Lossless Beam Splitter Research Articles

Metasurface-enabled non-orthogonal four-output polarization splitter for non-redundant full-Stokes imaging

Imaging polarimetry plays an essential role in various fields since it imparts rich information that cannot be obtained through mere intensity and spectral measurements. To retrieve full Stokes parameters, at least four sensor pixels are required, each of which projects incident light to a different polarization state in the Stokes space. Conventional full-Stokes division-of-focal-plane (DoFP) cameras realize this function by integrating angled polarizers and retarders on top of image sensors. Due to the inevitable absorption at the polarizers, however, the maximum efficiency of these schemes is limited to 50% in theory. Instead of polarizers, three sets of lossless polarization beam splitters can be used to achieve higher-efficiency polarimetry, however, at the cost of reduced spatial resolution due to the need for six redundant sensor pixels. In this paper, we reveal that low-loss four-output polarization splitting (without filtering) is possible using a single-layer dielectric metasurface. Although these four states are not orthogonal to each other, our metasurface enables simultaneous sorting and focusing onto four sensor pixels with an efficiency exceeding 50%. The designed metasurface composed of silicon nanoposts is fabricated to experimentally demonstrate complete retrieval of full Stokes parameters at a near-infrared wavelength range from 1500 to 1600 nm with −0.67-dB (85.8%) transmission and −2.28-dB (59.2%) overall efficiency. Finally, multi-pixel polarimetry is demonstrated using a 3×4 superpixel array.

Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization.

Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong-Ou-Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

Fundamental properties of beamsplitters in classical and quantum optics

A lossless beamsplitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws of classical and quantum optics to obtain general relations among the magnitudes and phases of these probability amplitudes. Proceeding to examine a pair of (nearly) single-mode wavepackets in the number-states n1 and n2 that simultaneously arrive at the splitter's input ports, we find the distribution of photon-number states at the output ports using an argument inspired by Feynman's scattering analysis of indistinguishable Bose particles. The result thus obtained coincides with that of the standard quantum-optical treatment of beamsplitters via annihilation and creation operators â and â†. A simple application of the Feynman method provides a form of justification for the Bose enhancement implicit in the well-known formulas ân=nn−1 and â†n=n+1n+1.

Anti-Hong–Ou–Mandel interference by coherent perfect absorption of entangled photons

Two-photon interference, known as the Hong–Ou–Mandel effect, has colossal implications for quantum technology. It was observed in 1987 with two photodetectors monitoring outputs of the beamsplitter illuminated by photon pairs: the coincidence rate of the detectors drops to zero when detected photons overlap in time. More broadly, bosons (e.g. photons) coalesce while fermions (e.g. electrons) anti-coalesce when interfering on a lossless beamsplitter. Quantum interference of bosons and fermions can be tested in a single—photonics platform, where bosonic and fermionic states are artificially created as pairs of entangled photons with symmetric and anti-symmetric spatial wavefunctions. We observed that interference on a lossy beamsplitter of a subwavelength thickness, or a coherent perfect absorber, reverses quantum interference in such a way that bosonic states anti-coalesce while fermionic states exhibit coalescent-like behavior. The ability to generate states of light with different statistics and manipulate their interference offers important opportunities for quantum information and metrology.

Configurable lossless broadband beam splitters for semi-guided waves in integrated silicon photonics

We show that narrow trenches in a high-contrast silicon-photonics slab can act as lossless power dividers for semi-guided waves. Reflectance and transmittance can be easily configured by selecting the trench width. At sufficiently high angles of incidence, the devices are lossless, apart from material attenuation and scattering due to surface roughness. We numerically simulate a series of devices within the full 0-to-1-range of splitting ratios, for semi-guided plane wave incidence as well as for excitation by focused Gaussian wave bundles. Straightforward cascading of the trenches leads to concepts for 1×M-power dividers and a polarization beam splitter.

Phase stabilization of a coherent fiber network by single-photon counting.

