We present recent results on high energy, high repetition rate 2090 nm Ho:YAG laser system resonantly pumped by the radiation of efficient Tm-doped CW fiber lasers. The laser consists of a master oscillator power amplifier (MOPA) with two additional amplification stages. We demonstrate maximum energy of 120 mJ per pulse with a 15 ns pulse width at 500 Hz, corresponding to a peak power of 8 MW. The results presented in a wide 100-1000 Hz range of repetition rates.
We report an approach to generation of optical frequency combs in the spectral range 2 – 20 µm. The 2-cycle, multi-Watt laser at the repetition rate 80 MHz is based on a polycrystalline Cr:ZnS. The bandwidth of the super-octave ultrafast Cr:ZnS laser source at the central wavelength 2.4 µm is extended to the long-wave IR range (5 – 20 µm) via optical rectification in non-oxide nonlinear materials: GaSe, ZGP. The key advantages of Cr:ZnS frequency comb technology is high efficiency of optical-to-optical conversion from low-cost cw EDFL light to fs MIR pulses, and ultra-low timing jitter. These advantages, in turn, has allowed us to implement shoe-box-sized, light-weight, frequency combs that open new avenues in imaging, sensing, and spectroscopy. Our preliminary evaluations confirm the applicability of the developed sources for dual-comb spectroscopy.
KEYWORDS: Frequency combs, Long wavelength infrared, Spectroscopy, Molecular spectroscopy, Mode locking, Femtosecond phenomena, Mid-IR, Optical amplifiers, High power lasers, Synchrotrons
Femtosecond mid-IR and long wave IR lasers provide tremendous opportunities for imaging and sensing because they combine high spatial coherence of the laser beams (crucial for remote sensing), high temporal coherence of mode-locked oscillators (enabling dual comb spectroscopy in important molecular fingerprint region), and few-optical-cycle pulses (enabling IR sensing with high dynamic range via electric field sampling with low cost room temperature near-IR photodetectors). The development of such a sources (especially compact and field-deployable sources) is a challenging task that relies on the most advanced bulk laser technologies, new gain and nonlinear materials for a wide range of laser wavelengths. We present a viable route to the generation of power and energy scalable few-cycle pulse trains in the IR and describe the application of the developed sources for dual comb spectroscopy. The laser architecture is based on a combination of laser and nonlinear interactions in polycrystalline Cr:ZnS media that enables simultaneous amplification of ultrashort pulses, nonlinear pulse compression to 2-optical-cycle, and nonlinear broadening of pulses’ spectrum to an optical octave. Importantly, all of the necessary optical signals for stabilization of the frequency comb with the large lever arm are generated directly inside polycrystalline Cr:ZnS. This, in turn, has allowed us to implement robust and reliable shoe-box sized middle-IR frequency combs with ultra-low timing jitter of the pulse trains, broad instantaneous spectra, and Watt-level average power.
We report a technique for generation of ultra-broadband coherent femtosecond continua in the infrared. The laser architecture is based on the Cr:ZnS–GaSe and Cr:ZnS–ZGP tandem arrangements that enable simultaneous amplification of ultrashort middle IR pulses and augmentation of pulses’ spectrum via a chain of intrapulse three-wave mixings. The first part of the tandems is based on a single-pass polycrystalline Cr:ZnS amplifier, which is optically pumped by off-the-shelf continuous wave Er-doped fiber laser and outputs 2-cycle pulses with multi-Watt average power at 80 MHz repetition rate, at the central wavelength 2.5 μm. The second stage of the tandems comprises a GaSe or ZGP crystals configured for intrapulse difference frequency generation. The Cr:ZnS–GaSe tandem has allowed us to achieve multi-octave 2–20 μm continuum with 2 W power in the range 2–3 μm and power in excess of 20 mW in the important range 3–20 μm. On the other hand, Cr:ZnS–ZGP tandem features long-wave infrared (6–12 μm) output pulses with record braking sub-Watt power level. Last but not least, Cr:ZnS–GaSe and Cr:ZnS–ZGP IR sources have small footprints and are easily convertible to the optical frequency combs with low carrier-to-envelope timing jitter.
