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Developing algorithms that produce approximate solutions is always interesting when we are generating the final solution for a problem. Progressive algorithms report a partial solution to the user which approximates the final solution in some specific steps. Thus, the user can stop the algorithm if the error of the partial solution is tolerable in terms of the application. In this paper, we study the closest pair problem under the Euclidean metric. A progressive algorithm is designed for the closest pair problem, which consists of steps and spends time in each step. In step r, the error of the partial solution is bounded by , where αis the ratio of the maximum pairwise distance and the minimum pairwise distance of points.

We numerically investigate and design a compact electrically pumped edge-emitting photonic crystal waveguide (PCW) quantum dot (QD) laser operating at room temperature. Use of a narrowband folded directional coupler as the output mirror has made the proposed structure an edge-emitting single-mode laser. Moreover, we propose a set of rate equations to model the performance of the PCW-QD laser. In the proposed model, we take the effects of the homogeneous and inhomogeneous broadenings and the slow-light effects on the modal gain and loss coefficient into account. Simulations show that threshold current as low as ∼26  μA can be achieved for the PCW-QD laser with a 50-μm-long cavity and output power in the range of micro-watts. The proposed low-threshold edge-emitting PCW-QD laser is a promising light source for the off-chip and on-chip photonic network applications.

We have simulated multiexciton generation (MEG) processes in Si and Ge nanocrystals, employing the equation of motion coupled cluster single and double as a high-level ab initio approach. Simulations, consistent with the experimental results reported so far, reveal the key role of the d-polarized valence component in the chosen basis set on the accuracy and reliability of the results. Moreover, the MEG thresholds calculated with def2SVP basis set are ∼8.23(8.07) eV for seven (eight)-atom Si clusters and ∼7.58(6.84) eV for similar Ge clusters. The normalized MEG thresholds of Ge nanocrystals are 8% smaller with respect to Si. Thus, in contrast to Si, they are more appealing to the optical device designers for enhancing the device quantum efficiency. Furthermore, the resemblance of the symmetry of the simulated seven-atom clusters to those of the experimentally domelike grown nanocrystals makes the behavior of their MEG quantum probability similar.

A new generation unbiased antennaless CW terahertz (THz) photomixer emitters array made of asymmetric metal–semiconductor–metal (MSM) gratings with a subwavelength pitch, operating in the optical near-field regime, is proposed. We take advantage of size effects in near-field optics and electrostatics to demonstrate the possibility of enhancing the THz power by 4 orders of magnitude, compared to a similar unbiased antennaless array of the same size that operates in the far-field regime. We show that, with the appropriate choice of grating parameters in such THz sources, the first plasmonic resonant cavity mode in the nanoslit between two adjacent MSMs can enhance the optical near-field absorption and, hence, the generation of photocarriers under the slit in the active medium. These photocarriers, on the other hand, are accelerated by the large built-in electric field sustained under the nanoslits by two dissimilar Schottky barriers to create the desired large THz power that is mainly radiated downward. The proposed structure can be tuned in a broadband frequency range of 0.1–3 THz, with output power increasing with frequency.

Taking advantage of the Kerr nonlinearities of metallic nanolayers and graphene (G) and the well-known pump–probe method, we show that 200-nm-wide slabs of hyperbolic metamaterial (HMM) composed of 14 vertically stacked unit cells can be switched all optically between the negative refraction regime (ON state) and the no-transmission regime (OFF state), when illuminated by appropriately chosen TE-polarized Gaussian pump and TM-polarized CW probe. Finite element method numerical simulations show that the HMM slab with unit cells made of Au/Al_2O_3 nanolayers suffering from a relatively large plasmonic loss exhibits an ON state transmittance spectrum limited to 52%–72% over the visible range of 585–600 nm, when a 500 V/μm pump signal is utilized. Similar numerical results obtained for the HMM slab whose unit cells are made of Au/Al_2O_3/G/Al_2O_3/Au nanolayers show that a 4 V/μm pump signal is enough to stimulate the Kerr effect, resulting in a ∼97% ON state transmittance over the ultra-narrowband of 803–805 nm. Moreover, simulations show that when the unit cells are made of Ag/Si/G/Si/Ag nanolayers, a 95-nm-wide ON state transmittance of 49%–99% over the IR range of 800–895 nm can be obtained with a 19.5 V/μm pump. The proposed HMM structures can be used as all-optical switches in future optical digital systems.

