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Order to disorder transitions are important for two-dimensional (2D) objects such as oxide films with cellular porous structure, honeycomb, graphene, Bénard cells in liquid, and artificial systems consisting of colloid particles on a plane. For instance, solid films of porous alumina represent almost regular crystalline structure. We show that in this case, the radial distribution function is well described by the smeared hexagonal lattice of the two-dimensional ideal crystal by inserting some amount of defects into the lattice.Another example is a system of hard disks in a plane, which illustrates order to disorder transitions. It is shown that the coincidence with the distribution function obtained by the solution of the Percus-Yevick equation is achieved by the smoothing of the square lattice and injecting the defects of the vacancy type into it. However, better approximation is reached when the lattice is a result of a mixture of the smoothed square and hexagonal lattices. Impurity of the hexagonal lattice is considerable at short distances. Dependencies of the lattice constants, smoothing widths, and contributions of the different type of the lattices on the filling parameter are found. The transition to order looks to be an increase of the hexagonal lattice fraction in the superposition of hexagonal and square lattices and a decrease of their smearing.

UDC 621.373.826Based on equations for the evolution of the polarization density matrix for laser emission, we have shown that when a laser with an anisotropic cavity is turned on in a magnetic field higher than some critical value, we will observe a new optical effect: pulsations between the polarized and completely unpolarized states of the laser emission. In a magnetic field much higher than the critical value, practically complete suppression of polarization occurs, which may serve as a method for obtaining unpolarized laser emission.Introduction. Magnetooptic phenomena, discovered back in the 19th Century [1-3], have attracted attention of researchers even today [4] because of their broad application in optics, laser physics [5,6], and also for high-current polarization measurements [7]. In this paper, we demonstrate the possibility that there is one more interesting magnetooptic effect which can be used to control the polarization properties of laser radiation. This effect arises when lasing in a gas laser is initiated in a magnetic field that was previously turned on.As we know, for sufficiently small cavity anisotropy, there is a time interval between the process of establishing the single-mode lasing regime [8] and the process of polarization of the laser emission in this established mode. In this paper, we assume that the laser has already gone to the single-mode lasing regime, and we consider the process of establishing its polarization.In the absence of a magnetic field, the process of establishing the polarization of the laser occurs due to residual cavity anisotropy, which for technological reasons cannot be made to be completely isotropic. 1 In the general case, we can choose a basis in which the cavity loss matrix is diagonal. For example, let us assume that absorption for a wave propagating along the z axis and polarized in the xz plane is stronger than for a wave polarized in the yz plane. Then, taking into account the fact that the gain is the same for both polarizations (isotropic pumping), we can conclude that polarization is established for laser emission along the y axis.On the other hand, we know that due to the Faraday effect, the plane of polarization for the laser begins to rotate if the laser (with already established polarization) is placed in a magnetic field. This effect has been well studied both experimentally and theoretically [5,6,[9][10][11][12][13][14][15][16][17][18][19]. One of the many applications of this effect is measurement of small magnetic fields (laser magnetometry) [20,21]. We should also note that the electrical analog of the laser Faraday effect can be used to search for parity violation and time-reversal invariance [22].The question arises concerning how the process of establishing the polarization of the laser emission changes if lasing is initiated in a magnetic field that has been previously turned on. The indicated problem cannot be solved on the basis of the equation for the electromagnetic field amplitude in a laser cavity [5,[15][16][17][18], or within the ...

Order to disorder transitions are important for 2D objects such as oxide films with a cellular porous structure, honeycomb, graphene, and Bénard cells in liquid and artificial systems consisting of colloid particles on a plane. For instance, solid films of the porous alumina represent an almost regular quasicrystal structure (perfect aperiodic quasicrystals discovered in 1991 is not implied here). We show that, in this case, the radial distribution function is well described by the quasicrystal model, i.e., the smeared hexagonal lattice of the two-dimensional ideal crystal by inserting a certain amount of defects into the lattice. Another example is a system of hard disks in a plane, which illustrates the order to disorder transitions. It is shown that the coincidence with the distribution function, obtained by the solution of the Percus-Yevick equation, is achieved by the smoothing of the square lattice and injecting the defects of the vacancy type into it. However, a better approximation is reached when the lattice is a result of a mixture of the smoothened square and hexagonal lattices. Impurity of the hexagonal lattice is considerable at short distances. Dependences of the lattices constants, smoothing widths, and impurity on the filling parameter are found. Transition to the order occurs upon an increasing of the hexagonal lattice contribution and decreasing of smearing.

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