Higher-order Light Research Articles

Reverse design of multifunctional cascade devices based on the adjoint method

In this paper, a 1×4 ultra-compact wavelength division multiplexing cascaded device(DMC) with an arbitrary splitting ratio based on adjoint topology optimization reverse design is proposed, which is approximately two orders of magnitude smaller than that of conventional waveguide devices. It can simultaneously perform wavelength demultiplexing, mode conversion, and arbitrary ratio power splitting. The DMC separates 1310 nm and 1550 nm wavelengths, converts the input light from fundamental transverse mode (TE0) to first-order transverse mode (TE1) and second-order transverse modes (TE2), and performs arbitrarily proportional power splitting of the converted higher-order light source.

Photonic integrated processor for structured light detection and distinction

Integrated photonic devices are pivotal elements across research fields that involve light-based applications. Particularly versatile platforms are programmable photonic integrated processors, which are employed in applications like communication or photonic computing. Free-space distributions of light can be coupled to such processors, which subsequently control the coupled light on-chip within meshes of programmable optical gates. This enables access to the spatial properties of free-space light, particularly its relative phase, which is usually challenging to measure. Here, we discuss and show the detection of amplitude and phase distributions of structured higher-order light beams using a multipurpose photonic processor. This can be used to directly distinguish light’s orbital angular momentum without including additional elements interacting with the free-space light. We envision applications in a range of fields that rely on the spatial distributions of light’s properties, such as microscopy or communications.

Quantifying signal quality in scanning transmission X-ray microscopy

While the general effects of experimental conditions such as photon flux and sample thickness on the quality of data acquired by scanning transmission X-ray microscopy (STXM) are widely known at a basic level, the specific details are rarely discussed. This leaves the community open to forming misconceptions that can lead to poor decisions in the design and execution of STXM measurements. A formal treatment of the uncertainty and distortions of transmission signals (due to dark counts, higher-order photons and poor spatial or spectral resolution) is presented here to provide a rational basis for the pursuit of maximizing data quality in STXM experiments. While we find an optimum sample optical density of 2.2 in ideal conditions, the distortions considered tend to have a stronger effect for thicker samples and so ∼1 optical density at the analytical energy is recommended, or perhaps even thinner if significant distortion effects are expected (e.g. lots of higher-order light is present in the instrument). (Note that X-ray absorption calculations based on simple elemental composition do not include near-edge resonances and so cannot accurately represent the spectral resonances typically employed for contrast in STXM.) Further, we present a method for objectively assessing the merits of higher-order suppression in terms of its impact on the quality of transmission measurements that should be useful for the design of synchrotron beamlines.

Revealing higher-order light and matter energy exchanges using quantum trajectories in ultrastrong coupling

The dynamics of open quantum systems is often modelled using master equations, which describe the expected outcome of an experiment (i.e., the average over many realizations of the same dynamics). Quantum trajectories, instead, model the outcome of ideal single experiments -- the ``clicks'' of a perfect detector due to, e.g., spontaneous emission. The correct description of quantum jumps, which are related to random events characterizing a sudden change in the wave function of an open quantum system, is pivotal to the definition of quantum trajectories. In this article, we extend the formalism of quantum trajectories to open quantum systems with ultrastrong coupling (USC) between light and matter by properly defining jump operators in this regime. In such systems, exotic higher-order quantum-state- and energy-transfer can take place without conserving the total number of excitations in the system. The emitted field of such USC systems bears signatures of these higher-order processes, and significantly differs from similar processes at lower coupling strengths. Notably, the emission statistics must be taken at a single quantum trajectory level, since the signatures of these processes are washed out by the ``averaging'' of a master equation. We analyze the impact of the chosen unravelling (i.e., how one collects the output field of the system) for the quantum trajectories and show that these effects of the higher-order USC processes can be revealed in experiments by constructing histograms of detected quantum jumps. We illustrate these ideas by analyzing the excitation of two atoms by a single photon~[Garziano et al., Phys. Rev. Lett.117, 043601 (2016)]. For example, quantum trajectories reveal that keeping track of the quantum jumps from the atoms allow to reconstruct both the oscillations between one photon and two atoms, as well as emerging Rabi oscillations between the two atoms.

Surface-Enhanced Spectroscopy for Higher-Order Light Scattering: A Combined Experimental and Theoretical Study of Second Hyper-Raman Scattering.

