Numerical modeling of optical levitation and trapping of the "stuck" particles with a pulsed optical tweezers

We present the theoretical analysis and the numerical modeling of optical levitation and trapping of the stuck particles with a pulsed optical tweezers. In our model, a pulsed laser was used to generate a large gradient force within a short duration that overcame the adhesive interaction between the stuck particles and the surface; and then a low power continuous - wave (cw) laser was used to capture the levitated particle. We describe the gradient force generated by the pulsed optical tweezers and model the binding interaction between the stuck beads and glass surface by the dominative van der Waals force with a randomly distributed binding strength. We numerically calculate the single pulse levitation efficiency for polystyrene beads as the function of the pulse energy, the axial displacement from the surface to the pulsed laser focus and the pulse duration. The result of our numerical modeling is qualitatively consistent with the experimental result. (C) 2005 Optical Society of America.

Nanofabrication for On-Chip Optical Levitation, Atom-Trapping, and Superconducting Quantum Circuits

Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO₂ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_m = 5.8(1.1) x 10⁵, representing more than an order of magnitude improvement over the conventional limits of SiO₂ for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d₀ ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si₃N₄ membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

Wave-front analysis method of circular aperture sampling for collimation testing

A new type of wave-front analysis method for the collimation testing of laser beams is proposed. A concept of wave-front height is defined, and, on this basis, the wave-front analysis method of circular aperture sampling is introduced. The wave-front height of the tested noncollimated wave can be estimated from the distance between two identical fiducial diffraction planes of the sampled wave, and then the divergence is determined. The design is detailed, and the experiment is demonstrated. The principle and experiment results of the method are presented. Owing to the simplicity of the method and its low cost, it is a promising method for checking the collimation of a laser beam with a large divergence. © 2005 Optical Society of America.

Highly sensitive wave-front sensor with a non-zero-order phase plate

We propose a novel highly sensitive wave front detection method for a quick check of a flat wave front by taking advantage of a non-zero-order pi phase plate that yields a non-zero-order diffraction pattern. When a light beam with a flat wave front illuminates a phase plate, the zero-order intensity is zero. When there is a slight distortion of the wave front, the zero-order intensity increases. The ratio of first-order intensity to that of zero-order intensity is used as the criterion with which to judge whether the wave front under test is flat, eliminating the influence of background light. Experimental results demonstrate that this method is efficient, robust, and cost-effective and should be highly interesting for a quick check of a flat wave front of a large-aperture laser beam and adaptive optical systems. (c) 2005 Optical Society of America.

Composite second-order performance improvement in optical fibre CATV transmission system using chirped fibre grating

Theoretically, we analyse the dispersion compensation characteristics of the chirped fibre grating (CFG) in an optical fibre cable television (CATV) system and obtain the analytic expression of the composite second-order (CSO) distortion using the time-domain form of the field envelope wave equation. The obtained result is in good agreement with the numerical simulation result. Experimentally, we verify the result by making use of the tunable characteristics of CFG to change the dispersion compensation amount and obtain an optimal CSO performance in a 125km fibre transmission link. Both the theoretical and experimental results show that the CSO performance can be improved by properly choosing the dispersion compensation amount for a certain fibre transmission link.

Effect of microcosmic optical parameters of dopants on the signal-to-noise ratio in doubly doped LiNbO3 crystals

We propose a united theory that describes the two-center recording system by taking scattering noise into account. The temporal evolution of the signal-to-noise ratio in doubly doped photorefractive crystals is described based on jointly solving material equations and coupled-wave equations with the fourth-order Runge-Kutta method. Roles of microcosmic optical parameters of dopants on the signal-to-noise ratio are discussed in detail. The theoretical results can confirm and predict experimental results. (c) 2005 Elsevier GmbH. All rights reserved.

Analysis of optical systems with extended depth of field using the Wigner distribution function

We describe the use of a Wigner distribution function approach for exploring the problem of extending the depth of field in a hybrid imaging system. The Wigner distribution function, in connection with the phase-space curve that formulates a joint phase-space description of an optical field, is employed as a tool to display and characterize the evolving behavior of the amplitude point spread function as a wave propagating along the optical axis. It provides a comprehensive exhibition of the characteristics for the hybrid imaging system in extending the depth of field from both wave optics and geometrical optics. We use it to analyze several well-known optical designs in extending the depth of field from a new viewpoint. The relationships between this approach and the earlier ambiguity function approach are also briefly investigated. (c) 2006 Optical Society of America.

