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We present a comprehensive study of the temperature dependent electronic and optoelectronic properties of a tunnelling injection quantum dot laser. The optical power-voltage (P opt–V) characteristics are shown to be correlated with the current-voltage (I–V) and capacitance-voltage (C–V) dependencies at low and elevated temperatures. Cryogenic temperature measurements reveal a clear signature of resonant tunnelling manifested in periodic responses of the I–V and P opt–V characteristics, which diminish above 60 K. The C–V characteristics reveal a hysteresis stemming from charging and de-charging of the quantum dots, as well as negative capacitance. The latter is accompanied by a clear peak that appears at the voltage corresponding to carrier clamping, since the clamping induces a transient-like effect on the carrier density. C–V measurements lead also to a determination of the dot density which is found to be similar to that obtained from atomic force microscopy. C–V measurements enable also to extract the average number of trapped electrons in each quantum dot which is 0.95. As the important parameters of the laser have signatures in the electrical and electro-optical characteristics, the combination serves as a powerful tool to study intricate details of the laser operation.

We describe the fabrication process and properties of an InP based quantum dot (QD) laser structure grown on a 5° off-cut silicon substrate. Several layers of QD-based dislocation filters embedded in GaAs and InP were used to minimize the defect density in the QD active region which comprised eight emitting dot layers. The structure was analyzed using high resolution transmission electron microscopy, atomic force microscopy and photoluminescence. The epitaxial stack was used to fabricate optical amplifiers which exhibit electroluminescence spectra that are typical of conventional InAs QD amplifiers grown on InP substrates. The amplifiers avail up to 20 dB of optical gain, which is equivalent to a modal gain of 46 cm−1.

Entangled photon pairs are a fundamental component for testing the foundations of quantum mechanics, and for modern quantum technologies such as teleportation and secured communication. Current state-of-the-art sources are based on nonlinear processes that are limited in their efficiency and wavelength tunability. This motivates the exploration of physical mechanisms for entangled photon generation, with a special interest in mechanisms that can be heralded, preferably at telecommunications wavelengths. Here we present a mechanism for the generation of heralded entangled photons from Rydberg atom cavity quantum electrodynamics (cavity QED). We propose a scheme to demonstrate the mechanism and quantify its expected performance. The heralding of the process enables non-destructive detection of the photon pairs. The entangled photons are produced by exciting a rubidium atom to a Rydberg state, from where the atom decays via two-photon emission (TPE). A Rydberg blockade helps to excite a single Rydberg excitation while the input light field is more efficiently collectively absorbed by all the atoms. The TPE rate is significantly enhanced by a designed photonic cavity, whose many resonances also translate into high-dimensional entanglement. The resulting high-dimensionally entangled photons are entangled in more than one degree of freedom: in all of their spectral components, in addition to the polarization—forming a hyper-entangled state, which is particularly interesting in high information capacity quantum communication. We characterize the photon comb states by analyzing the Hong-Ou-Mandel interference and propose proof-of-concept experiments.

Using quantum dot (QD) structures as active material for optoelectronics was already in focus before the development of quantum well (QW) lasers and before semiconductor lasers occupied an important place in the market. The big step in reducing laser threshold conditions by substituting bulk gain materials with QWs should find a logical continuation by further reducing the dimensionality toward full 3D carrier confinement by QDs. This was predicted by theoretical considerations at the beginning of the 1980s [1], [2]. However, no practical technologies were available at that time. Top-down approaches, as originally addressed, to produce nanoscale species on very large surfaces and interface areas resulted in the accumulation of a large defect density within the active region and the domination of nonradiative carrier recombination mechanisms. Only during the early 1990s was a major breakthrough achieved with the introduction of the bottom-up approach of strain-driven, self-organized epitaxial QD growth. The first lasers were obtained in the gallium arsenide (GaAs)-based material system [3].

Resonant and non-resonant tunneling injection of charge carriers in a quantum dot optical gain medium in the form of an optical amplifier operating in the telecom wavelength range were identified using multi wavelength pump probe measurements. Since the inhomogeneously broadened ensemble of quantum dots exhibits a very wide spectrum of transition energies, both tunneling injection processes take place simultaneously at different spectral locations and thus can be identified. These findings highlight the fact that at least one of the tunneling processes must occur at a wavelength at or near the gain peak, where laser oscillations take place. An energetic misalignment leads to reduced laser performance since in that case, the tunneling process becomes a carrier loss mechanism.