Motivated to explore the ultimate limits of surface-enhanced nonlinear spectroscopies, we report on the first observation of molecular second hyper-Raman scattering with the aid of surface enhancement and provide a new theoretical framework for first-principles calculations of the second hyper-Raman effect. Second hyper-Raman enhancement factors, determined to be a minimum of 10(5) times stronger than those in Raman scattering, demonstrate a clear trend toward larger enhancements for nonlinear phenomena, and the nearly quantitative agreement between simulation and experiment provides a unique spectroscopic window into higher-order molecular responses.

Strategies for reducing the light shift in atomic clocks

Recent progress in optical lattice clocks requires unprecedented precision in controlling systematic uncertainties at $10^{-18}$ level. Tuning of nonlinear light shifts is shown to reduce lattice-induced clock shift for wide range of lattice intensity. Based on theoretical multipolar, nonlinear, anharmonic and higher-order light shifts, we numerically demonstrate possible strategies for Sr, Yb, and Hg clocks to achieve lattice-induced systematic uncertainty below $1\times 10^{-18}$.

Impact Analyses of High-Order Light Reflections on Indoor Optical Wireless Channel Model and Calibration

This paper analyzes the impact of high order light reflections on indoor optical wireless communication (IOWC) channel models. Based on observing the results of computer simulations, a calibration method is proposed to reduce model errors. Channel models are generated by tracing and adding up diffuse light reflections and sequential sub-reflections along its traveling path. As computation complexity increases significantly with the number of reflection orders considered, researchers traditionally, though incorrectly, take the contribution of first a few reflection orders, most commonly three, to represent the complete channel. Discarded high-order reflections bring no significant performance difference to low-speed transmission systems; however, major contemporary IOWC research institutions focus on high-speed Gigabits per second (Gbps) communications and the model errors resulting from discarded high-order reflections are no longer negligible. This is where the importance of our proposed method lies. root-mean-square (RMS) delay-spread, for instance, is severely underestimated by neglecting higher-order reflections. We simulate an IOWC system in an ordinary 6 m × 6 m × 3 m room and calculate the contributions of each order of reflections at 841 locations. It shows the RMS delay-spread estimation using the first three orders underestimates the true value by 15.3% on the average and by at most 26.6% as maximum. To limit error within half a symbol period, 1 Gbps and 10 Gbps systems tolerate underestimations up to 13.7% and 1.4%, respectively. These must be achieved by applying first five and nine orders. To maintain the computation efficiency of low-order reflection models and improve their accuracies, we propose a statistical calibration method. It reduces average model error of first three reflection orders from 15.7% to 4.3%. The numbers of orders required by 1 and 10 Gps systems are individually reduced to 3 and 7.

Design and performance of a new VIS–VUV photoluminescence beamline at UVSOR-III

A new bending-magnet beamline with a 2.5 m normal-incidence monochromator has been constructed to serve with a light source in the visible-vacuum-ultraviolet region for photoluminescence, transmission and reflection spectroscopies of solids at the UVSOR-III 750 MeV synchrotron radiation light source. The aim is to pave the way to establishing a beamline with high photon flux, high brilliance, high energy-resolution, high linear-polarization and low higher-order light. To obtain high photon flux and brilliance, the acceptance angle of the bending-magnet radiation was designed to be 40 mrad (H) × 14 mrad (V) and the post-mirror system employed Kirkpatrick-Baez optics. The incidence angle of the incoming light to the optical elements, except to the gratings, was set to a grazing angle in order to keep a degree of linear polarization. For achieving high energy-resolution, an off-plane Eagle-type monochromator was adopted. Higher-order unwanted light in the energy range below ∼11 eV was suppressed to be less than 0.1%.

Characteristics of an absolutely calibrated flat-field extreme ultraviolet spectrometer in the 10-130 Å range for fusion plasma diagnostics

A flat-field extreme ultraviolet (EUV) spectrometer with a nominal 2400 grooves/mm aberration-corrected ruled grating has been developed to analyze the emission spectrum in the wavelength range of 10 to 130 A from large helical device (LHD) plasmas. Spectral properties such as resolution, sensitivity, contribution of higher-order light, and background stray light have been studied using emission spectra mainly from intrinsic impurities, e.g., C and Fe. It is found that the spectrometer well resolves closely existing spectral lines of highly ionized medium- and high-Z impurities even in a very short wavelength range such as 10 to 20 A. As a result, it allows one to study the charge state distribution of elements in high-temperature fusion plasma. The ruled grating was then replaced by a laminar type holographic grating for the comparative study. The spectral resolution for the ruled grating (Dlambda approximately 0.08 A at 33.73 A) is clearly better than the holographic grating (Dlambda approximately 0.13 A at 33.73 A). Both gratings well suppress the higher-order light, e.g., the second-order light is only less than 11% of the first-order light for C vi(33.73 A). Relative sensitivity calibration with the wavelength has been done using bremsstrahlung continuum from the LHD plasmas. Absolute intensity calibration has been done by comparing the spectral intensities directly with the absolutely calibrated 1200 grooves/mm EUV spectrometer in the overlapping range of 90-120 A due to the absence of a good branching pair in 10-130 A. As a typical result on the present spectrometer well-resolved n=2-3 full transition arrays from Ne- to Li-like ions are measured for Fe and Ti and wavelengths of the spectral array are tabulated for each charge state. Spectroscopic comparison is also made between the 1200 grooves/mm and 2400 grooves/mm gratings in a range of 50-130 A.

