Biomedical subjects

D J Kaup

Publications and source records attributed to D J Kaup.

4 recordsLinked to original sources

PubMed2006

Optical breathers in nonlinear anisotropic and dispersive media.

Anisotropic crystals containing impurity atoms, when the principal optical axis of the uniaxial crystal and the vector of electrical dipole moment of the impurity atoms are perpendicular to each other and are directed along different crystallographic axes, are shown to have three different mechanisms of the formation of breathers depending on the direction of the wave propagation and on the symmetry of the medium. Explicit analytic expressions for the parameters of breathers and the effective nonlinear susceptibilities for extraordinary waves are obtained. All uniaxial crystals with quadratic susceptibilities can be divided into three different groups, according to the crystal classes. Each group is characterized by a universal structure of the breather zones. The structure of the breather zones of the trigonal, tetragonal, and hexagonal crystals with cubic susceptibilities depends neither on the crystallographic system nor on the crystal classes and coincides with the structure of the breather zones of the trigonal and hexagonal crystals with quadratic susceptibilities and crystal classes 3, 3m, 6, 6m2. It is shown that structure of breather zones of the different groups of crystals for the cases when the principal optical axis of the uniaxial crystal and the vector of electrical dipole moment of the impurity atoms are mutual parallel or perpendicular to each other are significantly different.

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PubMed2004

Optical nonresonance and two-photon resonance breathers in anisotropic media.

Anisotropic optical crystals with two-photon resonance impurity atoms are shown to have three different mechanisms of the formation of breathers depending on the direction of the wave propagation and on the symmetry of the medium. Explicit analytic expressions for the parameters of nonresonance and resonance two-photon breathers of extraordinary waves are obtained. It is shown that, unlike one-photon breathers, for two-photon breathers in the media with quadratic susceptibilities and the crystal classes 3, 3m, 4, 4mm, 6, 6mm, and Kerr media two different structures of the breathers zones are realized.

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PubMed2004

Three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities.

We formulate a general model of three-wave optical interactions (in the spatial domain), which combines quadratic (chi(2)) and cubic (chi(3)) nonlinearities, the latter including four-wave mixing. The model can be realized in chi(2) materials where an effective chi(3) nonlinearity is engineered by means of the quasi-phase-matching technique. Both self-focusing and self-defocusing chi(3) nonlinearities are considered. The birefringence of the two fundamental-frequency (FF) waves is taken into regard. Several types of solitons in this system are found, by means of the variational approximation and numerical methods. These are exact single-component solitons and generic three-wave (3W) ones, which are classified by relative signs of their components. Stability of the solitons is investigated by means of the Vakhitov-Kolokolov (VK) criterion, and then tested by direct simulations. One type of the single-component FF solitons (the "fast" one, in terms of the known two-component birefringent chi(3) model) is, chiefly, unstable, as in that model, but nevertheless a stability interval is found for it, which provides for the first example of stable fast solitons. The other FF soliton (the "slow" one, in terms of the same chi(3) model, where it is always stable) has its stability and instability regions. A single-component soliton in the second harmonic (SH) is found too; it also has its stability region, contrary to the common belief that such a soliton must always be unstable due to the parametric interaction. The 3W solitons are stable indeed if this is predicted by the VK condition, in the case when all the three components are positive. Following variation of the chi(2) mismatch parameter, the 3W soliton bifurcates from the SH one, and at another point it bifurcates back into the slow-FF single-component soliton; conjectured normal forms of the respective bifurcations are given. 3W solitons with different signs of their components may be unstable contrary to the VK criterion, which is explained by consideration of the chi(2) term in the system's Hamiltonian. In direct simulations, unstable solitons evolve into stable breathers. A different instability takes place in the case of the self-defocusing chi(3) nonlinearity, when all the solitons blow up into a turbulent state. Parallel to the solitons, continuous-wave solutions are studied too. In terms of the existence and stability, they resemble solitons of similar types.

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PubMed1999

Three-wave interaction solitons in optical parametric amplification.

This paper applies three-wave interaction (TWI)-soliton theory to optical parametric amplification when the signal, idler, and pump wave can all contain TWI solitons. We use an analogy between two different velocity regimes to compare the theory with output from an experimental synchronously pumped optical parametric amplifier. The theory explains the observed inability to compress the intermediate group-velocity wave and 20-fold pulse compression in this experiment. The theory and supporting numerics show that one can effectively control the shape and energy of the optical pulses by shifting the TWI solitons in the pulses.

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