<title>Theory of optical resonator with plane-dispersive elements</title>

Abstract

Dispersion optical resonators of tunable lasers often contain one or more plane dispersive elements (PDE), e.g. , refracting boundaries or diffraction gratings. The characteristic feature of such structures is that their optical length varies over resonator cross-section; this causes specific difiuaction distortions of the light beam. But conventional ideas concerning processes in dispersion resonators are based on the analysis of simplified models, where each PDE conditionally is removed or replaced by certain thin optical element, so that particular nature ofPDE is neglected.An attempt of systematic theoretical consideration of optical resonator with PDE is presented. On the base of general formulae for paraxial beam transformation in PDE the integral equation describing wide class of dispersion resonators is derived. It is analyzed and discussed; for some cases there are given approximate analytical and numerical solutions. They demonstrate slight asymmetry in beam profile and in dependence of resonator losses on its misalignment. Besides, it is shown that tuning of the resonator can be changed not only by angular but by certain progressive shifts of resonator elements. These effects can give new possibilities for the control of tunable laser radiation and must be allowed for in precision measurements.

Asymmetric optical vortex in plasma density gradient

“…The AOAM is the surplus which contributes to the transformation of the beam profile, so it is the asymmetric part of the beam OAM. When a LG beam with both VOAM and AOAM passes through a quadratic phase corrector, M 12 obtains a transformation described by [49]…”

“…In the Bekshaev's approach, the beam evolution is described by means of the beam Wigner function which is the amplitude associated to a light ray passing through a point along a certain direction [49,50]. The irradiance matrix, calculated from the Wigner function, contain some characteristic parameters about the beam profile and propagation direction and change with the beam evolution.…”

“…To determine the VOAM, one must perform such transformation that the whole asymmetric part of the beam OAM is removed. It has been shown that the corresponding quadratic phase corrector must have the form as[49] VOAM and the AOAM of the laser beam are expressed as[35], calculate the second irradiance matrix M C relative to the center of the laser beam[35], r C represents the transverse coordinates of energy center of the laser beam, and p C determines the inclination angle between the trajectory of beam center and the x axis. They are defined as[49] These moments in M C describe the essential internal beam properties excluding the effect of the motion of energy center.…”

Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction

“…Like in case of a deformed high-order LG mode [21], it is interesting to inspect the relative separation of the secondary OVs with respect to the current beam profile, which may be useful in the context of creation of the OV arrays. Since the diffracted beam intensity distribution is represented by complicated functions without explicit analytical expression, it is convenient to characterize the beam profile by means of the second intensity moments [37][38][39][40] which form the symmetric positive definite matrix…”

Transformation of optical-vortex beams by holograms with embedded phase singularity

“…In this case, in contrast to the incident beam (6), whose amplitude falls down exponentially, the diffracted beam shows much slower power-law falloff (however, for non-zero m this circumstance is not so drastic as in the case of OV generation [16] and does not prevent the existence of the second-order intensity moments [16,32,33]). An interesting detail is that the term (13) disappears (and, correspondingly, the diverging ''singular" wave is not excited at all) if condition (15) does hold.…”