“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure

Two different spatial levels are involved concerning damage accumulation to eventual failure. nucleation and growth rates of microdamage nN* and V*. It is found that the trans-scale length ratio c*/L does not directly affect the process. Instead, two independent dimensionless numbers: the trans-scale one * * ( V*)including the * **5 * N c V including mesoscopic parameters only, play the key role in the process of damage accumulation to failure. The above implies that there are three time scales involved in the process: the macroscopic imposed time scale tim = /a and two meso-scopic time scales, nucleation and growth of damage, (* *4) N N t =1 n c and tV=c*/V*. Clearly, the dimensionless number De*=tV/tim refers to the ratio of microdamage growth time scale over the macroscopically imposed time scale. So, analogous to the definition of Deborah number as the ratio of relaxation time over external one in rheology. Let De be the imposed Deborah number while De represents the competition and coupling between the microdamage growth and the macroscopically imposed wave loading. In stress-wave induced tensile failure (spallation) De* < 1, this means that microdamage has enough time to grow during the macroscopic wave loading. Thus, the microdamage growth appears to be the predominate mechanism governing the failure. Moreover, the dimensionless number D* = tV/tN characterizes the ratio of two intrinsic mesoscopic time scales: growth over nucleation. Similarly let D be the “intrinsic Deborah number”. Both time scales are relevant to intrinsic relaxation rather than imposed one. Furthermore, the intrinsic Deborah number D* implies a certain characteristic damage. In particular, it is derived that D* is a proper indicator of macroscopic critical damage to damage localization, like D* ∼ (10–3~10–2) in spallation. More importantly, we found that this small intrinsic Deborah number D* indicates the energy partition of microdamage dissipation over bulk plastic work. This explains why spallation can not be formulated by macroscopic energy criterion and must be treated by multi-scale analysis.

Space-frequency coupling, conical waves, and small-scale filamentation in water

Numerical simulations of fs laser propagation in water have been made to explain the small-scale filaments in water we have observed by a nonlinear fluorescence technique. Some analytical descriptions combined with numerical simulations show that a space-frequency coupling mainly from the interplay among self-phase modulation, dispersion and phase mismatching will reshape the laser beam into a conical wave which plays a major role of energy redistribution and can prevent laser beam from self-guiding over a long distance. An effective group velocity dispersion is introduced to explain the pulse broadening and compression in the filamentation. (c) 2005 American Institute of Physics.

Relativistic channel-coupling focusing enhanced nonlinear guiding of an intense laser beam in a plasma channel

We employ the variational method to study the optical guiding of an intense laser beam in a preformed plasma channel without using the weakly relativistic approximation. Apart from the dependence on the laser power and the nonlinear channel strength parameter, the beam focusing properties is shown also to be governed by the laser intensity. Relativistic channel-coupling focusing, arising from the coupling between relativistic self-focusing and linear channel focusing, can enhance relativistic self-focusing but its strength is weaker than that of linear channel focusing. (C) 2008 Elsevier B.V. All rights reserved.

Optimization of the multiwavelength erbium-doped fiber laser in a unidirectional cavity without an isolator

A highly uniform multiwavelength erbium-doped fiber ring laser with an intracavity sine phase modulator is demonstrated. The flat output spectrum is achieved by optimizing the cavity structure, modulation amplitude, and frequency of the sine phase modulator. Fifteen lasing lines with wavelength spacing of 0.9 nm appear simultaneously and stably with power differences less than 2 dB and side-mode suppression ratio higher than 32 dB. In addition, the proposed cavity can support unidirectional operation without optical isolators. An output power difference of about 20 dB is realized between the counterclockwise and clockwise directions, which is almost independent of the pump power and lasing wavelengths. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

Influence of birefringence dispersion on distributed measurement of polarization coupling in birefringent fibers

A white light interferometer is developed to measure the distributed polarization coupling in high-birefringence polarization-maintaining fibers (PMFs). Usually the birefringence dispersion between two orthogonal eigenmodes of PMFs is neglected in such systems. Theoretical analysis and experimental results show that the birefringence dispersion becomes a nonnegligible factor in a long-fiber test. Significant broadening of interferograms and loss of longitudinal coherence are observed. The spatial resolution and measurement sensitivity of the system decrease correspondingly. Optimum spectrum width selection is presented for better spatial resolution and measurement range. c 2007 Society of Photo-Optical Instrumentation Engineers.

