Pump-probe phase spectroscopy with submilliradian sensitivity and nanosecond time delay using Michelson interferometers

Using two Michelson interferometers, we describe an experimental scheme for sensitive pump-probe spectral interferometry measurements at long time delays. It has practical advantages over the Sagnac interferometer method typically used when long-time delays are required. First, with the Sagnac interferometer, achieving many nanosecond delays requires expanding the size of the interferometer so that the reference pulse arrives before the probe pulse. Because the two pulses still pass through the same region of the sample, long-lived effects can still affect the measurement. In our scheme, the probe and reference pulses are spatially separated at the sample, alleviating the need for a large interferometer. Second, in our scheme, a fixed delay between probe and reference pulses is straightforward to produce and is continuously adjustable while maintaining alignment. Two applications are demonstrated. First, transient phase spectra are presented in a thin tetracene film with up to 5 ns probe delay. Second, impulsive stimulated Raman measurements are presented in Bi₄Ge₃O₁₂. The signal-to-noise using the double Michelson technique is comparable to previously described methods with the added advantage of arbitrarily long pump-probe time delays.

Analysis of complex multidimensional optical spectra by linear prediction

We apply Linear Prediction from Singular Value Decomposition (LPSVD) to two-dimensional complex optical data in the time-domain to generate spectra with advantages over discrete Fourier transformation (DFT). LPSVD is a non-iterative procedure that fits time-domain complex data to the sum of damped sinusoids, or Lorentzian peaks in the spectral domain. Because the fitting is linear, it is not necessary to give initial guess parameters as in nonlinear fits. Although LPSVD is a one-dimensional algorithm, it can be performed column-wise on two-dimensional data. The method has been extensively used in 2D NMR spectroscopy, where spectral peaks are typically nearly ideal Lorentzians, but to our knowledge has not been applied in the analogous optical technique, where peaks can be far from Lorentzian. We apply LPSVD to the analysis of zero, one, and two quantum electronic two-dimensional spectra from a semiconductor microcavity. The spectra consist of non-ideal, often overlapping peaks. We find that LPSVD achieves a very good fit even on non-ideal data. It reduces noise and eliminates discrete distortions inherent in the DFT. We also use it to isolate and analyze weak features of interest.

Two-beam coupling by a hot electron nonlinearity

Transparent conductive oxides such as indium tin oxide (ITO) bear the potential to deliver efficient all-optical functionality due to their record-breaking optical nonlinearity at epsilon near zero (ENZ) wavelengths. All-optical applications generally involve more than one beam, but, to our knowledge, the coherent interaction between beams has not previously been discussed in these materials, which have a hot electron nonlinearity. Here we study the optical nonlinearity at ENZ in ITO and show that spatial and temporal interference has important consequences in a two-beam geometry. Our pump-probe results reveal a polarization-dependent transient that is explained by diffraction of pump light into the probe direction by a temperature grating produced by pump-probe interference. We further show that this effect allows tailoring the nonlinearity by tuning the frequency or chirp. Having fine control over the strong and ultrafast ENZ nonlinearity may enable applications in all-optical neural networks, nanophotonics, and spectroscopy.

Nonlinearity and ionization in Xe: experiment-based calibration of a numerical model

Recently proposed universality of the nonlinear response is put to the test and used to improve a previously designed model for xenon. Utilizing accurate measurements resolving the nonlinear polarization and ionization in time and space, we calibrate the scaling parameters of the model and demonstrate agreement with several experiments spanning the intensity range relevant for applications in nonlinear optics at near-infrared and mid-infrared wavelengths. Applications to other species including small molecules are discussed, suggesting a self-consistent way to calibrate light-matter interaction models.

Absolute Measurement of Laser Ionization Yield in Atmospheric Pressure Range Gases over 14 Decades

Strong-field ionization is central to intense laser-matter interactions. However, standard ionization measurements have been limited to extremely low density gas samples, ignoring potential high density effects. Here, we measure strong-field ionization in atmospheric pressure range air, N_{2}, and Ar over 14 decades of absolute yield, using mid-IR picosecond avalanche multiplication of single electrons. Our results are consistent with theoretical rates for isolated atoms and molecules and quantify the ubiquitous presence of ultralow concentration gas contaminants that can significantly affect laser-gas interactions.

