Showing papers on "High harmonic generation published in 1993"
TL;DR: During strong-field multiphoton ionization, a wave packet is formed each time the laser field passes its maximum value, and one important parameter which determines the strength of these effects is the rate at which the wave packet spreads in the direction perpendicular to the laser electric field.
Abstract: During strong-field multiphoton ionization, a wave packet is formed each time the laser field passes its maximum value Within the first laser period after ionization there is a significant probability that the electron will return to the vicinity of the ion with very high kinetic energy High-harmonic generation, multiphoton two-electron ejection, and very high energy above-threshold-ionization electrons are all conssequences of this electron-ion interaction One important parameter which determines the strength of these effects is the rate at which the wave packet spreads in the direction perpendicular to the laser electric field; another is the polarization of the laser It will be essential for experimentalists to be aware of these crucial parameters in future experiments
5,334 citations
TL;DR: This work presents high sensitivity electron energy spectra for xenon in a strong 50 ps, 1.053 [mu]m laser field and calculates using the single active electron approximation show excellent agreement with the observed electron distributions.
Abstract: We present high sensitivity electron energy spectra for xenon in a strong 50 ps, 1.053 \ensuremath{\mu}m laser field. The above threshold ionization distribution is smoothly decreasing over the entire kinetic energy range (0--30 eV), with no abrupt changes in the slope. This is in direct contrast to the sharp cutoff observed in xenon optical harmonic generation spectra. Calculations using the single active electron approximation show excellent agreement with the observed electron distributions. These results directly address the unresolved relationship between the electron and photon emission from an atom in an intense field.
1,020 citations
TL;DR: Results of harmonic generation using a 1-ps 1015-W/cm2 Nd-glass laser are presented and different ways of optimizing the number of photons by defocusing the laser beam or increasing the density are discussed.
Abstract: We present experimental results of harmonic generation using a 1-ps ${10}^{15\mathrm{\ensuremath{-}}}$W/${\mathrm{cm}}^{2}$ Nd-glass laser. We see up to the 29th harmonic in Xe, 57th in Ar, and at least up to the 135th harmonic in Ne (160 eV), being then limited by our monochromator's resolution. The conversion efficiencies in Xe, Ar, Ne, and He are compared and different ways of optimizing the number of photons by defocusing the laser beam or increasing the density are discussed.
581 citations
TL;DR: Blueshifting of the laser and harmonic wavelengths indicates a small degree of ionizatoin until the threshold for highest harmonics (>91 st) is reacthed, compared to recent calculations of the strong-field atomic response.
Abstract: Neon gas excited by 800-nm laser pulses (15 mJ, 125 fsec) at an intensity near ${10}^{15}$ W/${\mathrm{cm}}^{2}$ generates harmonics up to 109th order. The appearance of successively higher harmonics as the laser intensity is increased is compared to recent calculations of the strong-field atomic response. Blueshifting of the laser and harmonic wavelengths indicates a small degree of ionization until the threshold for the highest harmonic (g91st) is reached.
514 citations
TL;DR: In this paper, the screw dislocations of different charges produced by diffraction on the computer-synthesized grating or by nonlinear processes of second- harmonic generation are experimentally studied and discussed.
367 citations
01 Jan 1993
TL;DR: In this paper, the authors present a model for double ionization in femtosecond laser fields, which is based on the Lagmago-Kamta model and is shown to have a minimal correlation approach.
