Quantitative analysis of slow light experiments utilising coherent population oscillation (CPO) in a range of saturably absorbing media, including ruby and alexandrite, Er3+:Y2SiO5, bacteriorhodopsin, semi-conductor quantum devices and erbium doped optical fibres, shows that the observations may be more simply interpreted as saturable absorption phenomena. A basic two-level model of a saturable absorber displays all the effects normally associated with slow light, namely phase shift and modulation gain of the transmitted signal, hole burning in the modulation frequency spectrum and power broadening of the spectral hole, arising from the finite response time of the non-linear absorption. Only where hole-burning in the optical spectrum is observed (using independent pump and probe beams), or pulse delays exceeding the limits set by saturable absorption are obtained, can reasonable confidence be placed in the observation of slow light in such experiments. Superluminal ('fast light') phenomena in media with reverse saturable absorption (RSA) may be similarly explained.
The saturable absorption characteristics of two-, three-, and five-core one-dimensional fiber coupler arrays and the seven-core hexagonal fiber coupler array are investigated. It is shown that the performance of all these saturable absorbers are comparable and not much is gained, if anything, by going from a two-core nonlinear coupler geometry to a higher number of cores. This observation is supported by the similarity of the saturable absorption curves, as well as comparable pulse characteristics obtained from the simulation of a generic mode-locked fiber laser cavity.
A series of benchmark tests of slow light in saturable absorbers is proposed. Stage I concerns experimental tests of saturable absorption, which can mimic slow light in saturable media. Stage II outlines the more demanding requirements for practical observation of spectral hole-burning in the absorption line, which is responsible for the reduction in group velocity.
We report on the response of graphene to high intensity mid-IR radiation and show that graphene exhibits saturable absorption and significant two-photon absorption in the spectral region from 1.55 $μ$m to 3.50 $μ$m (0.35 eV to 0.80 eV). We find that the effective modulation depth of multilayer graphene is limited by two-photon absorption which will affect its performance as a laser mode-locking element. The measured saturation intensities of femtosecond pulses were found to depend on the third power of photon energy when we combined our results with others reported in literature, while those o…
Nonlinear absorption in four and five energy level systems have been studied with the aid of steady-state rate equation approach. We report on the tunability of saturable and reverse saturable absorption as a function of spectroscopic parameters (lifetimes and absorption cross-sections). Detailed information is given on the estimation of spectroscopic parameters in the nonlinear absorption spectroscopy. The exhaustive graphical analysis of this article can provide the brief idea about transmittance curves of the nonlinear absorption to the experimentalists. In four and five level cascade model…
The nonlinear absorption of two-dimensional molybdenum disulfide was analyzed using the Z-scan technique. Sample size corresponding to a number of layer determines the band gap in the materials which play the key role for nonlinearity. Exciton dipole transition from ground state to excited state for monolayer and bilayer/multilayer is determined by the excitation source, ESA and GSA values. If the band gap is wider than the excitation source, two-photon excitation process is dominant which requires the larger ESA than GSA. For narrower bandgap, one-photon excitation is favorable because of the…
We fabricate a free-standing molybdenum diselenide (MoSe2) saturable absorber by embedding liquid-phase exfoliated few-layer MoSe2 flakes into a polymer film. The MoSe2-polymer composite is used to Q-switch fiber lasers based on ytterbium (Yb), erbium (Er) and thulium (Tm) gain fiber, producing trains of microsecond-duration pulses with kilohertz repetition rates at 1060 nm, 1566 nm and 1924 nm, respectively. Such operating wavelengths correspond to sub-bandgap saturable absorption in MoSe2, which is explained in the context of edge-states, building upon studies of other semiconducting transit…
We present a superconducting metamaterial saturable absorber at terahertz frequencies. The absorber consists of an array of split ring resonators (SRRs) etched from a 100nm YBaCu3O7 (YBCO) film. A polyimide spacer layer and gold ground plane are deposited above the SRRs, creating a reflecting perfect absorber. Increasing either the temperature or incident electric field (E) decreases the superconducting condensate density and corresponding kinetic inductance of the SRRs. This alters the impedance matching in the metamaterial, reducing the peak absorption. At low electric fields, the absorption…
