Phase Step Modulation Research Articles

Dual projectile beams.

Accelerating beams, of which the Airy beam is an important representative, are characterized by intensity maxima that propagate along curved trajectories. In this work we present a simple approach to directly generate accelerating beams with controllable trajectories by means of binary phase structures that consist of only a π phase step modulation in comparison to previous studies where two-dimensional cubic phase modulations for example are required, and which have practical limitations due to their challenging fabrication with phase plates or diffractive optical elements (DOEs), or the spatially extended system needed for their generation at the Fourier plane. In our approach, two intensity maxima are formed that propagate along root parabolic trajectories in contrast to Airy and higher order caustic beams that propagate along a parabolic curve, hence we call these beams Dual Projectile Beams (DPBs). By tailoring a step or slit phase patterns with additional Fresnel lenses, we either generate hollow-core or abruptly focusing beams and control their curvatures. Moreover, using DPBs as a simpler complement to complex structured light fields, we demonstrate their versatility at the example of their interaction with nonlinear matter, namely the formation of a spatial soliton in a photorefractive material. We show that the formed solitary state propagates almost unchanged for a distance of several Rayleigh lengths. This light matter interaction can be regarded as a light beam deceleration. The simplicity of this approach makes these beams suitable for integrated optics and high-power laser applications using DOEs or meta-surfaces.

Valence state manipulation of Sm^3+ ions via a phase-shaped femtosecond laser field

The ability to manipulate the valence state conversion of rare-earth ions is crucial for their applications in color displays, optoelectronic devices, laser sources, and optical memory. The conventional femtosecond laser pulse has been shown to be a well-established tool for realizing the valence state conversion of rare-earth ions, although the valence state conversion efficiency is relatively low. Here, we first propose a femtosecond laser pulse shaping technique for improving the valence state conversion efficiency of rare-earth ions. Our experimental results demonstrate that the photoreduction efficiency from Sm3+ to Sm2+ in Sm3+-doped sodium aluminoborate glass using a π phase step modulation can be comparable to that using a transform-limited femtosecond laser field, while the peak laser intensity is decreased by about 63%, which is very beneficial for improving the valence state conversion efficiency under the laser-induced damage threshold of the glass sample. Furthermore, we also theoretically develop a (2+1) resonance-mediated three-photon absorption model to explain the modulation of the photoreduction efficiency from Sm3+ to Sm2+ under the π-shaped femtosecond laser field.

Observing quantum control of up-conversion luminescence in Dy3+ ion doped glass from weak to intermediate shaped femtosecond laser fields

Controlling the up-conversion luminescence of rare-earth ions in real-time, in a dynamical and reversible manner, is very important for their application in laser sources, fiber-optic communications, light-emitting diodes, color displays and biological systems. In previous studies, the up-conversion luminescence control mainly focused on the weak femtosecond laser field. Here, we further extend this control behavior from weak to intermediate femtosecond laser fields. In this work, we experimentally and theoretically demonstrate that the up-conversion luminescence in Dy3+ ion doped glass can be artificially controlled by a π phase step modulation, but the up-conversion luminescence control behavior will be affected by the femtosecond laser intensity, and the up-conversion luminescence is suppressed by lower laser intensity while enhanced by higher laser intensity. We establish a new theoretical model (i.e. the fourth-order perturbation theory) to explain the physical control mechanism by considering the two- and four-photon absorption processes, and the theoretical results show that the relative weight of four-photon absorption in the whole excitation process will increase with the increase in laser intensity, and the interference between two- and four-photon absorptions results in up-conversion luminescence control modulation under different laser intensities. These theoretical and experimental works can provide a new method to control and understand up-conversion luminescence in rare-earth ions, and also may open a new opportunity to the related application areas of rare-earth ions.

Effect of laser spectral bandwidth on coherent control of resonance-enhanced multiphoton-ionization photoelectron spectroscopy

The high-resolution (2 + 1) resonance-enhanced multiphoton-ionization photoelectron spectroscopy (REMPI-PS) can be obtained by measuring the photoelectron intensity at a given kinetic energy and scanning the single π phase step position. In this paper, we further demonstrate that the high-resolution (2 + 1) REMPI-PS cannot be achieved at any measured position of the kinetic energy by this measurement method, which is affected by the laser spectral bandwidth. We propose a double π phase step modulation to eliminate the effect of the laser spectral bandwidth, and show the advantage of the double π phase step modulation on achieving the high-resolution (2 + 1) REMPI-PS by considering the contributions involving on- and near-resonant three-photon excitation pathways.

HIGH-RESOLUTION PHOTOELECTRON SPECTROSCOPY BY SPECTRAL PHASE STEP MODULATION

Femtosecond-induced resonance-enhanced multi-photon ionization photoelectron spectroscopy (REMPI-PES) has the drawback of low spectral resolution due to broadband spectrum of the laser. In this paper, we theoretically demonstrate that high-resolution REMPI-PES can be achieved by shaping the femtosecond laser pulse with spectral phase step modulation. Our results show that, by manipulating the phase step position and the modulation depth, a narrowband peak or hole in the photoelectron spectrum can be observed, and the position of the narrowband peak or hole is correlated with the eigenenergy of the excite state. Therefore, both high-resolution REMPI-PES and the excited state structure can be obtained by observing the narrowband peaks or holes.

Resolution enhancement of photoelectron spectra by coherent phase control

In this paper, we study theoretically, the coherent phase control of (2+1) resonantly enhanced multiphoton ionization photoelectron spectra in cesium atom system by shaping the femtosecond pulse with π phase step modulation under weak laser field. Our results show that the photoelectron spectra can be greatly narrowed and the photoelectron intensity can be enhanced after π phase step modulation by precisely setting the phase step position. Also, we show that the high-resolution photoelectron spectra and the fine energy-level diagram of the two closed excited states can be obtained.