Abstract: Preface. SILAP 2000: an overview. Part I: Double Ionization of Complex Atoms. Energy distribution of two-electron ionization of helium in an intense field R. Lafon, et al. Double ionization in strong fields: ion momenta and correlated electron momenta A. Staudte, et al. Mechanism of the non sequential double ionization of helium D.G. Lappas, et al. Electron momentum distributions for double ionization in the strong field limit S.P. Goreslavski, S.V. Popruzhenko. S-matrix theory of 'recoil-ion' momentum distribution for double ionization in femtosecond laser fields F.H.M. Faisal, A. Becker. Non-sequential double ionization: a minimal correlation approach R. Kopold, W. Becker. Non-sequential double ionization of atoms in strong fields K. Sacha, B. Eckhardt. Double-electron ionization of two-electron system in strong laser field D.V. Tikhonova. Calculation of double ionization of helium H.G. Muller. The two-electron response in laser driven helium L.R. Moore, et al. The helium atom in strong and short laser pulses: multielectron H. Bachau, R. Hasbani. Dynamics of a two-electron system driven by an ultrashort and intense laser pulse B. Piraux, G. Lagmago-Kamta. Angular distributions for double ionization by an ultrashort, intense laser pulse: the case of Li- G. Lagmago-Kamta, A.F. Starace. Two-and-three electron atoms in strong laser fields P. Lambropoulos, et al. Part II: Ionization and Dissociation of Molecules. Tunnelling ionization and the Franck-Condon principle J.H. Posthumus, et al. Dissociative ionization of few-electron molecules in intense laser fields D. Dundas, et al. One-photon breakup of H+2 in a strong DC field Z. Mulyukov, R. Shakeshaft. Part III: Interaction of Clusters with Very Intense Femtosecond Laser Pulses. Nuclear fusion in gases of deuterium clusters and hot electron generation in droplet sprays under irradiation with an intense femtosecond laser T. Ditmire, et al. The absorption of energy by large atomic clusters from superintense laser pulses V.P. Krainov, M.B. Smirnov. Part IV: Production of Very Intense Femtosecond Laser Pulses. A semi-classical model for high-harmonic generation D.B. Milosevic. Beyond the simple maris model for high harmonic generation M. Brewezyk, K. Rzazewski. Anisotropy induced polarization effects in harmonic generation by an absorptive medium B. Borca, et al. About a new method of high harmonic amplification E.A. Nersesov, et al. X-ray generation via stimulated recombination of electrons and Bohr's correspondence principle A. Jaron, et al. Part V: Stabilization and Relativistic Effects in Super Strong Fields. Interference stabilization: LAMBDA- and V-schemes, dynamics of ionization, initial coherent population of Rydberg levels and quantum phase control of the ionization yield M.V. Fedorov, N.P. Poluektov. Computer experiments on atomic stabilization in a strong laser field A.M. Popov, et al. Quasistationary stabilization of the decay of a weakly-bound level and its breakdown in a strong laser field N.L. Manakov, et al. The strong field limit of atomic stabilization in ultrashort pulses M. Dorr, et al. 3-D numerical calculations of laser atom interactions -- subrelativistic and weakly relativistic regime A. Scrinzi, et al. Momentum space description of hydrogen atom interacting with a low frequency strong laser field A. de Bohan, et al. Relativistic effects in the atomic res
241 citations
TL;DR: The dependence of the high-order harmonic cutoff with the laser intensity in neon and argon is found to be lower than that predicted in single-atom theories.
Abstract: We present experimental studies of high-order harmonic generation in the rare gases performed with a short-pulse titanium sapphire laser operating at 794 nm in the 10(14)-10(15) W/cm2 range. The harmonic yields generated in neon and in argon are studied for all orders as a function of the laser intensity. They vary first rather steeply, in the cutoff region, then much more slowly in the plateau region, and, finally, they saturate when the medium gets ionized. The dependence of the high-order harmonic cutoff with the laser intensity in neon and argon is found to be lower than that predicted in single-atom theories. We observe high-order harmonics in argon and xenon (up to the 65th and 45th, respectively) at 10(15) W/cm2, which we attribute to harmonic generation from ions. We also show how the harmonic and fundamental spectra get blueshifted when the medium becomes ionized. (Less)
223 citations
TL;DR: Results of experiments testing the influence of elliptical polarization on the production of high-order harmonics are presented and some of these data are compared with the predictions of lowest-order perturbation theory.
Abstract: We present results of experiments testing the influence of elliptical polarization on the production of high-order harmonics. Experiments were conducted both with a 600-nm, 1-psec dye laser and with an 825-nm, 140-fsec Cr:${\mathrm{LiSAF}}_{6}$ (Cr:LiSAF) laser system, over a wide range of intensities and target gases (xenon, argon, and neon), using a detection system with a dynamical range of more than three orders of magnitude. The decrease of the harmonic strength with the ellipticity of the pump beam is rather slow for the low-order harmonics, and becomes much steeper for the high-order harmonics. We compare some of these data with the predictions of lowest-order perturbation theory.
191 citations
TL;DR: It will be shown that symmetric molecular ions should in general produce more efficient harmonic generation than atoms, due to the presence of molecular charge-resonance (CR) states, which have no atomic analogues.