Time domain synthesis of electro-optical birefringent system for optical waveform generation

In this paper is described a novel technique for producing an electro-optical intensity synthesizer which can generate different periodic time domain waveforms through only sine or cosine wave applied-voltages. The synthesizer presented here consists of a series of stages between two polarizers, with each stage consisting of an electro-optic element and a compensator. Every electro-optical element has the same applied-voltage function but different azimuth angles and ratios between the longitudinal and transverse lengths. The main principle is the synthesis of an electro-optic effect and a polarization interference effect in the time domain. This technique is based on an expanded Fourier positive-direction searching algorithm, which can not only simplify the calculation process but also produces many choices of structural parameters for different waveforms generation. A three-stage synthesis of an electro-optical birefringent system for continuous square waveform is undertaken to prove the principle.

An Optically recombined laser interferometer for gravitational wave detection

Kilometer scale interferometers for the detection of gravitational waves are currently under construction by the LIGO (Laser Interferometer Gravitational-wave Observatory) and VIRGO projects. These interferometers will consist of two Fabry-Perot cavities illuminated by a laser beam which is split in half by a beam splitter. A recycling mirror between the laser and the beam splitter will reflect the light returning from the beam splitter towards the laser back into the interferometer. The positions of the optical components in these interferometers must be controlled to a small fraction of a wavelength of the laser light. Schemes to extract signals necessary to control these optical components have been developed and demonstrated on the tabletop. In the large scale gravitational wave detectors the optical components must be suspended from vibration isolation platforms to achieve the necessary isolation from seismic motion. These suspended components present a new class of problems in controlling the interferometer, but also provide more exacting test of interferometer signal and noise models.

This thesis discusses the first operation of a suspended-mass Fabry-Perot-Michelson interferometer, in which signals carried by the optically recombined beams are used to detect and control all important mirror displacements. This interferometer uses an optical configuration and signal extraction scheme that is planned for the full scale LIGO interferometers with the simplification of the removal of the recycling mirror. A theoretical analysis of the performance that is expected from such an interferometer is presented and the experimental results are shown to be in generally good agreement.

The resolution of the thermodynamic paradox and the theory of guided wave propagation in anisotropic media

The resolution of the so-called thermodynamic paradox is presented in this paper. It is shown, in direct contradiction to the results of several previously published papers, that the cutoff modes (evanescent modes having complex propagation constants) can carry power in a waveguide containing ferrite. The errors in all previous “proofs” which purport to show that the cutoff modes cannot carry power are uncovered. The boundary value problem underlying the paradox is studied in detail; it is shown that, although the solution is somewhat complicated, there is nothing paradoxical about it.

The general problem of electromagnetic wave propagation through rectangular guides filled inhomogeneously in cross-section with transversely magnetized ferrite is also studied. Application of the standard waveguide techniques reduces the TM part to the well-known self-adjoint Sturm Liouville eigenvalue equation. The TE part, however, leads in general to a non-self-adjoint eigenvalue equation. This equation and the associated expansion problem are studied in detail. Expansion coefficients and actual fields are determined for a particular problem.

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously. (C) 2007 Optical Society of America

Stabilization of optical Fabry-Perot sensor by active feedback control of diode laser

This paper presents the design and characterization of a fiber Fabry-Perot interferometer (FFPI) acoustic wave detector with its Q point being stabilized actively. The relationship between the reflectivity of the F-P cavity facets and cavity length was theoretically analyzed, and high visibility of 100% was realized by optimized design of the F-P cavity. To prevent the drifting of the Q point, a new stabilization method by actively feedback controlling of the diode laser is proposed and demonstrated, indicating the method is simple and easy operating. Measurement shows that good tracing of Q point was effectively realized. (c) 2008 Elsevier B.V. All rights reserved.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

Optical properties of a square-lattice photonic crystal within the partial bandgap

Optical properties of a two-dimensional square-lattice photonic crystal are systematically investigated within the partial bandgap through anisotropic characteristics analysis and numerical simulation of field pattern. Using the plane-wave expansion method and Hellmann-Feynman theorem, the relationships between the incident and refracted angles for both phase and group velocities are calculated to analyze light propagation from air to photonic crystals. Three kinds of flat slab focusing are summarized and demonstrated by numerical simulations using the multiple scattering method. (c) 2007 Optical Society of America