Search

In this letter, excitation of discrete levels in a quantum system is considered, when the duration of the driving pulse is changed from multi-cycle to ultra-short half-cycle regime. It is shown that, as the number of optical cycles decreases, the system passes from the periodic-driven regime to the “kick-driven” action. In both cases the effect depends on the pulse area. However for subcycle pulses the area is equal to the time integral of the field strength, whereas for multi-cycle pulses it is determined by the time integral of the pulse envelope. The interference of the envelope pulse area and the electric pulse area and its possible manifestations in experiments are discussed.

Electromagnetically induced gratings (EMIGs) of atomic populations are formed in the resonant media at the interference of two or more overlapping monochromatic beams. They are of great interest in the view of the possibility of numerous applications in optics and spectroscopy. The significant progress has been achieved recently in the generation of ultrashort femto- and attosecond pulses. Such ultrashort pulses cannot provide an interference pattern because the region of their overlapping is very small and insufficient to form even few interference fringes. However, when the pulse duration is shorter than the relaxation times in the medium in the presence of a coherent interaction with the medium, they can rapidly change of the population of atomic levels owing to carrier-wave Rabi flopping. In this case, population gratings can be formed without the instantaneous overlapping of ultrashort light pulses in the medium. The latest results on the production and control of EMIGs received by means of a sequence of single- and subcycle light pulses have been reviewed. It has been shown that the unipolar subcycle pulses can be used to control more efficiently the EMIGs compared to multipolar multicycle pulses. Various applications of these gratings have been discussed in the ultrafast optics and for the holographic recording.

Our recent theoretical studies of generation of ultrashort pulses based on collective spontaneous emission from a thin resonant medium layer excited by a pair of high-frequency (compared to the transition frequency of the medium) pulses are reviewed. The source of generated radiation is a resonant polarization pulse in the medium (“stopped polarization pulse”), which is excited and switched off by a pair of light pump pulses. This method allows obtaining attosecond pulses in the optical and ultraviolet ranges, as well as femtosecond terahertz pulses. The effect of the superradiance in generation is discussed. The use of coherent and collective processes makes it possible to achieve a high efficiency of the generation of terahertz radiation. The proposed method is an alternative method of obtaining ultrashort pulses compared to the currently well-developed methods such as the high-harmonic generation method.

The possibility of selective population of the energy levels of quantum systems using a single unipolar subcycle pulse and a pair of pulses has been studied. The possibility of selective population of quantum levels has been clearly illustrated based on the numerical solution of a system of equations for the density matrix of a three-level medium that interacts with a pair of subcycle attosecond and terahertz pulses. The possibility of creating a population inversion in a three-level medium using a pair of such pulses has been shown. The dynamics of population gratings in a three-level medium exposed to the action of a pair of Gaussian pulses of large amplitude on the system is studied. Whereas the shape of the gratings in a weak field is harmonic, according to analytical calculations performed by the perturbation theory, in the case of a strong field, the spatial profile of the gratings may differ from the sinusoidal profile and may have a complex structure of peaks.

A method of coherent controlling the polarization of a medium has been proposed recently for the generation of extremely short pulses. The method is based on the excitation of atomic polarization oscillations and their subsequent stop using a pair of ultrashort pulses. The so-called stopped pulse of the polarization of a medium, which arises in the interval between its excitation and deexcitation, can be a source of an extremely short radiation pulse. In this work, the above-indicated possibility of generation of an isolated attosecond ultraviolet pulse in a three-level resonant medium whose parameters correspond to a hydrogen atom excited by a pair of unipolar X-ray pulses is considered theoretically. In this case, the generation mechanism is of the antenna-type, that is, it is caused by the collective spontaneous emission of pre-phased atoms in the absence of a noticeable decay of their free polarization.

A variant of the experiment to observe the optical Aharonov—Bohm effect has been discussed. In the experiment, a unipolar subcycle light pulse has been proposed as a source of the vector potential acting on electrons and having zero electric field strength in the region of a nonzero vector potential. Such a relation between the field and potential appears because the unipolar pulse has a nonzero electric area. An unusual situation where the fact of the passage of the pulse in one of the arms of two-beam interferometer is stored for a very long time after the passage and can be recorded in a two-beam electronic interferometer by a shift of fringes has been discussed. Detailed analysis of the phase shift under the influence of the vector potential created by the inhomogeneous unipolar pulse removes this contradiction and shows the equality of phase incursions in both arms that is unobvious at first glance.

