scispace - formally typeset
Search or ask a question

Showing papers on "Chirp published in 2004"


Journal ArticleDOI
TL;DR: This work compensates for the angular dispersion and the first-order chirp of the highly stable UV pulses with a second prism sequence and fully characterize the temporal pulse shape with zero-additional-phase spectral phase interferometry for direct electric-field reconstruction (ZAP-SPIDER).
Abstract: Tunable UV pulses shorter than 10 fs are generated by achromatic frequency doubling of a noncollinear optical parametric amplifier. With a suitable two-prism sequence we achieve first- and second-order achromatic phase matching and increase the natural bandwidth of the nonlinear crystal by a factor of 80. Extremely broad UV spectra with a Fourier limit of 2.9 fs are generated in a 360-microm-thick beta-barium borate crystal at a conversion efficiency of 20%. We compensate for the angular dispersion and the first-order chirp of the highly stable UV pulses with a second prism sequence and fully characterize the temporal pulse shape with zero-additional-phase spectral phase interferometry for direct electric-field reconstruction (ZAP-SPIDER). Pulses as short as 7 fs are generated by controlling the higher-order chirp with a deformable mirror.

172 citations


Journal ArticleDOI
TL;DR: It is proved that the combination of spatial and temporal chirp also produces pulse-front tilt in ultrashort laser pulses, and this is verified experimentally using a GRENOUILLE.
Abstract: Pulse-front tilt in an ultrashort laser pulse is generally considered to be a direct consequence of, and equivalent to, angular dispersion. We show, however, that, while this is true for certain types of pulse fields, simultaneous temporal chirp and spatial chirp also yield pulse-front tilt, even in the absence of angular dispersion. We verify this effect experimentally using GRENOUILLE.

150 citations


Proceedings Article
16 May 2004
TL;DR: In this article, the combination of spatial and temporal chirp also produces pulse-front tilt, and the authors verify this experimentally using a GRENOUILLE and show that it is equivalent to angular dispersion in ultrashort laser pulses.
Abstract: Pulse-front tilt in ultrashort laser pulses is usually considered equivalent to angular dispersion. We prove, however, that the combination of spatial and temporal chirp also produces pulse-front tilt. We verify this experimentally using a GRENOUILLE.

125 citations


Journal ArticleDOI
Kyung Taec Kim1, Chul Min Kim1, Moon-Gu Baik, G. Umesh1, Chang Hee Nam1 
TL;DR: In this paper, a method for obtaining a single sub-50-attosecond pulse using harmonic radiation is proposed, where the chirped structure of the harmonic radiation imposes a limit on the minimum achievable pulse duration, but its positive chirp can be compensated by the negative group delay dispersion of an appropriately selected x-ray filter material, used also for the spectral selection.
Abstract: A method for obtaining a single sub-50-attosecond pulse using harmonic radiation is proposed. For the generation of broad harmonic radiation during a single half-optical cycle, atoms are driven by a femtosecond laser pulse with intensity above the saturation intensity for optical field ionization and hence experience a large nonadiabatic increase of the laser electric field between optical cycles. Although the chirped structure of the harmonic radiation imposes a limit on the minimum achievable pulse duration, we demonstrate that its positive chirp can be compensated by the negative group delay dispersion of an appropriately selected x-ray filter material, used also for the spectral selection, resulting in a single attosecond pulse with a duration less than 50 as.

110 citations


Journal ArticleDOI
TL;DR: Coupling femtosecond light pulses from an all-fiber Er:laser system into a dispersion-shifted and highly non-linear fiber generates output spectra exhibiting two broadband and mutually coherent maxima.
Abstract: Coupling femtosecond light pulses from an all-fiber Er:laser system into a dispersion-shifted and highly non-linear fiber, we generate output spectra exhibiting two broadband and mutually coherent maxima. Depending on the chirp of the input pulse, the spectral separation is easily tunable over a wide range up to values exceeding 100 THz. In this way, the source provides access to an ultrabroadband wavelength interval from 1130 to 1950 nm. Because of soliton effects, the long-wave component exhibits a transform-limited pulse width of 40 fs directly after the nonlinear element. The high-frequency part propagating in the dispersive regime is recompressed to pulse durations as short as 24 fs with an optimized prism sequence.

