Jesús Liñares -Beiras-

• PhD in Physics
• Professor (Full) at University of Santiago de Compostela

We analyze autocompensation possibilities in entanglement-based QKD protocols. In particular, we study the seminal BBM92 protocol and find that an autocompensating technique is possible, although with severe limitations. This prompts the introduction of a different, more practical protocol based on Bell state exchange parity (BSEP), which allows fo...

Ion-exchanged glass as a platform for quantum photonics is proposed. Quantum projectors are implemented with integrated optical directional couplers fabricated by ion-exchange K $^+$ /Na $^+$ in soda-lime glass. We consider devices composed of concatenated directional couplers which implement $N$ -dimensional quantum projective measurements, an...

Single photon or biphoton states propagating in optical fibers or in free space are affected by random perturbations and imperfections that disturb the information encoded in such states and accordingly quantum key distribution is prevented. We propose three different systems for autocompensating such random perturbations and imperfections when a m...

Ion exchange in glass has a long history as a simple and effective technology to produce gradient-index structures and has been largely exploited in industry and in research laboratories. In particular, ion-exchanged waveguide technology has served as an excellent platform for theoretical and experimental studies on integrated optical circuits, wit...

We present a communication system based on quantum degenerate four-wave mixing for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings (cross-talking) among 2N optical modes (spatial and polarization modes), represented by arbitrary SU(2N) transformations and due to mechanical and...

A systematic study of light propagation in anisotropic and metamaterial media is presented by using a Finslerian vector eikonal method, that is, by considering the approximation of very short wavelengths of light in Maxwell’s equations and using particular metric tensors of the general Finsler metric tensor induced by an anisotropic medium. Green’s...

We propose a simple polygonal model to describe the phase profile of ion-exchanged gratings. This model enables the design of these gratings, as well as the characterization of the ion-exchange process itself. Several ion-exchanged gratings were fabricated to validate the model and to characterize the process involved in their fabrication. From thi...

We present a preliminary theoretical and experimental study of quantum projectors implemented by integrated optical directional couplers fabricated by ion-exchange Na/K processes in soda-lime glass. Theoretical considerations about devices formed by concatenated 2x2 directional couplers are presented in order to show their capabilities for implemen...

Single photon or biphoton states propagating in optical bers or in free space are affected by random perturbations or imperfections along optical bers or free space that disturb the information encoded in such states and accordingly quantum key distribution is prevented. We propose three different systems for autocompensating such random perturbati...

In this work, we present the physical simulation of the dynamical and topological properties of atom-field quantum interacting systems by means of integrated quantum photonic devices. In particular, we simulate mechanical systems used, for example, for quantum processing and requiring a very complex technology such as a spin-1/2 particle interactin...

Featured Application Spatial mode MUX/DEMUX for elliptical-core few-mode fibers in intra-datacenter networks. Abstract Few mode optical fibers are a promising way to continue increasing the data rate in optical communications. However, an efficient method to launch and extract separately each mode is essential. The design of a interferometric spat...

We present a bidirectional quantum communication system based on optical phase conjugation for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings among 2N spatial and polarization optical modes described by SU(2N) transformations due to perturbations are autocompensated after a si...

We present theoretical and laboratory experimental results on a robust interferometric device based on pupil inversion, or 180° rotational shearing interferometry. The image of an astronomical object degraded by the atmosphere turbulence can be restored (ideally up to the diffraction limit) by a numerical post-processing of the interferogram. Unlik...

We study the production of entangled two- and N-mode quantum states of light in optical waveguides. To this end we propose a quantum photonic circuit which produces a reconfigurable superposition of photon subtraction on two single-mode squeezed states. Under post-selection, continuous variable or discrete variable entangled states with possibiliti...

We study both manipulation and detection of two-mode spatial quantum states of light by means of a reconfigurable integrated device built in an electro-optical material in a Kolgelnik-Schmidt configuration, which provides higher error tolerance to fabrication defects and larger integration density than other current schemes. SU(2) transformations a...

Photolithography combined with ion-exchange in glass is a well-known technology that can be applied to develop many different optical devices. In this work, we present the complete procedure to generate small circular phase-shift masks with diameters of only a few microns and high control in the phase change produced. It is a strategic element in a...

We present a system based on phase conjugation in optical fibers for autocompensating highdimensional quantum cryptohraphy. Phase changes and coupling effects are auto-compensated by a single loop between Alice and Bob. Bob uses a source of coherent states and next Alice attenuate them up to a single photon level and thus 1-qudit states are generat...