Optical lattice clock with atoms confined in a shallow trap

We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunneling leads to a residual sensitivity to the atom dynamics hence requiring large depths [$(50\text{--}100){E}_{r}$ for Sr] to avoid any frequency shift or line broadening of the atomic transition at the ${10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}18}$ level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g., higher-order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunneling. We show that using the Earth's gravity, much shallower traps (down to $5{E}_{r}$ for Sr) can be used for the same accuracy goal.

Beamline for high-resolution angle-resolved photoemission at Saga Light Source

A new beamline for high-resolution angle-resolved photoemission study on solids and surfaces has been constructed at BL13 of Saga Light Source. In order to realize high-resolution in a wide energy range, the monochromator system is composed of the grazing-incidence mount with two varied line spacing plane gratings (VLSPG) and the normal incidence mount with a multilayer-coated plane grating. Relatively, high photon flux and low higher-order light can be obtained using the multilayer-coated plane grating in the boundary region between grazing-incidence and normal-incidence mounts. It is found from ray-tracing simulations that resolving power better than 10,000 and photon flux of 10 10–10 12 photon/s can be obtained. A high-resolution photoemission system with a gated-detector and a mode-locked Ti:Sapphire laser with the regenerative amplifier is installed at the beamline. Using these systems, we can perform the time-resolved high-resolution photoemission study for various photo-excited phenomena and surface dynamics.

Ultrastable optical clock with neutral atoms in an engineered light shift trap.

An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the 5s(2) 1S0-->5s5p 3P0 transition of 87Sr atoms as a "clock transition." Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10(-17).

Performance of laminar-type holographic grating for a soft x-ray flat-field spectrograph in the 0.7–6 nm region

A laminar-type holographic grating having a groove density of 2400 lines/mm was designed and fabricated for use with a soft x-ray flat-field spectrograph covering the 0.7–6 nm region. The varied-line-spaced grating pattern was generated by use of an aspheric wave front recording system and the laminar-type grooves were formed by a reactive ion-etching method. The performance of the grating was evaluated by using a molybdenum K x-ray generator and a spectrograph with a charge coupled device imaging detector. Also, the absolute diffraction efficiencies of the zeroth, first, second, and third, spectral orders were measured by use of the reflectometers installed at Synchrotron Radiation Beamlines. The experimental results showed that the holographic grating indicated comparable spectral resolution and maximum first-order diffraction efficiency (>2%) at ∼2 nm with a replica grating made from a mechanically ruled varied-line-spacing grating. It also showed higher efficiency in the <1.0 nm region and lower level higher-order light over the whole wavelength range than the replica grating.

Beamline-induced chromium structure in carbon K-edge absorption spectra

We show that Cr subcoatings in beamline optical elements can introduce an additional structure in C K-edge X-ray absorption measurements, which somewhat resembles the well-known losses produced by carbon contamination. The photon throughput variations induced by Cr and C require different treatments when correcting absorption spectra. The potential difficulties in unravelling the two effects could be avoided with efficient filtration of higher-order light.

Performance of a very high resolution soft x-ray beamline BL25SU with a twin-helical undulator at SPring-8

We report on the excellent performance of a newly constructed soft x-ray helical undulator beamline BL25SU of SPring-8 for photon energies 500–1800 eV. The full beamline was designed to perform very high resolution soft x-ray spectroscopy of solids with using high brilliance, highly circularly polarized undulator radiation. The grazing incidence monochromator employs varied-line-spacing plane gratings which operate in convergent light from a spherical mirror and focuses monochromatic light onto the exit slit. A resolving power in excess of 15 000 was measured at 540 and 870 eV for a grating with a central groove density of 600 lines/mm from the photoemission spectra of Au. A resolving power of more than 20 000 is estimated near 870 eV for a grating with a central groove density of 1000 lines/mm. A photon flux of more than 1×1011 photons/s/100 mA/0.02% b.w. is supplied onto the sample between 500 and 1800 eV with very low amount of higher-order light. The low heat load from the twin-helical undulator gives high stability to all optical components, which is essential to obtain high resolution in a wide energy region. Three experimental stations are installed in tandem on this beamline for various high resolution spectroscopy measurements.

