velocity, which is the condition for negative refraction. Indeed, negative phase velocity serves as a definition of negative index materials. While mechanical and radio frequency devices exhibiting such effective negative indices were known at the time of Veselago's writing, bulk materials with negative phase velocity were not found in nature and were not readily attainable.
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