A variable lateral-shearing Sagnac interferometer with high numerical aperture for measuring the complex spatial coherence function of light

High-Tc superconductivity is surpassed by few, if any, other unsolved problems in contemporary physics in terms of its richness, complexity, impact on other fields, and potential technological importance in energy applications. Recent discoveries reveal that the highest transition temperatures emerge under extraordinary experimental conditions such as the strong perturbation of a single atomic layer material by the underlying substrate, application of ~200 GPa pressure or ~MV/cm static electric fields, or irradiation by intense femtosecond optical fields. Research in superconductivity under extreme experimental conditions is challenging and requires the development of novel experimental methods and new theoretical tools suitable to tackle the problem. Our team has approached the challenges of transient superconductivity under intense optical fields by rethinking the types of experimental observables that are best suited to elucidate the physics of light-induced effects. This exercise has identified the need for: i) ultra-fast spatio-temporal probes enabling access to plasmonic properties and also nano-scale inhomogeneities that are ubiquitous in unconventional superconductors; ii) meso-scale structures and hybrid meta-surfaces imperative for strong enhancement of optical fields and iii) theoretical approaches suitable to explain and predict the response of superconductors under ultra-fast photo-excitation. Co-PIs have already made major advances with developing capabilities i)-iii). Therefore, our team is poised to make significant progress in transient superconductivity by exploring novel spatio-temporal effects that currently remain unattainable. Co-investigators will search for light-induced superconductivity in the high-Tc cuprates to build upon spectacular recent results still lacking independent confirmations. Novel data acquisition methods combined with nano-plasmonic imaging will allow our team to test the hypothesis of photo-induced superconducting pairing. Spatio-temporal experiments will provide insights into the interplay between superconductivity and competing orders in the cuprates. Co-PIs will also investigate strong light-matter interaction and superconductivity in FeSe monolayers. Finally, we will study spatio-temporal electrodynamics of planar Josephson junctions. This latter direction will allow our team to thoroughly characterize one of the most fundamental examples of inhomogeneity in all of unconventional superconductivity. The proposed experiments in combination with theoretical analysis will provide information that is difficult to obtain using alternative methods. Basov and Averitt will carry out pump-probe spectroscopy and nano-imaging experiments. Averitt and Hone will design and fabricate state-of-the-art meta-surfaces. Theoretical and computational studies of ultrafast transient phenomena will be carried out by Millis and Fogler. Modeling of time-resolved nano-optical effects will be done by Fogler. The bulk of the requested budget will be used to support graduate students at Columbia & UCSD that will be co-supervised by co-PIs. The proposed program is transformative, since it will enable an entire suite of experiments previously either impossible or technically implausible. It will deliver critically important insights not only into mechanisms of unconventional superconductivity but also to many other correlated quantum materials.

We investigate the possibility of interferometric optical field sensor with DMD forming a series of sampling interferometers in the pupil of an optical system. Our preliminary experiment validates the feasibility of our approach for the field reconstruction in the case of coherent field. We believe that this approach can be extended to sensing of speckle patterns and even incoherent fields, by analyzing not only the intensity and phase, but also the amplitude and the visibility of the interference patterns. Such analysis would yield the complete complex amplitude and/or coherence function, making the approach directly applicable to a wide range of inverse source problems in optics.

The existence of a spatial correlation singularity or a ring dislocation in the spatial coherence function when a vortex is present has been demonstrated recently. Here, we investigate how the spatial correlation singularity is affected by both the radial and azimuthal mode indices (p, ℓ) in a partially coherent light field. Theoretically, we find that the spatial correlation singularity may exist even in a non-vortex beam (ℓ = 0) due to the radial index. Numerical simulations show the number of ring dislocations in the far-field cross correlation function is equal to 2p + |ℓ| for the low coherence cases. This is confirmed by our experimental results. This phenomenon may occur in any partially coherent vortex wave.

The demonstration of optical binding of micro-particles placed in intense optical fields has resulted in unique and exciting prospects for studying new forms of condensed matter. The ability to tailor optical fields in the spatial and temporal domains elicits the possibility of creating novel condensed matter with the structure controlled by tailoring the optical field. Here, we theoretically calculate the transverse optical binding forces for nanoparticles within monochromatic and broadband optical fields. We demonstrate the decrease in amplitude of the optical binding forces for broadband fields as a function of inter-particle separation and attribute the effect to the averaging effect of spectrally dependent optical forces. We also examine multiple particle optically bound systems and use the interacting dipole method to find self-organized positions for six and ten particles illuminated by a monochromatic plane wave.