103 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the second harmonic generation of ultraviolet pulses with mixed orders of chirp and explicitly discussed the transfer of the spectral phase in frequency doubling and found that chirped SHG avoids spectral narrowing and allows for precompression of dispersion encountered in the ultraviolet beam path.
Abstract: Ultraviolet pulses with a duration of 7 fs are efficiently generated by frequency doubling the output of a noncollinear optical parametric amplifier. The ultraviolet pulses are tunable between 275 to 335 nm. The acceptance bandwidth of the doubling crystal is increased by a factor of 80 through high-order achromatic phase matching. The chirp of the visible pulses and the dispersion introduced along the beam path are compensated partially before and partially after the doubling crystal. For the design of the dispersion management, we investigate the second harmonic generation of pulses with mixed orders of chirp and explicitly discuss the transfer of the spectral phase in frequency doubling. A simple analytic theory is derived that correctly describes frequently observed spectral narrowing effects. We find that chirped SHG avoids spectral narrowing and allows for precompression of dispersion encountered in the ultraviolet beam path. We apply chirped SHG to generate 18.7 fs ultraviolet pulses in an extremely simple setup.

101 citations


Journal ArticleDOI
TL;DR: In this article, the authors compare two definitions of spatial chirp, which they call "spatial dispersion" and "frequency gradient" for Gaussian beams and pulses, and the relationship between the two definitions is found to be analogous to that between the definitions of time and frequency domains.

95 citations


Journal ArticleDOI
TL;DR: In this paper, the inhomogeneous nonlinear Schrodinger equation with the loss/gain and the frequency chirping is considered, and the N-solitary solution is presented by employing the Darboux transformation.

94 citations


Journal ArticleDOI
TL;DR: A method for flow estimation using synthetic aperture imaging and focusing along the flow direction and using spherical wave emissions with a number of defocused elements and a linear frequency-modulated pulse to improve the signal-to-noise ratio is presented.
Abstract: A method for flow estimation using synthetic aperture imaging and focusing along the flow direction is presented. The method can find the correct velocity magnitude For any flow angle, and full color flow images can be measured using only 32 to 128 pulse emissions. The approach uses spherical wave emissions with a number of defocused elements and a linear frequency-modulated pulse (chirp) to improve the signal-to-noise ratio. The received signals are dynamically focused along the flow direction and these signals are used in a cross-correlation estimator for finding the velocity magnitude. The flow angle is manually determined from the B-mode image. The approach can be used for both tissue and blood velocity determination. The approach was investigated using both simulations and a flow system with a laminar flow. The flow profile was measured with a commercial 7.5 MHz linear array transducer. A plastic tube with an internal diameter of 17 mm was used with an EcoWatt 1 pump generating a laminar, stationary flow. The velocity profile was measured for flow angles of 90 and 60 degrees. The RASMUS research scanner was used for acquiring radio frequency (RF) data from 128 elements of the array, using 8 emissions with 11 elements in each emission. A 20-/spl mu/s chirp was used during emission. The RF data were subsequently beamformed off-line and stationary echo canceling was performed. The 60-degree flow with a peak velocity of 0.15 m/s was determined using 16 groups of 8 emissions, and the relative standard deviation was 0.36% (0.65 mm/s). Using the same setup for purely transverse flow gave a standard deviation of 1.2% (2.1 mm/s). Variation of the different parameters revealed the sensitivity to number of lines, angle deviations, length of correlation interval, and sampling interval. An in vivo image of the carotid artery and jugular vein of a healthy 29-year-old volunteer was acquired. A full color flow image using only 128 emissions could be made with a high-velocity precision.

91 citations


Journal ArticleDOI
TL;DR: In this paper, a method based on the Biot model was proposed for estimating the physical and acoustic properties of surficial ocean sediments from normal incidence reflection data acquired by a chirp sonar.
Abstract: This paper proposes a method, based on the Biot model, for estimating the physical and acoustic properties of surficial ocean sediments from normal incidence reflection data acquired by a chirp sonar. The inversion method estimates sediment porosity from reflection coefficient measurements and, using the estimated porosity and the measured change in fast wave attenuation with frequency, estimates the permeability of the top sediment layer. The spectral ratio of echoes from the interface at the base of the upper sediment layer and from the sediment-water interface provides a measure of the change in attenuation with frequency. Given the porosity and permeability estimates, the Kozeny-Carman equation provides the mean grain size and the inversion method yields the acoustic properties of top sediment layer. The inversion technique is tested using chirp sonar data collected at the 1999 Sediment Acoustics Experiment (SAX-99) site. Remote estimates of porosity, grain size, and permeability agree with direct measurements of those properties.

