Quantum optimal control theory of high harmonic generation. Highharmonic generation from solids nature physics. We show that highharmonic generation can produce higher photon energies and flux by using higher laser intensities than are typical, strongly ionizing the medium and creating plasma that. Both methods have, in theory, a tendency to produce a train of closely spaced pulses rather than a single pulse. High harmonics generation is a process in which an atom absorbs q photons of energy. Second harmonic generation in nonlinear optical crystal diana jeong 1. Theoretical aspects of intense field harmonic generation. Introduction we present theoretical aspects of highharmonic generation hhg in this chapter. High harmonic generation hhg is a nonlinear process during which a target gas, plasma, or solid sample is illuminated by an intense laser pulse. Highharmonic generation in solids university of arizona. The approach includes the relevant interband polarizations and intraband currents. Highorder harmonic generation provides a new method for generating coherent, xuv radiation. High harmonic generation is the phenomenon that very high harmonics of an intense input laser beam are generated in a gas.
Generation of excessive free electrons in the medium at high peak intensity results in a phase mismatch 9. Theory of highorder harmonic generation for gapless graphene. The frequency of the generated radiation extends into the xuv region. This dissertation is a study of both the physical mechanism of harmonic generation as well as its development as a source of coherent xuv radiation. We show the emergence of the typical nonperturbative spectral features, harmonic plateau and cutoff, for midinfrared driving fields. We address theoretically and numerically the possibility of observing ellipticity in highorder harmonic generation hhg from aligned molecules driven by linearly polarized fieldsa subject of controversy in the recent literature with significant implications. Its possible implications for numerical calculations of the high harmonic signal are discussed. High harmonic generation in bulk solids is a new research topic while the atomic hhg has been studied for about 30 years now. Sapphire lasers as well as many other wavelength ranges, covering second harmonic generation shg, third harmonic generation thg and fourth harmonic generation fhg. Corkum, theory of high harmonic generation by lowfrequency laser fields. The harmonic generation topology adopts an oscillator operating at a subharmonic of the rf carrier frequency i. We study the highharmonic spectrum emitted by a singlelayer graphene, irradiated by an ultrashort intense infrared laser pulse. Theoretical description of highorder harmonic generation. High order harmonic generation in rare gases unt digital.
We demonstrate highharmonic spectroscopy in manyelectron molecules using timedependent densityfunctional theory. Using timedependent density functional theory, highharmonic generation hhg is studied in onedimensional structures of sizes from a single nucleus up to hundreds of nuclei. On the quantumoptical nature of high harmonic generation. An overview the nonlinear interaction of an ultrashort laser pulse with matter generates coherent radiation at multiples harmonics of the laser frequency. Sources operating with long interaction lengths produce soft xrays with a high degree of spatial coherence, allowing focusing to high intensity. Highharmonic generation by a laserdriven solid slab is simulated using timedependent density functional theory. Multiple harmonic plateaus up to very high harmonic orders are observed already.
Specifically, the understanding of the hhg process in rare gases has played a. Perturbation theory study of highharmonic generation osa. The paper semiglobal approach for propagation of the timedependent schr odinger. Theoretical description of highorder harmonic generation in solids a. We have computed nonlinear susceptibilities for harmonic generation in hydrogenic ions, as described by lowestand nextlowestorder perturbation theory. Quantitative rescattering theory for highorder harmonic. High harmonic generation physics 208a presentation october 11, 2004 tom allison uc berkeley. However, free electrons in the partially ionized gas medium are known to prevent phase matching and limit upconversion to lowenergy harmonics only. First, we describe an analytical estimate using the hghg parameters in the duvfel project at bnl as an example. Therefore it would be desirable to compare the generation process in solid and gas phase same atomic constituents. We present a simple, analytic, and fully quantum theory of high harmonic generation by lowfrequency laser fields. A very intense laser pulse i approximately10sup 10sup 14 wcmsup 2 is focused into a dense approximately10sup l7 particlescmsup 3 atomic.