We present deep sub-wavelength measurement of the field distribution inside nanophotonic dielectric laser accelerator structures, using photon-induced nearfield electron microscopy. Comparing the measured field with theory provides new insight into accelerators’ performance and structural sensitivity.

Tunneling-injection structures are incorporated in semiconductor lasers in order to overcome the fundamental dynamical limitation due to hot carrier injection by providing a carrier transport path from a cold carrier reservoir. The tunneling process itself depends on band alignment between quantum-dot levels and the injector quantum well, especially as in these devices LO-phonon scattering is dominant. Quantum dots with their first excited state near the quantum well bottom profit the most from tunnel coupling. As inhomogeneous broadening is omnipresent in quantum dot structures, this implies that individual members of the ensemble couple differently to the injector quantum well. Quantum dots with higher energy profit less, as the phonon couples to higher, less occupied states. Likewise, if the energy difference between ground state and quantum well exceeds the LO-phonon energy, scattering becomes increasingly inefficient. Therefore, within 20–30 meV, we find quantum dots that benefit substantially different from the tunnel coupling. Furthermore, in quantum dots with increasing confinement depth, excited states become successively confined. Here, scattering gets more efficient again, as subsequent excited states reach the phonon resonance with the quantum well bottom. Our results provide guidelines for the optimization of tunnel-injection lasers. Theoretical results for electronic state calculations in connection with carrier–phonon and carrier–carrier scattering are compared to the experimental results of the temporal gain recovery after a short pulse perturbation.

The fundamental interaction between free electrons and light stands at the base of both classical and quantum physics, with applications in free-electron acceleration, radiation sources, and electron microscopy. Yet, to this day, all experiments involving free-electron light interactions are fully explained by describing the light as a classical wave, disregarding its quantum nature. Here, we observe quantum statistics effects of photons on free-electron-light interactions. We demonstrate interactions passing continuously from Poissonian to super-Poissonian and up to thermal statistics, unveiling a surprising manifestation of Bohr's Correspondence Principle: the transition from quantum walk to classical random walk on the free-electron energy ladder. The electron walker serves as the probe in non-destructive quantum detection, measuring the photon-correlation ${g^{(2)} (0)}$ and higher-orders ${g^{(n)} (0)}$. Unlike conventional quantum-optical detectors, the electron can perform both quantum weak measurements and projective measurements by evolving into an entangled joint-state with the photons. Our findings suggest free-electron-based non-destructive quantum tomography of light, and constitute an important step towards combined attosecond-temporal and sub-A-spatial resolution microscopy.

We demonstrate the hallmark concept of periodic collapse and revival of coherence in a room-temperature ensemble of quantum dots (QDs) in the form of a 1.5-mm-long optical amplifier. Femtosecond excitation pulses induce coherent interactions with a number of discrete homogeneous QD subgroups within an inhomogeneously broadened ensemble, which interfere constructively to induce coherent revival (CR). The amplitude decay of CR is dictated by the QD homogeneous linewidth, thus enabling its extraction in a double-pulse Ramsey-type experiment. The more common photon echo technique is also invoked and yields the same linewidth provided that both experiments use the same bias. A dephasing time ${T}_{2}$ longer than 5 ps is extracted. This is a record long ${T}_{2}$ for a room-temperature QD ensemble and testifies to the high quality of the InAs/InP QDs used in the experiments. Measured electrical bias and temperature dependencies of the transverse relaxation times (${T}_{2}$ and ${T}_{2}^{*}$) enable the determination of the two main decoherence mechanisms: carrier-carrier and carrier-phonon scatterings.

