Quaternary adaptive optics.

We present a new Point Diffraction Interferometer (PDI). Binary adaptive optics (BAO) and Quaternary Adaptive Optics (QAO) can be performed with the help of this PDI as a wavefront sensor. The PDI interferogram, once binarized, is used in two consecutive steps to produce a quaternary mask with phase values 0, π/2, π and 3π/2. The addition of the quaternary mask compensates for the aberrated wavefront and allows us to reach a Strehl ratio of about 0.81. We have verified through computer simulations that the use of QAO depends on the number of actuators of the compensating device to achieve effective compensation. The technique was successfully validated through an experiment.

Ion-exchanged binary phase plates for mode multiplexing in graded-index optical fibers.

Few-mode graded-index optical fibers are being increasingly relevant in spatial division multiplexing. Likewise, multi-region binary phase plates are fundamental elements for some mode multiplexing schemes in such optical fibers. In this work, we propose a coupling configuration for mode multiplexing based on collimating-focusing graded-index lenses together with binary phase plates, and calculate, in a fully analytical and quasi-analytical way, the theoretical conversion efficiencies and crosstalks between the fields generated by such plates and the Laguerre-Gaussian modes. These modes describe, directly or by a linear combination of them, the first optical modes of many graded-index optical fibers. The results obtained provide both the illumination conditions of the plates and their optical characteristics. The fabrication of the plates is made by using ion-exchange technology and their optical characterization by beam profilometry. The experimental conversion efficiencies are in agreement with the theoretical results.

Interferometric space-mode multiplexing based on binary phase plates and refractive phase shifters.

A Mach-Zehnder interferometer (MZI) that includes in an arm either a reflective image inverter or a Gouy phase shifter (RGPS) can (de)multiplex many types of modes of a few mode fiber without fundamental loss. The use of RGPSs in combination with binary phase plates for multiplexing purposes is studied for the first time, showing that the particular RGPS that shifts π the odd modes only multiplexes accurately low order modes. To overcome such a restriction, we present a new exact refractive image inverter, more compact and flexible than its reflective counterpart. Moreover, we show that these interferometers remove or reduce the crosstalk that the binary phase plates could introduce between the multiplexed modes. Finally, an experimental analysis of a MZI with both an approximated and an exact refractive image inverter is presented for the case of a bimodal multiplexing. Likewise, it is proven experimentally that a RGPS that shifts π/2 demultiplexes two odd modes which can not be achieved by any image inverter.

Spatial mode multiplexing/demultiplexing by Gouy phase interferometry.

We present a theoretical study about spatial mode multiplexing/demultiplexing (mux/demux) without theoretical losses by means of interferometry with selective control of the Gouy phase of optical beams, that is, Gouy phase interferometry (GPI). Different Gouy phase values can be obtained by inserting appropriate optical systems at each arm of an interferometer. Thus, spatial mode mux/demux operations of strategic interest in optical communications with few-mode optical fibers are implemented by means of constructive interference and regardless of the parity and separability of the optical beams. Consequently, unachievable mux/demux by interferometry based on image inversion methods becomes possible with GPI. This kind of operation can also be interesting for optical sensors, optical metrology, image processing, and so on.

Chromatic characterization of ion-exchanged glass binary phase plates for mode-division multiplexing.

Mode-division multiplexing (MDM) in few-mode fibers is regarded as a promising candidate to increase optical network capacity. A fundamental element for MDM is a modal transformer to LP modes which can be implemented in a free-space basis by using multiregion phase plates, that is, LP plates. Likewise, several wavelengths have to be used due to wavelength multiplexing purposes, optical amplification tasks, and so on. In this work we show that efficient monolithic binary phase plates for different wavelengths can be fabricated by ion-exchange in glass and used for MDM tasks. We introduce an optical characterization method of the chromatic properties of such phase plates which combines the inverse Wentzel-Kramers-Brillouin (IWKB) together with Mach-Zehnder and Michelson-based interferometric techniques. The interferometric method provides a measurement of the phase step for several wavelengths, which characterizes the chromatic properties of the phase plate. Consequently, it is shown that the IWKB method allows us to design and characterize the phase plates in an easy and fast way.

Ion-exchanged glass binary phase plates for mode-division multiplexing.

Significant efforts are being made to increase optical network capacity in response to ever-growing data traffic. One promising candidate is mode-division multiplexing (MDM) in few-mode fibers. A fundamental element for MDM is a modal transformer. Modal transformation can be implemented in a free-space basis by using multiregion phase plates. In this work, we show that efficient monolithic binary phase plates can be fabricated by ion exchange in glass and used for MDM tasks. We present an optical characterization method of such plates, which is based on a combination of the inverse Wentzel-Kramers-Brillouin (IWKB) method and Mach-Zehnder interferometric techniques. The IWKB method allows us to design and characterize the phase plates in an easy and fast way, whereas interferometry gives us a precise measurement of the phase step. Far-field optical intensities are measured, and a high-quality mode transformation is confirmed.