By driving the highorder harmonic generation process using longerwavelength midinfrared light, we show that, in theory, fully phasematched frequency upconversion can extend into the hard xray region of the spectrum. The response of a single atom to the drive laser eld, the microscopic aspect, is described semiclassically in section 1. Intesities as high as 1014 wcm2 have been observed. A highgain harmonicgeneration freeelectron laser is demonstrated. Origin and implication of ellipticity in high harmonic. At these intensities we can start to look for nonlinear optics in the xray regime. We show the emergence of the typical nonperturbative spectral features, harmonic plateau and cutoff, for midinfrared driving fields, at fluences below the damage threshold.
It is commonly assumed that a complete theory for selection rules in optical nonlinear harmonic generation was developed previously. Hhg is most easily understood using the threestep model 2, 3, 4. Presented next are selected experimental results related to optimizing the. Devereaux1,2 1stanford institute for materials and energy science, slac national accelerator laboratory, menlo park, ca 94025, usa 2geballe laboratory for advanced materials, stanford university, stanford, ca 94305, usa. High harmonic generation an overview sciencedirect topics. We illustrate the high oam harmonics generation in a plasma using several examples including the. We have demonstrated experimentally and theoretically an unconventional phasematching scheme.
High harmonic generation hhg of an intense laser pulse is a highly nonlinear optical phenomenon that provides the only proven source of tabletop attosecond pulses, and. Observation of highorder harmonics from bulk crystals was, however, reported much more recently, in 2010. Ishikawa photon science center, graduate school of engineering, university of tokyo japan 1. Highharmonic generation hhg is a signature optical phenomenon of strongly driven, nonlinear optical systems. High order harmonic generation in rare gases thesis. Recollision dynamics analysis of highorder harmonic. The phenomenon of hhg in solids is not yet well understood and has triggered a wide range of theoretical studies. Fully quantum treatment explicitly presents the high harmonic generation as a threestage process. Fully quantum treatment explicitly presents the high harmonic generation as a threestep process. Theory of highharmonic generation in solids iopscience. In this picture the process is treated in two steps. Theory of high harmonic generation by low frequency laser fields. The theory recovers the classical interpretation of kulander et al.
Quantum theory of a high harmonic generation as a three. Highharmonic generation hhg in bulk crystals exposed to intense midinfrared lasers with photon energies below the bandgap is investigated theoretically. High harmonic generation hhg is a technique for producing spatially and. Our approach uses a laserseeded freeelectron laser to produce amplified, longitudinally coherent, fourier transformlimited output at a harmonic of the seed laser. Observation of a train of attosecond pulses from high. We reproduce many observed characteristics of high harmonic generation experiments in solids including the formation of only odd harmonics in inversionsymmetric materials, and the nonlinear formation of high harmonics with increasing field. However, it can be difficult to compare theory and experiment, since the dynamics under investigation are often very sensitive to the laser intensity, which. The quantitative rescattering theory qrs for highorder harmonic generation hhg by intense laser pulses is presented. Quantumorbit theory of highorder harmonic generation hhg by bicircular laser field is presented.
The harmonixx product line is a series of frequency converters for ultrafast lasers. Theory of highorder harmonic generation from molecules by intense laser pulses 2 highorder harmonic generation hhg is one of the most studied nonlinear phenomena in intense lasermatter interaction 1. A microscopic theory is presented to describe highharmonic generation in solids with the semiconductorbloch equations. Theory of highharmonic generation chapter 1 theory of highharmonic generation in considering the generation of high harmonic radiation with high intensities, two main aspects can be distinguished. Theory of highorder harmonic generation in relativistic. Harmonic generation is a nonlinear optical proc ess in which the frequency of laser light is. Harmonic generation is a nonlinear optical process in which the frequency of laser light is converted into its integer multiples. High harmonic generation hhg is an extremely nonlinear effect, where a medium is driven by a strong laser field, generating coherent broadband radiation with photon energies ranging up to the xray and pulse durations reaching attosecond timescales. High harmonic generation hhg is a nonlinear process during which a target is illuminated by. Hhg is a strong laserfieldinduced process in which the energy absorbed from the laser field is emitted in the form of a highenergy photon.