Abstract: The harmonic-generation (HG) spectra of the ${\mathrm{H}}_{2}^{+}$ molecular ion generated by short, intense, linearly polarized laser pulses are calculated nonperturbatively by solving a three-dimensional time-dependent Schr\"odinger equation. It is found that while ${\mathrm{H}}_{2}^{+}$ radiates in a similar manner to an atomic system such as H or ${\mathrm{He}}^{+}$ at high frequencies, the molecular ion in high-vibrational states or at large internuclear distances behaves analogously to a two-level system in an intense, relatively-long-wavelength laser field. It will be shown that symmetric molecular ions should in general produce more efficient harmonic generation than atoms, due to the presence of molecular charge-resonance (CR) states, which have no atomic analogues. Two HG plateaus, one molecular due to CR transitions and one atomiclike, appear for a long-wavelength excitation. Each plateau has its own maximum harmonic-number cutoff, which can be rationalized in terms of the maximum energy which can be acquired by an electron in the laser field.
183 citations
TL;DR: In this paper, the harmonic generation cutoff as a function of the laser intensity in neon was determined using an intense, short-pulse Ti:sapphire laser, and the experimental cutoff was lower than that obtained in single-atom calculations.
Abstract: We have experimentally determined the harmonic-generation cutoff as a function of the laser intensity in neon using an intense, short-pulse Ti:sapphire laser. The experimental cutoff is lower than that obtained in single-atom calculations. Using a simple quantum-mechanical approach to harmonic generation valid at high intensity, we show that the difference is due to the effect of propagation.
175 citations
TL;DR: In this article, a nonlinear cold fluid model is formulated and used to analyze relativistic harmonic generation, and the plasma density response is included self-consistently and is shown to significantly reduce the current driving the harmonic radiation.
Abstract: A linearly polarized, ultraintense laser field induces transverse plasma currents which are highly relativistic and nonlinear, resulting in the generation of coherent harmonic radiation in the forward direction (i.e., copropagating with the incident laser field). A nonlinear cold fluid model, valid for ultrahigh intensities, is formulated and used to analyze relativistic harmonic generation. The plasma density response is included self-consistently and is shown to significantly reduce the current driving the harmonic radiation. Phase detuning severely limits the growth of the harmonic radiation. The effects of diffraction are considered in the mildly relativistic limit. No third-harmonic signal emerges from a uniform plasma of near-infinite extent. A finite third-harmonic signal requires the use of a semi-infinite or finite slab plasma. For an initially uniform plasma, no second-harmonic radiation is generated. Generation of even harmonics requires transverse gradients in the initial plasma density profile. >
TL;DR: In this article, high-order harmonic spectra which are flat over 20 eV were generated using intense laser pulses, and this bandwidth corresponds to temporal pulses on the order of ∼ 5 × 10-17 s, and thereby motivated a search for a new regime of short-pulse generation.
TL;DR: By controlling the relative polarization of the two fields, this work can control the mixing efficiency and produce coherent extreme ultraviolet (XUV) radiation polarized orthogonally to the strong driving field.
Abstract: Production of sum-frequency radiation and even'' harmonics from the mixed 1[omega] (1053 nm) and 2[omega] (527 nm) field is observed and compared to measurements of the relative conversion efficiency of the independent fields. By controlling the relative polarization of the two fields, we can control the mixing efficiency and produce coherent extreme ultraviolet (XUV) radiation polarized orthogonally to the strong driving field. Extension to produce XUV radiation of arbitrary polarization is discussed.
TL;DR: In this article, a general nonlinear optical (NLO) interaction, one or two laser beams are directed into a suitable material in which an output beam of the desired frequency is generated.
Abstract: Although the wen-known properties of laser radiation are desirable for a wide variety of applications, only limited segments of the optical spectrum can be directly produced by practical, high-performance laser systems. Through nonlinear optics, laser radiation can be converted from one frequency to another, significantly increasing the range of applications that can be addressed. In a general nonlinear optical (NLO) interaction, one or two laser beams are directed into a suitable material in which an output beam of the desired frequency is generated. NLO interactions include harmonic generation, sum and difference frequency generation, and parametric oscillation, the latter generating a pair of tunable output beams at lower frequency from a single input beam. The physics of an NLO interaction impose severe demands on potential NLO materials. In general, a material must be optically transparent to the incident and generated radiation, possess a quadratic susceptibility of
TL;DR: This work has obtained superior results for the high-order harmonic generation by using ions compared to using neutral rare gases, and has demonstrated the advantages of using ions as nonlinear media to generate extreme ultraviolet radiation.