II-VI chalcogenides (e.g. ZnSe/S) doped with transition metal (TM) ions such as Cr, and Fe are arguably the materials of choice for fabrication of effective mid-IR gain media. TM:II-VI materials feature a favorable blend of laser spectroscopic parameters: a four-level energy structure, absence of excited state absorption, close to 100% quantum efficiency of fluorescence (for Cr doped II-VI media), broad mid-IR vibronic absorption and emission bands. This talk summarizes progress in fabrication of high quality Cr:ZnS/Se and Fe:ZnS/Se by cation vacancy and cation interstitial enhanced post growth thermal diffusion. We also describe recent breakthrough on recrystallization and effective doping of ZnS ceramics under hot isostatic pressing resulting in a large cm-scale monocrystalline domains formation and an increase of the Fe diffusion coefficient by three orders of magnitude.
We report recent advances in high-power Cr:ZnS/Se and Fe:ZnSe laser systems, enabling a wide range of tunability (1.8-5.0µm) with output power levels of up to 140 W near 2500 nm, 32 W at 2940 nm, and 35 W at 4300 nm with corresponding optical efficiencies of 62%, 29%, and 35%.
Current improvements of output characteristics of polycrystalline Cr:ZnS/Se oscillators in Kerr-Lens-Mode-Locked (KLM) regime are reported: up to 2 W output power at 75-1200 MHz repetition rate, up to 2 cycle pulse duration (16 fs) with efficiency of 20-25% with regards to Er-fiber laser pump power. The effects of efficient up-conversion of mid-IR fs pulses in the laser medium as well as supercontinuum generation are demonstrated.
Further extension of mid-IR spectral coverage to 3-8 m is demonstrated by Cr:ZnS KLM laser pumped degenerate (subharmonic) parametric oscillators (OPOs) based on based on quasi-phase matching in orientation-patterned gallium arsenide, and random phase matching in polycrystalline ZnSe.
II-VI binary and ternary chalcogenides (e.g. ZnS, ZnSe; CdZnTe, ) doped with transition metal (TM) ions such as Cr, and Fe are arguably the materials of choice for effective mid-IR lasers potentially covering 1.8-9 µm spectral range. This talk summarizes progress in Cr:ZnS/Se and Fe:ZnSe laser systems, enabling a wide range of tunability (1.8-5.0µm) with output power levels of up to 140 W, as well as Fe doped ternary chalcogenides with tunability potentially extended up to 9 um.
TM:II-VI media feature a unique combination of superb ultra-fast laser capabilities with high nonlinearity enabling exceptional output characteristics of polycrystalline Cr:ZnS/Se oscillators in Kerr-Lens-Mode-Locked (KLM) regime over 2-2.6 um and effective up and down conversion of fs pulses via random phase matching (RFM). Extension of mid-IR spectral coverage to 3-8 um is demonstrated by Cr:ZnS KLM laser pumped subharmonic parametric oscillators (OPOs) based on quasi-phase matching in OP-GaAs, and RFM in polycrystalline ZnSe.
Fe:II-VI semiconductors are complimentary to Cr doped compounds and 3-8 um KLM ultrafast oscillators based on Fe doped chalcogenides are feasible. Another important feature of Fe:II-VI media is excellent energy storage capability at 77-200K (~60 µs luminescence life time) enabling efficient Q-switched regime and high energy amplification of ns and ultrafast pulses.
One of the major problems in the development of CW, gain switched, Q-switched and KLM ultrafast Fe:II-VI lasers was the absence of convenient pump sources overlapping with absorption band (2.7-4.5 um) of Fe: gain media. Potential utilization of Quantum Cascade Lasers (QCL) as pump sources of Fe:II-VI lasers will be discussed in the form QCL-solid state laser hybrid platforms as well as Fe doped active layers integrated in QCL structures.
This paper summarizes recent improvements of output characteristics of polycrystalline Cr:ZnS/Se master oscillators in Kerr-Lens-Mode-Locked regime. We developed a flexible design of femtosecond polycrystalline Cr:ZnS and Cr:ZnSe lasers and amplifiers in the spectral range 2–3 μm. We obtained few-optical-cycle pulses with multi-Watt average power in very broad range of repetition rates 0.08–1.2 GHz. We also report on efficient nonlinear frequency conversion directly in the polycrystalline gain elements of ultra-fast lasers and amplifiers. In this work we also report on recent progress in spinning ring gain element technology and report to the best of our knowledge the highest output power of 9.2 W Fe:ZnSe laser operating in CW regime at 4150nm.
