Ubiquity of Fourier transformation in optical sciences.

Fourier transformation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. I discuss some of its applications in optical science and engineering to provide a broad perspective on the intimate relation between the physical and mathematical concepts that are elegantly interwoven within the theory of Fourier transforms.

Ultrahigh Aspect Ratio Copper-Nanowire-Based Hybrid Transparent Conductive Electrodes with PEDOT:PSS and Reduced Graphene Oxide Exhibiting Reduced Surface Roughness and Improved Stability.

Copper nanowires (CuNWs) with ultrahigh aspect ratio are synthesized with a solution process and spray-coated onto select substrates to fabricate transparent conductive electrodes (TCEs). Different annealing methods are investigated and compared for effectiveness and convenience. The CuNWs are subsequently combined with the conductive polymer poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) ( PEDOT: PSS) or with reduced graphene oxide (rGO) platelets in order to reduce the surface roughness and improve the durability of the fabricated TCEs. Our best-performing PEDOT: PSS/CuNW films have optical transmittance T550 = 84.2% (at λ = 550 nm) and sheet resistance Rs = 25 Ω/sq, while our best CuNW/rGO films have T550 = 84% and Rs = 21.7 Ω/sq.

An effective nanosensor for organic molecules based on water-soluble mercaptopropionic acid-capped CdTe nanocrystals with potential application in high-throughput screening and high-resolution optical microscopy.

Specially-treated glass substrates coated with a thin film of water soluble mercaptopropionic acid (MPA) capped CdTe nanocrystals (NCs) were prepared and found to undergo photoluminescence changes by as much as 40% when micro-droplets of organic molecules were placed in the nanometer-range proximity of the NCs. This imaging technique involving close proximity between a nano-crystal and an organic molecule is found to provide a 2 × -3 × enhanced contrast ratio over the conventional method of fluorescence imaging. Photoluminescence of NCs is recoverable upon removal of the organic molecules, therefore validating these NCs as potential all-optical organic molecular nanosensors. Upon optimization and with proper instrumentation, these nano-crystals could eventually serve as point-detectors for purposes of super-resolution optical microscopy. No solvents are required for the proposed sensing mechanism since all solutions were dried under argon flow. Fluorophores and fluorescent proteins were investigated, including fluorescein, Rhodamine 6G, and green fluorescent protein (GFP). Furthermore, NC photoluminescence changes were systematically quantified as a function of the solution pH and of the organic molecule concentration. Long duration (> 40 minutes) continuous excitation studies were conducted in order to evaluate the reliability of the proposed sensing scheme.

Thermally robust and blinking suppressed core/graded-shell CdSe/CdSe1-xSx/CdS 'giant' multishell semiconductor nanocrystals.

We demonstrate that core/graded-shell CdSe/CdSe1-xSx/CdS giant semiconductor nanocrystals (g-NCs) have robust photoluminescence (PL) temperature response. At a size of 10.2 nm in diameter, these g-NCs undergo a PL drop of only 30% at 355 K relative to their PL intensity at 85 K. In comparison, the core/step-shell CdSe/CdS g-NCs at the same diameter exhibit 80% PL drop at 355 K. Spectral shifting and broadening were found to be, respectively, 5-10 times and 2-4 times smaller than those observed in standard CdSe core and CdSe/CdS core/shell NCs. These core/graded-shell g-NCs are largely blinking suppressed and have insignificant photoluminescence decay even after excitation at very high irradiance (44 kW cm(-2)) for over an hour. These types of g-NC have potential applications as the active medium for thermally robust laser devices (in the visible range) or as temperature-insensitive bioprobes for biomedical imaging.

Mansuripur replies.

A Reply to the Comments by Vanzella, Barnett, Saldanha, and Khorrami.

An effective and simple oxygen nanosensor made from MPA-capped water soluble CdTe nanocrystals.