Abstract: We have investigated the high-order harmonic generation of a subpicosecond KrF laser (248 nm) using nine ionic species in laser-produced plasmas. The highest order of the 21 st harmonic (11.8 nm) has been observed in a lead plasma. The maximum observed harmonic orders in various ions and neutral rare gases are found to be proportional to the ionization potentials of these species. We have obtained superior results for the high-order harmonic generation by using ions compared to using neutral rare gases, and have demonstrated the advantages of using ions as nonlinear media to generate extreme ultraviolet radiation
TL;DR: It is studied how a strong semi-infinite laser pulse affects an electron confined by a potential whose parameters mimic an AlAs-GaAs-AlAs double quantum well.
Abstract: We study how a strong semi-infinite laser pulse affects an electron confined by a potential whose parameters mimic an AlAs-GaAs-AlAs double quantum well. Interesting phenomena take place for special values of laser frequency, intensity, and pulse rise time. There are values of these parameters for which the dipole moment of the system has a low-frequency Fourier component whose magnitude is higher than that of the fundamental (i.e., the component having the same frequency as the laser). For other parameter values, the low-frequency component disappears and the Fourier transform of the dipole moment has a large zero-frequency component and intense even-harmonic components (i.e., with frequency 2n\ensuremath{\omega}, where n is an integer and \ensuremath{\omega} is the laser frequency). The presence of the even harmonics is intriguing: The system has inversion symmetry and even harmonics are forbidden by symmetry rules valid to all orders in perturbation theory. Finally, a laser pulse with well-chosen parameters can drive an electron that was initially in a delocalized eigenstate, to a state in which it is almost completely localized in one well. These processes are systematically investigated by numerical calculations and are rationalized with the help of a simple model which predicts the qualitative behavior observed numerically. The model suggests that these phenomena occur at those values of the parameters for which two Floquet states having different generalized parities become degenerate or nearly degenerate. This condition is rather general and we see no reason why it will not be fulfilled in systems other than double quantum wells (e.g., atoms or molecules).
TL;DR: Experimental results of harmonic generation at 1064 nm using a 36-ps neodymium-doped yttrium aluminum garnet laser tightly focused in a gas jet of xenon bring information about how the high harmonics are phase matched in the medium and also about the single-atom dynamics of the process.
Abstract: We present experimental results of harmonic generation at 1064 nm using a 36-ps neodymium-doped yttrium aluminum garnet laser tightly focused in a gas jet of xenon. The harmonic yields are studied as a function of the position of the focus in the jet at several laser intensities and as a function of intensity at several focus positions. These results bring information about how the high harmonics are phase matched in the medium and also about the single-atom dynamics of the process. The harmonic yields as a function of the position of the focus in the jet exhibit regular oscillations that are due to the interference effects inherent to the generation of harmonics in the nonlinear medium. The intensity dependences present structures that we attribute to single-atom resonance effects.
TL;DR: In this article, gain-guided vertical-cavity surface-emitting laser (VCSEL) with a modulation bandwidth of 14 GHz is described, and it is shown that the relative intensity of the second-harmonic response decreases rapidly at higher drive currents.
Abstract: Planar, gain-guided vertical-cavity surface-emitting lasers (VCSELs) with a modulation bandwidth of 14 GHz are described. This bandwidth is reached at a drive current of only 8 mA. The intrinsic bandwidth of these devices is estimated to be greater than 50 GHz. Nonlinear light-current characteristics of these lasers may lead to a high level of nonlinear harmonic distortion of the high-frequency output. It is shown that the relative intensity of the second-harmonic response decreases rapidly at higher drive currents, in agreement with a phenomenological model based on the DC characteristics of the laser. >
TL;DR: In this article, the relativistic harmonic content of large-amplitude electromagnetic waves propagating in underdense plasmas is investigated and the steady-state harmonic content for nonlinear linearly polarized waves is calculated.