The interest in unipolar pulses in optics is related to the possibility of their efficient action on quantum objects. In this work, we study the interaction of a short rectangular unipolar pulse with a two-level resonant medium under conditions that the pulse duration is shorter than the relaxation times of the medium. It is paradoxical that the polarization and the population difference of the medium oscillate not at the Rabi frequency, but, rather, at a frequency that is proportional to the sum of the squared frequency of the resonant transition of the medium and the squared Rabi frequency of the pulse. This phenomenon is similar to the Stark effect, which consists of a shift of the transition frequencies of a medium in a constant external electric field. The possibility of generating radiation at frequencies that exceed the resonant transition frequency of the medium upon its excitation by a rectangular unipolar pulse is discussed.

Conventionally, attosecond pulses are obtained using generation of high-order optical harmonics upon excitation of various media by femtosecond laser pulses with the central frequency in the infrared range. Here, we consider theoretically an alternative possibility of obtaining an isolated extreme ultraviolet (XUV) attosecond pulse in a thin layer of helium atoms excited by a pair of half-cycle (quasi-unipolar) X-ray pulses. The approach is based on the free polarization decay of an atomic medium. An analogy of the processes under consideration with the phenomenon of superradiance is discussed.

A new parameter of “the atomic scale of an electrical area” has been introduced. It shows the effect of unipolar pulses on a quantum system. This parameter is equal to the ratio of the Planck constant to the characteristic size of the quantum system and the electric charge of the quantum particle. This new parameter is universal and can be used to assess the efficiency of the action of unipolar and quasi-unipolar pulses on various quantum systems.

Based on an approximate solution of the Schrodinger equation, the effect that a pair of extremely short small-amplitude subcycle pulses has on a quantum system is studied. It is shown that, if the pulses are shorter than the inverse frequencies of atomic transitions, the probability of transitions between levels is determined by the electric area of the pulses and the time delay between them. As a consequence, a unipolar pulse can more efficiently affect the system than a bipolar one, while a sequence of pulses realizes a selective action on quantum objects, despite a nonresonant character of the interaction.

Recent theoretical and experimental results on coherent passive mode locking in lasers due to self-induced transparency are revised. In contrast to traditional laser systems, where passive mode locking occurs due to the effects of incoherent gain and absorption saturation, this regime of mode locking arises due to coherent interaction between light and matter. Theoretical results are presented that demonstrate the possibility of obtaining single-cycle pulses in a laser with a linear cavity of ultrashort length. Results are also presented from what are apparently the first experiments on coherent mode locking due to self-induced transparency in lasers.

The radiation of a two-level resonant medium that is placed into a cavity and is excited by a periodically phase modulated laser pulse is studied theoretically. The radiation is analyzed based on the analytical and numerical solutions of the system of Maxwell–Bloch equations under conditions of a strong coupling between the field and the matter. Under these conditions, this system is similar to a polariton laser. The excitation efficiency of a polariton laser by a phase-modulated radiation pulse is shown to be high compared to a pulse without phase modulation of the carrier frequency. It is shown that the main reason for the efficient excitation of polariton modes in the medium is the appearance of difference combination parametric resonance. The obtained results open up new possibilities for the excitation of radiation of polariton lasers by low-power frequency-modulated pump laser radiation.

Our recent studies of methods for obtaining ultrashort light pulses and analysis of the impact of ultrashort optical pulses on classical and quantum micro-objects with the identification of the determining role of the degree of unipolarity of pulses (maximum for strictly unipolar pulses) in the efficiency of direct laser acceleration of charged particles and excitation of atoms and molecules have been reviewed. Special attention has been paid to the coherent mode locking regime in lasers, which is implemented when the laser pulse duration is less than the relaxation time of the working transition in media with resonance amplification and absorption (laser analog of the phenomenon of self-induced transparency). Experimental data on coherent mode locking in a titanium-sapphire laser with a cell with rubidium vapor at self-induced transparency in rubidium have been presented. The interaction of ultrashort pulses in resonant media has also been analyzed.

The regime of passive mode locking in a Ti:sapphire laser with a coherent absorber resulting in the emission of pulses with a duration considerably shorter than the absorber relaxation times is demonstrated experimentally. A cell filled with rubidium vapor placed in the laser cavity serves as a coherent absorber. Mode locking arises when the laser oscillation frequency is tuned to the resonance transitions in rubidium. In our opinion, 2π pulses of self-induced transparency appear in the cavity, and the reported results represent the first experimental demonstration of passive mode locking caused by the effect of self-induced transparency, which has previously been discussed only theoretically.

