Integral equations for photonic-crystal fibers

The integral and integro-differential equations for photonic-crystal waveguides (fibers) with both infinite and finite quasi-periodic dielectric coatings have been obtained, with previous consideration of the equations for 2D periodic photonic crystals with magnetodielectric and metallic inclusions. The corresponding numerical results are presented.     

Calculated out-of-plane transmission loss for photonic-crystal slab waveguides

A fully three-dimensional finite-difference time domain numerical model is presented for calculating the out-of-plane radiation loss in photonic-crystal slab waveguides. The propagation loss of a single-line defect waveguide in triangular-lattice photonic crystals is calculated for suspended-membrane, oxidized-lower-cladding, and deeply etched structures. The results show that low-loss waveguides are achievable for sufficiently suspended membranes and oxidized-lower-cladding structures.     

Roughness losses and volume-current methods in photonic-crystal waveguides

We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green’s functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.     

Very large spontaneous-emission Beta factors in photonic-crystal waveguides

Through a new rigorous Bloch-mode formalism, we theoretically study the generation of photons in single-row-defect photonic-crystal waveguides. In contrast with previous related works relying on a reinforcement of the spontaneous emission (SE) through microcavity effects, we explore situations for which the SE into radiation modes is reduced to a very low level while the SE into the guided mode is maintained at a level comparable to that in the bulk material. Remarkably large SE beta factors in excess of 95% are obtained, and since no resonance effect is involved, this efficiency is achieved over a 40-nm-large spectral interval at lambda approximately 950 nm.     

The position independence of heterostructure coupled waveguides in photonic-crystal switch

Based on studying the propagation states of electromagnetic waves in heterostructure coupled waveguides produced by appropriately modulating the refractive index of rods, the realization of photonic-crystal switch is analyzed and the position effect of the heterostructure coupled waveguides on the switch function is investigated. The simulation results show that the output state is the result of the integral effect of different coupling regions; therefore, the switch function is independent on the distribution of heterostructure coupled waveguides. This property will bring great flexibility to fabricate photonic-crystal switch in practice.     

Effective theories for circuits and automata

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational, and social systems makes the problem harder. Here, we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.     

Slow-light enhanced optical forces between longitudinally shifted photonic-crystal nanowire waveguides

We reveal that slow-light enhanced optical forces between side-coupled photonic-crystal nanowire waveguides can be flexibly controlled by introducing a relative longitudinal shift. We predict that close to the photonic band edge, where the group velocity is reduced, the transverse force can be tuned from repulsive to attractive, and the force is suppressed for a particular shift value. Additionally the shift leads to symmetry breaking that can facilitate longitudinal forces acting on the waveguides, in contrast to unshifted structures where such forces vanish.     

Nanowire plasmonic waveguides,circuits and devices

As typical one‐dimensional nanostructures for waveguiding tightly confined optical fields beyond the diffraction limit, metal nanowires have been used as versatile nanoscale building blocks for functional plasmonic and photonic structures and devices. Metal nanowires, especially those fabricated by bottom‐up synthesis such as Ag and Au nanowires, usually exhibit excellent diameter uniformity and surface smoothness with diameters down to tens of nanometers, which offers great opportunities for plasmonic waveguiding of optical fields with deep‐subwavelength confinement, coherence maintenance and low scattering losses. Based on nanowire plasmonic waveguides, a variety of applications ranging from plasmonic couplers, interferometers, resonators to photon emitters have been reported in recent years. In this article, significant progresses in these nanowire plasmonic waveguides, circuits and devices are reviewed. Future outlook and challenges are also discussed.     

Modeling of single- and multimode photonic-crystal planar waveguides with the plane-wave admittance method

One-foil targets emit most transition radiation (TR) power in storage ring synchrotrons. Such one-foil TR emitting targets (OFTRTs) are optimized, with respect to the foil material and the foil thickness, for use as X-ray lithography (XRL) sources. The best possible elemental material and the foil thickness of OFTRTs for XRL are determined for our storage ring synchrotrons MIRROIRCLE-20SX and MIRRORCLE-6X, which operate with electrons accelerated to 20 MeV and 6 MeV, respectively. It is shown that the XRL efficiency of a OFTRT, with an optimum thickness, increases when the elemental foil material has a lower atomic number Z. The best elemental OFTRT, for performing XRL by MIRRORCLE-20SX, should contain one Be foil with a thickness of d≅240 nm, while the second best OFTRT should be made of one C foil with d≅220 nm. The best elemental OFTRT, for performing XRL by MIRRORCLE-6X, should contain one C foil with d≅35 nm, while the second best OFTRT should be made of one Be foil with d≅100 nm, because there are no thinner Be foils. The XRL efficiency of a C-foil OFTRT increases when a higher-density foil is used. A OFTRT containing one foil of a given material with optimum thickness, in MIRRORCLE-20SX, has approximately 100 times larger XRL efficiency in comparison with such a target in MIRRORCLE-6X. PACS 41.50.+h; 29.25.-t; 81.16.Nd; 41.60.Ap; 29.20.Dh     

Temporal self-action and compression of intense ultrashort laser pulses in hollow photonic-crystal waveguides

Hollow-core waveguides with a periodic (photonic-crystal) cladding are shown to allow efficient temporal compression of high-intensity ultrashort laser pulses and formation of megawatt soliton-like features in the regime of robust isolated guided modes. We numerically analyze the temporal envelope evolution and spectral transformation of the light field in air-guided modes of gas-filled hollow coaxial periodic Bragg waveguides. Based on this analysis, we define optimal compression regimes, permitting high compression ratios (of about six) and high compression efficiencies (up to 73%) to be achieved for microjoule laser pulses with an initial pulse length of 80–400 fs.     

