Intensity-dependent Phase Shifts Research Articles

Semi-empirical quantum optics for mid-infrared molecular nanophotonics.

Nanoscale infrared (IR) resonators with sub-diffraction limited mode volumes and open geometries have emerged as new platforms for implementing cavity quantum electrodynamics at room temperature. The use of IR nanoantennas and tip nanoprobes to study strong light-matter coupling of molecular vibrations with the vacuum field can be exploited for IR quantum control with nanometer spatial and femtosecond temporal resolution. In order to advance the development of molecule-based quantum nanophotonics in the mid-IR, we propose a generally applicable semi-empirical methodology based on quantum optics to describe light-matter interaction in systems driven by mid-IR femtosecond laser pulses. The theory is shown to reproduce recent experiments on the acceleration of the vibrational relaxation rate in infrared nanostructures. It also provides physical insights on the implementation of coherent phase rotations of the near-field using broadband nanotips. We then apply the quantum framework to develop general tip-design rules for the experimental manipulation of vibrational strong coupling and Fano interference effects in open infrared resonators. We finally propose the possibility of transferring the natural anharmonicity of molecular vibrational levels to the resonator near-field in the weak coupling regime to implement intensity-dependent phase shifts of the coupled system response with strong pulses and develop a vibrational chirping model to understand the effect. The semi-empirical quantum theory is equivalent to first-principles techniques based on Maxwell's equations, but its lower computational cost suggests its use as a rapid design tool for the development of strongly coupled infrared nanophotonic hardware for applications ranging from quantum control of materials to quantum information processing.

Nonclassical states of light in a nonlinear Michelson interferometer

Nonlinear quantum metrology schemes can lead to faster than Heisenberg-limited scalings for the measurement uncertainty. We study a Michelson interferometer embedded in a Kerr medium [Phys. Rev. A 92, 022104 (2015)] that leads to nonlinear, intensity dependent phase shifts corresponding to relative changes in the lengths of its two arms. The quantum Cram\'er-Rao bound on the minimum achievable measurement uncertainties is worked out and the requirements, in practice, to saturate the bound are investigated. The choice of input state of light into the interferometer and the readout strategy at the output end are discussed. The ideal nonclassical states of light that must be used to saturate the bound are found to be highly susceptible to photon loss noise. We identify optimal states at each noise level that are both resilient to noise and capable of giving the enhanced sensitivities and discuss practical implementations of the interferometry scheme using such states.

Prediction of Second-Harmonic Generation Wave-Front Distribution by Extreme Learning Machine

In the applications of wave-front detection using second-harmonic generation, the spatial phase distribution needs to calculate accurately before and after frequency doubling in real-time. This letter presents a learning-based method called extreme learning machine to fit the corresponding relationship of phase between the fundamental frequency wave and the second-harmonic. The Zernike coefficients of the fundamental frequency wave wave-front and the second-harmonic wave-front are used as input data for Extreme Learning Machine model training and testing. The effects of the intensity-dependent phase shift and walk-off are also considered. The reliability of the trained Extreme Learning Machine model was accessed based on simulation results. The proposed method has shown distinct competitive advantages in real-time calculation efficiency. The well-trained Extreme Learning Machine model only needs 0.026 seconds to accurately predict the phase distribution of the fundamental frequency wave. The runtime is three orders of magnitude smaller than the traditional numerical calculation method.

Unveiling the mechanism of wave-front distortion of superfluorescent pulses

We investigated the transverse properties of 420-nm yoked superfluorescence (YSF) emitted from the atomic vapor of rubidium by driving the $5S\text{\ensuremath{-}}5D$ two-photon transition with an ultrashort laser pulse. From the observed interferograms of the superfluorescent pulses, we derived both the amplitude and phase properties of their electric fields. By increasing the pump-pulse intensity, the spatial profile of the 420-nm YSF changed from a central bright spot into a ring-shaped radial profile, accompanied by a simultaneous distortion of the wave front. This behavior can be explained by considering the intensity-dependent phase shifts of the $5S\text{\ensuremath{-}}5D$ wave packets during the excitation process, which was further imprinted to the 420-nm YSF wave front. The single-shot experiments enabled us to clarify the locally coherent regions of the 420-nm YSF as well as their stochastic feature.