SELECTIVE EXCITATION OF COHERENT ANTI-STOKES RAMAN SCATTERING VIA PHASE STEP MODULATION

It is known that femtosecond coherent anti-Stokes Raman scattering (CARS) method suffers from the drawback of poor selectivity between neighboring Raman energy levels due to the large bandwidth of the pulses. Quantum coherent control based on the ultrashort pulse shaping technique is a promising solution. In this paper, we propose a simple approach to realize the selective excitation of CARS spectra by shaping both the probe and pump pulses with the π phase step. By phase step modulation of the probe pulse, we show that the CARS signals between neighboring Raman energy levels can be greatly narrowed and differentiated, and then selective excitation can be realized by modulating both the probe and pump pulses. Finally, the mechanism of the selective excitation by population transfer is briefly discussed.

High-resolution resonance-enhanced multiphoton-ionization photoelectron spectroscopy of Rydberg states via spectral phase step shaping

Femtosecond-induced resonance-enhanced multi-photon ionization (REMPI) photoelectron spectroscopy of the Rydberg states is faced with low spectral resolution due to the broadband laser spectrum. In this paper, we theoretically demonstrate that a high-resolution (2 + 1) REMPI photoelectron spectrum of the Rydberg states in a sodium (Na) atom can be obtained by shaping a femtosecond laser pulse with a spectral phase step modulation. Our results show that, by using a phase-shaped femtosecond laser pulse, some narrowband holes or peaks in the REMPI photoelectron spectrum can be created, and the positions of these holes or peaks are correlated with the eigenenergies of the Rydberg states. Thus, by observing these holes or peaks in the REMPI photoelectron spectrum, both the high-resolution REMPI photoelectron spectrum and the energy-level diagram of the Rydberg states can be obtained.

MANIPULATION OF THE MOLECULAR ORIENTATION BY COMBINED ELECTROSTATIC AND PHASE-SHAPED LASER FIELDS

We theoretically show that the field-free molecular orientation induced by the combined electrostatic and laser fields can be manipulated through shaping the femtosecond laser pulse with periodic phase step modulation. By adjusting the modulation time τ or the modulation depth δ, the maximum degree of the molecular orientation can be fully suppressed or reconstructed by the combined electrostatic and the transform-limited laser fields. The relations between the maximum degree of the field-free molecular orientation and the laser intensity, the amplitude of the electrostatic field, as well as the rotational temperature are also investigated.

Control of resonance enhanced multi-photon ionization photoelectron spectroscopy by phase-shaped femtosecond laser pulse

In this paper, we theoretically demonstrate that the (2+1+1) resonance enhanced multi-photon ionization photoelectron spectroscopy in sodium atom can be effectively controlled by shaping femtosecond laser pulse with a π phase step modulation in weak laser field, involving its total photoelectron energy, maximal photoelectron intensity, and spectroscopic bandwidth. Our results show that the total photoelectron energy can be suppressed but not enhanced, the maximal photoelectron intensity can be enhanced and also suppressed, and the photoelectron spectroscopy can be tremendously narrowed. These theoretical results can provide a feasible scheme to achieve the high-resolution photoelectron spectroscopy and study the excited state structure in atomic and molecular systems.

Intermediate state absorption enhancement in resonance-mediated (2+1) three-photon excitation process

In this paper, we theoretically study the control of intermediate state absorption in resonance-mediated (2+1) three-photon excitation process by shaping the femtosecond pulse with a π phase step modulation under weak laser field. Our results show that the intermediate state absorption can be enhanced, and the coherent enhancement increases with the increase of the pulse intensity and pulse duration. Our analysis indicates that the absorption enhancement results from the absorption reduction of the final state from the intermediate state in the shaped laser field. Furthermore, the effects of the population difference of the final and intermediate states in the unshaped laser field and the transition dipole moment from the intermediate state to the final state on the absorption enhancement are discussed and analyzed.

Field-free molecular alignment control by phase-shaped femtosecond laser pulse

In this paper, we theoretically show that the field-free molecular alignment can be controlled by shaping the femtosecond laser pulse with a periodic phase step modulation, involving the maximum degree and temporal structure of the molecular alignment. We show that the molecular alignment can be completely suppressed or reconstructed as that by the transform-limited laser pulse, the temporal structure of the alignment transient can be controlled with a desired shape, and the molecular alignment and antialignment for any temporal structure can be switched. Furthermore, we also show that both the degree and direction of the molecular alignment at a fix time delay can be continuously modulated.

Coherent control of molecular rotational state populations by periodic phase-step modulation

We theoretically demonstrate that the molecular rotational state populations through an impulsive nonresonant Raman process can be manipulated by shaping the femtosecond laser pulse with a periodic phase-step modulation. We show that, by precisely controlling these parameters characterizing the periodic phase-step modulation, both the odd and even rotational state populations can be completely suppressed or reconstructed as that induced by the transform-limited laser pulse, and the relative excitation between the odd and even rotational state populations can also be obtained. Furthermore, we show that the field-free molecular alignment can be manipulated due to the modulation of the odd and even rotational state populations.

Three-state selective population of dressed states via generalized spectral phase-step modulation

We present a joint experimental and theoretical study of selective population of dressed states (SPODS) in a three-level system. Control is exerted by shaped intense femtosecond laser pulses generated by a generalized spectral phase-step modulation function. We show that both control parameters (i.e., the phase-step amplitude and position) can be used to switch population among each three dressed states with high selectivity. The dynamics of the system, and hence the resulting photoelectron signal is studied theoretically by analyzing the time evolution of the adiabatic dressed-state energies and populations.