Wavelet Cross-Spectrum Analysis of Multi-Scale Disturbance Instability and Transition on Sharp Cone Hypersonic Boundary Layer

Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean andfluctuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in thefrequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance are demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.     

Temporal evolution of the emission spectra of color center lasers

The mode spectrum of a homogeneously broadened laser is mainly influenced by mode competition effects. In this paper the temporal evolution of the emission spectra of color center lasers caused by mode competition is investigated. The results are compared with a theoretical estimation.Dedicated to Prof. Dr. Herbert Welling on the occasion of his 60th birthday     

Analytical study of the splitting process of a multiply-quantized vortex in a Bose–Einstein condensate and collaboration of the zero and complex modes

We study the dynamics of a trapped Bose–Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross–Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov–de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.     

Scheme for Direct Measurement of the Wigner Function via Resonant Interaction

We propose a scheme for direct measurement of the Wigner function for a cavity mode. In the scheme the cavity field resonantly interacts with an atomic ensemble. Under certain conditions, the state of the cavity mode is transferred to the atomic system. After a displacement the measurement of the parity of the atomic excitation number directly yields the Wigner function of the initial state of the cavity mode.     

Doughnut-like beam generation of Laguerre-Gaussian mode with extremely high mode purity

An apparatus to achieve a single doughnut-like Laguerre-Gaussian (LG) mode with extremely high mode purity higher than 99.6% is reported. The proposed apparatus is a conceptual combination of a high-order HG mode selector and an astigmatic mode converter, which consists of only four simple and easily-made optical elements: three lens elements and one binary phase element. Theoretical simulations show that the apparatus has a good tolerance for both system production and alignment errors. With such high mode purity, the doughnut-like LG beam generated by the apparatus carrying an orbital angular momentum will be beneficial to numbers of studies including the trapping and rotating of micro and nano-particles, non-linear optics, and atom-light interaction.     

High Polarization Single Mode Photonic Crystal Microlaser

Generally, dipole mode is a doubly degenerate mode. Theoretical calculations have indicated that the single dipole mode of two-dimensional photonic crystal single point defect cavity shows high polarization property. We present a structure with elongated lattice, which only supports a single y-dipole mode. With this structure we can eliminate the degeneracy, control the lasing action of the cavity and demonstrate the high polarization property of the single dipole mode. In our experiment, the polarization extinction ratio of the y-dipole mode is as high as 51：1.     

Coupled modes of the torsion pendulum

The coupling of the swing modes of a torsion pendulum to the torsional mode has been solved analytically. Our solution provides a clear explanation of why a magnetic damper is effective in suppressing unwanted modes in most gravitational experiments. The analytic solution also shows that the amplitude of the mode coupling is greatest at the lowest frequencies. This explains why mode coupling at the lowest frequency is all that is observed in the experiments reported here.     

Global Structures and Multi-Temporal Variabilities of MLT Migrating Diurnal Tide

Migrating diurnal tide in the MLT region is examined by the application of Hough mode decomposition with the tide delineated from the SABER/TIMED temperatures over 2002-2006. The decomposition results show that in the height range 60-100km, the （1, 1） mode is the most predominant among eight leading Hough modes including four propagating and four trapped modes. It exhibits a sustained maximum at 97 km and significant semi-annual oscillation. Additionally, a novel feature of inter-annual variation with period of about two years is clearly seen in the （1, 1） mode, e.g., repeated maxima are seen at the March equinox of 2002, 2004 and 2006, respectively. This feature is further manifested by the tidal amplitudes in the height range 70-100km in the height-time cross-section at the equator. It is likely of the QBO as the height range just coincides to where the zonal mean zonal winds derived by using the UARS data exhibiting the QBO. The other results show that the （1, 2） mode is important at 〈 80 km exhibiting comparable amplitude to that of the （1, 1） mode, and in particular the nearly anti-correlation with the （1, 1） mode. The tide at about 85 km is suggested of rather complex as the four trapped modes exhibit maximum at these heights, which indicates the presence of local excitations or sources at below.     