Study of Nonlinear Optical Properties of Disperse Yellow – 7 Dye-doped Polymer Films using CW Laser

The materials with an ability of self-focusing/defocusing through their light intensitydependent refractive index and phase shift properties are potential candidates for all-optical photonic devices. Several organic materials including dye-doped polymer films are attracting many researchers due to their advantages in terms of enhanced efficiency, and acceptable mechanical properties to fabricate useful devices. In this paper, we have reported the nonlinear optical properties like nonlinear absorption and nonlinear refraction of an organic dye Disperse Yellow - 7 (DY-7) doped in Polymethyl methacrylate-methacrylic acid (PMMA-MA) polymer matrix using open aperture and closed aperture Z-scan experimental methods by means of low power continuous wave (CW) laser beam. The optical limiting properties of these films are also studied using Type 1 and Type 2 configurations at different input powers using continuous wave (CW) laser beams of 532 nm wavelength. The nonlinear refractive index n2, nonlinear absorption coefficient β, changes in refractive index with input intensity, and the magnitude of third-order optical nonlinearity of the dye-doped film are experimentally determined. The sample is tested for optical power limiting in which the input limiting threshold and saturated output power level for both type 1 and type 2 optical limiting configurations are recorded. DY-7 dye-doped in PMMA-MA polymer film has shown saturation absorption at lower input irradiance and reverse saturation absorption at higher input irradiance along with thermal nonlinearity and hence found to be a potential candidate for the third harmonic property based photonic devices.

Study of Third Order Optical Nonlinearity in Disperse Orange-25 Dye-doped Polymer Films using CW Laser

The organic materials with the ability of self-focussing/defocusing through their light intensity-dependent refractive index and phase shift properties are potential materials in alloptical photonic devices have become interesting topic of continuous research. Several organic materials including dye-doped polymer films are attracting many researchers due to their advantages in terms of enhanced efficiency, and acceptable mechanical properties tofabricate useful devices. In this paper, we have reported the nonlinear optical properties like nonlinear absorption and nonlinear refraction of an organic dye Disperse Orange-25 (DO-25) doped in Polymethyl methacrylate-methacrylic acid (PMMA-MA) polymer matrix usingopen aperture and closed aperture Z-scan experimental methods by means of low power continuous wave (CW) laser beam. The optical limiting properties of these films are also studied using Type 1 and Type 2 configurations at different input powers using continuous wave (CW) laser beams of 532 nm wavelength. The nonlinear refractive index n2, nonlinear absorption coefficient β, changes in refractive index with input intensity, and the magnitude of third-order optical nonlinearity of the dye-doped film are experimentally determined. The saturated output power for type 1 and type 2 optical limiting are determined. The inputlimiting threshold and saturated output power level for both type 1 and type 2 optical limiting configurations are recorded. DO-25 dye-doped in PMMA-MA polymer film has shown saturation absorption at lower input irradiance and reverse saturation absorption at higher input irradiance and hence found to be a potential candidate for the third harmonic property based photonic devices.

Study of Third Order Optical Nonlinearity in Disperse Orange-25 Dye-doped Polymer Films using CW Laser

The organic materials with the ability of self-focussing/defocusing through their light intensity-dependent refractive index and phase shift properties are potential materials in alloptical photonic devices have become interesting topic of continuous research. Several organic materials including dye-doped polymer films are attracting many researchers due to their advantages in terms of enhanced efficiency, and acceptable mechanical properties to fabricate useful devices. In this paper, we have reported the nonlinear optical properties like nonlinear absorption and nonlinear refraction of an organic dye Disperse Orange-25 (DO-25) doped in Polymethyl methacrylate-methacrylic acid (PMMA-MA) polymer matrix using open aperture and closed aperture Z-scan experimental methods by means of low power continuous wave (CW) laser beam. The optical limiting properties of these films are also studied using Type 1 and Type 2 configurations at different input powers using continuous wave (CW) laser beams of 532 nm wavelength. The nonlinear refractive index n2, nonlinear absorption coefficient β, changes in refractive index with input intensity, and the magnitude of third-order optical nonlinearity of the dye-doped film are experimentally determined. The saturated output power for type 1 and type 2 optical limiting are determined. The input limiting threshold and saturated output power level for both type 1 and type 2 optical limiting configurations are recorded. DO-25 dye-doped in PMMA-MA polymer film has shown saturation absorption at lower input irradiance and reverse saturation absorption at higher input irradiance and hence found to be a potential candidate for the third harmonic property based photonic devices.