87 citations


Patent
24 May 2004
TL;DR: By writing non-linear chirp into fiber Bragg gratings, greater control over dispersion compensation in CPA systems is obtained, such that the dispersion profile of the fiber grating and a bulk compressor may be matched.
Abstract: By writing non-linear chirp into fiber Bragg gratings, greater control over dispersion compensation in CPA systems is obtained, such that, for example, the dispersion profile of the fiber Bragg grating and a bulk compressor may be matched. An iterative method of writing the fiber grating can reduce the group delay ripple to very low levels; and adaptive control of the fiber grating dispersion profile can further reduce these levels, while in addition offering greater acceptable yield in the manufacture of such gratings. Fiber Bragg gratings may be designed so as to provide customized pulse shapes optimized for various end uses, such as micromachining, for example, and may also be used to counteract gain-narrowing in a downstream amplifier.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the operation of a mode-locked fiber laser system for application in gas spectroscopy as a multipoint multigas sensor and reported a tuning rate of /spl sim/0.014 nm per kHz change in mode-lock frequency (at the third harmonic) has been demonstrated.
Abstract: This paper reports on an initial investigation into the operation of a mode-locked fiber laser system for application in gas spectroscopy as a multipoint multigas sensor. Wavelength selection is performed by use of multiple chirped gratings and fine tuning by using the dispersion properties of the chirped gratings. A tuning rate of /spl sim/0.014 nm per kHz change in mode-lock frequency (at the third harmonic) has been demonstrated, which is suitable for scanning across gas absorption lines. Key issues that have an important bearing on the tuning are discussed, including gain flattening and polarization drift. This paper investigates a method of multiplexing the sensor cells with the mode-locked system. Preliminary results for a two cavity system are presented to verify the principles of the technique.

Journal ArticleDOI
TL;DR: In this article, the authors measured the chirp rate of harmonics 13 to 23 in argon by cross correlation with a 12 femtosecond probe pulse under low ionization conditions.
Abstract: We measure the chirp rate of harmonics 13 to 23 in argon by cross correlation with a 12 femtosecond probe pulse. Under low ionization conditions, we directly measure the negative chirp due to the atomic dipole phase, and show that an additional chirp on the pump pulse is transferred to the qth harmonic as q times the fundamental chirp. Our results are in accord with simulations using the experimentally measured 815 nm pump and probe pulses. The ability to measure and manipulate the harmonic chirp rate is essential for the characterization and optimization of attosecond pulse trains.

Journal ArticleDOI
TL;DR: An adaptive learning loop enhances the efficiency and tuning of high-order harmonic generation and indicates that a specific quantum path coupled with ionization effects determines the optimized harmonic spectrum.
Abstract: An adaptive learning loop enhances the efficiency and tuning of high-order harmonic generation. In comparison with simple chirp tuning, we observe a broader tuning range and a twofold to threefold enhancement in integrated photon flux in the cutoff region. The driving pulse temporal phase varies significantly for different tunings and is more complicated than a simple chirp. We compare our experimental results with a one-dimensional, time-dependent model that incorporates the intrinsic atomic response, the experimental pulse temporal phase, ionization effects, and transverse coherence of the spatial mode of the laser. The model agrees with our experimental results and indicates that a specific quantum path coupled with ionization effects determines the optimized harmonic spectrum.

Journal ArticleDOI
TL;DR: Photonic-crystal fibers provide a high efficiency of frequency upconversion of regeneratively amplified femtosecond pulses of a Cr: forsterite laser, permitting the generation of subpicosecond anti-Stokes pulses with a smooth temporal envelope and a linear positive chirp, ideally suited for femtOSEcond coherent nonlinear spectroscopy.
Abstract: Photonic-crystal fibers provide a high efficiency of frequency upconversion of regeneratively amplified femtosecond pulses of a Cr: forsterite laser, permitting the generation of subpicosecond anti-Stokes pulses with a smooth temporal envelope and a linear positive chirp, ideally suited for femtosecond coherent nonlinear spectroscopy. These pulses from a photonic-crystal fiber were cross correlated in our experiments with the femtosecond second-harmonic output of the Cr: forsterite laser in toluene solution, used as a test object, in boxcars geometry to measure the spectra of coherent anti-Stokes Raman scattering (CARS) of toluene molecules (XFROG CARS).