Low temperature Raman study on the site symmetry of ZnSe:P

Raman spectra of phosphorous doped ZnSe are recorded from 9 to 300 K. In addition to TO mode at 208 cm⁻¹ and LO mode at 253 cm⁻¹, a new mode around 240 cm⁻¹ is observed between 55 and 270 K. The spectra at lower and higher temperatures do not show the new mode. This new mode confirms that there is a reduction of (Se site) symmetry from T_d to C_3v when P substitutes for Se. This is due to Jahn Teller distortion.     

WG-Like Modes Selectivity in a Square Cavity with Posts

We investigate the characteristics of Whispering-Gallery（WG）-like modes in a square cavity with posts by employing the two-dimensional （2D） finite-difference time-domain （FDTD） technique combined with the effective index method. The results indicate that the posts can result in mode selection in the WG-like modes. The WG-like modes with odd mode numbers are not much sensitive to the sizes of the posts. However, the quality factor （i.e. Q-factor） of the WG-like modes with even mode numbers decreases sharply with the increasing size of the posts. The decreasing Q-factor is attributed to mode leakage and scattering loss due to the presence of the post. The mode selection increases the mode spacing of square cavity twice in an optimized structure.     

Mode competition in multi-core fiber amplifier

3D beam propagation numerical code and a newly developed optical mode solver were implemented for studies on the recently experimentally realized Yb fiber amplifier with 7-core hexagonal structure. It was found that the launched seven single-frequency beams matched with the cores converge to a wave field with permanently diminishing space beating patterns, but the result is sensitive to phases of separate beams. Namely, at a spread of phases of individual beams within a few tenths of radian, the convergence of the wave field to the in-phase mode is observed, while at phases random spread on the order of π the out-of-phase mode is dominating. Such behavior is observed at strong gain saturation in the cores. Both effects take place even if the guiding index of the cores fluctuates within a limited range. The mode solver predicts that the in-phase mode has the minimal small signal gain, and the gain of the out-of-phase mode is maximal one. This fact proves that there is no strict correlation between modal gains and amplification in strong saturated multi-core fiber. The smaller core index step significantly improves the convergence of the amplified radiation to the in-phase mode. An approach to the waveguide structure tailoring is described which assures the single in-phase mode stability.     

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.     

Step-selective measurement by grating-based lateral shearing interferometry for segmented telescopes

We present an original step-selective mode which allows to measure only the steps and not the slowly varying aberrations of a wave front. This mode can be implemented when measuring segmented wave front by a diffraction-grating-based lateral shearing interferometer. This set-up rests on the different chromatic response of these interferometers depending on the rate of change of the impinging wave front: for smooth defects, the response is classically achromatic whereas it is chromatic for a step variation, which was to our knowledge overlooked. The interest of this mode for astronomical measurements is highlighted. First we present theoretical considerations to show how this mode of measure is possible; then a numerical simulation illustrates them.     

Laser Mode-Dependent Size of Plasma Zones Induced by Femtosecond Laser Pulses in Fused Silica

We carry out the numerical simulations of femtosecond laser propagation with TEMoo mode, TEM10 mode and a beam combining both the modes in fused silica. It is found that the transverse size of plasma zones induced by laser pulses with the TEM10 mode is smaller than that induced by the TEM00 mode, while the longitudinal size is almost the same, and the saturated plasma density is higher. The transverse size, the longitudinal size and the ratio of the longitudinal to transverse size, for the beam combining both the modes, all could be reduced at the same time in comparison with the TEM00 mode under the same focusing conditions.     

A Three-Dimensional Ray-Tracing Study of R-X Mode Waves during High Geomagnetic Activity

We further present a three-dimensional (3D) ray-tracing study on the propagation characteristic of the superluminous R-X mode waves during high geomagnetic activity following our recent two-dimensional results [J. Geophys. Res. 112(2007)A10214]. We perform numerical calculations for this mode which originates at specific altitude r=2.0R_E in the source cavity along a 70° night geomagnetic field line. We demonstrate that the ray path of the R-X mode is essentially governed by the azimuthal angle of the wave vector k. Ray paths starting with azimuthal angle 180° (or in the meridian plane) can reach the lowest latitude, but stay at relatively higher latitudes with the azimuthal angles other than 180° (or off the meridian plane). The results further supports the previous finding that the R-X mode may be physicallypresent in the radiation belts under appropriate conditions.     