Multibeam coupling in photorefractive SBN:Ce

Theoretical and experimental results are presented for simultaneous multibeam coupling in photorefractive SBN:Ce. Within a single crystal, multiple signals are amplified through a coupling process that employs a single pump. The coupling gain of each signal results from coupling both between the pump and the signal and between different signals. The amount of gain that each signal receives is dependent on the intensity of the incident signal; thus a competition for the gain exists among the various signals.

Optimization of the multiwavelength erbium-doped fiber laser in a unidirectional cavity without an isolator

A highly uniform multiwavelength erbium-doped fiber ring laser with an intracavity sine phase modulator is demonstrated. The flat output spectrum is achieved by optimizing the cavity structure, modulation amplitude, and frequency of the sine phase modulator. Fifteen lasing lines with wavelength spacing of 0.9 nm appear simultaneously and stably with power differences less than 2 dB and side-mode suppression ratio higher than 32 dB. In addition, the proposed cavity can support unidirectional operation without optical isolators. An output power difference of about 20 dB is realized between the counterclockwise and clockwise directions, which is almost independent of the pump power and lasing wavelengths. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

Simple ABCD matrix method for evaluating optical coupling system of laser diode to single-mode fiber with a lensed-tip

In this paper, we present a simple technique to determine the coupling efficiency between a laser diode and a lensed-tip based on the ABCD transformation matrix method. We have compared our analysis technique to that of previous work and have found that the presented method is reliable in predicting the coupling efficiency of lensed-tip and has the advantage of simplicity of coupling efficiency calculation even by a pocket calculator. The results can be useful for designing coupling optics. (c) 2005 Elsevier GmbH. All rights reserved.

Influence of birefringence dispersion on distributed measurement of polarization coupling in birefringent fibers

A white light interferometer is developed to measure the distributed polarization coupling in high-birefringence polarization-maintaining fibers (PMFs). Usually the birefringence dispersion between two orthogonal eigenmodes of PMFs is neglected in such systems. Theoretical analysis and experimental results show that the birefringence dispersion becomes a nonnegligible factor in a long-fiber test. Significant broadening of interferograms and loss of longitudinal coherence are observed. The spatial resolution and measurement sensitivity of the system decrease correspondingly. Optimum spectrum width selection is presented for better spatial resolution and measurement range. c 2007 Society of Photo-Optical Instrumentation Engineers.

Laser diode array side-pumped acousto-optic induced unidirectional operation Q-switched Nd : YAG slab ring laser

A laser-diode array (LDA) side-pumped Nd:YAG slab ring laser is described that incorporates a prism-shaped acousto-optic modulator to enforce unidirectional operation and Q-switching. When pumped by the maximum power of 50 W, Q-switched energies of 3.6 mJ and 50 ns duration, corresponding to a peak power of 72 kW, are obtained. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)01306-9].

Prism coupling of ultrashort light pulses into waveguides

We discuss coupling of ultrashort light pulses into waveguides by use of a prism waveguide coupler configuration. Theoretical analysis indicates that an extra loss induced by the short coherence times of ultrashort pulses, which has a strong effect on the reflected light and the optimum coupling condition, appears in the waveguide. Numerical simulations show that the reflectance strongly depends on the coherence times of ultrashort pulses. A method for realizing optimum coupling by compensating for the extra loss is proposed as well in this paper. A preliminary experiment of employing ultrashort pulses with different coherence times was carried out, and good agreement between theory and experiment was obtained. (c) 2006 Optical Society of America.