Automated polarization-dependent multidimensional coherent spectroscopy phased using transient absorption

An experimental apparatus is described for multidimensional optical spectroscopy with fully automated polarization control, based on liquid crystal variable retarders. Polarization dependence of rephasing two-dimensional coherent spectra are measured in a single scan, with absolute phasing performed for all polarization configurations through a single automated auxiliary measurement at the beginning of the scan. A factor of three improvement in acquisition time is demonstrated, compared to the apparatus without automated polarization control. Results are presented for a GaAs quantum well sample and an InGaAs quantum well embedded in a microcavity.

Controlling femtosecond filament propagation using externally driven gas motion

The thermal density depression (or "density hole") produced by a high-repetition-rate femtosecond filament in air acts as a negative lens, altering the propagation of the filament. We demonstrate the effects of externally driven gas motion on these density holes and the resulting filament steering, and we derive an expression for the gas velocity that maximizes the effect. At gas velocities more than ∼3 times this value, the density hole is displaced from the filament, and it no longer affects filament propagation. We demonstrate density hole displacement using an audio speaker-driven sound wave, leading to a controllable, repeatable deflection of the filament. Applications are discussed, including quasi-phase matching in gas-based nonlinear optics. To the best of our knowledge, this is the first demonstration of femtosecond filament propagation control through controlled motion of the nonlinear medium.

Bound-Electron Nonlinearity Beyond the Ionization Threshold

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

Energy deposition of single femtosecond filaments in the atmosphere: erratum

In this erratum the funding section of Opt. Lett.41, 3908 (2016)OPLEDP0146-959210.1364/OL.41.003908 has been updated.

Energy deposition of single femtosecond filaments in the atmosphere

We present spatially resolved measurements of energy deposition into atmospheric air by femtosecond laser filaments. Single filaments formed with varying laser pulse energy and pulsewidth were examined using longitudinal interferometry, sonographic probing, and direct energy loss measurements. We measure peak and average energy absorption of ∼4  μJ/cm and ∼1  μJ/cm for input pulse powers up to ∼6 times the critical power for self-focusing.

Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths

We measure the nonlinear refractive index coefficients in N₂, O₂, and Ar from visible through mid-infrared wavelengths (λ=0.4-2.4  μm). The wavelengths investigated correspond to transparency windows in the atmosphere. Good agreement is found with theoretical models of χ((3)). Our results are essential for accurately simulating the propagation of ultrashort mid-infrared pulses in the atmosphere.

Multi-MeV Electron Acceleration by Subterawatt Laser Pulses

We demonstrate laser-plasma acceleration of high charge electron beams to the ∼10  MeV scale using ultrashort laser pulses with as little energy as 10 mJ. This result is made possible by an extremely dense and thin hydrogen gas jet. Total charge up to ∼0.5  nC is measured for energies >1  MeV. Acceleration is correlated to the presence of a relativistically self-focused laser filament accompanied by an intense coherent broadband light flash, associated with wave breaking, which can radiate more than ∼3% of the laser energy in a ∼1  fs bandwidth consistent with half-cycle optical emission. Our results enable truly portable applications of laser-driven acceleration, such as low dose radiography, ultrafast probing of matter, and isotope production.

Optical mode structure of the air waveguide

Analysis is performed on propagation of light in long-lived optical waveguides in air generated by arrays of femtosecond filaments. Mode structure, leakage losses, and coupling efficiency are studied analytically and numerically as a function of wavelength and time delay after the waveguide-initiating filaments.

Quantum control of molecular gas hydrodynamics

We demonstrate that strong impulsive gas heating or heating suppression at standard temperature and pressure can occur from coherent rotational excitation or deexcitation of molecular gases using a sequence of nonionizing laser pulses. For the case of excitation, subsequent collisional decoherence of the ensemble leads to gas heating significantly exceeding that from plasma absorption under the same laser focusing conditions. In both cases, the macroscopic hydrodynamics of the gas can be finely controlled with ∼40  fs temporal sensitivity.