We present an autocompensating quantum cryptography technique for Measurement-Device-Independent quantum cryptography devices with different kind of optical fiber modes. We center our study on collinear spatial modes in few-mode optical fibers by using both fiber and micro-optical components. We also indicate how the obtained results can be easily...

Ion-exchange in glass is a well-known technique to fabricate phase optical elements. For elements with reduced dimensions, the side diffusion, intrinsic to ion-exchange processes, can affect the performance of these elements if it is not taken into account. Here we present a procedure to optimise the zero-order suppression of ion-exchanged phase gr...

Space division multiplexing based on multicore fibers (MCFs) is an optimum candidate to further increase the data bandwidth in optical communications, and its interest for spatial high-dimensional quantum cryptography has increased in the last few years. However, the main shortcoming lies in the appearance of phases and polarization acquired indepe...

High-dimensional quantum cryptography through optical fibres with several spatial modes requires an efficient quantum key distribution (QKD). However, optical modes acquire different phases and lags due to modal dispersion and random fluctuations, and a modal crosstalk appears under prop- agation. At present, special optical fibres for spatial mult...

Autocompensating techniques have been suggested for polarization modes some years ago and therefore restricted to a bidimensional Hilbert space. However, if spatial modes are considered in order to get high-dimensional quantum key distribution (QKD) then new autocompensating and projective measurement devices are needed. In this work we propose a h...

In a recent article, Banerji et al. introduced a novel quantum state of light, coined as the perfect quantum optical vortex state [Phys. Rev. A 94, 053838 (2016)] due to its mathematical similarity with the classical perfect vortex beam. This state is obtained by means of the Fourier transform of a Bessel-Gaussian vortex state, and the authors clai...

In a recent article, Banerji et al. introduced a novel quantum state of light, coined as the perfect quantum optical vortex state [Phys. Rev. A 94, 053838 (2016)] due to its mathematical similarity with the classical perfect vortex beam. This state is obtained by means of the Fourier transform of a Bessel-Gaussian vortex state, and the authors clai...

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 lense...

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 particula...

A quantum photonic circuit with the ability to produce continuous variable quantum vortex states is proposed. This device produces two single-mode squeezed states which go through a Mach-Zehnder interferometer where photons are subtracted by means of weakly coupled directional couplers towards ancillary waveguides. The detection of a number of phot...

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 in...

In this article we propose a versatile integrated optical chip with the ability to generate both coherent and squeezed Bell-like states for quantum information processing purposes. This is a reconfigurable quantum photonic circuit in a lithium niobate substrate which produces both non-local addition and subtraction of photons on squeezed vacuum sta...

We study the production of entangled two- and N-mode quantum states of light in optical waveguides. To this end, we propose a quantum photonic circuit that produces a reconfigurable superposition of photon subtraction on two single-mode squeezed states. Under postselection, continuous variable or discrete variable entangled states with possibilitie...

We study the propagation of quantum states of light in separable longitudinally inhomogeneous waveguides. By means of the usual quantization approach this kind of media would lead to the unphysical result of quantum noise squeezing. This problem is solved by means of generalized canonical transformations in a comoving frame. Under these transformat...

We study the propagation of quantum states of light in separable longitudinally inhomogeneous waveguides based on the momentum operator. This is carried out in the optical field-strength space by means of the optical propagator obtained by the path integral formalism. We analyze virtual squeezing appearing in these media and its effect on quantum s...

We present an evanescent field optical biosensor based on a bimodal integrated optical waveguide made by a double ion-exchange process. The ion-exchange is optimized to achieve a high sensitivity of the guiding properties to changes in waveguide cover. The detection is performed by measuring the changes in the fringe spacing of bimodal interference...

We study the propagation of quantum states of light in separable longitudinally inhomogeneous media. By means of the usual quantization approach this kind of media would lead to the unphysical result of quantum noise squeezing. This problem is solved by means of generalized canonical transformations in a comoving frame. Under these transformations...

We experimentally demonstrate the first few-mode space division multiplexed (SDM) transmission of real-time 10Gb/s Ethernet (10GbE) traffic using commercial small form-factor pluggable SFP + transceivers without coherent detection or multiple input multiple output digital signal processing (MIMO-DSP) over 0.5km elliptical-core few-mode-fiber, achie...

We study both manipulation and detection of two-mode spatial quantum states of light by means of a reconfigurable integrated device built in an electro-optical material in a Kolgelnik–Schmidt configuration, which provides higher error tolerance to fabrication defects and larger integration density than other current schemes. SU(2) transformations a...