Photoabsorption and fluorescence cross sections of SiCl4 in the region of 6.2–31 eV

Absolute photoabsorption and fluorescence cross sections of gaseous SiCl4 have been measured in the energy region 6.2–31 eV using synchrotron radiation as the light source. Higher order light from the 1-m Seya monochromator was suppressed by use of an Ar gas filter in the energy range 11.3–15.5 eV (110–80 nm) and a LiF window at hν<11.8 eV (105 nm). Emissions have been observed for the C̃ 2T2→à 2T2 and C̃ 2T2→X̃ 2T1 processes of the SiCl4+ molecular ion and the à 1B1→X̃ 1A1 and B13→X̃ 1A1 of the SiCl2 radical. The total fluorescence cross section has been determined to be 22.4±1.0 Mb at 21.22 eV. By comparing with the partial cross section for formation of the C̃ 2T2 ionic state [Carlson et al., J. Chem. Phys. 84, 641 (1986)], it has been concluded that the SiCl4+(C̃ 2T2) formed decays via radiative processes with quantum yield φ≈1. The experimental results provide information on the breakdown pathways of the SiCl4+(C̃ 2T2) ion state. The bands observed in photoabsorption and fluorescence excitation spectra have been assigned as the (4s, np, and np)←3t2, (4s and np)←1e, (4s and np)←1e, (4s and 4p)←2t2, and (np and nd)←2a1 Rydberg series. The ionization energies for the (2t2)−1 and (2a1)−1 processes have been found to be 15.04±0.03 and 18.17±0.03 eV, respectively.

Characteristics and performance of the Los Alamos VUV beamline at the NSLS

We describe the design and performance of the Los Alamos VUV synchrotron radiation beamline, U3C, on the VUV ring of the National Synchrotron Light Source at Brookhaven National Laboratory. The beamline uses separate function optics to collect and focus the horizontally and vertically diverging beam. The monochromator is a grazing incidence Rowland circle instrument of the extended grasshopper design (ERG). A postmonochromator refocusing mirror is used to focus or collimate the diverging beam from the monochromator. The beamline control and diagnostics systems are also discussed. Particular emphasis in the design has been placed on the reduction of stray and harmonic light. Higher order light is reduced by a grazing angle mirror low pass filter installed immediately downstream from the monochromator while stray light is reduced through the use of baffles and thin film filters. Also included in the line is a differential pumping section that permits gas phase and other experiments requiring pressures in the 10 −5 to 10 −4 Torr range to be coupled to the beamline.

Macrodistribution of Light Scattered by Dispersions of Spherical Dielectric Particles*

The light scattered by an infinite plane layer of suspended dielectric particles is discussed without consideration of the interference from different particles. Let the first-order quantity function (q.f.) be defined as that fractional part of the total incident light energy subject to one scattering process, the second-order q.f. as the fraction subject to two scattering processes, etc. Then the first-order q.f. and its angular distribution from a very dilute medium is given by Mie’s theory. The second- and higher order q.f. from a denser medium are derived in terms of elementary exponentials. Polar plots are presented showing that for a Rayleigh medium (α→0, where α=particle circumference/wave-length) second- as well as higher order light is of substantially uniform distribution whereas such uniformity is attained only for light of order greater than eight for a medium with a pronounced Mie primary distribution (α=5 in Fig. 6). The fractions of scattered light were calculated in two ways: (1) as forward progressive quantity functions for the several orders, to be multiplied by angular factors for any direction; (2) as separate forward and backward progressive half-space q.f. for the several orders, to be multiplied by angular factors taken in the corresponding half-spaces. Comparison of the ratio r of total backward to total forward light as obtained from both calculations, (1) and (2), gives similar results in most cases. r becomes smaller as both, α and the medium dilution increase (r=1 for α→0, r=~1/1000 for α=5). For very dense dispersions (still neglecting interference) r approaches unity for all α according to method (1), while it decreases slightly from r=1 for α=0 with increasing α according to the more detailed method (2). The latter method, however, proves to be the only one appropriate to trace the large backward reflection combined with the low forward transmission in some absorbing media.Corrections are made for the q.f. of the several orders in terms of a slenderness factor where the medium is defined as a limited region of an infinite plane layer.A specific numerical example is given for a low density medium for which this correction is negligible and method (1) is good enough. The weight of suspended material necessary for a barely photographable vapor trail is calculated for various sizes of dielectric particles.