Direct imaging of the acoustic waves generated by femtosecond filaments in air

We present time-resolved measurements of the gas acoustic dynamics following interaction of spatial single- and higher-mode 50 fs, 800 nm pulses in air at 10 Hz and 1 kHz repetition rates. Results are in excellent agreement with hydrodynamic simulations. Under no conditions for single filaments do we find on-axis enhancement of gas density; this occurs only with multifilaments. We also investigate the propagation of probe beams in the gas density profile induced by a single extended filament. We find that light trapping in the expanding annular acoustic wave can create the impression of on-axis guiding in a limited temporal window.

Optical beam dynamics in a gas repetitively heated by femtosecond filaments

We investigate beam pointing dynamics in filamentation in gases driven by high repetition rate femtosecond laser pulses. Upon sudden exposure of a gas to a kilohertz train of filamenting pulses, successive filaments are steered from their original direction to a new stable direction whose equilibrium is determined by a balance among buoyant, viscous, and diffusive processes in the gas. The beam mode is preserved. Results are shown for Xe and air, but are broadly applicable to all configurations employing intense, high repetition rate femtosecond laser pulses in gases.

The effect of long timescale gas dynamics on femtosecond filamentation

Femtosecond laser pulses filamenting in various gases are shown to generate long- lived quasi-stationary cylindrical depressions or 'holes' in the gas density. For our experimental conditions, these holes range up to several hundred microns in diameter with gas density depressions up to ~20%. The holes decay by thermal diffusion on millisecond timescales. We show that high repetition rate filamentation and supercontinuum generation can be strongly affected by these holes, which should also affect all other experiments employing intense high repetition rate laser pulses interacting with gases.

High field optical nonlinearity and the Kramers-Kronig relations

The nonlinear optical response to high fields is absolutely measured for the noble gas atoms He, Ne, Ar, Kr, and Xe. We find that the response is quadratic in the laser field magnitude up to the ionization threshold of each gas. Its size and quadratic dependence are well predicted by a Kramers-Kronig analysis employing known ionization probabilities, and the results are consistent with calculations using the time-dependent Schrödinger equation.

Ionization-grating-induced nonlinear phase accumulation in spectrally resolved transient birefringence measurements at 400 nm

We report experimental confirmation of the ionization-grating-induced transient birefringence predicted by Wahlstrand and Milchberg [Opt. Lett. 36, 3822 (2011)] and discuss its impact on the higher-order Kerr effect interpretation by Loriot et al. of pump-probe transient birefringence measurements made at 800 nm [Opt. Express 17, 13429 (2009)]. Measurement of the transient birefringence in air at 400 nm shows a negative contribution to the index of refraction at zero delay for frequencies within the pump bandwidth, the degenerate case, and no negative contribution for frequencies exceeding the pump bandwidth, the nondegenerate case. Our findings suggest that a reevaluation of the higher-order Kerr effect hypothesis of Loriot et al. is necessary.

Electric field-induced coherent control in GaAs: polarization dependence and electrical measurement [Invited]

A static electric field enables coherent control of the photoexcited carrier density in a semiconductor through the interference of one- and two-photon absorption. An experiment using optical detection is described. The polarization dependence of the signal is consistent with a calculation using a 14-band k · p model for GaAs. We also describe an electrical measurement. A strong enhancement of the phase-dependent photocurrent through a metal-semiconductor-metal structure is observed when a bias of a few volts is applied. The dependence of the signal on bias and laser spot position is studied. The field-induced enhancement of the signal could increase the sensitivity of semiconductor-based carrier-envelope phase detectors, useful in stabilizing mode-locked lasers for use in frequency combs.

Effect of a plasma grating on pump-probe experiments near the ionization threshold in gases

Calculations are performed of the phase shift caused by the spatial modulation in the plasma density due to interference between a strong pump pulse and a weak probe pulse. It is suggested that a recent experiment [Opt. Express 17, 13429 (2009)] observed an effective birefringence from this plasma grating rather than from the higher-order Kerr effect.

Optical nonlinearity in Ar and N2 near the ionization threshold

We directly measure the nonlinear optical response in argon and nitrogen in a thin gas target to laser intensities near the ionization threshold. No instantaneous negative nonlinear refractive index is observed, nor is saturation, in contrast with a previous measurement [Opt. Express 17, 13429 (2009)] and calculations [Phys. Rev. Lett. 106, 183902 (2011)]. In addition, we are able to cleanly separate the instantaneous and rotational components of the nonlinear response in nitrogen. In both Ar and N2, the peak instantaneous index response scales linearly with the laser intensity until the point of ionization, whereupon the response turns abruptly negative and ∼constant, consistent with plasma generation.

Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz-Keldysh effect

In (100)-oriented GaAs illuminated at normal incidence by a laser and its second harmonic, interference between one- and two-photon absorption results in ballistic current injection, but not modulation of the overall carrier injection rate. Results from a pump-probe experiment on a transversely biased sample show that a constant electric field enables coherent control of the carrier injection rate. We ascribe this to the nonlinear optical Franz-Keldysh effect and calculate it for a two-band parabolic model. The mechanism is relevant to centrosymmetric semiconductors as well.

Contactless photoconductive terahertz generation

We describe a pulsed terahertz (THz) emitter that uses a rapidly oscillating, high-voltage bias across electrodes insulated from a photoconductor. Because no carriers are injected from the electrodes, trap-enhanced electric fields do not form. The resulting uniform field allows excitation with a large laser spot, lowering the carrier density for a given pulse energy and increasing the efficiency of THz generation. Compared to a dc bias, less susceptibility to damage is observed.

Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells

Detailed electronic many-body configurations are extracted from quantitatively measured time-resolved nonlinear absorption spectra of resonantly excited GaAs quantum wells. The microscopic theory assigns the observed spectral changes to a unique mixture of electron-hole plasma, exciton, and polarization effects. Strong transient gain is observed only under cocircular pump-probe conditions and is attributed to the transfer of pump-induced coherences to the probe.

The quantum-limited comb lineshape of a mode-locked laser: fundamental limits on frequency uncertainty

We calculate the quantum-limited shape of the comb lines from a mode-locked Ti:sapphire laser using experimentally-derived parameters for the linear response of the laser to perturbations. The free-running width of the comb lines is found across the laser spectrum. By modeling the effect of a simple feedback loop, we calculate the spectrum of the residual phase noise in terms of the quantum noise and the feedback parameters. Finally, we calculate the frequency uncertainty in an optical frequency measurement if the limiting factor is quantum noise in the detection of the optical heterodyne beat.

Quantitative measurement of timing and phase dynamics in a mode-locked laser

We present results of an experimental study of the timing and phase dynamics in a mode-locked Ti:sapphire laser. By measuring the response of two widely spaced comb lines to a sinusoidal modulation of the pump power, we determine quantitatively the response of both the central pulse time and the phase. Because of the distinct response of the pulse energy, central frequency, and gain to the modulation, we are able to distinguish their contributions to the timing and phase dynamics.

Coherent control of pulsed X-ray beams

Synchrotrons produce continuous trains of closely spaced X-ray pulses. Application of such sources to the study of atomic-scale motion requires efficient modulation of these beams on timescales ranging from nanoseconds to femtoseconds. However, ultrafast X-ray modulators are not generally available. Here we report efficient subnanosecond coherent switching of synchrotron beams by using acoustic pulses in a crystal to modulate the anomalous low-loss transmission of X-ray pulses. The acoustic excitation transfers energy between two X-ray beams in a time shorter than the synchrotron pulse width of about 100 ps. Gigahertz modulation of the diffracted X-rays is also observed. We report different geometric arrangements, such as a switch based on the collision of two counter-propagating acoustic pulses: this doubles the X-ray modulation frequency, and also provides a means of observing a localized transient strain inside an opaque material. We expect that these techniques could be scaled to produce subpicosecond pulses, through laser-generated coherent optical phonon modulation of X-ray diffraction in crystals. Such ultrafast capabilities have been demonstrated thus far only in laser-generated X-ray sources, or through the use of X-ray streak cameras.

Cherenkov radiation at speeds below the light threshold: phonon-assisted phase matching

Charged particles traveling through matter at speeds larger than the phase velocity of light in the medium emit Cherenkov radiation. Calculations reveal that a given angle of the radiation conical wavefront is associated with two velocities, one above and one below a certain speed threshold. Emission at subluminal but not superluminal speeds is predicted and verified experimentally for relativistic dipoles generated with an optical method based on subpicosecond pulses moving in a nonlinear medium. The dipolar Cherenkov field, in the range of infrared-active phonons, is identical to that of phonon polaritons produced by impulsive laser excitation.