An interferometric characterization of the phase angular shifting produced by rotation of an ion-exchanged glass binary phase plates is presented. The inverse WKB method is used as a starting point to fabricate the phase plates, because such a method can only characterize the phase shift for normal incidence of the light on the plate. A complete ph...

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 wav...

We present a wave-optics paraxial approach to the interference by amplitude division produced by plane-parallel films (or plates) and non-plane-parallel films, or by equivalent optical devices such as a Michelson interferometer, when they are illuminated with extended (spatially incoherent) quasi-monochromatic sources. To the best of our knowledge,...

A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-stren...

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 th...

Using a transmission fiber with a zero differential modal dispersion wavelength and a gain-equalized few-mode EDFA, we demonstrate mode-multiplexed transmission over a fiber recirculating loop with all few-mode components.

We measure the modal gain and noise figure characteristics of a ring-doped few-mode erbium-doped fiber amplifier. We obtained 1 dB higher gain in LP11 than LP01 at an average of 12.5 dB per mode.

We demonstrate wavelength-division multiplexed (WDM) and mode-division multiplexed (MDM) transmission over a fiber recirculating loop comprising of a 25-km span of low differential mode group dispersion (DMGD) few-mode fiber carrying the LP01 and LP11 mode groups, and an inline few-mode erbium-doped fiber amplifier (FM-EDFA) providing low mode-depe...

A seven-core few-mode multicore fiber in which each core supports both the LP01 mode and the two degenerate LP11 modes has been designed and fabricated for the first time, to the best of our knowledge. The hole-assisted structure enables low inter-core crosstalk and high mode density at the same time. LP01 inter-core crosstalk has been measured to...

We demonstrated 1.05-Pb/s transmission over 3km of multicore fiber with spectral efficiency of 109b/s/Hz, using twelve single-mode cores carrying DP-32QAM-OFDM signals and two few-mode cores carrying DP-QPSK in their LP01 and two LP11 modes.

We present the main theoretical results on spatial propagation of quantum light in nonlinear waveguiding devices together with a few applications. We show that the quantization of the classical momentum provides a consistent quantum mechanical formulation of both the linear and the nonlinear quantum light propagation in waveguiding devices. The mom...

We demonstrate mode-division multiplexed transmission using the LP01 and LP11 modes over three heterogeneous spans of few-mode fiber and investigate the impact of fusion splicing and free-space coupling on mode mixing.

A method that characterizes two-mode waveguides whose modes cannot be selectively excited (such as buried waveguides) is presented and demonstrated. The theoretical results are presented for $N$ modes, although for the sake of simplicity, only the two-mode case is developed. The values of the optical mode fields are recovered from several images of...

We demonstrate mode-division multiplexed transmission using the LP01 and LP11 modes over three heterogeneous spans of few-mode fiber and investigate the impact of fusion splicing and free-space coupling on mode mixing.

In response to ever growing data traffic, significant efforts are being made to increase optical network capacity. One promising candidate is mode-division multiplexing (MDM) in few-mode fibers, which uses space as a new information-bearing dimension. A fundamental element for MDM is a modal transformer. Modal transformation can be implemented in a...

We demonstrate mode-division multiplexed WDM transmission over 50-km of few-mode fiber using the fiber’s LP01 and two degenerate LP11 modes. A few-mode EDFA is used to boost the power of the output signal before a few-mode coherent receiver. A 6×6 time-domain MIMO equalizer is used to recover the transmitted data. We also experimentally characteriz...

A seven-core few-mode multi-core fiber in which each core supports three spatial modes has been designed and fabricated. Low inter-core crosstalk is achieved with a high mode density. This fiber allows multiplexed transmission of 21 spatial modes per polarization.

We demonstrate mode-division multiplexed WDM transmission using the LP₀₁ and LP₁₁ modes of a few-mode fiber. The signal is recovered using a 6×6 MIMO equalizer at the receiver after amplification by a few-mode EDFA.

We present a derivation of the paraxial geometrical laws starting from a wave-optics approach, in particular by using simple continuity conditions of paraxial spherical waves at boundaries (discontinuities) between optical media. Paraxial geometrical imaging and magnification laws, under refraction and reflection at boundaries, are derived for seve...

In this work we present a brief outlook of the main results of the research work developed by our group on quantum integrated optics. The major research of the group has been focused on integrated optics and besides in the last years several theoretical and applied quantum studies have been made about both linear and nonlinear integrated optical de...

A quantum analysis of the generalized polarization properties of multimode single photon states is presented. It is based on the optical field-strength probability distributions in such a way that generalized polarization is understood as a significant confinement of the probability distribution along certain regions of the multidimensional optical...