Pupil aberrations in Offner spectrometers.

The light path function (LPF) of an Offner spectrometer is presented. The evaluation of the LPF of this spectrometer enables its imaging properties to be studied for arbitrary object and image positions, while avoiding the more complicated analysis of intermediate images generated by the diffraction grating, which is often involved. A power series expansion of the LPF on the grating coordinates directly determines pupil aberrations of the generated spectrum and facilitates the search for configurations with small low-order aberrations. This analysis not only confirms the possibility of reducing low-order aberrations in Rowland-type mounts, namely astigmatism and coma, as predicted in previous studies, but also proves that all third-order terms in the series expansion of the aberration function can be canceled at the image of the design point and for the corresponding design wavelength, when the design point is located on a plane orthogonal to the optical axis. Furthermore, fourth-order terms are computed and shown to represent the most relevant contribution to image blurring. Third- and fourth-order aberrations are also evaluated for Rowland mounts with the design point located outside the aforementioned plane. The study described in this manuscript is not restricted to small angles of incidence, and, therefore, it goes beyond Seidel and Buchdahl aberrations.

Design of Dyson imaging spectrometers based on the Rowland circle concept.

We aim to show that Dyson imaging spectrometers can be easily designed by applying the concept of the Rowland circle to refracting surfaces. This allows us to conceive an analytical procedure that is based on the removal of astigmatism at two wavelengths. Following this procedure, high-optical-quality spectrometers can be designed even for high speeds. Root-mean-square spot radii less than 2.5 µm are obtained for speeds as high as f/1.5, slit lengths of 15 mm, and wavelength ranges of 0.4-1.7 µm. Design examples are presented for classical Dyson spectrometers in which the detector is glued to the glass plane surface and for spectrometers with an air gap between this surface and the image plane.

Off-plane anastigmatic imaging in Offner spectrometers.

In this paper, the imaging performance of an Offner concentric imaging spectrometer is analyzed when the spectrometer entrance slit is disposed arbitrarily on the plane that is parallel to the grating grooves and contains the common center of curvature. Astigmatism-corrected designs are obtained for off-plane incidence on the grating if one point on the slit is located on the Rowland circle of the primary mirror. In this case, the combined system of primary mirror plus diffraction grating provides two astigmatic line images oriented parallel and orthogonal to the plane of diffraction, with the former located on the same plane as the slit. Consequently, these images can be brought to a single focus on this plane by the tertiary mirror if its radius of curvature is chosen properly. In addition, coma aberration is simultaneously removed. These results can be applied to the design of two-mirror or three-mirror spectrometers, generalizing the concept of the best imaging circle and providing solutions to get anastigmatic imaging for two object points and two wavelengths.

Schwarzschild spectrometer.

This is a proposal and description of a new spectrometer based on the Schwarzschild optical system. The proposed design contains two Schwarzschild optical systems. Light diverging from the spectrometer entrance slit is collimated by the first one; the collimated light beam hits a planar diffraction grating and the light dispersed from the grating is focused by the second system, which is concentric with the first. A very simple procedure obtains designs that are anastigmatic for the center of the slit and for a particular wavelength. A specific example shows the performance of this type of spectrometer.

The Offner imaging spectrometer in quadrature.

This is a proposal and description of a new configuration for an Offner imaging spectrometer based on the theory of aberrations of off-plane classical-ruled spherical diffraction gratings. This new spectrometer comprises a concave mirror used in double reflection and a convex reflection grating operating in quadrature, in a concentric layout. A very simple procedure obtains designs that are anastigmatic for a given point on the entrance slit and a given wavelength. Specific examples show that the performance of this type of system improves the performance of analogous conventional in-plane systems, when compactness and/or high spectral resolution is of fundamental importance.

Two-wavelength anastigmatic Dyson imaging spectrometers.

High-quality Dyson imaging spectrometers are designed by applying a telecentric condition for off-axis image points. By imposing this condition for two different wavelengths, designs presenting low aberrations for the whole spectral range of the system are obtained. A UV-TO-NIR fast design (f/1.5) exhibiting excellent optical performance is presented.

Imaging with classical spherical diffraction gratings: the quadrature configuration.

We review the theory of spherical diffraction gratings with regard to their imaging properties in off-plane arrangements. Our study is restricted to gratings with equally spaced grooves, and it is focused on the quadrature configuration, where the incident and diffraction planes are orthogonal to each other. We identify regions of low astigmatism and propose some monochromator mounts.