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The transverse Poynting vector of the quadratically chirped Airy beams in RHM and LHM slabs at the same positions as those in Figs. 5(f1)-5(f8) with c 0 = −8 in (a1)-(a8), c 0 = 0 in (b1)-(b8), and c 0 = 8 in (c1)-(c8).
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We analytically and numerically investigate the dynamic propagation of the quadratically chirped Airy beams in right-handed material (RHM) and left-handed material (LHM) slabs. Based on the analytical expressions and numerical calculations, we find that through choosing the appropriate value of the quadratic chirp, one can modify the diffraction, t...
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... ω is the angular frequency. From Eq. (8), it is easy to find that the energy flowing in the z direction is proportional to the light intensity, which can be influenced by the quadratic chirp as demonstrated above. We perform numerical simulation of the transverse Poynting vector from the finite-energy Airy beams with different quadratic chirp in Fig. 6. From Fig. 6, we can observe that the variation trend of the transverse Poynting vector in the LHM slab is different from that in the RHM slab due to the specific characteristic of LHM. In addition, the quadratic chirp imposed on the finite-energy Airy beams would influence the distributions of the transverse energy flow, yet hardly affect the ...
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A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes are normally studied below the lightline where they exist continuously and emerge from points on the lightline,...
Citations
... The Poynting vector is the rate of electromagnetic energy flow per unit area, which is defined as = (c/4π) × , [42] where c is the speed of light, and are the electric and magnetic field, respectively. In the Lorenz gauge, the time-averaged Poynting vector of anx-polarized field can be written as [43,44] ...
Propagation dynamics of the cosh-Airy vortex (CAiV) beams in a chiral medium is investigated analytically with Huygens–Fresnel diffraction integral formula. The results show that the CAiV beams are split into the left circularly polarized vortex (LCPV) beams and the right circularly polarized vortex (RCPV) beams with different propagation trajectories in the chiral medium. We mainly investigate the effect of the cosh parameter on the propagation process of the CAiV beams. The propagation characteristics, including intensity distribution, propagation trajectory, peak intensity, main lobe’s intensity, Poynting vector, and angular momentum are discussed in detail. We find that the cosh parameter affects the intensity distribution of the CAiV beams but not its propagation trajectory. As the cosh parameter increases, the distribution areas of the LCPV and RCPV beams become wider, and the side lobe’s intensity and peak intensity become larger. Besides, the main lobe’s intensity of the LCPV and RCPV beams increase with the increase of the cosh parameter at a farther propagation distance, which is confirmed by the variation trend of the Poynting vector. It is significant that we can vary the cosh parameter to control the intensity distribution, main lobe’s intensity, and peak intensity of the CAiV beams without changing the propagation trajectory. Our results may provide some support for applications of the CAiV beams in optical micromanipulation.
... propagation path. Over recent years, with quadratic chirp, the Airy beam in a medium with parabolic potential [15], the Airy pulse in an optical fiber [16], in a quintic nonlinear fiber [17] and the quadratically chirp Airy (QCAi) beams in the LHMs and RHMs slabs [18] have been studied by researchers. ...
... As is known to all, the optical ABCD transmission matrix is different when the QCAiV beams propagate in different media. With the schematic diagram we discussed above, the ABCD matrix of the optical system under the paraxial approximation can be expressed as [11,12,14,18,21] ...
... In the Cartesian coordinate system, the optical field distribution of QCAiV beams in the initial plane can be written in terms of [2,3,12,18] ...
Based on the ABCD matrix and Huygens diffraction integral, the expressions for the quadratically chirped Airy vortex (QCAiV) beams with vortex’s arbitrary position and vortex’s topological charge propagating in the right-handed (RHMs) and left-handed materials (LHMs) slabs are deduced. The effects of the position and the topological charge m of the vortex on the intensity distribution, the intensity concentration, the peak intensity, diffraction range and radiation forces are deeply investigated in the paper. It is shown that the acceleration of the optical vortex is always bigger than that of the corresponding QCAiV beams in both RHMs and LHMs slabs. Therefore, with suitable position of the vortex, plurality of intersections of the vortex and the QCAiV beams can be achieved and the intensity concentration can be controlled during propagation. The range of the diffraction can be controlled by the off-axis vortex and it depends on the relative distance from vortex to the origin. At last, we demonstrate the effect of the vortex on the maximum scattering force and gradient force distribution on the Rayleigh dielectric particles respectively.
