When using multimode fibers as high-resolution endoscopes, advanced adaptive optics is needed to overcome the modal dispersion which scrambles the image. Additionally, for non-linear imaging methods, all the wavelengths of a femtosecond laser pulse must be simultaneously focused at the sample plane, with appropriate dispersion compensation, that might vary across the sample area. We investigate the bandwidth of the focused spot for a graded index fiber used as a point scanning imaging device. We demonstrate that with proper compensation for the dispersion of the spatial light modulator this can be <45 nm. We also measure the spectral phase at the sample plane, and demonstrate that this does not vary substantially with spot position.
Multimode fibers are a promising tool for high resolution, low-cost, minimally invasive endoscopic imaging. The fiber can be used both to illuminate the sample, which may be buried deep inside the tissue, and to collect the backreflected light. Except for the bare fiber, no other imaging optics have to be inserted, enabling a device with a very small diameter. However, light propagating through the fiber is scrambled before it hits the sample. This renders straightforward imaging impossible, but if this scrambling is known with high accuracy, for instance because the transmission matrix has been measured, the scrambling process can be compensated before the light enters the fiber. For step index multimode fibers, where the refractive index profile consists of a cylindrical core with a constant but higher refractive index than the cladding, it has been shown that the transmission matrix can be predicted for any fiber orientation. Graded index fibers (GIF), where the refractive index profile resembles a parabola, offer numerous advantages, most prominently they are much less sensitive to bending. We measured the transmission matrix of a large GIF and show that we can fully understand the transmission matrix in terms of guided fiber modes, and simultaneously acquire accurate knowledge of the refractive index profile. We also show that although the quality of a commercially available graded index fiber is not sufficient to perform the same analysis, imaging performance of a graded index fiber is much more resilient to bending than the imaging performance of a comparable step index fiber. This demonstrates the need for a graded-index fiber with a high quality refractive index profile.
Many of the properties of thick lenses can be understood by considering these as a combination of parallel ideal thin lenses that share a common optical axis. A similar analysis can also be applied to many other optical systems. Consequently, combinations of ideal lenses that share a common optical axis, or at least optical-axis direction, are very well understood. Such combinations can be described as a single lens with principal planes that do not coincide. However, in recent proposals for lens-based transformation-optics devices the lenses do not share an optical-axis direction. To understand such lens-based transformation-optics devices, combinations of lenses with skew optical axes must be understood. In complete analogy to the description of combinations of pairs of ideal lenses that share an optical axis, we describe here pairs of ideal lenses with skew optical axes as a single ideal lens with sheared object and image spaces. The transverse planes are no longer perpendicular to the optical axis. We construct the optical axis, the direction of the transverse planes on both sides, and all cardinal points. We believe that this construction has the potential to become a powerful tool for understanding and designing novel optical devices.
We recently showed how structures of ideal (thin) lenses can act as (ray-optical) transformation-optics devices. This was done by breaking the structure down into all sets of ideal lenses in the structure that share a common edge, and showing that these sets have very specific imaging properties. In order to start the development of a general understanding of the imaging properties of sets of ideal lenses that share a common edge, we investigate here particularly simple and symmetric examples of combinations of ideal lenses that share a common edge. We call these combinations ideal-lens stars. An ideal-lens star is formed by N identical ideal lenses, each placed such that they share a principal point (which lies on the common edge) and such that the angles between all neighbouring lenses are the same. We find that that passage through every single ideal lens in the ideal-lens star images any point to itself. Furthermore, light-ray trajectories in ideal-lens stars are piecewise linear approximations to conic sections. (In the limit of N approaching infinity, they are conic sections.)
We study, theoretically, omni-directional Euclidean transformation-optics (TO) devices comprising planar, light-ray-direction changing, imaging, interfaces. We initially studied such devices in the case when the interfaces are homogeneous, showing that very general transformations between physical and electromagnetic space are possible. We are now studying the case of inhomogeneous interfaces. This case is more complex to analyse, but the inhomogeneous interfaces include ideal thin lenses, which gives rise to the hope that it might be possible to construct practical omni-directional TO devices from lenses alone. Here we report on our progress in this direction.
Small, fibre-based endoscopes have already improved our ability to image deep within the human body. A novel approach introduced recently utilised disordered light within a standard multimode optical fibre for lensless imaging. Importantly, this approach brought very significant reduction of the instruments footprint to dimensions below 100 μm. The most important limitations of this exciting technology is the lack of bending flexibility - imaging is only possible as long as the fibre remains stationary. The only route to allow flexibility of such endoscopes is in trading-in all the knowledge about the optical system we have, particularly the cylindrical symmetry of refractive index distribution. In perfect straight step-index cylindrical waveguides we can find optical modes that do not change their spatial distribution as they propagate through. In this paper we present a theoretical background that provides description of such modes in more realistic model of real-life step-index multimode fibre taking into account common deviations in distribution of the refractive index from its ideal step-index profile. Separately, we discuss how to include the influence of fibre bending.