Coherent optical fiber networks are extremely sensitive to thermal, mechanical, and acoustic noise, which requires elaborate schemes of phase stabilization with dedicated auxiliary lasers, multiplexers, and photodetectors. This is particularly demanding in quantum networks operating at the single-photon level. Here, we propose a simple method of phase stabilization based on single-photon counting and apply it to quantum fiber networks implementing single-photon interference on a lossless beamsplitter and coherent perfect absorption on a metamaterial absorber. As a proof of principle, we show dissipative single-photon switching with visibility close to 80%. This method can be employed in quantum networks of greater complexity without classical stabilization rigs, potentially increasing efficiency of the quantum channels.

Controlled Quantum Teleportation of Superposed Coherent State Using GHZ Entangled Coherent State

Controlled quantum teleportation of superposed coherent states using GHZ entangled 3-mode coherent states is studied. Proposed scheme can be implemented experimentally using linear optical components such as a symmetric lossless beam splitter, two phase-shifters and two photon counters. Fidelity is found close to unity for appreciable mean number of photons in coherent states and is 0.99 for mean photon number equal to two.

Non-Hermitian Magnon-Photon Interference in an Atomic Ensemble.

The interference of photons in a lossy beam splitter (BS) exhibits anticoalescence, which is surprising for bosons. Such a non-Hermitian system involving open quantum dynamics is of particular interest for quantum information processing and metrology. The Hermiticity of photonic devices is generally fixed according to the material, but is controllable at the interface of photons and atomic systems. Here, we demonstrate a tunable non-Hermitian BS for the interference between traveling photonic and localized magnonic modes. The crossover from a Hermitian to a non-Hermitian magnon-photon BS is achieved by controlling the coherent and incoherent interaction mediated by the excited levels of atoms, which is reconfigurable via the detuning of a control laser. A correlated interference pattern between the photons and magnons is demonstrated by such a non-Hermitian BS. Our system has the potential to operate with photons and magnons at the single-quanta level, and it provides a versatile quantum interface for studying the non-Hermitian quantum physics and parity-time symmetry.

Beam splitter phase shifts: Wave optics approach

We investigate the phase relationships between transmitted and reflected waves in a lossless beam splitter having a multilayer structure, using the matrix approach as outlined in classical optics books. Contrarily to the case of the quantum optics formalism generally employed to describe beam splitters, these matrices are not unitary. In this note we point out the existence of general relations among the elements of the transfer matrix that describes the multilayer beam splitter. Such relations, which are independent of the detailed structure of the beam splitter, fix the phase shifts between reflected and transmitted waves. It is instructive to see how the results obtained by Zeilinger by using spinor algebra and Pauli matrices can be easily derived from our general relations.

Quantum optics of lossy asymmetric beam splitters.

We theoretically investigate quantum interference of two single photons at a lossy asymmetric beam splitter, the most general passive 2×2 optical circuit. The losses in the circuit result in a non-unitary scattering matrix with a non-trivial set of constraints on the elements of the scattering matrix. Our analysis using the noise operator formalism shows that the loss allows tunability of quantum interference to an extent not possible with a lossless beam splitter. Our theoretical studies support the experimental demonstrations of programmable quantum interference in highly multimodal systems such as opaque scattering media and multimode fibers.

Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting

If a single-mode nonclassical light is combined with the vacuum on a beam splitter, then the output state is entangled. As proposed in [Phys. Rev. Lett. 94, 173602 (2005)], by measuring the output-state entanglement for a balanced lossless beam splitter, one can quantify the input-state nonclassicality. These measures of nonclassicality (referred to as entanglement potentials) can be based, in principle, on various entanglement measures, leading to the negativity (NP) and concurrence (CP) potentials, and the potential for the relative entropy of entanglement (REEP). We search for the maximal nonclassicality, which can be achieved by comparing two entanglement measures for arbitrary two-qubit states and those which can be generated from a photon-number qubit via a balanced lossless beam-splitter, where the qubit basis states are the vacuum and single-photon states. Surprisingly, we find that the maximal nonclassicality, measured by the REEP for a given value of the NP, can be increased (if NP<0.527) by using either a tunable beam splitter or by amplitude damping of the output state of the balanced beam splitter. We also show that the maximal nonclassicality, measured by the NP for a given value of the REEP, can be increased by dephasing. The entanglement itself is not increased by these local losses, but the possible ratios of different measures are affected. Moreover, we show that partially-mixed states can be more nonclassical than both pure states and completely-mixed states, by comparing the NP for a given value of the REEP. This implies that not all entanglement measures can be used as entanglement potentials. Alternatively, a single balanced lossless beam splitter is not always transferring the whole nonclassicality of its input state into the entanglement of its output modes. Applying a lossy beam splitter can solve this problem at least for the cases analyzed in this paper.