CdTe semiconductor nanocrystals (NCs) with 3-mercaptopropionic acid as the ligand exhibit a reversible response towards inter-switching oxygen and argon environments. The photoluminescence response is investigated at multiple oxygen concentrations, NC coverage and excitation intensities, in which all conditions exhibit full recovery upon exposure to flowing argon. The CdTe NC's large surface-to-volume ratio results in high sensitivity towards oxygen molecules with significant photoluminescence quenching at a concentration of 40 ppm. This suggests a novel approach to the creation of simple, inexpensive and ultrasensitive oxygen nanosensors.

Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation.

The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume containing a distribution of electrical charges and currents. If electric and magnetic dipoles also happen to be present in a material medium, they are traditionally treated by expressing the corresponding polarization and magnetization distributions in terms of bound-charge and bound-current densities, which are subsequently added to free-charge and free-current densities, respectively. In this way, Maxwell's macroscopic equations are reduced to his microscopic equations, and the Lorentz law is expected to provide a precise expression of the electromagnetic force density on material bodies at all points in space and time. This Letter presents incontrovertible theoretical evidence of the incompatibility of the Lorentz law with the fundamental tenets of special relativity. We argue that the Lorentz law must be abandoned in favor of a more general expression of the electromagnetic force density, such as the one discovered by Einstein and Laub in 1908. Not only is the Einstein-Laub formula consistent with special relativity, it also solves the long-standing problem of "hidden momentum" in classical electrodynamics.

Fabrication of phase-change chalcogenide Ge2Sb2Te5 patterns by laser-induced forward transfer.

Femtosecond laser pulses are focused on a thin film of Ge2Sb2Te5 phase-change material, and the transfer of the illuminated material to a nearby substrate is investigated. The size, shape, and phase-state of the fabricated pattern can be effectively controlled by the laser fluence and by the thickness of the Ge2Sb2Te5 film. Results show multi-level electrical and optical reflection states of the fabricated patterns, which may provide a simple and efficient foundation for patterning future phase-change devices.

Fabrication of phase-change Ge2Sb2Te5 nano-rings.

Phase-change material Ge2Sb2Te5 rings with nanometer-scale thickness have been fabricated using the photo-thermal effect of a focused laser beam followed by differential chemical etching. Laser irradiation conditions and etching process parameters are varied to control the geometric characteristics of the rings. We demonstrate the possibility of arranging the rings in specific geometric patterns, and also their release from the original substrate.

Local electrical characterization of laser-recorded phase-change marks on amorphous Ge2Sb2Te5 thin films.

Amorphous thin films of Ge(2)Sb(2)Te(5), sputter-deposited on a thin-film gold electrode, are investigated for the purpose of understanding the local electrical conductivity of recorded marks under the influence of focused laser beam. Being amorphous, the as-deposited chalcogenide films have negligible electrical conductivity. With the aid of a focused laser beam, however, we have written on these films micron-sized crystalline marks, ablated holes surrounded by crystalline rings, and other multi-ring structures containing both amorphous and crystalline zones. Within these structures, nano-scale regions of superior local conductivity have been mapped and probed using our high-resolution, high-sensitivity conductive-tip atomic force microscope (C-AFM). Scanning electron microscopy and energy-dispersive spectrometry have also been used to clarify the origins of high conductivity in and around the recorded marks. When the Ge(2)Sb(2)Te(5) layer is sufficiently thin, and when laser crystallization/ablation is used to define long isolated crystalline stripes on the samples, we find the C-AFM-based method of extracting information from the recorded marks to be superior to other forms of microscopy for this particular class of materials. Given the tremendous potential of chalcogenides as the leading media candidates for high-density memories, local electrical characterization of marks recorded on as-deposited amorphous Ge(2)Sb(2)Te(5) films provides useful information for furthering research and development efforts in this important area of modern technology.

Laser-induced phase transitions of Ge2Sb2Te5 thin films used in optical and electronic data storage and in thermal lithography.

