Fractals are mathematical series that exhibit replicating patterns at every scale. If the repeated patterns are identical at every scale, the fractal is termed self-similar. Fractals have found their way into applications such as communication and cosmology. Theoretical simulations showed that the eigenmodes of unstable laser resonators possess a fractal character, in contrast with the well-known stable-cavity eigenmodes. Unstable laser resonators have a special plane, called self-conjugate, in which the eigenmodes not only have the same pattern, but are also magnified copies of themselves. Here, we show a novel optical resonator that is capable of generating eigenmodes with self-similar fractal features. Our novel resonator is considered as an analogue to both the monitor-insidemonitor effect and monitor-outside-monitor effects. The fractal feature is proved by finding a typical image of the eigenstate at different scales. More quantitatively, we measured the pattern dimension which had a non-integer value, as is characteristic of self-similar fractals.
Mathematical self-similar fractals manifest identical replicated patterns at every scale. Recently, fractals have found their way into a myriad of applications. In optics, it has been shown that manipulation of unstable resonator parameters such as cavity length, curvatures of mirrors, the design of aperture and its transverse position can reveal self-similar fractal patterns in the resonators eigenmodes. Here, we present a novel laser resonator that can generate self-similar fractal output modes. This resonator has a special plane termed self-conjugate, during each round trip inside the cavity, is imaged upon itself with either a magnification or demagnification depending on the direction of beam propagation inside the cavity. By imaging an aperture placed in the self-conjugate plane inside the cavity, we qualitatively show the fractal behaviour occurring at various scales which, are given by powers of the magnification at the self-conjugate plane. We computed the fractal dimension of the patterns we generated and obtained non-integer values, as is expected for fractals.
The use of beams carrying orbital angular momentum (OAM) has become ubiquitous and topical in a variety of research fields. More recently, there has been a growing interest in exotic OAM carrying beams with spatially variant polarization, so called Poincare sphere beams, with the well known cylindrical vector beams (CVBs) a particular example; for example, they can be used to obtain tighter focus in applications ranging from optical trapping and tweezing, to laser material processing. Here we outline how to generate such beams in a deterministic manner directly from a solid state laser by employing intra-cavity geometric phase control. Further, we show how to detect and quantify such beams and introduce a new beam quality factor for vector beams. Finally, we consider the effects of amplification on the quality of such beams. We show that the amplification process can be used to maintain, degrade or improve the overall quality of vector beams.
Vector beams that carrying orbital angular momentum (OAM) have become ubiquitous and topical in a variety of research fields. The quality of such beams usually degrades while propagating in space. Here, we report a noval technique to improve the quality of vector beams by amplifying these beams through birefringent amplifier. We demonstrated this experimentally over the different orientation of the amplifier to reach enhancement in the quality of maximum 20% of that for the incident beam.
Across various areas in the optical world, there has been a growing interest in exploiting the properties of non-separable optical fields. A class of non-separable fields, known as vector modes, exhibit a coupling between the spatial and polarisation degrees of freedom that is akin of entanglement in quantum mechanics. These vector modes, however, are typically characterized using qualitative measurements which are inadequate in determining to what extent an optical field is non-separable. Here, we present tools to characterize the degree of non-separability of an arbitrary optical field, exploiting the similarities between vector modes and quantum entangled states. As an example, we use vector modes carrying orbital angular momentum to demonstrate the effectiveness of our scheme, and note that the approach can be generalized to vector modes as a whole.
Vector beams are spatial modes of light with spatially variant polarization states in the transverse profile. Over the years, vector beams have found their way into plenty of applications ranging from material processing and lithography to electron acceleration and particle trapping. Though qualitative measurements are routinely used to analyse vector beams, there is currently no quantitative measure for vector beam purity. Here, we introduce a new measure, the vector quality factor (VQF), that maps the purity of vector beams to a scale ranging from 0 to 1. We demonstrate a simple optical setup to generate and detect vector beams using a birefringent phase plate known as a q-plate. Tomographic measurements are performed by decomposing the vector beam into its circular basis states, and measuring the expectation values of the Pauli matrices as intensity measurements which, are used to evaluate the VQF of vector beams.