Shearograms of an optical phase singularity

For sub half-micron lithography, control of the Critical Dimension, represents the key to a robust and manufacturable process. The lithographer must understand and tune the exposure system for critical dimension performance using variables such as Numerical Aperture (NA), Partial Coherence (PC), position of the Focal Plane. Exposure tool must be characterized for its lens signature and the tools must be matched for their CD variation within the optical field In a previous study, we demonstrated that the phase-shift focal plane monitor, PSFM accurately measures focal plane variations when appropriate calibrations are employed. That paper also described the development of a model to determine lens classic aberrations such as Coma, Astigmatism and Field Curvature. The publication correlated the results to an approximation of the stepper's Critical Dimension (CD) behavior for a matrix of NA and PC settings. The present study, continues to study CD uniformity through examination of the lens aberrations and field focal signature of optical steppers in a 0.35 um process. We describe a method of measuring the uniformity of numerical aperture (NA) and partial coherence (PC) across the exposure field this new tool is then applied as an aid in optical lens characterization and tool-to-tool matching. The information gathered is thereupon applied to measure lens aberrations and predict CD variation across the field under various settings of the lens focal plane, the predictions are validated by a comparison against CD uniformity as measured by an advanced critical dimension metrology system.

We studied response of calcium fluoride single crystal against intense optical field. It undergoes transition into semimetal, ensured by detecting optical-field-induced current. The transient conductivity jumps by 16 orders of magnitude within sub-femtosecond time scale.

The use of a Boltzmann transport equation with a drift term is physically incorrect for optical-field frequencies. Also, the use of a simple energy-balance equation is found to lead to an inaccurate estimation of electron temperature. Therefore, we have established a Boltzmann-scattering equation for the accurate description of the relative scattering motion of electrons interacting with an incident optical field by including impurity- and phonon-assisted photon absorption as well as Coulomb scattering between two electrons. Multiple peaks on the high-energy tail of a Fermi-Dirac distribution are predicted and the effect of pair scattering is analyzed. Moreover, the effective electron temperature is calculated as a function of both the incident-field amplitude and the photon energy so that the thermodynamics of hot electrons may be investigated.

We present an investigation of the dynamics of centre-of-mass of a neutral particle cloud in a cavity pumped by an optical field. We derive an expression for the pump threshold for spatial self-organization of the particles and analyze its scaling laws in terms of the system parameters. Using a newly developed statistical model, we simulate the dynamics of the particles and numerically obtain the scaling laws. We show good agreement between the analytic formulae and simulations. We further use the scaling relation to discuss the operating conditions for cavity cooling a large ensemble of particles. Finally, we study cavity cooling of an ensemble of molecules with an initial temperature of around 10 mK. We show that 35% of the molecules are trapped by the optical field intensity in the cavity and a final temperature below 1 mK is reached.

The second-order χ(2) process underpins many important nonlinear optical applications in the field of classical and quantum optics. Generally, the χ(2) process manifests itself only in a non-centrosymmetric dielectric medium via an anharmonic electron oscillation when driven by an intense optical field. Due to inversion symmetry, group-IV semiconductors, such as silicon (Si) and germanium (Ge), are traditionally not considered as ideal candidates for second-order nonlinear optics applications. Here, we report the experimental observation of the second-harmonic generation (SHG) in a Ge-on-insulator (GOI) sample under femtosecond optical pumping. We especially, report the measurement of the SHG signal from a GOI sample in the telecom S-band by pumping at ∼3000 nm.

The spreading properties of the Fraunhofer diffraction patterns of optical fields in any state of spatial coherence along the z‐axis are both theoretically and numerically analysed using the so called spatial coherence wavelets. The numerical analysis is performed by studying the one‐dimensional diffraction pattern produced when a single slit is uniformly illuminated with a Gaussian Schell‐model field. The diffraction pattern is understood as the result of contributions provided by spatial coherence wavelets coming from two different regions within the aperture, called the inner circle and the truncation crown respectively. It is shown that shape‐invariant spots with minimum spreading along the z‐axis can be obtained by properly modulating the spatial coherence properties along the truncation crown. Those spots can be regarded as finger prints of the spatially partially coherent optical field, in the sense that they only depend on the spatial coherence properties and not on the shape of the aperture itself. Numerical evidence shows that eliminating the contributions coming from the mentioned crown reduces the spreading to its minimum value for a given z distance. Therefore, the suppression of the contributions coming from the crown also suggests a way to eliminate spreading. The experimental implementation of this principle is a subject of research at the present.

