Soliton formation by interacting Airy beams

The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Airy spatial solitons can also be formed, which are similar to the states formed in the interaction between two Airy beams in nonlinear media. This quasi-equilibrium state is formed by the interaction of the main soliton beam and side lobes of Airy beam due to their different propagation trajectories in the nonlinear media. Moreover, it has been shown the Airy spatial solitons in tree structure can be formed by adjusting the initial parameters in the interaction between the Airy beam and Kerr media.

We study numerically and experimentally laser coherent combination (LCC) with multiple one- or two-dimensional Airy beams. It is shown that the method of LCC using Airy beams leads to a higher combining efficiency and a better feature of propagation than that using conventional Gaussian beams. Based on such coherent Airy beams combination, we propose a laser steering approach that could achieve large-angle beam steering (over 0.6°) without the need of using any mechanical steering component.

The common generation methods of two-dimensional airy beams were introduced briefly. The disadvantage of generation method by utilizing traditional two-dimensional digital phase masks was analyzed as well. Based on this, the digital blazed grating was introduced, as well as its corresponding theories. It was proposed that the traditional two-dimensional digital phase mask and the alterable digital blazed grating could be combined to generate a comprehensive phase mask. Thus, the diffraction orders of the airy beams could be controlled by changing the periods of improved comprehensive phase masks. Compared to the traditional two-dimensional digital phase masks, the airy beams generated by the proposed comprehensive phase mask had the advantage of controllable distances between different diffraction orders. At the same time, the specific order of the Airy beams could be strengthened, and the others could be weakened, which was useful to the subsequent study on the propagation and control of two-dimensional airy beams. The experimental results showed that: the proposed comprehensive phase masks could distinguish between the different diffraction orders of generated Airy beams. As a result, the mutual interference between different diffraction orders could be avoided effectively.

We have designed, fabricated, and tested an amplitude diffractive optical element for generation of two-dimensional (2D) Airy beams. The design is based on a detour-phase computer-generated hologram. Using laser ablation of metallic films, we obtained a 2 mm×2 mm diffractive optical element with a pixel of 5 μm×5 μm and demonstrated a fast, cheap, and reliable fabrication process. This device can modulate 2D Airy beams or it can be used as a UV lithography mask to fabricate a series of phase holograms for higher energy efficiency. Tests according to the premise and an analysis of the transverse profile and propagation are presented.

Two-photon flow cytometry with laser scanning two-dimensional airy beams

An Airy beam is a non-diffractive wave which propagates along a ballistic trajectory without any external force. Although it is impossible to implement ideal Airy beams because they carry infinite power, so-called finite Airy beams can be achieved by tailoring infinite side lobes with an aperture function and they have similar propagating characteristics with those of ideal Airy beams. The finite Airy beam can be optically generated by several ways: the optical Fourier transform system with imposing cubic phase to a broad Gaussian beam, nonlinear generation of Airy beams, curved plasma channel generation, and electron beam generation. In this presentation, a holographic generation of the finite Airy beams will be discussed. The finite Airy beams can be generated in virtue of holographic technique by ‘reading’ a hologram which is recorded by the interference between a finite Airy beam generated by the optical Fourier transform and a reference plane wave. Moreover, this method can exploit the unique features of holography itself such as successful reconstruction with the imperfect incidence of reference beam, reconstruction of phase-conjugated signal beam, and multiplexing, which can shed more light on the characteristics of finite Airy beams. This method has an advantage in that once holograms are recorded in the photopolymer, a bulky optics such as the SLM and lenses are not necessary to generate Airy beams. In addition, multiple Airy beams can be stored and reconstructed simultaneously or individually.