This paper summarizes recent improvements of output characteristics of polycrystalline Cr:ZnS/Se master oscillators in Kerr-Lens-Mode-Locked regime: 1.9 W average power at 41 fs pulse duration, 24 nJ pulse energy and 515 kW peak power with efficiency of 19% with regards to 1567 nm pump power from linearly polarized Er-fiber laser. A simple design of mid-IR fs Cr:ZnS MOPA enabled power scaling to 6.8 W at 79 MHz repetition rate. This was accompanied by a 2 fold spectral broadening to 600 nm at -10 dB level, pulse compression from 44 to <30 fs, and overall 25 % optical to optical efficiency. Improved dispersion management of the resonator enabled pulse duration of Cr:ZnS master oscillator approaching 2 optical cycles (<26 fs) and 500 nm (27 THz) bandwidth of the spectrum at half-maximum. Further improvements of the optical coatings will result in octave-spanning polycrystalline Cr2+:ZnS/ZnSe lasers. In this work we also report on recent progress in spinning ring gain element technology and show new unprecedented output power levels for Cr:ZnSe laser gain media: ~140 W at 2400-2500 nm spectral range and ~32 W at 2940-2950 nm in CW regime of operation. High gain of the spinning ring Cr:ZnSe power amplifier demonstrated in this work may potentially enable scaling up the femtosecond mid-IR Cr:ZnS MOPA up to 70-100W.
Cr2+ doped ZnS and ZnSe possess a unique blend of physical, spectroscopic, and technological parameters. These laser materials feature ultra-broadband gain in 1.9 – 3.3 μm mid-IR range, low saturation intensities, and large pump absorption coefficients. The II-VI semiconductor hosts provide a low phonon cut-off, broad IR transparency, and high second and third order nonlinearity. Cr:ZnS and Cr:ZnSe are available in polycrystalline form: the material consists of a multitude of microscopic single-crystal grains with a broad distribution of grain sizes and orientations, which results in random quasi-phase-matching (RQPM). The distinctive features of RQPM are a linear dependence of the conversion yield with length of the medium and ultra-wide bandwidth of three-wave mixing. We review resent experimental results on optically pumped mid-IR ultrafast lasers based on polycrystalline Cr:ZnS and Cr:ZnSe. We demonstrate that Kerrlens mode-locking of polycrystalline Cr:ZnS and Cr:ZnSe lasers allow for generation of few-cycle mid-IR pulses with MW-level peak power. This opens several avenues for efficient nonlinear frequency conversion of short optical pulses directly in the laser gain medium via RQPM process. We implemented Kerr-lens mode-locked Cr:ZnS oscillators, which feature high power (up to 0.25 W), spectrally broad (up to 22 THz) second harmonic generation (SHG) in the laser medium. We also demonstrate simple and robust ultrafast source based on single-pass continuously pumped polycrystalline Cr:ZnS laser amplifier: mid-IR pulses with 6.8 W average power and the spectrum spanning 2.0–2.6 μm as well as SHG pulses with 0.52 W average power and 1.05 – 1.25 μm spectral span were obtained.
Progress in fabrication and mid-IR lasing of Cr and Fe thermal-diffusion and radiation enhanced thermal diffusion doped II-VI binary and ternary polycrystals is reported. We demonstrate novel design of mid-IR Fe:ZnSe and Cr:ZnSe/S solid state lasers with significant improvement of output average power up to 35W@4.1 μm and 57W@2.5 μm and 20W@2.94 μm. We report significantly improved output characteristics of polycrystalline Cr:ZnS/Se lasers in gain-switched regime: 16 mJ at 200 Hz, pulse duration 5 ns with tunability over 2400-3000 nm as well as Kerr-Lens-Mode-Locked regime in terms of average power (up to 2 W), peak power and pulse energy (0.5 MW and 24 nJ, respectively), and pulse duration (less than 29 fs).
