Photonic lanterns are a powerful emerging technology with critical applications in wavefront sensing, ultra-resolution hyperspectral imaging, telecommunications, adaptive optics for deep turbulence, LIDAR, directed energy, and astronomical investigations of extrasolar planets. A photonic lantern is a monolithic optical fiber device consisting of a smooth, continuous 3-D waveguide transition that implements spatial transformations. The lantern effectively decomposes the input light into eigenmodes of the lantern, with each mode corresponding to an output SMF. Thus, we can measure the distribution of intensities among the output single-mode beams to reconstruct the incoming optical field. Our group has pushed lanterns to high coupling efficiencies, with demonstrated broadband (400-700nm) transmission >91%, with efficiency rising to >97% for wavelengths approaching 1000nm and beyond. A rapidly expanding application of photonic lanterns is in the area of wavefront sensing. We will present our recent developments for Photonic Lantern WaveFront Sensors (PLWFS), with particular emphasis on their potential applications for optical system metrology and aberration control.
Our team aims to demonstrate a photonic Quantum-Inspired Imager (QI2) which provides source reconstruction below the optical/NIR diffraction limit in the presence of atmospheric turbulence without the need for adaptive optics. Turbulent cells in the atmosphere reduce image resolution by causing fluctuations in the phase of propagating wavefronts. Rather than relying on conventional methods of wavefront sensing, our approach leverages the spectral diversity inherent in the factors which limit resolution, thus breaking the degeneracy between these aberrating processes. Though this concept has long been employed in astronomy to achieve diffraction limited imaging, our approach achieves this necessary spectral diversity with a passive photonic lantern mode multiplexer that converts a multimode wavefront input into an array of spatially distinct single-mode outputs, from which we can deduce the atmospheric phase variations and reconstruct the source function. We present detailed simulations and laboratory tests demonstrating the QI2 approach in measuring atmospheric turbulence and correcting phase distortions.
Fiber mode scrambling remains a key technology for fiber-fed EPRV measurements. Any change in mode excitation within the fiber will result in apparent centroid shifts (and thus artificial RV shifts) in the target spectrum. Technologies such as scramblers and mechanical agitators are currently used to mitigate this effect. Here, we present our experimental results on the modal illumination stability of “flat top” optical fibers. These fibers are fabricated with deliberately-introduced internal mode scrambling features which distribute light evenly among the fiber modes during transmission from input to output. Importantly, this scrambling occurs with minimal (few percent) light losses and without external optical alignment or mechanical motion to achieve excellent mode scrambling if the flat-top fiber is spliced into the existing fiber feed. We will present our measurements of flat-top fiber throughput and scrambling gain, and the expected benefits from incorporating such a fiber into existing EPRV spectrographs.
We present results from development of a photonic Quantum-Inspired Imager (QI2) providing source reconstruction below the optical/NIR diffraction limit through atmospheric turbulence without adaptive optics. Our group has demonstrated a photonic spatial mode sorter quantum-sensing device in practice — a photonic lantern — with capabilities in both spatial and spectral diversity, as well as future extensions to polarization sensitivity. Our team has developed high-efficiency photonic lantern mode-sorting/multiplexing devices fabricated in optical fibers. Our proposed passive imaging system is therefore based on three main innovations: (i) photonic lantern spatial mode sorters with spatial and spectral diversity, (ii) atmospheric blur removal enabled by mode-/wavelength-resolution, (iii) quantum-inspired image reconstruction techniques.
The ellipsoidal coordinate system has the interesting property that every other orthogonal coordinate system in which the three-dimensional Helmholtz equation is separable, is a special case of it. In this work, we explore the solutions to the wave equation in ellipsoidal coordinates in order to visualize the behavior of optical fields with ellipsoidal geometry. We show several parity properties which allow us to create fundamental modes of vibration with different symmetries around the (x; y), (x; z) and (y; z) planes. We discuss the resonant modes of an ellipsoidal cavity and the traveling waves with ellipsoidal geometry. We propose a method to calculate the second linearly independent solution to the ellipsoidal wave equation
We study the propagating and shaping characteristics of the novel one-dimensional Cartesian Parabolic-Gaussian
beams. The transverse profile is described by the parabolic cylinder functions and are apodized by a Gaussian
envelope. Their physical properties are studied in detail by finding the 2n-order intensity moments of the beam.