An advanced full-wave time-domain numerical model for reverse saturable absorption (RSA) is presented and verified against established methods. Rate equations, describing atomic relaxations and excitation dynamics, are coupled to Maxwell equations by using a Lorentzian oscillator. These oscillator models the kinetics-dependent light-matter interaction in the form of averaged polarizations. The coupled equations are discretized in space and time using a finite-difference time-domain method which provides a versatile platform to design complex structures and integrate diverse material models. We…
A detailed investigation of the nonlinear multimodal interference in a short graded-index multimode optical fiber is presented. The analysis is performed for a specific device geometry, where the light is coupled in and out of the multimode fiber via single-mode fibers. The same device geometry was recently used to obtain ultra-low-loss coupling between two single-mode optical fibers with very different mode-field diameters. Our results indicate the potential application of this simple geometry for nonlinear devices, such as in nonlinear switching, optical signal processing, or as saturable ab…
The two most commonly used models for passively modelocked lasers with fast saturable absorbers are the Haus modelocking equation (HME) and the cubic-quintic modelocking equation (CQME). The HME corresponds to a special limit of the CQME in which only a cubic nonlinearity in the fast saturable absorber is kept in the model. Here, we use singular perturbation theory to demonstrate that the CQME has a stable high-energy solution for an arbitrarily small but non-zero quintic contribution to the fast saturable absorber. As a consequence, we find that the CQME predicts the existence of stable model…
We study the breaking of reciprocity in non-Hermitian coupled photonic waveguides by the simultaneous action of the nonlinear effect of saturable absorption, and the presence of exceptional points. The nonlinear response of such a system is studied in depth, giving physical insight into the operational principles and fundamental limitations, while producing analytical and semi-analytical results for the transmission and nonreciprocal intensity range. We numerically validate the theoretical results and assess important performance metrics for the nonreciprocal operation of such a device. This n…
We proposed a narrow spectral bandwidth Erbium-doped fiber (EDF) laser Q-switched by a homemade saturable dynamic induced grating (SDIG) which is introduced via reforming the structure of a fiber saturable absorbers FSA with a piece of EDF and a fiber Bragg grating. The SDIG integrates both saturable absorption and spectral filtering effect simultaneously, which was confirmed through theoretical analysis and experimental results for the first time, to the best of our knowledge. Further study verified that the spectral width of the Q-switched emissions is decided by the length of the SDIG and t…
In connection with the experiments recently achieved on doped crystals, biological samples, doped optical fibers and semiconductor heterostructures, we revisit the theory of the propagation of a pulse-modulated light in a saturable absorber. Explicit analytical expressions of the transmitted pulse are obtained, enabling us to determine the parameters optimizing the time-delay of the transmitted pulse with respect to the incident pulse. We finally compare the maximum fractional delay or figure of merit so attainable to those which have been actually demonstrated in the experiments.
We present an experimental and theoretical study of modal nonlinear dynamics in a specially designed dual-mode semiconductor Fabry-Perot laser with a saturable absorber. At zero bias applied to the absorber section, we have found that with increasing device current, single mode self-pulsations evolve into a complex dynamical state where the total intensity experiences regular bursts of pulsations on a constant background. Spectrally resolved measurements reveal that in this state the individual modes of the device can follow highly symmetric but oppositely directed spiralling orbits. Using a g…
We employed open-aperture Z-scan technique to unveil the third-order optical nonlinearity in ZnCo2O4 (ZCO) microflowers. Our results indicate that intersystem crossing (ISC) lifetime can be used as simple tool to demonstrate remarkably contrasting optical nonlinearity in ZCO. Ultrafast transient absorption measurements reveal that ISC from singlet to triplet state takes place in 5 ps. For femtosecond laser pulses, when the pulse duration is shorter than ISC lifetime, saturable absorption (SA) takes place for all intensities. On the contrary, when the pulse duration is longer than ISC for nanos…
We firstly report mode-locked square-wave pulse in Yb-doped fiber laser based on graded index multimode fiber of reverse suturable absorption. By adjusting the pump power, the width of the square-wave can be tuned range from 350 ps to 52.6 ns with 3dB bandwidth spectrum of 0.73 nm. The supermode suppression ratio exceeds ~ 65 dB, which indicates excellent mode-locked operation state, and we also study the characteristic of pulse by the chirp measurement system. The mode-locked square-wave pulse fiber laser can sever as high power light source for industrial applications.