We study theoretically a novel possibility for the emission of few-cycle pulses via excitation of nonlinear oscillators arranged in a thin circular string by a spot of light moving along the string. Such excitation can be realized by a beam emitted from a source at some distance, when the beam rotates with high constant angular velocity. Here we analyze the possibility to realize such setup using ultrafast beam deflectors and a diffractive optical element (DOE). We show that the pulse duration, amplitude and spectrum can be controlled by the spot velocity, the resonance frequency of the medium as well as by the parameters of the DOE. Remarkably, the electric field area of the generated field does not depend on DOE characteristics. These theoretical predictions open novel opportunities in generation of few cycle pulses with controllable duration and waveshape.

We show that, using a pair of short terahertz pulses, it is possible to form light-induced gratings of the population difference, which can be applied to control terahertz radiation. The pulses coherently interact with the medium and do not overlap in it. The examined effect opens up new opportunities in terahertz spectroscopy with the use of such short pulses.

The dynamics of coherent propagation of a unipolar subcycle pulse of a large electric-field area (the integral of the electric-field strength with respect to time) in a nonlinear two-level resonant medium is studied theoretically. The propagating pulse is shown to be capable of splitting into a pair of individual components, each of which behaves like a pulse of self-induced transparency. This phenomenon is similar to the well-known phenomenon of splitting of a 4π or 6π pulse into a pair of 2π pulses of self-induced transparency, which occurs in the case of propagation of long pulses, when the notion of the pulse area is applicable and the area theorem holds.

The possibility of generation of quasi-unipolar extremely short pulses (with a duration of several periods of field oscillations) is theoretically analyzed for the excitation of a circular, nonlinear, and resonant medium with a light spot. The light spot rotates along a circle with a velocity that exceeds the speed of light in vacuum, while particles of the medium are distributed uniformly along the circle. It is shown that, by introducing a delay in the form of a phase plate into the system, one can control the shape, the duration, and the amplitude of generated pulses.

By numerically solving the system of Maxwell–Bloch equations, we have examined theoretically collisions of extremely short single-cycle and unipolar subcycle pulses in a nonlinear resonant medium under conditions that the light interacts coherently with the medium. The dynamics of the electric field of structures of light-induced polarization and inversion difference has been considered in the situation in which pulses are overlapped in the medium. We show that the states of the medium (to the right and to the left of the overlap region of the pulses) may differ. In particular, we show that polarization waves with different characteristics can exist in the regions of the medium that are located on opposite sides of the overlap region of the pulses. These waves travel in different directions and have different spatial frequencies.

Using the method of the Green’s function for a wave equation, it is shown that, in a one-dimensional geometry, the field emitted by a resonant medium that is composed by a system of coupled or free charges is proportional not to the acceleration of charges, as is usually assumed, but, rather, to their velocity that they acquire as a result of the action of a light pulse on initially stationary charges. This feature opens up new opportunities for the generation of ultrashort pulses of one-cycle and subcycle durations, as well as for the diagnostics of media and materials using such ultrashort pulses.

Collisions of unipolar subcycle pulses in a nonlinear resonant medium that coherently interact with it are studied theoretically. The dynamics of spatial polarization structures and population difference that the pulses induce in the medium are analyzed. A surprising feature is that the medium is capable of “remembering” the result of the interaction with the pulses and their collisions during times comparable to the polarization relaxation time. An analysis of the dynamics of light-induced structures makes it possible to judge the parameters of subcycle pulses at the times longer than the pulse duration, which, in the future, can be useful in their detection.

The possibility of diagnosing the linear and nonlinear electrodynamic susceptibilities of media by examining the time profiles of extremely short terahertz radiation pulses (using pulsed terahertz spectroscopy methods) that are incident on a thin layer of a medium under study, are reflected from the layer, and are transmitted through it is shown theoretically. In the general case, the linear and nonlinear susceptibilities of different orders can be found by solving linear integral equations. Diagnostics is considerably simplified in the case of an isolated resonance of a medium with homogeneous spectral broadening, which is modeled by the response of an anharmonic oscillator.