Controlling the multiport nature of Bragg diffraction in atom interferometry

Bragg diffraction has been used in atom interferometers because it allows signal enhancement through multiphoton momentum transfer and suppression of systematics by not changing the internal state of atoms. Its multi-port nature, however, can lead to parasitic interferometers, allows for intensity-dependent phase shifts in the primary interferometers, and distorts the ellipses used for phase extraction. We study and suppress these unwanted effects. Specifically, phase extraction by ellipse fitting and the resulting systematic phase shifts are calculated by Monte Carlo simulations. Phase shifts arising from the thermal motion of the atoms are controlled by spatial selection of atoms and an appropriate choice of Bragg intensity. In these simulations, we found that Gaussian Bragg pulse shapes yield the smallest systematic shifts. Parasitic interferometers are suppressed by a "magic" Bragg pulse duration. The sensitivity of the apparatus was improved by the addition of AC Stark shift compensation, which permits direct experimental study of sub-part-per-billion (ppb) systematics. This upgrade allows for a 310\,$\hbar k$ momentum transfer, giving an unprecedented 6.6\,Mrad measured in a Ramsey-Bord\'e interferometer.

Integrated nonlinear Mach Zehnder for 40 Gbit/s all-optical switching

We report on the experimental demonstration of a novel silicon based fully integrated nonlinear Mach Zehnder device. A standard silicon waveguide is used as a nonlinear arm, conversely a large mode SU-8 waveguide acts as a purely linear arm. Given this asymmetry, an intensity dependent phase shift can be introduced between the two interferometric arms. Thanks to a fine tuning of the silicon arm optical properties, a low power, ultrafast, picosecond operation is demonstrated, allowing the use of this device for ultrafast all-optical signal processing in high density communication networks.

Measuring small absorptions by exploiting photothermal self-phase modulation

We present a method for the measurement of small optical absorption coefficients. The method exploits the deformation of cavity Airy peaks that occur if the cavity contains an absorbing material with a nonzero thermorefractive coefficient dn/dT or a nonzero expansion coefficient α(th). Light absorption leads to a local temperature change and to an intensity-dependent phase shift, i.e., to a photothermal self-phase modulation. The absorption coefficient is derived from a comparison of time-resolved measurements with a numerical time-domain simulation applying a Markov-chain Monte Carlo algorithm. We apply our method to the absorption coefficient of lithium niobate doped with 7 mol. % magnesium oxide and derive a value of α(LN) = (5.9 ± 0.9) × 10(-4)/cm. Our method should also apply to materials with much lower absorption coefficients. Based on our modeling, we estimate that, with cavity finesse values of the order of 10(4), absorption coefficients of as low as 10(-8)/cm can be measured.

Understanding the nonlinear phase and frequency shift of an ultrashort light pulse induced by an inertial third-order optical nonlinearity

Inertia of optical nonlinearity is shown to distort the temporal profile of the intensity-dependent phase shift of an ultrashort laser pulse relative to the phase induced by the instantaneous optical nonlinearity. We demonstrate that a weakly inertial optical nonlinearity, whose response time is smaller than the pulse width, tends to redshift the light field and generates a cubic-phase correction to the quadratic phase, thus complicating the chirp of the spectrally broadened field. For very short light pulses with pulse widths shorter than the response times of optical nonlinearity, the redshift and cubic-phase terms often dominate the nonlinear phase shift, giving rise to phase profiles significantly different from those induced by instantaneous optical nonlinearity.

High speed response of nonlinear optical phase-shifter based on vertical micro-cavity saturable absorber

We present the modeling and experiment on the intensity-dependent phase shift of a nonlinear optical phase-shifter based on vertical micro-cavity saturable absorber for high-speed response. We demonstrated the 25ps transient response with a large negative nonlinear phase shift of over -0.7 radian. Our device would enable us to control the phase of high speed optical pulses including the compensation of fiber nonlinear effects in optical domain.

Focusing of Scanning Light Beams below the Diffraction Limit without Near-Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material

We show that a scanning light beam can be focused below the diffraction limit without the control of moving near-field elements using the combination of two main components: a light-controlled saturable absorber, which creates seed evanescent components from the beam, and a layer of negative-refraction material, which amplifies the evanescent waves. Focusing to spots with a FWHM in the range of 0.2-0.3 lambda is predicted. For slightly off-resonant input beams, an intensity-dependent phase shift leads to smaller spots.

Optical Transfer Functions of Kerr Nonlinear Cavities and Interferometers

We present the optical transfer functions for third-order nonlinear cavities that involve an optical carrier frequency and its modulation sideband fields. Our approach is based on linearized transformations and provides a convenient tool to calculate squeezed light sources as well as complex interferometer topologies, containing subsystems that involve intensity dependent phase shifts, i.e., optical Kerr media. As the result we present the noise spectral density of a Michelson interferometer with Kerr nonlinear arm cavities and resonant sideband extraction and find that quantum noise can be squeezed by arbitrary amounts even outside the cavity linewidth. Such a system might apply for future gravitational wave detectors or simply for a continuous wave source of squeezed states.