Entangled photon pairs are a fundamental component for testing the foundations of quantum mechanics, and for modern quantum technologies such as teleportation and secured communication. Current state-of-the-art sources are based on nonlinear processes that are limited in their efficiency and wavelength tunability. This motivates the exploration of physical mechanisms for entangled photon generation, with a special interest in mechanisms that can be heralded, preferably at telecommunications wavelengths. Here we present a mechanism for the generation of heralded entangled photons from Rydberg atom cavity quantum electrodynamics (cavity QED). We propose a scheme to demonstrate the mechanism and quantify its expected performance. The heralding of the process enables non-destructive detection of the photon pairs. The entangled photons are produced by exciting a rubidium atom to a Rydberg state, from where the atom decays via two-photon emission (TPE). A Rydberg blockade helps to excite a single Rydberg excitation while the input light field is more efficiently collectively absorbed by all the atoms. The TPE rate is significantly enhanced by a designed photonic cavity, whose many resonances also translate into high-dimensional entanglement. The resulting high-dimensionally entangled photons are entangled in more than one degree of freedom: in all of their spectral components, in addition to the polarization-forming a hyper-entangled state, which is particularly interesting in high information capacity quantum communication. We characterize the photon comb states by analyzing the Hong-Ou-Mandel interference and propose proof-of-concept experiments.

A technique to characterize arbitrary optical pulses based on dual comb spectroscopy was developed. We benchmark the method by comparison with conventional characterization methods. The limitations due to fluctuations of phase noise and timing jitters are overcome by implementing computational non-uniform sampling of measured interferograms.

Significant prolongation of the coherence time by means of photon echo has been observed in a room temperature quantum dot amplifier operating at telecom wavelength. A record-long room temperature pure dephasing time of 4.7 ps was demonstrated using a detection technique suitable for practical applications.

The small and large signal responses of InP-based 1.55 μm high-speed quantum dot (QD) lasers with and without tunnel-injection (TI) quantum well (QW) and/or p-type doping in the active region (incorporating nominally identical QDs) were designed, manufactured and compared. The structures were grown by a molecular beam epitaxy system equipped with group-V valved cracker cells. In all cases, the active region consisted of six QD or TI-QD structures, which were embedded in InAlGaAs barriers lattice matched to InP. The InGaAs TI-QWs were separated by a thin InAlGaAs tunnel barrier from the InAs QDs. The laser structures were processed into ridge waveguide lasers and analyzed. The results show, that the bandwidth and maximum data rates were reduced by incorporation of TI-QWs. P-doping resulted in slightly worse performance of the simple QD laser, but in an improvement of the TI QD laser. Furthermore, the large signal response of the tunneling injection QD laser is one of the first reports of digital modulation of such a laser. An optimization of the doping profile is promising to further improve the laser performance over the undoped counterparts.

We proposed a protocol to generate entangled photon-comb pairs using rubidium Rydberg atoms inside an optical cavity. Rydberg blockade isolates a single excitation and the heralding enables non-destructive detection of the presence of photon-pairs.

A technique to characterize arbitrary optical pulses based on dual comb spectroscopy was developed. Distortions due to timing and phase fluctuations were determined and a method to compensate for them was demonstrated.

The concept of tunneling injection was introduced in the 1990's to improve the dynamical properties of semiconductor lasers by avoiding the problem of hot carrier injection which increase the gain nonlinearity and hence limit the modulation capabilities. Indeed, tunneling injection led to record modulation speeds in quantum well lasers. Employing tunneling injection in quantum dot lasers is significantly more complicated. Tunneling injection is based on an energy band alignment between a carrier reservoir and the active region where laser oscillation takes place. However, the inherent inhomogeneity of self-assembled quantum dots prevents an unequivocal band alignment and can cause the tunneling injection process to actually deteriorate the laser performance compared to nominally identical quantum dot lasers that have no tunneling section. Understanding the complex process of tunneling injection in quantum dot lasers requires a comprehensive study where different aspects are analyzed theoretically and experimentally. In this paper we describe the technology of such lasers in the InP material system followed by a microscopic analysis of the detailed electrical characterization which is correlated to the electro-optic properties yields information about the exact carrier transport mechanism at bias levels of almost zero to well above threshold. A tunneling injection quantum dot optical amplifier was used for multi wavelength pump probe characterization from which it is clear why tunneling injection often deteriorates laser performance and determines how to design a structure which can take advantage of tunneling injection. Finally, we present a direct comparison between the modulation response of a tunneling injection quantum dot laser and a twin structure that has no tunneling injection section. The broad study sheds light on the fundamental tunneling injection process that can guide the design of an optimum laser where tunneling injection will be taken full advantage of and will improve the dynamical properties.