Phase dynamics in bistable and chaotic behaviour of a soft crystal mode parametrically driven by an optical field

A new class of planar optical components and devices has emerged using subwavelength metastructures with a strong contrast in refractive indices. High-contrast metastructures have shown promises to manipulate optical fields in an extraordinary way and to replace conventional bulky optical elements by their low-profile analogs, typically with subwavelength-scale features. We elucidate the underlying principle, how these seemingly low-profile geometries render unique optical responses, using the coupled-mode analysis in a multimode waveguide. Moreover, strong field localization in high-index structures allows us to interpret each single element in the metastructures as a low-quality-factor resonator (or a localized scatterer), permitting us to realize designer surface that shapes phase, amplitude, and polarization of light in free space, also known as an optical metasurface. The remainder of the thesis is devoted to explore novel applications in optics using high-contrast metastructures. One of the particularly interesting applications is to use them in an optical resonator. Specifically, we demonstrate to incorporate high-contrast subwavelength grating reflectors and dielectric metasufaces in a vertical Fabry–Perot cavity, and show that we can flexibly tune the resonance frequency by the subwavelength patterning. With this technique, we envision the realization of compact, on-chip spectrometers when integrating them on a photodetector array. Secondly, we investigate the use of high-contrast subwavelength gratings in visible wavelengths. We perform the optimization of their geometries and demonstrate a set of RGB color filters, down to near a micrometer in the pixel size. This platform exhibits unique performances such as high efficiency, angular insensitivity, and color tunability by the design. A novel device concept is also explored, where a high-contrast subwavelength grating reflector is integrated on a silicon platform to constitute an active resonant antenna, enabling high-speed, phase-dominant modulation by means of thermo-optic effect of silicon. We demonstrate an array of such active antennas, yielding a beam deflection capability. This justifies the robustness of our device design, enabling a large-scale integration of high-speed, phase-dominant spatial light modulators. Finally, we introduce a disorder-engineered metasurface in the context of wavefront shaping. Recently, wavefront shaping with disordered media has demonstrated optical manipulation capabilities beyond those of conventional optics, but translating this class of technology into a practical use has remained challenging due to enormous amounts of information needed to be characterized as the input-output responses. As a paradigm shift, we propose the use of disorder-engineered metasurface in wavefront shaping, where the disorder is programmatically designed and makes the system characterization-free prior to use. With this approach, we demonstrate high numerical aperture focusing in an extended volume as well as wide-field fluorescence imaging with unprecedented performances.

We compare designs and laser-induced damage thresholds (LIDTs) of hafnia/silica antireflection (AR) coatings for 1054 nm or dual 527 nm/1054 nm wavelengths and 0° to 45° angles of incidence (AOIs). For a 527 nm/1054 nm, 0° AOI AR coating, LIDTs from three runs arbitrarily selected over three years are ∼20 J/cm2 or higher at 1054 nm and <10 J/cm2 at 527 nm. Calculated optical electric field intensities within the coating show two intensity peaks for 527 nm but not for 1054 nm, correlating with the lower (higher) LIDTs at 527 nm (1054 nm). For 1054 nm AR coatings at 45° and 32° AOIs and S and P polarizations (Spol and Ppol), LIDTs are high for Spol (>35 J/cm2) but not as high for Ppol (>30 J/cm2 at 32° AOI; ∼15 J/cm2 at 45° AOI). Field intensities show that Ppol discontinuities at media interfaces correlate with the lower Ppol LIDTs at these AOIs. For Side 1 and Side 2 dual 527 nm/1054 nm AR coatings of a diagnostic beam splitter at 22.5° AOI, Spol and Ppol LIDTs (>10 J/cm2 at 527 nm; >35 J/cm2 at 1054 nm) are consistent with Spol and Ppol intensity behaviors.

We investigate the properties of a homogeneously broadened three-level system interacting with two optical fields, Eω1(x,t) and Eω2(x,t), with central frequencies ω1 and ω2 whose amplitudes are assumed to be slowly varying in time compared with dephasing times of the optical transitions. We calculate Raman susceptibilities allowing each transition to be induced by both fields and without employing the rotating wave approximation (RWA); this enables correct calculation of the optical response of the medium when the fields are on-resonance or arbitrarily far off-resonance with the Raman transition. In some frequency regions the RWA causes substantial errors. A distinction is drawn between two different types of RWA: (a) a neglect of off-resonant components of the polarization for direct optical transitions, and (b) neglect of off-resonant components of off-diagonal density matrix elements of order Eω1(x,t)Eω2(x,t)* in the field amplitudes. The first RWA is known to become inaccurate when the pump frequency is significantly off-resonance with the pump transition. We show that the second RWA becomes inaccurate when ‖ω1−ω2‖ is small or comparable to the active Raman mode frequency (even when the field are close to resonance). Calculations based upon our expressions show that when the pump frequency is close to resonance with the optical transition from the ground state, a nonlinear absorption at the Stokes shifted frequency occurs. This absorption can significantly decrease the Raman gain. Also, we find that Rabi splittings in a three-level system can occur even when the pulse durations of the incident fields are short compared with the T1 times of the system. We solve analytically for the optical response of the system to two fields of arbitrary strength and frequency. We analyze this solution and its perturbative expansion in the field amplitudes. We use the Maxwell–Bloch equations developed here to propagate time-dependent pulses.