Since the discovery of photorefractive spatial solitons [1, 2], these non-diffracting waves have been the subject of an intense research effort, because they are particularly interesting for building alloptical diodes, transistors, switches, and all-optical computers. Until now steady-state bright spatial solitons have been observed in BTO [3], SBN [4], InP:Fe [5], KNbO3 [6], KLTN [7], and BaTiO3 [8] crystals. Barium–calcium titanate (BCT) [9, 10] is a promising photorefractive material and an alternative to BaTiO3, which is much easier to grow and does not have any phase transition within the temperature range from 120 C to 100 C. This crystal also possesses slightly larger electrooptic coefficients r13 (20 pm/V) and r33 (130 pm/V) compared to BaTiO3. However, no studies of photorefractive spatial soliton formation have been reported so far in BCT crystals. In this contribution, we investigate photorefractive spatial soliton formation in iron-doped BCT crystals and observe, for the first time to our knowledge, the formation of steady-state two-dimensional (2D) screening solitons in this material. Samples of the congruently melting composition Ba0:23Ca0:77TiO3 are grown in the crystalgrowth laboratory of the Department of Physics at the University of Osnabr€uck [9, 10]. The dimension of our sample that is doped with 290 ppm Fe is 5 5 5 mm3. All surfaces are polished to optical quality. On both faces normal to the c-axis of the crystal, electrodes are prepared with silver paste. The light propagates along the a-axis in our experiment. Our experiments are conducted in a standard setup for soliton formation, in which an external electric field E0 is applied along the ferroelectric c-axis. A frequency-doubled Nd:YAG laser (l 1⁄4 532 nm) is used as the light source. Because of the low dark conductivity of our sample sd 6 10 14 W 1 cm 1 [9], a background illumination is necessary to tune the degree of saturation of the nonlinearity. This ordinarily polarized background light of the same wavelength 532 nm is made spatially incoherent by passing it through a rotating diffuser. The ratio r between the soliton light intensity (extraordinary polarization) and the background irradiance is r 5. The soliton intensity is always kept below 50 mW/cm2 to minimize photovoltaic self-defocusing. Figure 1 shows a characteristic result of 2D soliton formation. In this experiment, the beam intensity is I 30 mW/cm2. The beam diameter at the crystal’s input face is din 14 mm. Without an external electric field E0 applied, the beam width d increases during propagation due to both, phys. stat. sol. (a) 189, No. 1, R4–R5 (2002)

We demonstrate the existence of spatial soliton solutions in photonic crystal fibers (PCF's). These guided localized nonlinear waves appear as a result of the balance between the linear and nonlinear diffraction properties of the inhomogeneous photonic crystal cladding. The spatial soliton is realized self-consistently as the fundamental mode of the effective fiber defined simultaneously by the PCF linear and the self-induced nonlinear refractive indices. It is also shown that the photonic crystal cladding is able to stabilize these solutions, which would be unstable otherwise if the medium was entirely homogeneous.

In this study, we investigate the formation and stability of non-topological spatial solitons in a cubic-quintic nonlinear medium integrated with photonic Moiré lattices. This particular type of nonlinearity can be observed in carbon disulfide. For applying the competing nonlinearities of cubicand quintic orders, this study mitigates the catastrophic collapse that typically occurs in cubic nonlinear media, thereby stabilizing the soliton beams. Our approach is to identify fundamental soliton solutions by employing the Squared Operator Method (SOM), with further stability validation performed through the Split-Step Fourier method. Moiré lattices formed by the superposition of two periodic sublattices with a twist angle, exhibit unique properties that can significantly modify the light propagation characteristics. The shift from commensurate to incommensurate Moiré configurations influences critically soliton localization and power, highlighting the potential of cubicquintic nonlinear media for advanced soliton control in photonic and communication applications.

We present experimental evidence demonstrating that the photorefractive-index change responsible for the formation of photorefractive spatial screening solitons and coherent collisions between them is primarily isotropic in nature, even though the photorefractive medium is inherently anisotropic.

We investigate analytically and numerically propagation and spatial localization of light in nonlocal media with competing nonlinearities. In particular, we discuss conditions for the modulational instability of plane waves and formation of spatial solitons. We show that the competing focusing and defocusing nonlinearities enable coexistence of dark or bright spatial solitons in the same medium by varying the intensity of the beam.

Photorefractive and computational holography in the experimental generation of Airy beams

International audience

Exact self-bending soliton solutions for the equation of a beam in a photorefractive medium with diffusion and drift components of the nonlinear response are obtained and their stability is analysed. It is shown that the interaction of solitons in a medium with nonlocal nonlinearity is accompanied by energy exchange, which causes, as a rule, the annihilation of one of the solitons.

Spatial soliton formation in the bulk single-crystal polydiacetylene para-toulene sulfonate has been studied experimentally. The unique nonlinearity of this material at 1600 nm leads to stable solitons below an intensity maximum, and for higher intensities the input beams form a ring and a soliton.