Amorphous thin films of Ge(2)Sb(2)Te(5), sputter-deposited on a ZnS-SiO(2) dielectric layer, are investigated for the purpose of understanding the structural phase-transitions that occur under the influence of tightly-focused laser beams. Selective chemical etching of recorded marks in conjunction with optical, atomic force, and electron microscopy as well as local electron diffraction analysis are used to discern the complex structural features created under a broad range of laser powers and pulse durations. Clarifying the nature of phase transitions associated with laser-recorded marks in chalcogenide Ge(2)Sb(2)Te(5) thin films provides useful information for reversible optical and electronic data storage, as well as for phase-change (thermal) lithography.

Simple colloidal synthesis of single-crystal Sb-Se-S nanotubes with composition dependent band-gap energy in the near-infrared.

We report the first synthesis of high-quality binary and ternary Sb(2)Se(3-x)S(x) nanotubes across the entire compositional range from x = 0 to 3 via a simple, low-cost, colloidal synthetic method of injection of Sb(III)-complex solution into a hot paraffin liquid containing Se, S, or a mixture thereof. In contrast to the classic rolling mechanism, the modular formation of the reported nanotubes follows a four-stage self-seeding process: (i) amorphous nanospheres, (ii) short crystalline nanotubes growing out of relatively large amorphous nanospheres, (iii) long crystalline nanotubes attached to small amorphous nanospheres, and (iv) single-crystal nanotubes. The obtained single-crystal nanotubes have tunable composition, orthorhombic phase, well-defined rectangular cross sections, and growth direction along [001], as revealed by X-ray diffraction, scanning electron microscopy, energy-dispersive X-ray spectroscopy, transmission electron microscopy, and selected area electron diffraction studies. UV-vis-NIR absorption spectroscopy reveals that the optical bandgap energy of the Sb(2)Se(3-x)S(x) (0 < or = x < or = 3) nanotubes increases quadratically with the sulfur concentration x with these bandgap energies falling in the range from 1.18 to 1.63 eV at the red edge of the solar spectrum. The present study opens a new avenue to low-cost, large-scale synthesis of high quality semiconductor nanotubes with technological applications in solar energy conversion and also for a wide range of optical nanodevices operating in the near-infrared.

Maxwell's macroscopic equations, the energy-momentum postulates, and the Lorentz law of force.

We argue that the classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for actual (i.e., physical) models of polarization P and magnetization M , these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r,t) and M(r,t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with the requirements of the special theory of relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. One advantage of the proposed formulation is that it sidesteps the long-standing Abraham-Minkowski controversy surrounding the electromagnetic momentum inside a material medium by simply "assigning" the Abraham momentum density E(r,t)xH(r,t)/c2 to the electromagnetic field. This well-defined momentum is thus taken to be universal as it does not depend on whether the field is propagating or evanescent, and whether or not the host medium is homogeneous, transparent, isotropic, dispersive, magnetic, linear, etc. In other words, the local and instantaneous momentum density is uniquely and unambiguously specified at each and every point of the material system in terms of the E and H fields residing at that point. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.

Water-based route to ligand-selective synthesis of ZnSe and Cd-doped ZnSe quantum dots with tunable ultraviolet A to blue photoluminescence.

