J. Arriaga

Highly birefringent photonic crystal fibers

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.

Anomalous dispersion in photonic crystal fiber

We describe the measured group-velocity dispersion characteristics of several air-silica photonic crystal fibers with anomalous group-velocity dispersion at visible and near-infrared wavelengths. The values measured over a broad spectral range are compared to those predicted for an isolated strand of silica surrounded by air. We demonstrate a strictly single-mode fiber which has zero dispersion at a wavelength of 700 mm. These fibers are significant for the generation of solitons and supercontinua using ultrashort pulse sources.

Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber

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.

Photonic Crystal Optics and Homogenization of 2D Periodic Composites

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 uni-axial or bi-axial 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 the Physics of Inhomogeneous Media where exact, compact formulas are scarce. Our numerical method yields results with very high accuracy, even for very large dielectric contrasts and filling fractions.

Fundamental-mode cutoff in a photonic crystal fiber with a depressed-index core

We report a photonic crystal fiber with a depressed-index core doped with fluorine. The effective index of the cladding matches that of the core at an antiguiding wavelength, below which the fiber does not guide light at all.

PHOTONIC CRYSTALS AS OPTICAL COMPONENTS

Photonic crystals (PCs) have already found numerous applications associated with the photonic band gap. We point out that PCs could be also employed as custom-made optical components in the linear region well below the photonic gap. As an example, we discuss a birefringent PC lens that acts as a polarizing beam splitter. This idea is supported by a precise method of calculation of the optical constants of a transparent two-dimensional (2D) PC. Such a process of homogenization is performed for hexagonal arrays of polymer-based PCs and also for the mammalian cornea. Finally, 2D PCs are classified as optically uniaxial or biaxial.

ORDER-N PHOTONIC BAND STRUCTURES FOR METALS AND OTHER DISPERSIVE MATERIALS

We show how to calculate photonic band structures for idealized metals and other dispersive systems using an efficient order-N scheme. That is to say, we use a scheme where the calculation time scales linearly with the system size. The inverse dielectric function is treated as a simple pole. The method is applied to two simple periodic idealized metallic systems where it gives results in close agreement with calculations made with other techniques. Further, the approach demonstrates excellent numerical stability within the limits we give. By generalizing to an inverse dielectric function expanded as a series of poles, our method opens the way for efficient calculations on complex structures containing a whole different class of material.

Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index

For enhancing the omnidirectional photonic bandgap (OPBG), we report the fabrication of two different configurations of one-dimensional, wavelength scalable dielectric multilayer structures of porous silicon, consisting of a unit cell formed by varying the refractive index of the multilayers according to the envelope of a Gaussian function. As compared to the already reported OPBG of 88 nm (in the complete angular range of 0° to 89°), an enhancement up to 204 nm (2.3 times) was observed on stacking, six different Gaussian structures (balanced mirror) with only 8 periods each. An unbalanced mirror structure, consisting of the six similar Gaussian structures as the balanced mirror, but having different sequence of periods, (configuration with 13, 6, 5, 5, 6, and 13 periods for each Gaussian, respectively) was seen to demonstrate the OPBG of 252 nm (enhanced by 2.86 times). The total optical thickness of both the structures was kept to be the same. The omnidirectional nature of the PBG was verified experimen...

Omnidirectional photonic bandgaps in porous silicon based mirrors with a Gaussian profile refractive index

We have designed and fabricated one dimensional photonic bandgap (PBG) structures from dielectric multilayers of porous silicon, with a periodic repetition of a unit cell consisting of 21 layers (95%) with the refractive index varying according to the envelope of a Gaussian function and another layer (5%) with a fixed refractive index. The structures can be designed to demonstrate the wavelength scalability within the visible as well as near infrared region. Three different structures have been stacked together to enhance the width of the PBG. The omnidirectional nature of the PBG was verified experimentally and theoretically up to 68° and 89° angles of incidence, respectively.

Modelling photonic crystal fibres

Abstract One of the potential applications of photonic crystals is the so-called photonic crystal fibres. These systems can be constructed, for example, using a long thread of silica glass with a periodic array of airholes running down its length. If the central hole is absent, we generate a high-index “defect” in the repeating structure which acts like the core of an optical fibre. We study the propagation of light in these fibres. We solve the Maxwell equations using the plane wave expansion and the super cell method.