We have examined examples of nonlinear-photonics devices that are based on the coherent interaction of light with matter. Such interaction takes place if the duration of a light pulse is shorter than the relaxation times T 1 and T 2 in a resonant medium and if the strength of the light field is so high that Rabi oscillations arise. Theoretical analysis shows that these systems have a number of advantages compared to similar devices that operate under incoherent interaction conditions of light with matter.

Specific properties of the radiation emitted by a spatially modulated resonance medium excited by an ultrashort light pulse propagating through the medium at a variable superluminal velocity are analyzed. In so doing, frequencies different from that of the resonance transition of the medium may appear in the emission spectrum. It is demonstrated that, in contrast to an earlier studied case of medium excitation at constant velocity, variation of the excitation velocity leads to generation of a spectral continuum, the boundaries of which are determined by the range of variation of the medium-excitation velocity.

Quantum electrodynamics predicts the appearance of radiation in an empty cavity in which one of the mirrors is vibrating. It also predicts the appearance of radiation from an isolated vibrating mirror. Such effects can be described within the framework of classical electrodynamics. We present the qualitative explanation of the effect, along with the results of numerical simulation of the emission of radiation by an isolated vibrating metallic mirror, which can be induced by mirror illumination by an ultrashort pulse of light. The dynamics of conduction electrons in the metallic mirror is described by the classical Drude model. Simulation was performed for the cases of mirror illumination by either a bipolar or a unipolar pulse.

Methods recently proposed for generating unipolar pulses in nonlinear media in terahertz and optical electromagnetic ranges are reviewed. Such pulses have nonzero “electric area” (time integral of the field strength over the entire duration of a pulse) and, correspondingly, a significant component of the field with zero frequency, thus exhibiting quasistatic properties. Effective generation of unipolar pulses would allow, e.g., transferring mechanical momentum to charged particles and, thereby, controlling the motion of wave packets of matter, which can be useful for compact accelerators of charged particles and for other applications.

In the regime of coherent interaction of short optical pulses with a resonant medium, which is implemented with a pulse duration shorter than the relaxation times in the medium, the formation of population gratings can occur without overlapping the pulses therein. In this case, there are new possibilities for controlling optical pulses, which are especially pronounced for extremely short pulses. It is shown that, with the proper choice of the parameters of a sequence of extremely short optical pulses, not only the formation of population gratings, but also their erasure are possible. It is demonstrated that this effect can be used for the creation of an ultrahigh-speed optical deflector.

Particular features of the emission of radiation by a Raman-active medium excited by a sequence of ultrashort superluminal pulses have been studied theoretically. It is shown that such an excitation gives rise to the possibility of obtaining unipolar rectangular videopulses the duration and amplitude of which depend on the velocity of propagation of the excitation over the medium.

We investigate the possibility of controlling the radiation parameters of a spatially periodic one-dimensional medium consisting of classical harmonic oscillators by means of a sequence of ultrashort pulses that propagate through the medium with a superluminal velocity. We show that, in the spectrum of the transient process, in addition to the radiation at a resonant frequency of oscillators, new frequencies arise that depend on the period of the spatial distribution of the oscillator density, the excitation velocity, and the angle of observation. We have examined in detail the case of excitation of the medium by a periodic sequence of ultrashort pulses that travel with a superluminal velocity. We show that it is possible to excite oscillations of complex shapes and to control the radiation parameters of the resonant medium by changing the relationship between the pulse repetition rate, the medium resonant frequency, and the new frequency.

Using a delay differential equation model with two time delays, we investigate the dynamics of a semiconductor laser with an active cavity coupled to an external passive cavity. Our numerical simulations indicate that when the coupling between the two cavities is strong enough and the round-trip time of the active cavity is an integer multiple of the round-trip time of the external passive cavity, a harmonic mode-locking regime can develop in the laser with the pulse repetition period close to the passive cavity round-trip time. We also demonstrate that the output field intensity sensitively depends on the relative position of the frequency combs of the two cavities giving rise to a resonant behavior. The period and width of the resonances depend on the ratio of the round-trip times to the coupling between the two cavities. We show that the coupled cavity system under consideration can demonstrate a bistability between different regimes of generation.