Conditional average in a quantum system with postselection

A conditional average of an observable is considered for a quantum system, where measurement on a system is performed between an initial preparation and a postselection. It is shown that when the effect of measurement performed on a system can be described only in terms of eigenprojectors of a measured observable, the conditional average is represented by a mixture of the strong and weak values of the observable. Furthermore, a measurement process is constructed which provides the conditional average from measurement outcomes of pointer observables of an apparatus. In particular, when a qubit system is considered, the measurement apparatus consists of a lossless beam splitter, a single-qubit unitary gate and two controlled NOT gates.

Gain-assisted critical coupling for high-performance coherent perfect absorbers.

Balanced radiation and absorption rates of an optical resonator are necessary for coherent perfect light absorption in many active device applications. This balance is referred to as critical coupling condition. We propose a gain-assisted method for exact access to critical coupling conditions without altering any structure parameters. In a coherent absorber with additional internal gain media, critical coupling with arbitrarily high coherent signal extinction can be obtained by continuously tuning optical pumping density. Assuming a surface-plasmon resonance grating covered by a gain layer as a promising architecture, we numerically demonstrate gain-assisted continuous access to its critical coupling point with experimentally probable settings. In addition, the gain tuning further introduces switching of the coherent-absorber's functionality to a conventional lossless beam splitter.

Photon number distributions of output fields from a beam splitter

We examined the photon statistics of the output light field of a lossless symmetric beam splitter when a n-photon occupation number state and an arbitrary light field are present on the two input ports of the beam splitter. We showed that both the wave-like nature and the particle-like nature of light are contributed to the photon number distribution by investigation of the difference photon number probability at the output port.

Influence of a symmetric lossless beam splitter on a non-classical feature of an optical field

Recently, it was found [J. Phys. B: At. Mol. & Opt. Phys. 38, 665 (2005)] that amplitude-squared squeezing, a non-classical feature, can be enhanced during linear mixing with a coherent light beam using a symmetric lossless beam splitter. Here, another example is reported of enhancement of an easily detectable non-classical feature of an optical field in a similar mixing using a symmetric lossless beam splitter.

Entangling ability of a beam splitter in the presence of temporal which-path information

We calculate the amount of polarization-entanglement induced by two-photon interference at a lossless beam splitter. Entanglement and its witness are quantified, respectively, by concurrence and the Bell--Clauser-Horne-Shimony-Holt (CHSH) parameter. In the presence of a Mandel dip, the interplay of two kinds of which-path information---temporal and polarization---gives rise to the existence of entangled polarization states that cannot violate the Bell--CHSH inequality.

Generation of two-mode photon-added SU(2) coherent state and its quantum nonlocality property

A scheme for generating two-mode photon-added SU(2) coherent state by means of conditional measurement is proposed. Feeding three uncorrelated Fock states into three input ports of two cascade placed lossless beam splitters respectively and counting photons in one of the output channels, the conditional state in the other two output channels is a two-mode photon-added SU(2) coherent state. The quantum nonlocality property for this state is investigated using parity measurement.

Interference and the lossless lossy beam splitter

Interference and the lossless lossy beam splitter

Interference and the lossless lossy beam splitter

By directing the input into a particular mode it is possible to obtain as output all of the input light for a beam splitter which is 50% absorbing. This effect is also responsible for nonlinear quantum interference when two photons are incident on the beam splitter.

Equivalence of a lossless beam splitter and a nondegenerate parametric amplifier in conditional measurements

Ban [Opt. Commun. 143 (1977) 225] demonstrated an equivalence between a lossless beam splitter with one of the output modes in the vacuum state and a nondegenerate parametric amplifier with a vacuum input. We show that this equivalence can be extended to apply to all states.