In this paper, we report on the design procedure for developing subwavelength graphene-based plasmonic waveguide, performing as a THz switch or an AND/OR logic gate. The propagation length of the surface plasmons (SPs), stimulated by a 6 THz TM polarized incident wave along this waveguide with a top graphene layer whose chemical potential is held at $\mu_{\rm C}=300~{\hbox{meV}}$ (ON state) is more than 35 times larger than that in the waveguide with $\mu_{\rm C}= 0~{\hbox{eV}}$ (OFF state). Numerical results, obtained from full wave simulations using a finite element method, also show that the modulation depth density obtained for the straight plasmonic switching waveguide, whose length is just about 20% of the incident wavelength, is larger than those reported to date. Moreover, we also designed a logic AND gate composed of a straight waveguide, a Y-branch switch, and a logic OR gate composed of two face to face Y-branches, whose total lengths are ${\sim} {\hbox{37\%}}$, ${\sim} {\hbox{45\%}}$ , and ${\sim} {\hbox{53\%}}$ of the incident wavelength, respectively. Simulations show that the maximum ON/OFF ratios for these subwavelength plasmonic waveguides that occur between their ‘1 1’ and ‘0 0’ logical states are ${\sim} {\hbox{41.37}}$, ${\sim} {\hbox{39.87}}$, and ${\sim} {\hbox{40.76}}~{\hbox{dB}}$ , respectively. These numerical data also show that the modulation depth densities obtained for these devices are also greater than those reported to date. The proposed graphene-based plasmonic switches and gates offer potential building blocks for the future digital plasmonic circuits operating around 6 THz.

Using numerical analysis, we compare the results of optofluidic and rod filling techniques for the broadening of supercontinuum spectra generated by As_2Se_3 chalcogenide photonic crystal fibers (PCFs). The numerical results show that when air-holes constituting the innermost ring in a PCF made of As_2Se_3-based chalcogenide glass are filled with rods of As_2S_3-based chalcogenide glass, over a wide range of mid-IR wavelengths, an ultra-flattened near-zero dispersion can be obtained, while the total loss is negligible and the PCF nonlinearity is very high. The simulations also show that when a 50 fs input optical pulse of 10 kW peak power and center wavelength of 4.6 μm is launched into a 50 mm long rod-filled chalcogenide PCF, a ripple-free spectral broadening as wide as 3.86 μm can be obtained.

We propose a nanostructured hyperbolic metamaterial (HMM) that can make the transition between elliptic and hyperbolic regimes in the near infrared (IR) frequency range. This switchable HMM is a slab made of a periodic stack of metal/Al_2O_3/graphene/Al_2O_3/metal nano-layers. By tuning the graphene conductivity via tuning its chemical potential, through a variable external bias, the response of this highly anisotropic medium to a monochromatic TM incident light can be switched between a positive/negative refraction regime and a negative refraction/no-transmission regime. The proposed structure is suitable for applications such as beam splitters, modulators, four-port devices, and optical gates.

Using a nonstationary state solution to the nonlinear Schrödinger equation (NLSE), we report the results of our numerical investigation on the swing behavior of spatial solitons propagating along waveguides whose refractive indices in the transverse direction are perturbed by Scarf II type parity–time symmetric profiles. We show that solitons, after entering parity–time symmetry (PTS) cells with Scarf II profiles will, in general, swing along the waveguide with nonuniform amplitude and period. Nevertheless, it is demonstrated that when the average incident position in the transverse direction is set at the center of the profile symmetry and the amplitude of the incident soliton exceeds a specific value, the soliton behavior could be approximated by a stationary-state solution to the NLSE and say it is almost self-trapped. Simulation also shows that, depending on the soliton’s initial average transverse input position, the swing behavior could be greatly influenced by the nonreciprocity of PTS cells.