Generation of a variable linear array of phase-coherent supercontinuum sources

We investigate the coherence properties of a linear array of white-light sources produced in bulk media by ultrashort laser pulses. The array is generated out of the spatial interference pattern between two laser pump pulses, so that the number of supercontinuum sources and their separations can be easily manipulated by varying the geometry of the laser beam interaction. We find that all the secondary white-light sources which arise from the generation of filaments in the optical medium are well phase-locked and are thus able to generate stable and high-visibility multiple-beam interference patterns in the far-field. Observations are compared to the results of a simple model which takes into account a clamping of the peak laser intensity inside the filaments and includes intensity-dependent phase shifts among the different sources.

Nonlinear ellipsometric method for measuring second-order cascaded phase shift

An ellipsometric method for measuring second-order cascaded phase shift is experimentally demonstrated in a KNbO(3) single crystal. We analyze the polarization state composed of the two orthogonal polarizations of the transmitted fundamental wave, one of which experiences intensity-dependent depletion and phase shift while the other does not. This method does not require a well-defined beam profile or interferometric stability.

Observation of Optical Bistability in χ(2) Polyarylates

Results of measurements of optical bistability in a guest — host polymer structure are presented. A new type of polymer has been elaborated and its optical properties are described. The Fabry–Perot system has been used and the bistabile behaviour has been observed. The second order cascaded χ(2)(ω): χ(2)(2ω) process, leading to intensity dependent phase shift, has been suggested as the mechanism leading to this effect. A satisfactory model of this phenomenon was formulated.

Sources of phase noise in homodyne and heterodyne phase modulation devices used for tissue oximetry studies

The objective of this study was to characterize sources of phase noise in homodyne and heterodyne phase modulation devices (PMDs) used for tissue oximetry measurements. Each PMD incorporates a laser diode modulated at a radio frequency in the 50–200 MHz range, an optical detector and a homodyne/heterodyne phase sensitive detector. The intensity modulated light which propagates through tissue is attenuated and undergoes a phase shift, which reflects the mean time of flight of the photons through the tissue. The measured amplitude and phase can be used to determine hemoglobin saturation in tissues using equations based on diffusion theory. Four studies were performed to characterize the sources of phase noise. First, the signal to noise ratio was characterized to determine if the PMDs are operating at the shot noise or detector noise limit. Second, the accuracy of the three PMDs for measuring phase shifts in tissue were compared by using them to measure the phase shift as a function of path length change in air, at a constant amplitude, and at signal to noise ratios comparable to that measured from tissue. The third source of noise measured was the phase shift that results from optical attenuation of the signal (phase-amplitude cross talk) at a constant path length, to characterize intensity dependent phase shifts in the PMDs. Finally, the interchannel interference of a dual wavelength PMD which uses radio frequency multiplexing to perform phase measurements at two wavelengths simultaneously was compared to that of a dual wavelength PMD which uses time multiplexing to perform phase measurements at two wavelengths serially to determine the effect of each on phase error.

Numerical analysis of Z-scan experiments by use of a mode expansion

The Z-scan analysis technique has been developed to permit characterization of nonlinear refractive indices and nonlinear absorption of non-Gaussian laser beams by a numerical approach. The new approach is based on a mode expansion of the electric field of the laser beam into Gaussian–Laguerre or Gaussian–Hermite modes. The individual modes are propagated within the nonlinear sample under the influence of the intensity-dependent phase shifts. The resulting electric field at the exit plane is expanded as a new sum of Gaussian–Laguerre or Gaussian–Hermite modes. From the final mode expansion the field distribution at the detector plane is calculated. The method also makes it possible to simulate a variety of complex optical limiting devices, such as stacks of samples with different material parameters and thick samples with a variation of material parameters along the z axis. A series of test simulations is presented and compared with experimental Z-scan data of solutions of substituted phthalocyanine molecules.

Pulse-Shape Dependent Time Averaging Effects in Interferometric Nonlinear Phase Shift Measurements

When optical pulses of temporal width less than or comparable to a detector's response time are used to interferometrically measure intensity-dependent phase shifts, it becomes necessary to use time-averaging protocols to deduce the material nonlinearity. Relations between the actual peak nonlinear phase shifts and the measured values are numerically evaluated for Gaussian and sech square pulse shapes. We believe that these results are also very important to understand the pulse break-up effect in Mach-Zehnder type all-optical switching applications.