We report a novel design of CW Cr2+:ZnS/ZnSe laser systems and demonstrate record output powers of 27.5 W at 2.45 μm and 13.9 W at 2.94 μm with slope efficiencies of 63.7% and 37.4%, respectively. Power scaling of ultra-fast Cr2+:ZnS/ZnSe Kerr mode-locked lasers beyond 2 W level, as well as the shortest pulse duration of 29 fs, are also reported. New development of Fe:ZnSe laser with average output power > 35 W at 4.1 μm output wavelength and 100 Hz pulse repetition rate (PRR) was achieved in a nonselective cavity. With intracavity prim selector, wavelength tunability of 3.88-4.17 μm was obtained with maximum average output power of 23 W. We also report new results on Tm-fiber pumped passively and actively Q-switched Ho:YAG laser systems. High peak power actively Q-switched Ho:YAG laser demonstrates stable operation with pulse energy > 50 mJ, 12 ns pulse duration, and 100-1000 Hz PRR which correspondents to more than 4 MW peak power. The actively Q-switched Ho:YAG laser system optimized for high repetition rate delivers 40 W average output power at 10-100 kHz PRR. The Ho:YAG laser with passive Q-switcher demonstrates constant 5 mJ output energy from 200 Hz to 2.23 kHz PRR with optical slope efficiency with respect to Tm-fiber laser of ~43%.
In this paper, we report record nanosecond output energies of gain-switched Cr:ZnSe lasers pumped by Q-switched
Cr:Tm:Ho:YAG (100 ns @ 2.096 μm) and Raman shifted Nd:YAG lasers (7 ns @ 1.906 μm). In these experiments we
used Brewster cut Cr:ZnSe gain elements with a chromium concentration of 8x1018 cm-3. Under Cr:Tm:Ho:YAG
pumping, the first Cr:ZnSe laser demonstrated 3.1 mJ of output energy, 52% slope efficiency and 110 nm linewidth
centered at a wavelength of 2.47 μm. Maximum output energy of the second Cr:ZnSe laser reached 10.1 mJ under H2 Raman shifted Nd:YAG laser pumping. The slope efficiency estimated from the input-output data was 47%.
Middle infrared (mid-IR) chromium-doped zinc selenide (Cr:ZnSe) bulk lasers have attracted a lot of attention due to
their unique combination of optical and laser properties facilitating a wide range of potential scientific, industrial, and
medical applications. Utilization of thin film waveguide geometry enabling good thermal management and control of
beam quality is a viable pathway for compact chip-integrated optical laser design. Cr:ZnSe thin films are also promising
as saturable absorbers and mode-lockers of the cavities of solid state lasers operating over 1.3-2.1 μm. We recently
reported the first successful demonstration of mid-IR Cr:ZnSe planar waveguide lasing at 2.6 μm under gain-switched
short-pulse (5 ns) 1.56 μm excitation as well as the passive Q-switching of the cavity of a fiber-pumped Er:YAG laser
operating at 1645 nm using a highly doped Cr:ZnSe thin film. PLD grown Cr:ZnSe waveguide were fabricated on
sapphire substrates (Cr:ZnSe/sapphire) with chromium concentration of 1018-1019 cm-3. Further development of mid-IR
lasing in the Cr:ZnSe planar waveguide under continuous wave excitation were investigated. In addition, deposition of
Cr:ZnSe-based thin film structures on n-type GaAs substrates were also investigated for possible mid-IR
electroluminescence.
The objective of this work was to develop a compact and efficient Tm-fiber-Ho:YAG, hybrid laser passively Q-switched
by Cr:ZnSe saturable absorber. We used a folded semi-hemispherical 10 cm long cavity with a plane output coupler and
a 0.5 m concave high reflector. In these experiments we studied the performance of two high optical quality Cr:ZnSe
crystals as saturable absorbers with initial transmissions of 93.9% and 70% at 2.1 μm. With the 93.9% transmission
crystal, passive Q-switching was realized with a maximum output power of 5 W, pulse energy of 0.5 mJ, pulse duration
of 150 ns, and Q-switched-to-CW-mode extraction efficiency of 60%. With the 70% transmission crystal, passive Qswitching
was achieved with a 75% Q-switched-to-CW-mode extraction efficiency, pulse energy of 3 mJ, and duration
of 7ns. The laser demonstrated sustained damage-free, TEM000 operation with 0.5 MW of peak power showing promise
for applications requiring high-peak-power, diffraction-limited beams, and single-frequency regimes of operation.