Nanophotonics is based on the ability to construct structures with specific spatial distributions of the refractive index. Conventional nanophotonic structures are fabricated in planar settings, similar to electronic integrated circuits. We present a new class of nanophotonic structures with intricate design in three dimensions inspired by general relativity concepts, where the evolution of light is controlled through the space curvature of the medium. We demonstrate this concept by studying the evolution of light in a paraboloid structure inspired by the Schwarzschild metric describing the space surrounding a massive black hole. Our construction allows control over the trajectories, the diffraction properties and the phase and group velocities of wavepackets propagating within the curved-space structure. Finally, our structure exhibits tunnelling through an electromagnetic bottleneck by transforming guided modes into radiation modes and back. This generic concept can serve as the basis for curved nanophotonics and can be employed in integrated photonic circuits. Exploiting Einstein’s theory of general relativity, the curved space associated with specially designed nanophotonic structures is shown to be able to manipulate light propagation.

Further optimized high-quality InP-based quantum dot materials with low inhomogeneous linewidth broadening were used to realize $1.55\ \mu \mathrm{m}$ quantum dot distributed feedback lasers, which clearly show fundamental advantages in comparison to quantum well based devices in terms of new record values in emission linewidth $( , high output powers ( $> 17$ dBm at 20 °C) and high temperature stability ( $ kHz and $> 10\ \mathrm{dBm}$ at 80 °C).

Semiconductor DFB or DBR lasers with narrow linewidths are of outmost importance for a variety of applications, the most important ones being communication and LIDAR. Conventional single mode lasers based on quantum wells have linewidths of the order of one to a few MHz; reducing the linewidth requires the addition of an external feedback, and a stabilization scheme by means of some control circuitry which enables to reach linewidths of about 100 kHz. A much better solution is a diode laser chip that can provide very narrow linewidths without the need for complex external additions. Recent works suggest that such lasers are possible provided that the gain medium comprises quantum dots (QDs). This paper describes the spectral properties of state of the art 1550 nm InAs/InP QD DFB lasers grown by solid source MBE and comprising five highly uniform dot layers. The linewidth of these lasers was tested using delayed self-heterodyne as well as by beating against a highly stabilized optical frequency comb. The lasers exhibit linewidths of the order of 20 kHz at room temperature and below 70 kHz at 80 degrees C.

A comparison between QD lasers with and without tunnel-injection QW designs was performed. In both cases, six layers of a QD or TI-QD design were grown by molecular beam epitaxy equipped with group-V valved cracker cells. The InAs QDs are embedded in InAlGaAs barriers lattice matched to InP. The TI-QW consists of InGaAs separated by a thin InAlGaAs tunnel barrier. The lasers were processed into broad area and ridge waveguide lasers. Both laser designs exhibited high modal gain values in the range of 10-15 cm−1 per dot layer. The static and dynamic device properties of the different QD laser designs were measured and compared against each other.

Narrow linewidth InAs/InP QD DFB lasers with linewidths of less than 50kHz at 20°C which broadens to less than 80kHz at 80°C were demonstrated using delayed self-heterodyne as well as by optical frequency comb interferometry.

The integration of optical sources in Si photonic transceivers has relied so far on externally coupled III-V laser dies within the assembly. These hybrid approaches are however complex and expensive, as there are additional cost-increasing factors coming from the redundant testing of the pre- and post-coupled laser photonic chips. Further optimization of Photonic Integrated Circuits (PICs) cost and performance can be obtained only with radical technology advancements, such as the “holy grail” of Silicon Photonics; the monolithic integration of III-V sources on Si substrates. MOICANA project funded by EU Horizon 2020 framework targets to develop the technological background for the epitaxy of InP Quantum Dots directly on Si by Selective Area Growth with the best-in-class, in terms of losses and temperature sensitivity, in a CMOS fab, i.e. the SiN waveguide technology. In addition, MOICANA will develop the necessary interface for the seamless light transition between the III-V active and the SiN passive part of the circuitry featuring advanced multiplexing functionality and a combination of efficient and broadband fiber coupling. Through this unique platform, MOICANA aims to demonstrate low cost, inherent cooler-less and energy efficient transmitters, attributes stemming directly from the low loss SiN waveguide technology and the QD nature of the laser’s active region. MOICANA is targeting to exploit the advantages of the monolithic integrated PICs for the demonstration of large volume single-channel and WDM transmitter modules for data center interconnects, 5G mobile fronthaul and coherent communication applications.