Mixture multimode optical field classical states propagating in N × N integrated directional couplers are analyzed by using the density matrix formalism in a N-dimensional optical space. These mutimode optical fields present a kind of generalized polarization and accordingly a definition of a multimode polarization degree is proposed. It is based o...

In this work we present a brief outlook of the main results of the research work developed by our group on quantum integrated optics. The major research of the group has been focused on integrated optics and besides in the last years several theoretical and applied quantum studies have been made about both linear and nonlinear integrated optical de...

We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of th...

In this work a quantum mechanical derivation of the Spin operator in integrated isotropic and anisotropic photonic waveguides is obtained from both first principles of the electromagnetic theory and conservation laws, and moreover, within a phenomenological quantization approach. The Spin operator will be derived by starting from the spin conservat...

A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relat...

A quantum mechanical analysis of the guided light in integrated photonics waveguides is presented. The analysis is made starting from one-dimensional (1D) guided vector modes by taking into account the modal orthonormalization property on a cross section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time...

In this work is presented a macroscopic quantum-mechanical analysis of quantum light progression in different kinds of integrated photonic waveguide structures with coupled modes, and therefore with validity, for instance, for integrated optical waveguides (conventional integrated optics), photonic crystal waveguides, nano-optical waveguides (plasm...

In this work we present an analysis of the propagation, based on the Dirac equation, of spinor-electron quantum modes, that is, of spinor-electron guided waves in asymmetric 2D and 1D semiconductor nanostructures. Spinor-electron modes are calculated by means of Dirac equation in an asymmetric 2D semiconductor structures, analogous to the wellknown...

We present a quantum-mechanical analysis of progression of coupled modes in integrated photonic guides, that is, with validity, for instance, for integrated optical guides, photonic crystal guides and nano-optical guides. This analysis of quantization is consistent and accurate by using the Momentum operator, avoiding, in this way, inconsistent res...

A preliminary quantum analysis, based on the Dirac equation, of the propagation of spinor electron waves in electron waveguides is presented. The wave equations for spin-up (SU) and spin-down (SD) electron waves in electron guides are derived and their analogy with TE and TM light modes in dielectric guides is stressed. The spinor electron waveguid...

We present a theoretical study of all-optical multistability in an integrated device composed by a step-index nonlinear Kerr waveguide with a variable width film, providing an effective graded-index profile. The self- and cross-action of nonlinear Gaussian counterpropagating beams in this structure and a feedback controlling mechanism based on tran...

We present the design of an all-optical router based on the properties of both propagation and interaction of Gaussian beams in lenslike planar guides. Variational results of single co- and counterpropagation are derived and used to design three integrated optical devices, that is, a header extraction device, an optical bistable device and a data r...

We present both a derivation and a resolution method of a nonlinear equations system describing counterpropagation in a nonlinear guiding planar medium with linear and nonlinear losses (and/or gain). These equations system can be quasi-decoupled in a thin slice of the medium and they can be solved by exact or approximate methods, like the variation...

We present the theory and design of a fiber compatible all-optical integrated device which, by means of the swing effect experimented by a Gaussian beam propagating in a nonlinear planar waveguide with variable core width, presents a new kind of all-optical self-routing operation. The corresponding local modal amplitude distribution in this guide p...

We present a study of the spatial propagation of light in a third order planar step-index waveguide with a transverse parabolic width film. By using the Lagrangian formalism, the width and phase evolution of a Gaussian beam has been completely described showing both the refractive contributions of the lens-like waveguiding geometry and self-focusin...

A method to obtain the complete electromagnetic scattering properties of discontinuities between arbitrary integrated optical waveguides is presented. The method involves a new generalized scattering matrix concept, together with the generalized telegraphist equations formulism and the modal matching technique. Radiation losses, as well as reflecti...

A quantum mechanical analysis of the propagation of coupled modes in integrated optical waveguides is given. The modal orthonormalization property on a cross-section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry are taken into account to derive the quantum momentum operator and Heisenberg's...

A nonlinear integrated optical device, presenting an intrinsic bistable behaviour by means of the Kerr effect produced by counterpropagating beams, is presented. The proposed feedback mechanism, which preserves the spatial shape of the beams, is based on the transverse modal coupling of the beams to optical fibers through integrated multilenses. An...

In this work we present the study of step-index channel directional couplers which can be fabricated on a buffer planar guide in a such a way that they can be properly designed to support separable modal fields, though the index profile is non separable. The main advantage of this approach is the great simplicity in the analysis, design and fabrica...