... Here Fig. 9(a) shows the normalized maximum scattering force. For chirp parameter = 3, and beam order = 1, the magnitude of the maximum scattering force corresponds to 10 −30 N. When = 2, the magnitude of the maximum scattering force corresponds to 10 −29 N. When = 3, the magnitude of the maximum scattering force corresponds to 10 −27 N and when = 4, the magnitude of the maximum scattering force corresponds to 10 −25 N. Compared with the maximum scattering force of a Gaussian (10 −12 N) [45], Airy (10 −25 N) [46] and Bessel (10 −18 N) [47] beams, the maximum scattering force of the CAiHG wave packets is close to the value of the Airy beams but it is much smaller than the value of the Gaussian or Bessel beams due to the influence of the chirped Airy pulse and multi-beam combination. It is not difficult to find that although the order of the CAiHG wave packets increases, the normalized maximum scattering force of the CAiHG wave packets first increases and then decreases with increasing propagation distance. ...
Based on the analytic expression of the chirped Airy hollow Gaussian (CAiHG) wave packets derived from the (3 + 1)-dimensional ((3 + 1) D) Schrödinger equation, their propagation properties are investigated in detail for the first time. The results show that a focusing of the chirped Airy Gaussian pulses is found, which leads to the same focusing of the propagation trajectory and the maximum scattering force. The distribution factor α can modulate the convergence of the side wave rings at Z = 0. During the propagation process, with the increase of the β, when the β is negative, the side wave rings rise along the main wave axis but their moving is opposite when the β is positive. When the beam order n = 1, the intensity, the angular momentum and the gradient force gradually tend to the center but they move radially when n = 2. The direction of the peripheral gradient force points to the center but the direction is opposite in the center. The beam orders only affect the magnitude of the normalized maximum scattering force but have little effects on their distribution.
... On the other hand, the propagation of FAiB in different optical systems, such as the free space [3], the nonlinear medium [7], the turbulence atmosphere or the water [8], the uniaxial crystals [9], etc. have been studied extensively, among which the wave transmission characteristics in metamaterials so-called the double negative materials (DNM) has been attracted peculiar attention in recent years. Vaveliuk et al. discussed the negative propagation effect in nonparaxial Airy beams [10], Lin et al. analyzed the propagation of Airy beams from right-handed material to left-handed material [11], Deng et al. researched a good deal of Airy derivative beams propagation characteristics in DNM [12,13]. In the above mentioned theses, the coaxial grazing is required when discuss the beam transmission behavior, however, most of the optical instruments are slightly misaligned more or less in practical application [14], therefore, to take the misalignment into considerations is very necessary. ...
... What is more, what we want to emphasize is that Eqs. (21)- (23) are essential results of this paper and which is the particular case of Eq. (13) in Ez-zariy's article [15]. According to what we have learnt, not only the thin lens but also other optical instruments made of different kinds of shapes could be explored though generalized Huygens-Fresnel optical integral formula so long as the physical model and relevant factors in Eq. (13) are elaborate deduced and optimized, therefore, refer to [15], the evolution properties of the finite Airy Gaussian beam in a misaligned slab system with rectangular aperture, circular aperture and annular aperture [29] will be our next research target. ...
... DNM can act like a perfect lens [30]. Our conclusions agree with the results of relevant literatures, such as [11,13,31]. ...
In this letter, we deduce the approximate analytical formula for the finite Airy beam propagating in the misaligned slab system with a rectangular aperture by using the generalized Huygens-Fresnel integral equation, the light transfer matrix and expanding the hard-edged rectangular function into a finite sum of complex Gaussian function. The particular cases of this beam propagating in the apertured aligned slab system, unapertured misaligned slab system and unapertured aligned one are further illustrated through numerical examples as well. The effects of aperture size and misaligned factors on beam evolution in these slab structures are developed, which can provide a fast and effective method for investigating other kinds of pseudo non-diffracting laser beams through the rectangularly apertured misaligned slab system because most of the optical devices are slightly misaligned more or less in the practical application.
Combining the ABCD transfer matrix and the generalised Huygens-Fresnel integral equation method, the closed-form expression of a finite Airy Gaussian array beam (FAGAB) threading through a paraxial optical system was established in a space domain. We systematically investigated the evolution of the FAGAB's properties travelling through a curved slab system based on previously derived formula. The wave's characteristics through the flat slab system were the special cases of the main findings. We also assess the influence of the truncation factor and adjustment parameter on the FAGAB's intensity distribution on the slab system model's input and output cross-sections.