Fluorescence microscopy has emerged as a pivotal platform for imaging in the life sciences. In recent years, the overwhelming success of its different modalities has been accompanied by various efforts to carry out imaging deeper inside living tissues. A key challenge of these efforts is to overcome scattering and absorption of light in such environments. Multiple strategies (e.g. multi-photon, wavefront correction techniques) extended the penetration depth to the current state-of-the-art of about 1000μm at the resolution of approximately 1μm. The only viable strategy for imaging deeper than this is by employing a fibre bundle based endoscope. However, such devices lack resolution and have a significant footprint (1mm in diameter), which prohibits their use in studies involving tissues deep in live animals. We have recently demonstrated a radically new approach that delivers the light in/out of place of interest through an extremely thin (tens of microns in diameter) cylindrical glass tube called a multimode optical fibre (MMF). Not only is this type of delivery much less invasive compared to fibre bundle technology, it also enables higher resolution and has the ability to image at any plane behind the fibre without any auxiliary optics. The two most important limitations of this exciting technology are (i) the lack of bending flexibility and (ii) high demands on computational power, making the performance of such systems slow. We will discuss how to overcome these limitations.
Small, fibre-based endoscopes have already improved our ability to image deep within the human body. A novel approach introduced recently utilised disordered light within a standard multimode optical fibre for lensless imaging. Importantly, this approach brought very significant reduction of the instruments footprint to dimensions below 100 μm. The most important limitations of this exciting technology is the lack of bending flexibility - imaging is only possible as long as the fibre remains stationary. The only route to allow flexibility of such endoscopes is in trading-in all the knowledge about the optical system we have, particularly the cylindrical symmetry. In perfect cylindrical waveguides we can find optical modes that do not change their spatial distribution as they propagate through. We show that typical fibers retain such highly ordered propagation of light over remarkably large distances, which allows correction operators to be introduced in imaging geometries in order to maintain high-quality performance even in such flexible micro-endoscopes.
Ray-optically, optical components change a light-ray field on a surface immediately in front of the component into a different light-ray field on a surface behind the component. In the ray-optics limit of wave optics, the incident and outgoing light-ray directions are given by the gradient of the phase of the incident and outgoing light field, respectively. But as the curl of any gradient is zero, the curl of the light-ray field also has to be zero. The above statement about zero curl is true in the absence of discontinuities in the wave field. But exactly such discontinuities are easily introduced into light, for example by passing it through a glass plate with discontinuous thickness. This is our justification for giving up on the global continuity of the wave front, thereby compromising the quality of the field (which now suffers from diffraction effects due to the discontinuities) but also allowing light-ray fields that appear to be (but are not actually) possessing non-zero curl and there by significantly extending the possibilities of optical design. Here we discuss how the value of the curl can be seen in a light-ray field. As curl is related to spatial derivatives, the curl of a light-ray field can be determined from the way in which light-ray direction changes when the observer moves. We demonstrate experimental results obtained with light-ray fields with zero and apparently non-zero curl.
Transformation optics1-5 uses the fact5 that optical media alter the geometry of space and time for light. A
transformation medium performs an active coordinate transformation: electromagnetism in physical space, including
the effect of the medium, is equivalent to electromagnetism in transformed coordinates where space
appears to be empty. Some of the most striking applications of transformation optics include invisibility 1,2,4 or
perfect lensing based on negative refraction.5
Here we discuss an idea for a superantenna based on coordinate transformations. This device is invisible for
most of the rays while it condenses others into a single point. Our device relies on a three-dimensional extension
of optical conformal mapping 2,3 as we describe below.
We present an experimental scheme to perform continuous variable (2,3) threshold quantum secret sharing on the quadratures amplitudes of bright light beams. It requires a pair of entangled light beams and an electro-optic feedforward loop for the reconstruction of the secret. We examine the efficacy of quantum secret sharing in terms of fidelity, as well as the signal transfer coefficients and the conditional variances of the reconstructed output state. We show that, in the ideal limit, perfect secret reconstruction is possible. We discuss two different definitions of quantum secret sharing: the sharing of a quantum secret and the sharing of a classical secret with quantum resources.
We discuss sharing quantum secrets via optical interferometry and
squeezing. A secret quantum state for a single-mode field is encoded
into a multimode field as an entangled state and distributed
to a set of players so that certain subsets can decode the secret
states, and others cannot learn anything about the state. In
particular, we discuss the (k,n)-threshold scheme for optics
and specifically the (2,3) scheme. An arbitrary (k,n)-threshold
scheme can be achieved with no more than two single-mode squeezers.