Polarization-Independent Guided-Mode Resonance Filters under Oblique Incidence

We present the dispersion relation of guided-mode resonances in planar periodic waveguides, both for s-polarized （TF, mode） and p-polarized （TM mode） incident waves. For a fixed homogeneous planar waveguide, dispersion curves of the TE eigenmode cannot cross that of the TM eigenmode at all. That is to say, at a certain wavelength, TE and TM modes cannot be excited with the same propagation constant. Due to Bragg reflection in the planar periodic waveguide, dispersion curves of the TE leaky mode may intersect with that of the TM leaky mode in the first Brillouin zone. We employ these intersections to achieve polarization-independent guided-mode resonance filters.     

Photonic crystal fiber for fundamental mode operation of multicore fiber lasers and amplifiers

A mode-selection method based on a single-mode photonic crystal fiber (PCF) in the multicore fiber (MCF) lasers is presented. The designed PCF has a central core region formed by a missing air-hole, and three air-hole rings. With an appropriate choice of the design parameters of the PCF, the power coupling between the fundamental mode (FM) of the PCF and the fundamental MCF mode can be much higher than those between the FM and the other supermodes. As a result, the fundamental MCF mode has the maximum power reflection coefficient on the right-hand side of the MCF laser cavity, and dominates the output laser power. Since the maximum power of the fundamental MCF mode will lead to the desired laser beam profile, higher the fraction of the fundamental MCF mode power contained in the total output power contributes to higher beam quality. The numerical simulations show that the effectiveness of the fundamental MCF mode-selection is higher in the MCF lasers with the PCF as a mode-selection component than in the MCF lasers based on the free-space Talbot cavity method. Additionally, for the MCF amplifiers, an approach is presented to decrease the sensitivity of the amplifier performance to the variation of Gaussian beam waist utilizing the coupling between the Gaussian beam and the FM of the PCF. The numerical results show that this method can effectively increase the design flexibility for a broad range of the Gaussian beam waist.     

Instability of spatially periodic patterns due to a zero mode in the phase-field crystal equation

Weakly nonlinear spatially periodic patterns coupled to a Goldstone (zero) mode of the phase-field crystal model are investigated. Rotationally invariant equations for the dynamics of the amplitudes of a hexagonal pattern are derived first, which then allows us to determine stability regions for stripes and hexagons. There are parameter regimes in which all periodic patterns become unstable as a result of long-wavelength instabilities generated by the zero mode.     

Incident-angle dependence of the longitudinal optic mode and the Doppler effect in silica glass

The infrared reflection spectra of silica glass were monitored at different incident angles of the wave. The density of states (DOS) and frequency ω_LO of the longitudinal optic (LO) mode were found to be the functions of the incident angle. The DOS of the LO mode increases with increasing incident angle as a whole. However, two regions can be divided in which one is below ∼30° and the other is above 30°. The frequency ω_LO of the LO mode increases linearly with incident angle. The earlier proposed relationship between the shifted frequency produced by the Doppler effect and the source frequency of the main transverse optic (TO) mode was investigated by studying the infrared spectra of the annealed glass capillaries. The shifted frequency was found to be linearly proportional to the source frequency of the TO mode, as depicted by the Doppler effect.     

Flat-topped beam output from a double-clad rectangular dielectric waveguide laser with a high-index inner cladding

A novel method to produce a flat-topped laser beam by using a double-clad rectangular waveguide laser with high-index inner cladding is presented. The waveguide dispersion equation for cosine mode was deduced, the condition for the flattened mode was given out, relative gains for guided modes were calculated numerically and analyzed. Results indicate that a gain advantage for the flattened mode is clear, a flat-topped laser beam can be achieved when the optical confinement factor, the gain intensity and the output coupler are chosen suitably.