Abstract: The relativistic harmonic content of large-amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady-state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense (w/sub p//w/sub 0/) >
TL;DR: In this article, the results of a harmonic generation experiment in a simple gas (hydrogen) using 1-ps, 1- mu m laser pulses with a range of intensities extending from below to far above the laser ionization saturation threshold were reported.
Abstract: Reported are the results of a harmonic generation experiment in a simple gas (hydrogen) using 1-ps, 1- mu m laser pulses with a range of intensities extending from below to far above the laser ionization saturation threshold. The scaling with intensity above saturation of the third harmonic generated by a single laser-pulse in a filled gas cell is observed not to fit with a simple model that takes into consideration volume ionization effects alone. In another experiment, a pump-probe type, an upper limit on the conversion efficiency of third-harmonic generation in a preformed plasma is determined. It is found to be in agreement with the efficiency predicted by a relativistic harmonic generation theory. >
TL;DR: In this paper, it was shown that even for very high fields for which perturbation theory breaks down the even peaks in harmonic generation (HG) spectra are suppressed for a model Hamiltonian which is symmetric with respect to the reflection of coordinate space combined with translation of time by half period of the field.
Abstract: The present work shows that even for very high fields for which perturbation theory breaks down the even peaks in harmonic generation (HG) spectra are suppressed for a model Hamiltonian which is symmetric with respect to the reflection of coordinate space combined with translation of time by half period of the field. The proof presented utilizes the combination of Floquet theory and complex coordinate method. Numerical examples are included, which illustrate that even harmonics appear only when the above mentioned symmetry property of the Hamiltonian is broken.
TL;DR: In this paper, a method of generating odd harmonics from an intense laser incident upon a sharp vacuum-overdense plasma interface is presented, which results in efficient odd harmonic generation.
Abstract: A method of generating odd harmonics from an intense laser incident upon a sharp vacuum-overdense plasma interface is presented. One- and two-dimensional simulations are used to investigate the interaction of ultra-intense laser pulses with a sharp vacuum-plasma interface. With an intensity greater than 10/sup 18/ W/cm/sup 2/, these pulses have a pressure greater than 10/sup 3/ Mbar creating large density oscillations and relativistic electron velocities at the surface. This results in efficient odd harmonic generation. The author present is a physical model for this harmonic generation mechanism, along with some scaling of the power in the third harmonic. This is compared with relativistic particle-in-cell simulations that include mobile and immobile ions, as well as a variety of upper shelf densities. A discussion on how ion profile modifications influence the harmonics is also presented. >
01 Jan 1993
TL;DR: In this article, a sub-picosecond KrF excimer laser focused to a peak intensity in the region of 1014 W/cm2 (adiabaticity parameter in the range 8 < γ < 10).
Abstract: Plasma-induced spectral blue shifting in rare gases has been investigated with a subpicosecond KrF excimer laser focused to a peak intensity in the region of 1014 W/cm2 (adiabaticity parameter in the range 8 < γ < 10). The quiver energy of a free electron under these conditions is sufficiently small to ensure that ionization occurs solely by optical-field-induced processes. Blue shifts as large as 2 nm have been observed, and the blue-shifted spectrum shows an interferencelike oscillatory structure. Experimental results are compared with numerical simulations to show that the blue-shifted spectra are the result of plasma-induced self-phase modulation and can be modeled qualitatively by assuming tunneling ionization and plane-wave pulse propagation. The structure in the spectrum is closely related to that observed in earlier experiments on self-phase modulation in quite different systems.
TL;DR: High conversion efficiency can be achieved with nonlinear crystals of relatively low nonlinear coefficient for cw harmonic generation for the situation in which both fundamental and harmonic waves are resonant.
Abstract: Conversion efficiency for cw harmonic generation is calculated for the situation in which both fundamental and harmonic waves are resonant Compared with the situation of a singly resonant cavity at the fundamental, the doubly resonant geometry can lead to an increase of the effective nonlinear coefficient High conversion efficiency can thus be achieved with nonlinear crystals of relatively low nonlinear coefficient and with modest pump power for the fundamental input,
TL;DR: A fluid jet, enclosed in a vacuum chamber, is described that allows this technique of self-induced plasma shuttering to be used at high repetition rates and has excellent stability and a fast recovery time.