Propagation through complex ABCD optical systems, normalization factor, beam width, the quality M2 factor
and its kurtosis parameter are derived. We discuss its behavior for different beam parameters and the relation
between them. The Cartesian Parabolic-Gaussian beams carry finite power and form a biorthogonal set of
solutions of the paraxial wave equation in Cartesian coordinates.
We study the propagating and shaping characteristics of the novel Whittaker-Gaussian beams (WGB). The transverse profile is described by the Whittaker functions. Their physical characteristics are studied in detail by finding the 2n-order intensity moments of the beam. Propagation through complex ABCD optical systems, normalization factor, beamwidth, the quality M2 factor and its kurtosis parameter are derived. We discuss its behavior for different beam parameters and the relation between them. The WGBs carry finite power and form a biorthogonal set of solutions of the paraxial wave equation (PWE) in circular cylindrical coordinates.
We review the three types of laser beams - Hermite-Gaussian (HG), Laguerre-Gaussian (LG) and the newly discovered Ince-Gaussian (IG) beams. We discuss the helical forms of the LG and IG beams that consist of linear combinations of the even and odd solutions and form a number of vortices that are useful for optical trapping applications. We discuss how to generate these beams by encoding the desired amplitude and phase onto a single parallel-aligned liquid crystal display (LCD). We introduce a novel interference technique where we generate both the object and reference beams using a single LCD and show the vortex interference patterns.
The vector Mathieu-Gauss beams of integer order are examined as the solutions of the vector paraxial wave equation in elliptical coordinates. The propagation of the vector components and the three-dimensional intensity distribution of focused vector Mathieu-Gauss beams are analyzed for a variety of polarizations. Conditions in which the linearly polarized Mathieu-Gauss beams can be approximated by the scalar solutions of the paraxial wave equation are also discussed.
In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.
We present the experimental generation and characterization of each one of the four fundamental families of Helmholtz-Gauss beams: cosine-Gauss beams, stationary and helical Mathieu-Gauss beams, stationary and traveling parabolic-Gauss beams, and Bessel-Gauss beams. Both the transverse intensity profile and power spectrum that each one of the beams exhibits upon propagation is observed and compared to the theoretical model with good quantitative agreement. Emphasis is made on the fact that each of the four families of HzG beams is complete and orthogonal, and thus of fundamental relevance.
We study the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptic coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded index media. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence between the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation between the three definitions.
The term Helmholtz-Gauss beam refers to a field whose disturbance at the plane z =0 reduces to the product of the transverse field of an arbitrary nondiffracting beam (i.e. a solution of the two-dimensional Helmholtz equation) and a two-dimensional Gaussian function. In this work, the transverse shape and the propagation of Helmholtz-Gauss beams is experimentally studied for the four fundamental orthogonal families of Helmholtz-Gauss beams: cosine-Gauss beams, Bessel-Gauss beams, stationary and helical Mathieu-Gauss beams, and stationary and traveling parabolic-Gauss beams. The power spectrum of the Helmholtz-Gauss beams is also recorded and its intensity distribution is assessed. Potential applications are discussed.
Ince-Gaussian modes form a complete family of exact and orthogonal solutions of the paraxial wave equation for elliptical coordinates. The transverse distribution of these fields is described by the Ince polynomials and have an inherent elliptical symmetry. These modes constitute a smooth transition from Hermite-Gaussian modes to Laguerre-Gaussian modes. We report the experimental observation of Ince-Gaussian modes directly generated in a stable resonator. By slightly breaking the symmetry of the cavity of a diode pumped Nd:YVO4 laser and its pump beam configuration we were able to generate single high order Ince Gaussian modes with very high quality. The observed transverse modes and nodal patterns have the proposed elliptic structure and exhibit remarkable agreement with the theoretical predictions.
Propagation of light beams with apparent nondiffracting properties have intrigued the scientific community since they were introduced. In this talk we will introduce the fundamentals of nondiffracting beams and discuss the dynamics of optical vortices embedded in the new two families of nondiffracting beams we have recently discovered, Mathieu and parabolic beams.
Recently, a new class of nondiffracting beams has been demonstrated theoretically. Namely, Parabolic nondiffracting optical wavefields constitute the last member of the family of fundamental nondiffracting wavefields. Additionally, the existence of a new class of parabolic traveling waves associated to these wavefields has been demonstrated along the same lines. We have succeeded in demonstrating experimentally the fundamental odd and even parabolic wavefields in the laboratory. In this work, we present and discuss the experimental generation of higher-order parabolic nondiffracting wavefields. Because these fields show a complex structure, their generation relies in the successful construction of the field.
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