Modulation properties and temperature stability of short cavity ridge waveguide lasers based on high-quality InAs quantum dots exhibiting a total modal gain of ~90 cm -1 are reported. The 338-μm-long lasers show a threshold current of 20 mA at room temperature and an output powers of up to 36 mW. A maximum small signal modulation bandwidth of 15 GHz was obtained at 14 °C, which degrades to 13 GHz at 60 °C and 8 GHz at 80 °C. Digital modulation at 25 Gb/s between 15 °C and 50 °C was obtained with clear open eyes under constant drive conditions (dc and ac). The maximum data rates of 32 and 35 Gb/s were obtained for 338- and 230-μm-long lasers, respectively, at 14 °C.

We describe the optical properties of nonvolatile memory cells based on metal–insulator–semiconductor structures with embedded Pt nanoparticles, fabricated by atomic layer deposition. We show the effect of illumination on the static as well as dynamic properties of two devices, which differ by their respective thicknesses of the tunneling layer. The device with the thicker tunneling layer exhibits a faster response under illumination and significantly better retention properties, while the device with the thinner tunneling layer is faster under dark conditions.

We report phase sensitive amplification in a 1.5mm long, Ga0.5In0.5P dispersion engineered photonic crystal waveguide which has a flattened dispersion profile. A signal degenerate configuration with pulsed pumps whose total peak power is only 0.5W yields a phase sensitive extinction ratio of 10dB.

We present a planar three terminal device fabricated on a silicon-on-insulator substrate. The device is based on a two-layer dielectric stack comprising SiO2 tunneling and HfO2 layers. A so-called gate electrode is placed between two other contacts, of the source and drain, all deposited on the insulator stack. In the dark as well as under illumination, the current–voltage characteristic can be shifted in an ideal linear manner with changes in a positive gate voltage with the shift being somewhat larger under illumination. The reason for the change of shift is the ability of high-density oxygen vacancies, arranged in the filament regions within an HfO2 sublayer that was voltage stress. Namely, holes or electrons are trapped in the HfO2 sublayer, respectively, from the inverted or accumulated Si layer. This process is controlled by the gate and drain bias levels. Moreover, under illumination and at negative gate and drain voltages, the device exhibits negative differential resistance caused by capture of photo-generated minority carriers induced in the depletion region of the Si after they tunnel through the SiO2 layer by negative oxygen vacancies that migrate to the SiO2/HfO2 interface through the filament regions. Finally, the low level of saturation current in the dark and the ability to precisely control its value by illumination intensity, together with a large sensitivity of 80–85 A/W and 25 A/W, at 490 nm and 365 nm, respectively, allow additional applications that cannot be achieved with conventional MIS devices.

Electrical characteristics: I-V and C-V of InAs/InP quantum-dot lasers are analyzed and yield important parameters. The origin of the nonlinear I-V curve, the dot density and the number of carriers per dot are examples of what parameters can be extracted.

Carrier dynamics following a short pulse perturbation in a tunneling-injection quantum dot (QD) gain medium are analyzed. A hybrid state comprising the injection-well and QD first excited state dominate the dynamics with a time constant of 1ps. The role of the perturbation wavelength is discussed.

We report spectral characteristics of InAs/InP QD DFB lasers. Owing to low linewidth enhancement factor and high modal gain, lasers with 5 QD layers exhibit record linewidth of 55 kHz measured by the heterodyne beat note between the laser and an ultra-stable optical frequency comb.

Light matter coherent interactions require that the coherent state induced in the matter be maintained for the duration of the observation. The only way to induce and observe such interactions in room temperature semiconductors, where the coherence time is of the order of a few hundred femtoseconds, is to use ultrashort pulse excitations and an ultrafast characterization technique. For media comprising an ensemble of nanostructure semiconductors such as self-assembled quantum dots, the gain broadening inhomogeneity also affects the interaction. Moreover, when gain media in the form of an active waveguide, such as optical amplifiers, are used, the interaction is distributed and includes nonresonant incoherent phenomena that occur simultaneously with the coherent effects. Such a complex system can exhibit, nevertheless, clear coherent interactions even at room temperature. Using InAs/InP quantum dot and wirelike quantum dash amplifiers, Rabi oscillations, self-induced transparency, coherent control using spectral pulse shaping, Ramsey interference, and photon echo have been demonstrated. The characterization employed cross frequency resolved optical gating, and the experiments were accompanied by a comprehensive finite difference time domain model that solves the Maxwell and Lindblad equations. This work has major implications on the understanding of the details of dynamical processes in active semiconductor devices, on short pulse generation from semiconductor lasers, and on various future quantum devices.