They have a great potential to overcome the limitations of current laser sources and to extend attosecond pulses towards the xray regime. Citeseerx quantum theory of high harmonic generation via. Harmonic generation is a nonlinear optical process in which photons of intense incoming laser radiation interact with a nonlinear material and radiation with corresponding harmonics frequencies is generated. High harmonic spectroscopy utilizes the extremely nonlinear optical process of highorder harmonic generation hhg to measure complex attosecondscale dynamics within the emitting atom or molecule subject to a strong laser field. Harmonic generation is a nonlinear optical process in which the frequency of. The appearance of even harmonic orders is shown to require at least three electronic bands and a mutual interband coupling between them. This typically occurs at optical intensities of the order of 1014 wcm 2 or higher. Highharmonic generation hhg of femtosecond lasers produces unique shortwavelength light pulses with femtosecond to attosecond duration. C r mcdonald, g vampa1, g orlando1, p b corkum1 and t brabec1.
This phenomenon is known as high order harmonic generation hhg 1. We demonstrate from ab initio simulations that it is possible to generate highorder. Phase matching of high harmonic generation in the soft and. Subsequently iii stimulated or laser assisted recombination brings the electron back into the initial state. High harmonic generation from surface states of solids arxiv. Osa extended phase matching of high harmonic generation.
According to the qrs, hhg spectra can be expressed as a product of a returning electron wave packet and the photorecombination differential cross section of the laserfree continuum electron back to the initial bound state. Generation of high harmonics by the interaction of intense laser fields with periodic crystal structures is investigated theoretically. There are two known kinds of sources with the potential to produce coherent radiation over such bandwidths. Introduction the generation of high order harmonics hhg of intense. Rp photonics encyclopedia high harmonic generation, hhg. Under such conditions, the sample will emit the high harmonics of the generation beam above the fifth harmonics. Theory of high harmonic generation by low frequency laser. Abstract we study the highharmonic spectrum emitted by a singlelayer graphene, irradiated by an ultrashort intense infrared laser pulse. We show with theory and particleincell simulations that the orders of the oam harmonics can be tuned according to a selection rule that depends on the initial oam of the interacting waves. The papers optimal control theory of harmonic generation and optimization of high harmonic generation by optimal control theoryclimbing a mountain in extreme conditions represent the work of ido schaefer under the supervision of prof. We present theoretical aspects of highharmonic generation hhg in this chapter. Highorder harmonic generation due to the interaction of a short ultrarelativistic laser pulse with overdense plasma is studied analytically and numerically.
We discuss the theory of the high gain harmonic generation hghg. Harmonic generation an overview sciencedirect topics. Quantumorbit analysis of highorder harmonic generation. We present a simple, analytic, and fully quantum theory of highharmonic generation by lowfrequency laser fields. We find that the harmonic spectra are fairly robust against elastic and inelastic scattering. On the basis of the ultrarelativistic similarity theory we show that the highorder harmonic spectrum is universal, i. Introduction in traditional electromagnetism textbooks, polarization in the dielectric material is linearly proportional to the applied electric field. Obtaining efficiently similar photon energy from solidstate systems could lead, for instance, to more compact extreme ultraviolet and soft xray sources. Highgain harmonicgeneration freeelectron laser science. A nonperturbative floquetbloch theory of the interacting system crystal plus laser field is developed and applied to obtain the fieldmodified band structure of the system. Atomiclike highharmonic generation from twodimensional. Chapter high harmonic generation ultrafast optics and xrays.
Phase matching and coherence of highorder harmonic. Harmonics of very high orders are generated from atoms and molecules exposed to intense usually nearinfrared laser fields. Theory of highorder harmonic generation from molecules by. We compared high harmonic generation in the solid and gas phases of argon and krypton. Rather than by the perturbation theory found in standard textbooks of.
Theory of highharmonic generation by lowfrequency laser. These harmonics are characterized by a rapid, pertubative drop at low orders, followed by a broad plateau extending to photon energies of 150 ev in the lighter, rare gas atoms. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet xuv. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. Laserdriven highharmonic generation provides the only demonstrated route to generating stable, tabletop attosecond xray pulses but has low flux compared to other xray technologies. The generation of highorder harmonics from atomic and molecular gases enables the production of highenergy photons and ultrashort isolated pulses. We show that a weak attosecondpulsetrain ionization seed that is properly synchronized with the strong driving midinfrared laser field can produce experimentally relevant highharmonic generation hhg signals, from which we extract both the spectral amplitude and the target. Second harmonic generation in nonlinear optical crystal.
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