We present the design procedure for an ultracompact low-power all-optical modulator based on a dispersion-engineered slow-light regime in a photonic crystal Mach–Zehnder interferometer (PhC MZI), selectively infiltrated by nonlinear optical fluids. The dispersionless slow-light regime enhancing the nonlinearities enabled a 22 μm long PhC MZI to operate as a modulator with an input power as low as 3??mW/μm. Simulations reveal that the switching threshold can be controlled by varying the optofluidic infiltration.

We are proposing a procedure to enhance the transmission efficiency of 60° photonic crystal (PhC) waveguide bends by means of selective optofluidic infiltration of an air hole, which is created as a point defect at the center of the conventional 60° PhC bend. Numerical studies demonstrate that by varying the defect radius and indices of optical fluids, one may enhance the bend transmission level and tune its 3 dB bandwidth over a substantial range of 88–138 nm. In order to perform the numerical simulations, we have used two-dimensional (2D) finite difference time domain plane wave method, keeping in mind that the spectral features obtained by these 2D calculations are about 15% redshifted from those of real three-dimensional structures.

We have obtained a simple numerical model that explains the temperature behavior of multi-quantum-dot (QD) nanophotonic devices whose operations are based on optical near-field (ONF) interactions between any two resonant QDs that are in thermal equilibrium. This model involves a set of coupled rate equations that govern the temporal behavior of the QDs' energy level occupancies. Under a certain operating condition, this simple model can substitute for the more complex density matrix (DM) approach in modeling the temperature dependence of the ONF energy transfer rate (R_ONF) between any two resonant QDs in thermal equilibrium. The same applies for modeling the system state-filling time (τ_S). Applying our simple model to a two-QD system, we have derived analytical formulas for the interdot and the intradot transfer rates at finite temperatures (T≥0). Furthermore, by assuming a unidirectional energy transport operating condition, we have also derived an analytic formula for calculating τ_S for a two-QD system. To the best of our knowledge, this work is the first instance of reporting such analytic equations. Approximated values of τ_S obtained from our simple analytic equation are in reasonable agreements with those calculated by the DM approach.

We report the behavior of spatial optical solitons propagating through inhomogeneous waveguides with Gaussian, single triangular, and double-triangular refractive index profiles. In a given Gaussian profile, as the soliton amplitude decreases below a certain value, its behavior deviates from that of a particlelike soliton. Dependence of the swing period of a spatial soliton in a single triangular index profile on its amplitude, η, is less significant than that in a Gaussian profile. We also report the interacting behavior of two solitons propagating simultaneously through a waveguide with a double-triangular index profile. Furthermore, we present the effects of the solitons' initial phase factors and amplitude on their behavior.

Using the coupled-mode and carrier rate equations, we have derived a dynamic model for the distributed feedback semiconductor optical amplifier (DFB-SOA) all-optical flip-flop (AOFF). We have analyzed the effects of the coupling coefficient and the corrugation position on the dynamic response of the device. We have also investigated the effects of cross-phase modulation on the switching speed of the DFB-SOA with the distributed coupling coefficient (DCC), known as the DCC-DFB-SOA AOFF. Furthermore, it is shown that by optimizing the coupling coefficient value and the corrugation position, the AOFF speed limitation is improved significantly. The ON and OFF switching time values, in an optimized condition, are 300 and 100 ps, respectively, while the carrier lifetime is about 780 ps. In comparison with those of a conventional DFB-SOA-AOFF, these values show reductions of more than 2 and 14 times in the ON and the OFF switching times, respectively. Under such conditions, a maximum bit rate of 1.4 GHz is achieved. The finite difference time-domain method is utilized for the numerical simulations.