How short time scales substitute for cryogenic cooling: Quantum Coherent Effect in Room Temperature QD Amplifiers Gadi Eisenstein1 and Johann Peter Reithmaier2 1Electrical Engineering Dept. and Russell Berrie Nanotechnology Institute Technion – Israel Institute of Technology, Haifa 32000 Israel 2Technological Physics, Institute of Nanostructure Technologies and Analytics, CINSaT, University of Kassel, 34132 Kassel, Germany Abstract Semiconductor quantum dots (QDs) serve often as a two-level system for studying quantum coherent phenomena. Observation of quantum coherent effects requires observation times that are shorter than the coherence time. In room temperature semiconductor QDs, those times are of the order of 350 fs and therefore it is common to cool the QDs to cryogenic temperatures. A few years ago, we have introduced an alternative approach by which the cooling is substituted for by operation with ultra-short pulses having durations of 100-200 fs. The platform we employ is a 1.5 mm long InAs/InP QD optical amplifier. Measurements use the cross frequency resolved gating (X-FROG) technique and the experiments are accompanied by a comprehensive model that treats the QD amplifier as a cascade of two level system and also considers the QD gain inhomogeneity as well as non-resonant interactions such as two photon absorption and an accompanying Kerr-like effect. Several quantum coherent effects have been demonstrated including Rabi oscillations and self- induced transparency as well as coherent control of the Rabi oscillations achieved by shaping the pulses spectral phase. A modification of the experimental set up by which two pulses in a pump probe configuration are used with each pulse being separately measured using the X-FROG technique enables to demonstrate the optical analog of Ramsey-Resonances. Setting a nominal delay between the input pulses and changing the delay in 1 fs steps, we observe clear Ramsey fringes in the probe amplitude, instantaneous frequency and surprisingly also the separation between the two output pulses. The latter stems from the coupling between the real and imaginary parts of the susceptibility. It is unique to our system as it a cumulative effect that requires a reasonably long propagation distanced and can therefore only be seen in a waveguide configuration and never in a single QD which was used in all previous Ramsey experiments. The last effect is photon echo which was only studied numerically up to now. The talk will survey the various experimental results and will highlight the essence of operating with short pulses to induce and observe quantum coherent effects in room temperature QD amplifiers.

The dynamical properties of InP-based quantum dot (QD) gain media are surveyed and analyzed for three time scales ranging from tens of picoseconds to less than 200 fs, where quantum coherent phenomena are observable. Each of these time scales determines the important properties of QD devices, i.e., modulation capabilities, nonlinear gain, and coherent light-matter interactions. Experimental investigations and modeling results are described, highlighting the state of the art in QD devices for the important 1550-nm telecom wavelength range.

International audience; Continuous thin films of Pt on A-plane 1 1 2 0 À Á sapphire substrates were dewetted to characterize the morphological evolution and dew-etting kinetics at 800 °C using an oxygen partial pressure of 10 À20 atm. Hole growth was studied, focusing on partially dewetted samples. Four different low-index orientation relationships were found between the Pt and sapphire substrate by electron backscattered diffraction combined with transmission electron diffraction patterns. Abnormal grains adjacent to the holes with a small deviation from one of the low-index orientation relationships were observed. The difference in the heights of the abnormal grains adjacent to the holes (rim-height) is influenced by the initial position of the hole, and the existence of grains with a low-energy interface orientation relationship, and not only by diffusivity rates dictated by surface orientation as described in existing edge-retraction models. The existence of low-index orientation relationships is seen as the driving force for abnormal grain growth in the vicinity of the holes, and is a dominant factor in controlling the dewetting rate of thin metal films on oxide surfaces.

Storage and manipulation of quantum information requires (nearly) perfect timing---or precisely timed pulse sequences, anyhow. In quantum memory based on photon echoes, for example, the appearance time of the echo must be determined with great accuracy. This study shows how to control photon echoes in a quantum-dot optical amplifier operating at room temperature. As the amplifier is a distributed device, propagation effects are dominant in the generation of the echo pulse, and shaping the excitation pulse serves to control the echo's appearance time and strength.