In this article, we studied intensity dependent third order nonlinear optical response in ternary As40Sb7Se53 and As40Sb10Se50 chalcogenide glasses by employing nanosecond Z-scan technique. At low intensity, we observed saturable absorption in As40Sb7Se53 which makes a remarkable transition to reverse saturable absorption at higher intensities. On the other hand, when the Sb concentration increased in As40Sb10Se50, saturable absorption disappears and the sample exhibits only two-photon absorption. Experimental results further indicate that the strong two-photon absorption in our samples can be…
Quantitative evaluation of some recent 'slow light' experiments based on coherent population oscillations (CPO) shows that they can be more simply interpreted as saturable absorption phenomena. Therefore they do not provide an unambiguous demonstration of 'slow light'. Indeed a limiting condition on the spectral bandwidth is not generally satisfied, such that the requirements for burning a narrow spectral hole in the homogeneously broadened absorption line are not met. Some definitive tests of 'slow light' phenomena are suggested, derived from analysis of phase shift and pulse delay for a satu…
Intensity-dependent enhancement of saturable absorption in a film of PbS-Au4 nanohybrid composites has been observed by femtosecond time-resolved transient absorption measurement at 780 nm. The nonlinear absorption coefficient of saturable absorption in PbS-Au4 nanohybrid composites is found to be dependent on excitation irradiance and it is determined to be -2.9 cm/GW at 78 GW/cm2, an enhancement of nearly fourfold in comparison with that of pure PbS quantum dots (QDs). The enhancement is attributed to excitation of surface plasmon by resonant energy transfer between PbS QDs and Au nanopartic…
Fast saturable absorbers (FSAs) play a critical role in stabilizing many passively modelocked lasers. The most commonly used averaged model to study these lasers is the Haus modelocking equation (HME) that includes a third-order nonlinear FSA. However, it predicts a narrow region of stability that is inconsistent with experiments. To better replicate the laser physics, averaged laser models that include FSAs with higher-than-third-order nonlinearities have been introduced. Here, we compare three common FSA models to each other and to the HME using the recently-developed boundary tracking algor…
To shorten the duration of x-ray pulses, we present a nonlinear optical technique using atoms with core-hole vacancies (core-hole atoms) generated by inner-shell photoionization. The weak Coulomb screening in the core-hole atoms results in decreased absorption at photon energies immediately above the absorption edge. By employing this phenomenon, referred to as saturable absorption, we successfully reduce the duration of x-ray free-electron laser pulses (photon energy: 9.000 keV, duration: 6-7 fs, fluence: 2.0-3.5$\times$10$^5$ J/cm$^2$) by $\sim$35%. This finding that core-hole atoms are appl…
The ultrashort pulse laser operation is crucially defined by engaging explicit modulators. Conventionally, they are laborious to incorporate into an all-fibre design or involve the design of sophisticated cavities. We exploit Thulium-doped fibre as the gain and simple, highly integrated saturable absorber with a modulation depth of 23% and a high thermal damage threshold. Hence, pulses as short as 350fs carrying 1nJ energy at a repetition rate of 45MHz have been demonstrated. The laser average output power showed long-term stability with ~1%. The utilised concept of all-fibre saturable absorbe…
Saturable absorption is a non-perturbative nonlinear optical phenomenon that plays a pivotal role in the generation of ultrafast light pulses. Here we show that this effect emerges in graphene at unprecedentedly low light intensities, thus opening avenues to new nonlinear physics and applications in optical technology. Specifically, we theoretically investigate saturable absorption in extended graphene by developing a non-perturbative single-particle approach, describing conduction-electron dynamics in the atomically-thin material using the two-dimensional Dirac equation for massless Dirac fer…
In this work, a new model of effective lift-off threshold of oxide/metal target is presented. The influence of nonlinear processes in the oxide layer on its removal from the metallic samples using picosecond laser was investigated. Nonlinear and saturable absorption in the layer was incorporated into modeling for prediction of effective laser lift-off threshold fluence change with varying peak intensities in z-scan type experiment for the first time. The new model coincides well with the experimental results.