A water-based route has been demonstrated for synthesizing ZnSe and Cd-doped ZnSe (Zn(x)Cd(1-x)Se, 0 < x < 1) quantum dots (QDs) that have tunable and narrow photoluminescence (PL) peaks from the ultraviolet A (UVA) to the blue range (350-490 nm) with full-width at half-maximum (fwhm) values of 24-36 nm. Hydrazine (N(2)H(4)) was used to maintain oxygen-free conditions, allowing the reaction vessel to be open to air. The properties of the QDs were controlled using the thiol ligands, 3-mercaptopropionic acid (MPA), thiolglycolic acid (TGA), and l-glutathione (GSH). On the basis of optical spectra, linear three-carbon MPA attenuated nucleation and growth, yielding small ZnSe QDs with a high density of surface defects. In contrast, TGA and GSH produced larger ZnSe QDs with lower surface defect densities. The absorption spectra show that growth was more uniform and better controlled with linear two-carbon TGA than branched bifunctional GSH. After 20 min of growth TGA-capped ZnSe had an average diameter of 2.5 nm based on high-resolution transmission electron microscopy images; these nanocrystals had an absorbance peak maximum of approximately 340 nm (3.65 eV) and a band gap PL emission peak at 372 nm (3.34 eV). Highly fluorescent Zn(x)Cd(1-x)Se QDs were fabricated by adding a Cd-thiol complex directly to ZnSe QD solutions; PL peaks were tuned in the blue range (400-490 nm) by changing the Zn to Cd ratio. The Cd-bearing nanocrystals contained proportionally more Se based on X-ray photoelectron spectroscopy, and Cd-Se bonds had ionic character, in contrast to primarily covalent Zn-Se bonds.

Electromagnetic force and torque in ponderable media.

Maxwell's macroscopic equations combined with a generalized form of the Lorentz law of force are a complete and consistent set of equations. Not only are these five equations fully compatible with special relativity, they also conform with conservation laws of energy, momentum, and angular momentum. We demonstrate consistency with the conservation laws by showing that, when a beam of light enters a magnetic dielectric, a fraction of the incident linear (or angular) momentum pours into the medium at a rate determined by the Abraham momentum density, E x H/c(2), and the group velocity V(g) of the electromagnetic field. The balance of the incident, reflected, and transmitted momenta is subsequently transferred to the medium as force (or torque) at the leading edge of the beam, which propagates through the medium with velocity V(g). Our analysis does not require "hidden" momenta to comply with the conservation laws, nor does it dissolve into ambiguities with regard to the nature of electromagnetic momentum in ponderable media. The linear and angular momenta of the electromagnetic field are clearly associated with the Abraham momentum, and the phase and group refractive indices (n(p) and n(g)) play distinct yet definitive roles in the expressions of force, torque, and momentum densities.

Electromagnetic stress tensor in ponderable media.

We derive an expression for the Maxwell stress tensor in a magnetic dielectric medium specified by its permittivity epsilon and permeability micro. The derivation proceeds from the generalized form of the Lorentz law, which specifies the force exerted by the electromagnetic E and H fields on the polarization P and magnetization M of a ponderable medium. Our stress tensor differs from the well-known tensors of Abraham and Minkowski, which have been at the center of a century-old controversy surrounding the momentum of the electromagnetic field in transparent materials.

All-fiber bidirectional passively mode-locked ring laser.

We report the design and operation of a novel all-fiber bidirectional passively mode-locked ring laser. An erbium-doped fiber was chosen as the active element in a ring cavity arrangement. A short segment of a fiber taper embedded in carbon nanotubes/polymer composite, acting as a saturable absorber, was used to enable bidirectional mode locking. The laser generates two stable femtosecond pulse trains in opposite directions. A beat note of about 2 MHz, having a bandwidth of less than 2 kHz, is measured when the pulses propagating in opposite directions are (temporally) overlapped at a photodetector. We believe this device will find important applications in precision rotation sensing.

Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite.

We propose and demonstrate a new saturable absorber based on a fiber taper embedded in a carbon nanotube/polymer composite. Greater than a 10% reduction in absorption (due to saturation) is directly measured for our saturable absorber. Using an embedded fiber-taper saturable absorber, we built an all-fiber mode-locked ring laser, which produces 594 fs/1.7 nJ pulses with a repetition rate of 13.3 MHz.

Fiber laser using a microsphere resonator as a feedback element.

We show that a glass microsphere resonator can be used as a wavelength-selective mirror in fiber lasers. Due to their high quality factor (Q approximately 10(8)), microsphere resonators possess a narrow reflection bandwidth. This feature enables construction of single-frequency fiber lasers even when the laser cavity is long. Nonlinear effects (such as stimulated Raman lasing) were also observed in our setup at relatively low pump powers.