By modifying the design of an existing two-input nanophotonic AND gate, whose operation is based on optical near-field (ONF) interactions among three neighboring quantum dots (QDs), we have improved the gate ON/OFF ratio by up to about 9 dB. To do this, we have eliminated the possibility of direct ONF interaction between the input and output dots. Then, by adding another QD, as the second control dot to both existing and the modified two-input architectures, we have proposed two new three-input nanophotonic AND gate schemes—one with direct ONF interaction between its input and output dots, and the other without such interaction. Although, the former gate turns on relatively faster, one of its three possible ON/OFF ratios are shown to be about 7.3 dB lower than the latter. The differences in two other possible ON/OFF ratios of the two new gates are insignificant.

We propose a new numerical model to analyze heat induced by two-photon absorption and free-carrier absorption, while high intensity optical pulses propagate along silicon-on-insulator (SOI) nanowaveguides (NWGs). Using this model, we demonstrate that such induced heat causes a shift in the amount of wavelength conversion and hence deteriorates the converter output characteristics for pulses in the picosecond regime. The wavelength shift induced by a pulse with maximum input intensity and full width at half-maximum of I_max=1.5×10^10 W.cm^−2 and T_FWHM=30 ps, propagating along a SOI NWG with an effective cross-sectional area of a_eff=0.15 μm^2, is shown to be Δλ_s≈8 pm. We also demonstrate that such a shift can be compensated by tuning the pump intensity down by approximately 6.33%.

Chromatic dispersion compensation is an essential feature of high speed dense wavelength-division multiplexing (DWDM) systems. We propose a dispersion compensator structure whose characteristics meet the optical DWDM system requirements. The proposed structure is based on Fibonacci quasi-periodic multilayer structures composed of layers with large index differences. Studying the dispersive properties of Fibonacci structures with generation numbers j=3 and 4, and calculating group delay (GD) and group velocity dispersion (GVD) of their reflection bands, we have demonstrated that to have a smooth GD and almost a constant GVD in each band of a DWDM system, one needs not only to suitably chirp the structure refractive index profile, but also must properly apodize it. We also demonstrate the possibility of achieving high slope GDs and large GVDs by means of high order Fibonacci structures with thicker layers. Finally, by varying the layer dimensions and refractive indices as well as Fibonacci's order, one can design DWDM dispersion compensators suitable for distances as long as 220 km.

We propose a photodetector (PD) based on the internal photoemission effect over a Schottky barrier on a CMOS-compatible Si microring resonator for 1.55 μm. To analyze the device, we model the microring waveguide partially covered by a metal/silicide nanolayer, using the Z-transform method. The proposed structure benefits from the resonant-cavity-enhanced (RCE) waveguide PDs enjoying high efficiency and wavelength selectivity. Simulations show that the maximum value of the bandwidth-efficiency product for the proposed structure is in the order of 10 GHz, which is much higher than those reported for other RCE-based PDs.

We show a PT-symmetric coupler having an arm with a tunable gain and a no-loss arm when appropriately designed to possess reciprocal behavior, unlike its rivals having a fixed gain/loss arm, can perform as a tunable 2×2 spatial optical switch. The degree of the tunability equals the ratio of the coupler’s length to the total coupling length.

We propose a novel and compact all-optical tunable filter with embedded preamplifier and channel selector. This filter is based on cross-Raman scattering (XRS) in a silicon nanowire waveguide, suitable for multichannel optical communications. Tuning is performed by means of tuning the pump center wavelength. With this tuning approach the separation between the pump wavelength and that of the desired channel should equal the Raman shift in Si. Spanning over 40 optical communication channels following the ITU-T G.694.1 standard (100 GHz grid), our simulation results have demonstrated an excellent channel selectivity and tunabilty for the proposed all-optical filter. The XRS process in Si nanowire has amplified the desired channel by about 11.5+/-0.38 dB, while the suppression ratios for the first and the second neighboring channels are about 28+/-0.25 and 33.6+/-0.31 dB, respectively.