We present the theory and design of a nonlinear integrated optical device, which, by means of the Kerr effect produced by counterpropagating beams, presents an intrinsic bistable behaviour. The feedback mechanism proposed maintains the spatial shape of the beams and is based on both the transverse modal coupling of the beams to channel guides and a...

We present a theoretical model to describe the feature size produced by direct laser writing upon a photoresist relative to various experimental parameters. The model allows the number of parameters required for describing the linewidth to be reduced and shows how the description can be made in terms of the ratio of laser power to writing velocity....

The first example of hybrid diffractive/graded-index optical integration is presented. The demonstrated 1:3 beamsplitter for fiber optics consists of two GRIN lenses and one diffractive element, which are fabricated by ion exchange and stacked together to form a solid unit. The unit is coupled with the input optical fiber and with three output ones

Preliminary results are presented of a theoretical modelling of ionexchange processes to fabricate monomode channel guides such that the modal propagation can be solved by the effective index method in a quasi-exact form. With these results both the design and fabrication of integrated optical devices based on ion-exchanged channel guides, such as...

We employ interference microscopy to characterize in a direct and local way the graded index transitions at the boundaries of integrated optical elements fabricated by multistep ion-exchange processes, a task not yet possible by other technologies. A particular fabrication method based on purely thermal ion-exchange, which allows local single-mode...

A new kind of integrated optical sensor based on planar waveguiding elements is proposed. The sensing technique is by means of interference and transverse coupling to a single mode guide by using waveguiding lenses. The optical sensitivity function and the minimum detectable signal are obtained.

We present a technique to directly process silver ion- exchanged planar waveguides fabricated in soda-lime glass. The technique, that is regarded as complementary to the conventional lithography but with the inherent advantages of the direct processing of the material, is based on laser writing with a focused laser bema from an Ar+ laser, which ind...

We have designed novel glasses for the formation of graded-index diffractive optical structures. In these glasses silver ion exchange and rapid diffusion produce a large refractive-index variation (0.085). We model the non-linearity of the diffusion process by applying the Boltzmann–Matano technique to the optical profiles and use index variation r...

It is shown by numerical computations that self-similar index profiles imply self-similar mode spectra in planar waveguides. This leads to a simple method to estimate the diffusion activation energy and to evaluate the validity of Fick's second law in diffusion modeling, under given processing condition, from measurements of mode spectra. The feasi...

Ion-Exchanged Glass Integrated Optics has received a considerably attention during the laser years because of their well-known advantages. On the other hand, ion- exchanged waveguide components are finding important applications in the implementation of analogue processing devices, optical sensing devices and some kind of circuit for optical commun...

We report the fabrication of a high-concentration Er-doped phosphate-niobate glass. The glass composition has been optimized for doping with erbium and for ion-exchange processing. Formation and modelling of planar ion-exchanged waveguides with silver and potassium dopants are also presented to confirm that this glass is a prospective candidate for...

A model of lateral diffusion in the ion-exchange fabrication of integrated optical elements, based on two regions with different effective index in the same substrate, is demonstrated. A nondestructive method based on interference microscopy is used to characterize the corresponding graded-index transition regions between the outer and the inner zo...

We present the preliminary results about the paraxial design of graded-index (GRIN) bifocal spectacle lenses fabricated by a local ion-exchange technique in glass. Paraxial formulae for the optical power are calculated for two refractive index profiles modelling the GRIN region, Erfc and Gaussian, which correspond to a linear and nonlinear ion-exch...

A perturbative theory has been used to investigate the nonlinearly laser-induced grating formed by the superposition of two elliptical beams inside a Kerr medium. The effect on both soliton propagation and induced guiding of a weak beam has been studied.

The use of total reflection at the boundary between the guiding region and the substrate (or another guiding region) to implement waveguide achromatic elements is discussed. Two geometries of the boundary, parabolic and elliptical, are proposed and analyzed. The parabolic boundary was fabricated by selective ion exchange, and both its focusing capa...

A new fabrication method of waveguide integrated elements immersed in shallow buried single-mode planar waveguides fabricated in glass substrates is proposed in order both to avoid scattering losses, by minimizing the interaction of the propagating field with surface irregularities, and to improve fibre–waveguide coupling performance. Likewise, by...

Transmission of a guided mode through a graded refractive-index boundary generated beneath the mask edge in an ion-exchanged planar waveguide is considered by means of the overlap integral method and a precise electromagnetic scattering model. It is shown that, with optimized post-baking, virtually lossless transmission can be obtained for a wide r...