We present compact, highly-efficient, widely-tunable CW lasers based on Cr2+:ZnS and Cr2+:ZnSe gain media
longitudinally pumped by a single-emitter, 1.5 W, 1685 nm InP semiconductor laser. The Cr2+:ZnSe laser demonstrates
35% slope, and 24% real optical efficiency, respectively, up to 400 mW of output power, and is tunable from 2200 to
2700 nm. The Cr2+:ZnS laser shows 44% slope, and 31% real optical efficiency, respectively, up to 500 mW of output
power, and is tunable over 2100-2700 nm. The single-emitter diode pumping of chromium-doped chalcogenides allows
for fabrication of middle-infrared tunable laser sources where low- or mid-range output powers are sufficient, while low
footprint and miniature packaging are strictly required. In our presentation we will discuss the laser design issues
specific to diode pumping, demonstrate the performance of the Cr:ZnS and Cr:ZnSe laser systems with different
transmissions of the output couplers, describe several approaches for convenient wavelength tuning, and perform a
comparison of diode pumping efficiency to that of fiber-laser pumping.
We demonstrate, for the first time, room-temperature, 10 W (at 2400 nm), Er-fiber laser pumped, pure CW, thermally
diffusion doped, polycrystalline Cr2+:ZnS laser. We also show Littrow-grating, single-knob, wavelength tuning of the
laser over 1940-2780 nm with the maximum output power of 7.4 W at 2400 nm and above 2 W over 1970-2760 nm
wavelength range. The laser performs with 40% real optical efficiency (with 43% slope) and shows no output power
roll-off up to the highest available pump of 26 W.
Here we report a new method for transition-metal (TM) doped II-VI Quantum Dots (QD) fabrication and first mid-IR (2-3 μm) lasing
at 77K of Cr2+:ZnS QD powder (~ 27 nm grain size). Cr2+:ZnS nanocrystalline dots (NCDs) were prepared using laser ablation. The mid-IR photoluminescence (PL) and lasing were studied. The dependence of PL spectrum profile on pump energy demonstrated a threshold behavior accompanied by the appearance of a sharp stimulated emission band around 2230 nm. The stimulated emission band is shifted to the longer wavelength with respect to the spontaneous emission and corresponds to the peak of the Cr:ZnS gain spectrum. This was also accompanied by a considerable lifetime shortening.
Recent progress in transition metal doped II-VI semiconductor materials (mainly Cr2+:ZnSe) makes them the laser
sources of choice when one needs a compact system with continuous tunability over 2-3.1 &mgr;m, output powers up to
2.7 W, and high (up to 70%) conversion efficiency. The unique combination of technological (low-cost ceramic
material) and spectroscopic characteristics make these materials ideal candidates for "non-traditional" regimes of
operation such as microchip and multi-line lasing. This article reviews these non-traditional Cr-doped mid-IR lasers as
well as describes emerging Fe2+:ZnSe lasers having potential to operate at room temperature over the spectral range
extended to 3.7-5.1 &mgr;m. In addition to effective RT mid-IR lasing transition metal doped II-VI media, being wide band
semiconductors, hold potential for direct electrical excitation. This work shows the initial steps towards achieving this
goal by studying Cr2+, Co2+, and Fe2+ doped quantum dots. We have demonstrated a novel method of TM doped II-VI
quantum dots fabrication based on laser ablation in liquid environment. TM doped II-VI quantum dots demonstrated
strong mid-IR luminescence. It opens a new pathway for future optically and electrically pumped mid-IR lasers based
on TM doped quantum confined structures.
We demonstrate an Er-fiber-laser-pumped, CW, high-power, single-longitudinal-mode Cr2+:ZnSe laser, tunable in the 2-
3 &mgr;m spectral region. The laser is operating in a single longitudinal mode regime with a linewidth of 80-130 MHz over a
120 nm tuning range around 2.5 &mgr;m, and delivers up to 150 mW of output power. The laser design is very compact and
is based on Kogelnik/Littman cavity configuration with the total optical length of the folded cavity of 10 cm. The
narrow-linewidth output spectrum can be quickly scanned over a 10 nm spectral range with a repetition rate of 220 Hz by
a piezo-controlled tuning mirror which allows for an extremely fast wavelength tuning of the output spectrum over a
large number of absorption spectral lines of trace gases of interest. As a test experiment, we performed a Dopplerlimited-
resolution intracavity laser absorption spectroscopy of ro-vibrational transitions of the &ngr;3 and &ngr;1 bands of H2O
with minimum detectable absorption coefficient of ~3x10-7 cm-1, which corresponds to 9 parts per billion by volume
water vapor detection limit. The laser is currently in active stage of development and its further optimization will allow
for full 2-3 &mgr;m fast tuning range and Watt-level output powers. This laser is being designed as a seeding source for an
OPG-OPA-based, highly sensitive trace-gas sensor system for real-time detection of gas traces of biological pathogens
and explosives in the molecular fingerprint mid-IR spectral region of 2-10 &mgr;m.