On gravitational conductors,waveguides, and circuits

We show that a material with sufficiently large elastic shear modulus or shear viscosity will act like a gravitational conductor or metal. It will reflect gravitational waves, and it can be used to make gravitational waveguides and circuits. Unlike electromagnetism, a gravitational wave can be guided by a single conductor in transverse mode. Gravitational conductors can obey the dominant energy condition, and they can be larger than their Schwarzschild radius, but they must violate a new condition that is probably satisfied by all existing forms of matter. Direct-current gravitational circuits, although limits of guided gravitational waves, have a simple Newtonian interpretation.This essay is a slightly expanded version of one that received an honorable mention (1978) from the Gravity Research Foundation-Ed.Work supported in part by NSF grant No. PHY78-09616.     

Disposition density of waveguides on printed circuits

The dependencies of the maximum permissible disposition density of waveguides on printed circuits on the contrast value of Δn of refractive indices are computed. It has been shown that minimum cross coupling between adjacent waveguides are observed when the dimension of the core is optimal for providing the maximum fundamental mode confinement within the core.     

Effective and flexible analysis for propagation in time varying waveguides

The equivalence between the propagation of dispersive modal fields in two-dimensional waveguides, and plane waves in a one-dimensional plasma is presented. Exploitation of this equivalence allows a time domain variant of the effective index approach to be used to model dispersive waveguides problems very efficiently. A time domain integral equation is developed for this important practical case and the stability of a computer algorithm based upon it is improved by means of both a semi-implicit formulation and the use of a modified space–time mesh.     

Pedestal antiresonant reflecting waveguides for robust coupling to microsphere resonators and for microphotonic circuits

Strip-line pedestal antiresonant reflecting waveguides are high-confinement, silica integrated optical waveguides in which the optical modes are completely isolated from the substrate by thin high-index layers. These waveguides are particularly well suited for whispering-gallery mode excitation in high-Q microspheres. They can also be used in microphotonic circuits, such as for microring resonators. The theory and design of these structures are highlighted. Experiments that show high coupling efficiency to microspheres are also demonstrated.     

Effective non-linear coefficients of optical waveguides

Using the weakly guiding approximation, and with the assumption that the non-linearities are sufficiently weak so as not to change the transverse mode profile, perturbation theory is used to derive simple expressions for evaluating the modal, or effective, non-linear coefficients of optical waveguide structures based on the non-linear coefficients of the constituent materials. In particular, the third-order and fifth-order optical non-linearities of refraction and absorption are discussed. The expressions are used to estimate the effective modal non-linear refraction coefficients for various types of slab waveguides, focusing primarily on femtosecond refractive non-linearities in semiconductor amplifiers, including quantum-well structures. The results are of particular relevance to the design of all-optical switches based on these effects.     

Amorphous Si waveguides with high-quality stacked gratings for multi-layer Si optical circuits

To realize a stacked multi-layer silicon-based photonic device, a waveguide with a stacked grating was fabricated by using amorphous Si (a-Si) material, which is suitable for constructing layered structures. The fabrication method was based on forming a flat a-Si layer on a non-flat structure by using only spin-on-glass (SOG) coating technique. The a-Si grating was precisely constructed on the a-Si waveguide with gold alignment marks for electron beam lithography. Transmitted and reflected light power dependence on the grating period, wavelength, and polarization was systematically measured and compared with the designed dependence. As a result, the reflected light power exhibited a characteristic peak structure at a particular wavelength. Remarkable transverse electric/transverse magnetic (TE/TM) mode dependence was also observed. Furthermore, the measured and the designed properties were in excellent agreement with each other. Consequently, the designed structure was well reproduced in the actual stacked structure based on the a-Si material. These results pave the way for novel a-Si based integrated photonic devices such as polarization selectors and wavelength filters, indicating that a-Si is an excellent material for implementing Si-based multi-layer optical circuits.     

Effective equations for disordered one-dimensional systems

Using the method of supersymmetry, effective equations are derived for the one-particle Green's function of various one-dimensional disordered models. As an example, explicit expressions for the density of states and the localization length are derived for the two-band model of a one-dimensional semiconductor.     

Effective potential for complex Langevin equations

We construct an effective potential for the complex Langevin equation on a lattice. We show that the minimum of this effective potential gives the space–time and Langevin time average of the complex Langevin field. The loop expansion of the effective potential is matched with the derivative expansion of the associated Schwinger–Dyson equation to predict the stationary distribution to which the complex Langevin equation converges.