Abstract: The technique of self-induced plasma shuttering can be used to suppress prepulse energy from an ultrashort pulse If a femtosecond pulse is incident upon a transparent target, the leading edge passes through while the peak reflects owing to ionization breakdown at the surface We describe a fluid jet, enclosed in a vacuum chamber, that allows this technique to be used at high repetition rates The jet has excellent stability and a fast (~500 micros) recovery time At normal incidence, we demonstrate a reflection efficiency of 70% with a prepulse-to-main-pulse energy suppression ratio of >10, while at Brewster incidence we measure a reflection efficiency of 38% with a suppression ratio of nearly 400
TL;DR: In this paper, a time-dependent complex coordinate Flcquet method was developed for the study of non-linear phenomena for atoms (or small molecules) in smng laser fields and a simple timeindependent expression for the probability to obtain high harmonics was derived.
Abstract: The time-dependent complex coordinate Flcquet method was developed for the study of non-linear phenomena ohserved for atoms (or small molecules) in smng laser fields. On the basis of this method and by laking use of the special definition of the imr product for non-Hennitian operators a simple time-independent expression for the probability to obtain high harmonics was derived. This novel formula is used to investigate the phenomenon of harmonic generation for a model potential representing a single electmn in the presence of an intense laser field. The parameters of the one-dimensional potential are chosen to fit hvo electronic states of the xenon atom. Numerical results indicate the existence of a correlation between harmonic generation and other non-linear effects occurring in this system such as avoided crossings of Floquet resonance stales as the field strength amplitude is varied. The harmonic generation spectra obtained by the model presented here qualitatively agree with experimenral mulls on rare gas atoms placed in strong laser fields. For svong laser fields (> IO'' W cm-l). very- high-order harmonic generation is obsewed in numerical studies using both complex Flcquet analysis and a simulation by a pseudo-spectral grid solution to the time-dependent Schradinger equation with a =-periodic Hamiltonian. For eriremely suong laser fields, numerical results predict that the most intense frequency emiued by an atom interacting with a monwhmmatic laser field might not be the irradiating laser frequency, but rather a high multiple of it.
TL;DR: In this article, a microwave lifetime measurement method has been used at a frequency of 2.8 GHz in which the reflected microwave power is proportional to the average excess concentration over the whole thickness of the sample.
Abstract: One of the main problems in measuring the lifetime is how to distinguish the bulk and surface contributions to the total recombination process. The lifetime measured by any method is not only affected by bulk but also by surface recombination processes. Various methods have been suggested, such as immersing the sample in the HF solution, or measuring the fundamental lifetime on wafers which are identical except for the thickness. A microwave lifetime measurement method has been used at a frequency of 2.8 GHz in which the reflected microwave power is proportional to the average excess concentration over the whole thickness of the sample. The advantage of the harmonic generation method and analysis of the amplitude and phase of the reflected microwaves, is that it not only is highly accurate, but also gives the bulk lifetime and the surface recombination velocities at the front and back surfaces separately.
TL;DR: The ring-shaped beam is shown to provide self-organized phase matching for a wide range of refractive index variation, which may automatically compensate the spatially nonuniform phase mismatch created by the optical Kerr effect.
Abstract: A new type of phase matching based on the ring-shaped pump beam for efficient harmonic generation is observed. The ring-shaped beam is shown to provide self-organized phase matching for a wide range of refractive index variation, which may automatically compensate the spatially nonuniform phase mismatch created by the optical Kerr effect. Self-phase-matching is expected to be very efficient for frequency tripling of broadband and/or ultrashort pulses, as well as for high order harmonic generation. The high conversion efficiency ∼1.5% of 1.06 μm radiation tripling in a pure Rb vapor for a very short interaction length ∼4 cm is obtained, when a disk-shaped beam has been replaced by a ring-shaped beam
TL;DR: In this article, a phase-matching scheme based on a resonant density modulation was proposed to overcome the saturation of the third-harmonic wave amplitude, and the limitations of this scheme were analyzed.
Abstract: Relativistic third-harmonic generation in a plasma is investigated. The growth of a third-harmonic wave is limited by the difference between the phase velocity of the pump and driven waves. This phase velocity mismatch results in a third-harmonic amplitude saturation and oscillation. In order to overcome this saturation, a phase-matching scheme based on a resonant density modulation is described. The limitations of this scheme are analyzed. >