Currently existing lasers with passive mode-locking are two-section systems including an amplifier section and a saturable absorber section. The mechanism of generation of short pulses in them is based on the effects of saturation of the gain in the amplifier and absorption in the absorber, which prevent obtaining pulses with durations shorter than the relaxation time of the polarization in the amplifying and absorbing media. In this work, the new possibility of the generation of ultrashort pulses in a laser with passive mode-locking owing to the coherent character of the interaction of light with matter in the amplifying and absorbing media in ring and linear cavities has been theoretically analyzed. A practically interesting case where the amplifying and absorbing media are separated in the space of the cavity, rather than being homogeneously mixed in its volume, as was previously considered for such type of lasers, has been studied. It has been shown that the width of the spectrum of generated pulses can be much larger than the width of the amplification line and can vary depending on the parameters of the amplifying and absorbing media of the laser. The existence of nonsoliton scenarios of the regime of coherent passive mode synchronization, as well as the possibility of generation without injection of an auxiliary pulse, has been demonstrated.

Mode-locking in a cw narrowband tunable dye laser whose cavity contains absorbing cells with molecular iodine vapor has been studied experimentally. When the wavelength of radiation of the dye laser is tuned to absorption lines of molecular iodine vapor in a cell in the cavity, short pulses following with a period equal to or multiple of the round-trip time of light around the cavity appear. The duration of the generated pulses is about 1 ns, which is much shorter than the phase memory time in iodine vapor. In such a situation, modelocking occurs owing to the coherent character of the interaction of laser radiation with narrow absorption resonances in molecular iodine vapor.

We report the results of computer simulation of the emission of radiation by an extended two-level medium in a ring cavity. The cases of using strong external monochromatic, quasi-monochromatic, and biharmonic radiation for pumping the two-level medium are analyzed. It is shown that the emission of radiation with spectral content different from that of the pump radiation, which is interpreted as the inversionless oscillation, is the result of the spatiotemporal dynamics of light propagation in an extended two-level medium imbedded in a cavity. The appearance of this radiation is not related to known resonances of amplification of a weak probe field in a thin layer of the two-level system (the effect of inversionless oscillation) induced by strong resonance monochromatic or biharmonic field, as was thought before.

Specific characteristics of the radiation of a resonant medium excited by an ultrashort light pulse propagating through the medium with a superluminal velocity are considered. The medium is assumed to consist of identical linear harmonic oscillators with a spatial density periodically modulated along the direction of propagation of the superluminal excitation. The field of radiation of the resonant medium under these conditions is calculated. It is shown that, under the superluminal excitation, the radiation spectrum of the medium shows, along with the fundamental frequency of the oscillators, new frequencies that depend on the spatial frequency of the distribution of oscillators and on the angle of observation. Possible application of the effect is discussed.

We present a significantly different reflection process from an optically thin flat metallic or dielectric layer and propose a strikingly simple method to form approximately unipolar half-cycle optical pulses via reflection of a single-cycle optical pulse. Unipolar pulses in reflection arise due to specifics of effectively one-dimensional pulse propagation. Namely, we show that in considered system the field emitted by a flat medium layer is proportional to the velocity of oscillating medium charges instead of their acceleration as it is usually the case. When the single-cycle pulse interacts with linear optical medium, the oscillation velocity of medium charges can be then forced to keep constant sign throughout the pulse duration. Our results essentially differ from the direct mirror reflection and suggest a possibility of unusual transformations of the few-cycle light pulses in linear optical systems.

In this paper, we study the dynamics of a passively mode-locked semiconductor laser with dual-frequency coherent optical injection. The locking regions, where the laser pulse repetition rate is synchronized to the separation of the two injected frequencies, were calculated numerically using a delay differential equation model and measured experimentally. Asymptotic analysis performed in the limit of the small injection field amplitude revealed the dependence of the locking regions on the model parameters, such as optical bandwidth, absorber recovery time, and linear losses.

Hybrid mode locking in a two-section edge-emitting semiconductor laser is studied numerically and analytically using a set of three delay differential equations. In these equations, the external RF signal applied to the saturable-absorber section is modeled by the modulation of the carrier relaxation rate in this section. The estimation of the locking range where the pulse repetition frequency is synchronized with the frequency of the external modulation is performed numerically and the effect of the modulation shape and amplitude on this range is investigated. Asymptotic analysis of the dependence of the locking range width on the laser parameters is carried out in the limit of small-signal modulation. Our numerical simulations indicate that hybrid mode locking can be also achieved in the cases when the frequency of the external modulation is approximately twice and half of the pulse repetition frequency of the free-running passively mode-locked laser fP . Finally, we provide an experimental demonstration of hybrid mode locking in a 20-GHz quantum-dot laser with the modulation frequency of the reverse bias applied to the absorber section close to fP/2.