Journal ArticleDOI
TL;DR: Preliminary results performed on rubber samples and solid tissue phantoms indicate that the FD-PTA technique has the potential to be a reliable tool for biomedical depth-profilometric imaging.
Abstract: In conventional biomedical photoacoustic imaging systems, a pulsed laser is used to generate time-of-flight acoustic information of the subsurface features. This paper reports the theoretical and experimental development of a new frequency-domain (FD) photo-thermo-acoustic (PTA) principle featuring frequency sweep (chirp) and heterodyne modulation and lock-in detection of a continuous-wave laser source at 1064 nm wavelength. PTA imaging is a promising new technique which is being developed to detect tumor masses in turbid biological tissue. Owing to the linear relationship between the depth of acoustic signal generation and the delay time of signal arrival to the transducer, information specific to a particular depth can be associated with a particular frequency in the chirp signal. Scanning laser modulation with a linear frequency sweep method preserves the depth-to-delay time linearity and recovers FD-PTA signals from a range of depths. Preliminary results performed on rubber samples and solid tissue phantoms indicate that the FD-PTA technique has the potential to be a reliable tool for biomedical depth-profilometric imaging.

Journal ArticleDOI
TL;DR: Numerical simulations show that the supercontinuum bandwidth increases with the linear chirp, and that the coherence ofsupercontinuum improves as frequency chirping increases, and an optimal positive chirP is identified that maximizes the superContinuum bandwidth.
Abstract: Pre-chirp of the input pulse has a significant effect on pulse evolution in a photonic crystal fiber. We present numerical simulations which show that the supercontinuum bandwidth increases with the linear chirp, and that the coherence of supercontinuum improves as frequency chirping increases. An optimal positive chirp is identified that maximizes the supercontinuum bandwidth, corresponding to the formation of only one red-shifting Raman soliton.

Journal ArticleDOI
TL;DR: A BBO-based chirped-pulse optical parametric amplifier employing an angularly dispersed signal beam to yield a full-octave gain bandwidth, sufficient for the direct amplification of sub-10-fs pulses and the suppression of parasitic second harmonic generation of the signal beam.
Abstract: We propose a BBO-based chirped-pulse optical parametric amplifier employing an angularly dispersed signal beam to yield a full-octave gain bandwidth, sufficient for the direct amplification of sub-10-fs pulses. Numerical simulations show that this power-scalable amplifier configuration has a small-signal gain of 10(7) at a pumping intensity of 45 GW/cm(2). The additional phase-matching flexibility compared to alternative configurations permits the suppression of parasitic second harmonic generation of the signal beam.

Patent
09 Jul 2004
TL;DR: In this paper, an optical transmission network includes an optical transmitter photonic integrated circuit (TxPIC) chip and a plurality of monolithic modulated sources integrated for multiple signal channels on the same semiconductor chip is provided with channel equalization at the optical receiver side of the network.
Abstract: An optical transmission network includes an optical transmitter photonic integrated circuit (TxPIC) chip, utilized in an optical transmitter and has a plurality of monolithic modulated sources integrated for multiple signal channels on the same semiconductor chip is provided with channel equalization at the optical receiver side of the network that permits one or more such integrated modulated sources in the TxPIC chip to be out of specification thereby increasing the chip yield and reducing manufacturing costs in the deployment of such TxPIC chips. FEC error counts at the FEC decoder on the optical receiver side of the network includes counters that accumulate a plurality of bit pattern-dependent error counts based on different N-bit patterns in the received data bit stream. The accumulated counts of different N-bit patterns are utilized to provide for corrections to threshold and phase relative to the bit eye pattern as well as provided for weight coefficients for the optical receiver equalization system. The deployment of this type of equalization in a digital OEO REGEN network substantially reduces, if not eliminates, the need for dispersion compensating fiber (DCF) or EDFAs in an optical link of the network and enhances the optical receiver tolerance to chromatic dispersion (CD) so that an increase in chip yield is realized for TxPIC chips not operating with acceptable operational parameters, particularly with a desired frequency chirp parameter relative to at least one of the TxPIC modulated sources.

