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We report a strongly anisotropic photonic crystal fiber. Twofold rotational symmetry was introduced into a single-mode fiber structure by creation of a regular array of airholes of two sizes disposed about a pure-silica core. Based on spectral measurements of the polarization mode beating, we estimate that the fiber has a beat length of approximately 0.4 mm at a wavelength of 1540 nm, in good agreement with the results of modeling.

We consider the low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals). Exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived. We apply our formulas to the well-known phenomenon of the drop of the speed of sound in mixtures. For air bubbles in water we obtain a perfect agreement with the recent results of coherent potential approximation obtained by M. Kafesaki, R. S. Penciu, and E. N. Economou [Phys. Rev. Lett. 84, 6050 (2000)] if the filling of air bubbles is far from close packing. When air spheres almost touch each other, the approximation gives 10 times lower speed of sound than the exact theory does. DOI: 10.1103/PhysRevLett.91.264302 PACS numbers: 43.20.+g, 43.58.+z, 43.90.+v Acoustic waves play an important role in our life, being a universal carrier of information in vivid nature. In most cases, the media where the acoustic waves propagate are inhomogeneous. A common example is a mixture of water and air. During the past century the problem of propagation of sound in heterogeneous media has been extensively studied [1]. In the last few years artificial periodic elastic structures, phononic crystals, have been successfully fabricated [2]. Because of the presence of acoustic gaps -regions of frequencies where sound does not propagate [3] -phononic crystals can be used as soundless background for many technological devices. Phononic crystal with point, linear, and surface defects permit manipulation of sound: they guide the acoustic waves, split, and bend them [4]. At low frequencies phononic crystals possess a property to focus a sound beam [5] and thus may find numerous applications in acoustic surgery [6]. To design an acoustic lens one needs to know the refractive index of the material or the effective speed of sound. At low frequencies (well below the band gap) the dispersion relation is linear, ! c eff k, since one wavelength covers many periods of the structure, thus averaging the inhomogeneous medium. Calculation of the effective parameters of the uniform medium (effective speed of sound, c eff , and the effective elastic moduli) is a long-standing problem of the mathematical theory of homogenization [7]. Although the theory itself is well developed and predicts that different media homogenize at low frequencies, there are no explicit formulas that can be used for calculation of the effective parameters (see recent review [8] on homogenization for different types of the wave equations). There are also approximate methods that allow calculations of the effective parameters for particular structures [9][10][11]. Sometimes the effective elastic moduli can be evaluated from the exact upper and lower bounds [12].In this Letter we develop an exact analytical theory of homogenization of periodic elastic structures. Our approach is based on the plane wave method that has been successfully used for homogenization of pe...

We study the long-wavelength limit for an arbitrary photonic crystal (PC) of 2D periodicity. Light propagation is not restricted to the plane of periodicity. We proved that 2D PC's are uniaxial or biaxial and derived compact, explicit formulas for the effective ("principal") dielectric constants; these are plotted for silicon-air composites. This could facilitate the custom design of optical components for diverse spectral regions and applications. Our method of "homogenization" is not limited to optical properties, but is also valid for electrostatics, magnetostatics, dc conductivity, thermal conductivity, etc. Thus our results are applicable to inhomogeneous media where exact, explicit formulas are scarce. Our numerical method yields results with unprecedented accuracy, even for very large dielectric contrasts and filling fractions. [S0031-9007 (98)08154-X] PACS numbers: 42.70.Qs, 41.20.Jb, 42.25.LcPhotonic crystals (PC's) are arrays of dielectric materials with one-, two-, or three-dimensional periodicity. Since the suggestion [1] that PC's may be useful for controlling light emission, their properties have been researched intensively [2,3]. Recently, it was proposed that PC's could advance photonic information technology [4][5][6]. These ideas rely on the existence of a photonic band gap-a frequency region in which light propagation is forbidden. The region well below the gap received much less attention [7][8][9][10][11][12]. Here the wavelength is much greater than the lattice period; hence light "sees" a homogeneous medium. This situation is analogous to light propagation in natural crystals, whose optical properties like birefringence are described in crystal optics [13]. We studied analytically, for the first time, propagation in an arbitrary direction in space for a 2D PC.

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By coupling femtosecond pulses at lambda - 1.55mum in a short length (Z - 95 cm) of photonic crystal fiber, we observe the simultaneous generation of two visible radiation components. Frequency-resolved optical gating experiments combined with analysis and modal simulations suggest that the mechanism for their generation is third-harmonic conversion of the fundamental pulse and its split Raman self-shifted component.