PbWO4 crystals with Ho concentration ranging from 0.2% to 4% were grown by the Czochralski method. Polarized
optical absorption, emission and kinetics of fluorescence were studied over 20-300K temperature and 0.2-8&mgr;m spectral
ranges. Stimulated Raman scattering in PbWO4 crystal was studied under 1.6 and 2.0 &mgr;m excitation.
We report the study of middle-infrared electroluminescence of n-type, Cr doped bulk ZnSe crystals. n-type, Cr-doped
ZnSe samples were prepared in three stages. At the first stage, the undoped polycrystalline ZnSe samples were grown
by chemical vapor deposition. During the second stage, the doping of 1 mm thick ZnSe polycrystalline wafers was
performed by post-growth thermal diffusion of Cr. Finally, Cr:ZnSe wafers were annealed with Al2Se3 and ZnSe
powders in sealed vacuumed ampoules at 950°C for 96 hours. Comparison of the absorption spectra of the crystals
before and after thermal diffusion with Aluminum indicates the preservation of the desired Cr2+ ions. Ohmic contacts
for electrical measurements were formed by polishing the facets and wetting the surface of the crystals with In. The best
crystals demonstrated conductivity of up to 10-100 ohm*cm. The electroluminescence measurements were taken using
synchronous detection methods with an InSb detector. A pulse generator output (100V) at 5 kHz and a lock-in amplifier
were used to distinguish luminescence signals from other possible noise sources. We report the observation of middleinfrared
(2-3μm and 8μm) and visible (~600 nm) electroluminescence of n-type Cr doped bulk ZnSe crystals.
This paper is focused on a design of flexible laser systems capable to provide spatial transformation of the pump radiation into the spectral domain of the output laser oscillation using specially designed “spatially dispersive” laser cavity. These systems also provide ultrabroadband or controlled spectral linewidth of the output laser oscillation. The theoretical analysis based on gaussian approximation for the designed laser cavities with “spatial dispersion” was used to provide maximum spatial resolution of the spatial-spectral transformation. The transformations of the spatial distribution of the pump radiation into the spectral domain of the output laser oscillation were experimentally demonstrated in the gain-switched LiF:F2+** and LiF:F2- lasers with total efficiencies of up to 20% and output pulse spectrum width wider than 140 nm, centered at 0.96 μm and 1.14 μm, correspondingly. As a result of the optimization of the angular dispersion of the output radiation, the simultaneous phase-matching for second harmonic generation in the single nonlinear crystal was realized for the whole oscillation spectral range. This technique allows to use a nonlinear frequency conversion for nonlinear transformation of the beam spatial distribution. Due to this, the ultra broadband (>100 nm) or multiline (20 lines) second harmonic and sum frequency oscillations were demonstrated in a LiIO3 nonlinear crystal with an overall efficiencies of up to 12%.
We present a novel technical approach to build a multiwavelength/superbroadband laser source based on a combination of spectral and spatial domains. This approach provides a direct transformation of spatial domain of the pumping beam into spectral domain of the output oscillation. Several spatially dispersive laser cavities were designed and studied both theoretically and experimentally for optimal spatial to spectral transformation. This spatial to spectral transformation was demonstrated for LiF:F2+** color center laser, single broad-stripe diode laser operating at 660nm and 1560 nm multi-stripe diode laser.
A novel technical approach to build a multiwavelength laser source for DWDM applications is described. The basic idea of this system is to maintain simultaneous lasing operation in a gain medium at different wavelengths without mode competition. The system uses a novel dispersive cavity. By designing this cavity structure appropriately, the system creates its own microcavities-channels each lasing independently at different wavelengths across the complete gain spectrum of the laser active material. Multifrequency lasing on the basis of a single diode laser chip was analyzed theoretically and demonstrated experimentally.
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