Journal ArticleDOI
TL;DR: In this paper, photoassociation of ultracold atoms induced by chirped picosecond pulses is analyzed in a nonperturbative treatment by following the wavepacket dynamics on the ground and excited surfaces.
Abstract: Photoassociation of ultracold atoms induced by chirped picosecond pulses is analyzed in a non-perturbative treatment by following the wavepacket dynamics on the ground and excited surfaces. The initial state is described by a Boltzmann distribution of stationary continuum states. The chosen example is photoassociation of cesium atoms at temperature $T = 54 \mu$ K from the $a^3 \Sigma_u^ + (6s,6s)$ continuum to bound levels in the external well of the 0 g -(6s + 6p 3/2) potential. We study how the modification of the pulse characteristics (carrier frequency, duration, linear chirp rate and intensity) can enhance the number of photoassociated molecules and suggest ways of optimizing the production of stable molecules.

Patent
17 Dec 2004
TL;DR: In this article, the authors provided a fiber optic transmission system, comprising of an optical signal source adapted to produce a frequency modulated signal; and a multi-ring resonator optical spectrum reshaper (OSR) adapted to convert the frequency-modulated signal into a substantially amplitude modulated (SAM) signal.
Abstract: There is provided a fiber optic transmission system, comprising: an optical signal source adapted to produce a frequency modulated signal; and a multi-ring resonator optical spectrum reshaper (OSR) adapted to convert the frequency modulated signal into a substantially amplitude modulated signal. And there is provided a method for transmitting an optical signal through a fiber comprising: producing a frequency modulated signal; passing the frequency modulated signal through a multi-ring resonator optical spectrum reshaper (OSR) so as to convert the frequency modulated signal into a substantially amplitude modulated signal; and passing the substantially amplitude modulated signal into the fiber.

Journal ArticleDOI
Yitang Dai1, Xiangfei Chen1, Li Xia1, Yejin Zhang1, Shizhong Xie1 
TL;DR: The reconstruction algorithm is first applied to a sampled Bragg grating with chirp in the sampling period and a tunable dispersion compensator is fabricated with a tuning range of 300 ps/nm in a flat band of 1 nm.
Abstract: The reconstruction algorithm is first applied to a sampled Bragg grating (SBG) with chirp in the sampling period. This method is demonstrated to achieve various profiles of both reflection and group delay within one channel of the SBG. This method has the advantage that the phase mask does not need any chirp, and only submicrometer precision is needed in the fabrication process. Based on this method, a tunable dispersion compensator is fabricated with a tuning range of 300 ps/nm in a flat band of 1 nm.

Journal ArticleDOI
TL;DR: A linear array imaging system with coded excitation is considered, where the proposed excitation/compression scheme maximizes the signal-to-noise ratio (SNR) and minimizes sidelobes at the output of the compression filter.

Patent
G.A. Fish1, Y.A. Akulova1
30 Jul 2004
TL;DR: In this article, a monolithically-integrated semiconductor optical transmitter that can index tune to any transmission wavelength in a given range, wherein the range is larger than that achievable by the maximum refractive index tuning allowed by the semiconductor material itself (i.e., Δλ/λ>Δn/n), is presented.
Abstract: A monolithically-integrated semiconductor optical transmitter that can index tune to any transmission wavelength in a given range, wherein the range is larger than that achievable by the maximum refractive index tuning allowed by the semiconductor material itself (i.e. Δλ/λ>Δn/n). In practice, this tuning range is >15 nm. The transmitter includes a Mach-Zehnder (MZ) modulator monolithically integrated with a widely tunable laser and a semiconductor optical amplifier (SOA). By using an interferometric modulation, the transmitter can dynamically control the chirp in the resulting modulated signal over the wide tuning range of the laser.

Journal ArticleDOI
TL;DR: A novel method for synthesizing chirP-free pulses of any desired temporal shape by means of chirp compensation and spectral filtering of optical Raman similaritons is proposed and demonstrated experimentally.
Abstract: We propose and demonstrate experimentally a novel method for synthesizing chirp-free pulses of any desired temporal shape by means of chirp compensation and spectral filtering of optical Raman similaritons. The synthesized pulse shape is independent of the waveform, wavelength and energy of the initial pulses that are used for the similariton generation. Pulses are fully characterized by means of different techniques including cross-correlation and spectrum measurements, and the PICASO technique.

