We report on a simple experimental scheme to generate and control the orbital angular momentum (OAM) spectrum of the asymmetric vortex beams in a nonlinear frequency conversion process. Using a spiral phase plate (SPP) and adjusting the transverse shift of the SPP with respect to the incident Gaussian beam axis, we have transformed the symmetric (intensity distribution) optical vortex of order l into an asymmetric vortex beam of measured broad spectrum of OAM modes of orders l, l − 1, l − 2, …, 0 (Gaussian mode). While the position of the SPP determines the distribution of the OAM modes, we have also observed that the modal distribution of the vortex beam changes with the shift of the SPP of all orders and finally results in a Gaussian beam (l = 0). Using single-pass frequency doubling of the asymmetric vortices, we have transferred the pump OAM spectra, l, l − 1, l − 2, …, 0, into the broad spectra of higher order OAM modes, 2l, 2l − 1, 2l − 2, …, 0 at green wavelength, owing to OAM conservation in nonlinear processes. We also observed an increase in single-pass conversion efficiency with the increase in asymmetry of the pump vortices producing a higher power vortex beam of mixed OAM modes at a new wavelength than that of the pure OAM mode.

We study the annihilation of topological solitons in the simplest setting: a one-dimensional ferromagnet with an easy axis. We develop an effective theory of the annihilation process in terms of four collective coordinates: two zero modes of the translational and rotational symmetries Z and Φ, representing the average position and azimuthal angle of the two solitons, and two conserved momenta ζ and ϕ, representing the relative distance and twist. Comparison with micromagnetic simulations shows that our approach captures well the essential physics of the process.The dynamics of topological solitons in ferromagnets [1] poses a class of problems of fundamental interest. Time evolution of magnetization is governed by the Landau-Lifshitz-Gilbert (LLG) equation [2,3] Here m(r, t) = M/|M| is the unit-vector field of magnetization, J = |M|/γ is the angular momentum density, h eff (r) = −δU/δm(r) is the effective magnetic field obtained from the potential energy functional U [m(r)] and α 1 is the Gilbert damping constant. Since the magnetization field has infinitely many modes that are coupled non-linearly, full analytic solution to a dynamical problem is unavailable in most cases.A powerful alternative approach is to identify a small number of relevant soft modes, parametrized in terms of collective coordinates, and formulate an effective theory only in terms of these. This method was first applied to magnetic solitons by Schryer and Walker [4] to describe the dynamics of a domain wall in an easy-axis ferromagnet in one spatial dimension, m = m(z, t), with the Lagrangian [1]and the potential energyHere θ and φ are the polar and azimuthal angles of magnetization m, A is the exchange constant, K is the anisotropy, andẑ is the direction of the easy axis. The unit of length is the width of the domain wall 0 = A/K and the unit of time is the inverse of the ferromagnetic resonance frequency,In what follows, we work in these natural units and set J = A = K = 0 = t 0 = 1. A topological soliton interpolating between the two ground states m = ±ẑ and minimizing the potential energy (3) is a domain wallThe position of a domain wall Z and its azimuthal angle Φ are collective coordinates describing the zero modes associated with the translational and rotational symmetries. Schryer and Walker showed that, in the presence of weak perturbations, the dynamics of a domain wall reduces to a time evolution of Z and Φ. By substituting the domain-wall Ansatz (4) into the LLG equation (1) or into the Lagrangian (2), one obtains an effective theory for this system in terms of the two collective coordinates arXiv:1702.02248v1 [cond-mat.mes-hall]

Nonlinear frequency conversion processes depend on the polarization state of the interacting beams. On the other hand, vector vortex beams have space-variant polarization in the transverse beam plane. In light of these two points, is it possible to do nonlinear frequency conversion of the vector vortex beam in single-pass geometry and retain the characteristics of the beam? To address this question, here, we report an experimental scheme for single-pass second harmonic generation (SHG) of vector vortex beams. Using an ultrafast Ti:Sapphire laser of pulse width ∼17 fs and a set of spiral phase plates in a polarization based Mach–Zehnder interferometer (MZI), we have generated vector vortex beams of order as high as lp = 12 at an average power of 860 mW. Using two contiguous bismuth borate crystals with the optic axis orthogonal to each other, we have frequency-doubled the near-IR vector vortex beam into visible vector vortex beam with order as high as lsh = 24. The maximum output power of the vector vortex beam of order, lsh = 2, is measured be as high as 20.5 mW at a single-pass SHG efficiency of 2.4%. Controlling the delay in MZI, we have preserved the vector vortex nature of both the pump and frequency-doubled beams. Measurement on the mode purity confirms the generation of high quality vector vortex beams at pump and SHG wavelengths. This generic scheme can be used to generate vector vortex beams across the electromagnetic spectrum in all time scales, continuous-wave to ultrafast.

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Spontaneous parametric down‐conversion (SPDC), a primary resource of photonic quantum entangled states, strongly depends on the intrinsic phase matching condition. This makes it susceptible to changes in factors such as the pump wavelength, crystal temperature, and crystal axes orientation. Such intolerance to changing environmental factors prohibits  deployment of SPDC‐based sources in non‐ideal environments outside controlled laboratories. Here, a novel system architecture based on a hybrid linear and non‐linear solution that is shown to make the source tolerance‐enhanced without sacrificing brightness. This linear solution is a lens‐axicon pair, judiciously placed, which is tested together with two common non‐linear crystals, quasi‐phase‐matched periodically‐poled KTiOPO4, and birefringent‐phase‐matched BiB3O6. This approach has the benefit of simultaneous tolerance to the environment and high brightness, which is demonstrated by using the proposed architecture as a stable entangled photon source and a spectral brightness as high as 22.58 ± 0.15 kHz mW−1 with a state fidelity of 0.95 ±3.33333pt0.02$\pm \nobreakspace 0.02$, yet requiring a crystal temperature stability of only ±0.8 °C, a 5 × enhanced tolerance as compared to the conventional high brightness SPDC configurations is reported. This solution offers a new approach to deployable high‐brightness quantum sources that are robust to their environment, for instance, in satellite‐based quantum applications.