Patent
02 Jun 2004
TL;DR: In this paper, a narrow-band optical filter with a band center frequency offset from a central optical frequency of the optical signal is proposed to reduce the phase difference between FM and AM of the modulated optical signal.
Abstract: An optical transmission system has a directly modulated laser for modulating data directly on an optical signal, and a narrow band optical filter having a band center frequency offset from a central optical frequency of the optical signal, to reduce the phase difference between FM and AM of the modulated optical signal, the filter having a bandwidth sufficiently narrow to substantially remove frequencies outside a spectrum of adiabatic frequency chirp resulting from the modulation, combined with Fourier broadening caused by the data modulation. This is a cost effective way of improving the dispersion tolerance to give greatly improved system reach and to make it practical to use directly modulated lasers with existing NDSF. The narrow band filter can be located at the transmitter or the receiver, and can have a center frequency locked to a feature in the frequency spectrum of the laser.

Journal ArticleDOI
TL;DR: In this article, an analytical model from which the atomic origin of the harmonic chirp is clearly understood is presented, and the behavior of the chirps as a function of experimental parameters such as laser intensity is inferred.
Abstract: We demonstrate and evaluate the importance of an intrinsic chirp inherent to attosecond pulse creation accompanying high-order harmonic generation in recently published experimental data by Dinu et al. [Phys. Rev. Lett. 91, 063901 (2003)]. We present an analytical model, from which the atomic origin of the harmonic chirp is clearly understood. Moreover, the behavior of the chirp as a function of experimental parameters such as laser intensity is inferred. The comparison between our model and the experimental data provides us with useful information about the conditions in which the high-order harmonics is generated.

Journal ArticleDOI
TL;DR: A high-power laser system is demonstrated that employs a new scheme in which pulses with negative chirp are amplified and then recompressed by dispersion in a block of transparent material, which is believed to be the highest-average-power single-stage Ti:sapphire amplifier system with 11-W compressed output.
Abstract: We demonstrate a high-power laser system that employs a new scheme in which pulses with negative chirp are amplified and then recompressed by dispersion in a block of transparent material. This scheme has significant advantages for amplification of intermediate energy pulses at high average power, including insensitivity to small misalignments of the pulse compressor, elimination of compressor gratings and their thermal loading issues, low compressor energy and bandwidth throughput losses, and a simplified optical design. Using this scheme, we demonstrate what we believe is the highest-average-power single-stage Ti:sapphire amplifier system with 11-W compressed output.

Journal ArticleDOI
TL;DR: In this article, the optical power spectrum of a signal externally modulated using a Mach-Zehnder modulator is calculated analytically for binary signals for which the drive signal has either raised-cosine or Bessel-filtered pulse shape as well as for duobinary signals created by Bessel filtering.
Abstract: The optical power spectrum of a signal externally modulated using a Mach-Zehnder modulator is calculated analytically. Optical power spectra are calculated for binary signals for which the drive signal has either raised-cosine or Bessel-filtered pulse shape as well as for duobinary signals created by Bessel filtering. While the optical power spectrum is often approximated by the electrical power spectrum of the drive signal, this approximation usually underestimates the spectral spreading of the optical signal. Differences between the optical spectrum and the drive-signal electrical spectrum are most significant for drive signals having longer rise and fall times. Modulator chirp also broadens the optical spectrum. Chirp-induced spectral broadening is more significant for drive signals having longer rise and fall times.

Journal ArticleDOI
TL;DR: In this article, a self-referenced technique based on digital holography and frequency-resolved optical gating is proposed in order to characterize the complete complex electric field E(x,y,z,t) of a train of ultrashort laser pulses.
Abstract: A self-referenced technique based on digital holography and frequency-resolved optical gating is proposed in order to characterize the complete complex electric field E(x,y,z,t) of a train of ultrashort laser pulses. We apply this technique to pulses generated by a mode-locked Ti:Sapphire oscillator and demonstrate that our device reveals and measures common linear spatio-temporal couplings such as spatial chirp and pulse-front tilt.