From the point of view of the differential phase delay experienced by the two counterpropagating optical fields, the self-starting of the mode-locked fiber laser with a nonlinear amplifying loop mirror (NALM) is theoretically studied. Although it is generally believed that NALM shows a saturable absorption effect on both continuous wave (CW) light and pulses, we find a counter-intuitive fact that cross-phase modulation (XPM) leads to opposite signs of differential nonlinear phase shifts (NPSs) in these two cases, resulting in inverse saturable absorption (ISA) during pulse formation process. T…
The enhanced nonlinear optical response of a one-dimensional (1D) photonic crystal (PC) made from polymers and graphene composites is observed. The graphene PC was fabricated by spin-coating. It shows obvious bandgaps at two wavelengths in transmittance. Femtosecond Z-scan measurement at 515 nm and 1030 nm reveals a distinct enhancement in the effective nonlinear absorption coefficient Beff (and imaginary part of third-order dielectric susceptibility ImX(3)) for graphene nanoflakes embedded in the PC, when compared with the bulk graphene-polymer dispersion. The effect is studied in a wide rang…
We present the study of a proof-of-concept integrated device that can be used as a nonlinear broadband isolator. The device is based on the asymmetric loading of a highly-confining silicon-slot photonic coupler with graphene layers, whose ultrafast and low-threshold saturable absorption can be exploited for nonreciprocal transmission between the cross-ports of the coupler. The structure is essentially a non-Hermitian system, whose exceptional points are briefly discussed. The nonlinear device is modeled with a coupled Schrodinger equation system whose validity is checked by full-vector finite …
There are two opposing models in the analysis of the slow transmission of light pulses through saturable absorbers. The canonical incoherent bleaching model simply explains the slow transmission by combined effects of saturation and of non-instantaneous response of the medium resulting in absorption of the front part of the incident pulse larger than that of its rear. The second model, referred to as the coherent-population-oscillations (CPO) model, considers light beams whose intensity is slightly pulse modulated and attributes the time delay of the transmitted pulse to a reduction of the gro…
To date, MXene has been discovered for its viability as alternatives to conventional saturable absorber such as carbon nanotube and graphene. The characteristics of high nonlinear saturable absorption, astounding modulation depth, flexible bandgap tunability, and high electron density near Fermi level are the fundamentals of the MXene as an excellent saturable absorber candidate. In particular, the research effort contributed to MXene in nonlinear ul-trafast optics are extensively growing because MXene comprises one of the largest families in 2D nanomaterials that provides huge combination pos…
AgInSe2 nanorods (NRs) with diameter of 15 nm have been investigated for their nonlinear optical responses by using Z-scan and transient absorption techniques with femtosecond laser pulses of photon energy greater than the bandgap. At excitation irradiance of 20 GW/cm2, AgInSe2 NRs reveal saturation in the nonlinear absorption and optical Kerr nonlinearity with a recovery time determined to be a few ten picoseconds. Such large saturable absorption and Kerr nonlinearity exhibit a third-order susceptibility of 1.2 x 10-8 esu and a figure of merit of 0.04 esu.cm.s-1, making AgInSe2 NRs a promisin…
The paper presents a critical analysis of publications devoted to one of the methods for production of the so-called "slow light" (the light with an anomalously low group velocity) due to extremely high local steepness of the dispersion curve of the medium. The method in point employs for this purpose the effect of coherent population oscillations accompanied by burning of a narrow spectral hole in the homogeneously broadened absorption spectrum. Physical model of the effect proposed in the studies under consideration is based on analysis of response of a nonlinear medium to a low-frequency in…
We experimentally demonstrate a passively Q-switched erbium-doped fiber laser (EDFL) operation by using a saturable absorber based on Fe3O4 nanoparticles (FONP) in magnetic fluid (MF). As a kind of transition metal oxide, the FONP has a large nonlinear optical response with a fast response time for saturable absorber. By depositing MF at the end of optical fiber ferrule, we fabricated a FONP-based saturable absorber, which enables a strong light-matter interaction owing to the confined transmitted optical field within the single mode fiber. Because of large third-order optical nonlinearities o…
We report the first observation of robust self-trapping of vortex beams propagating in a uniform condensed medium featuring local saturable self-focusing nonlinearity. Optical vortices with topological charge m=1, that remain self-trapped over ~ 5 Rayleigh lengths, are excited in carbon disulfide using a helical light beam at 532 nm and intensities from 8 to 10 GW/cm^2. At larger intensities, the vortex beams lose their stability, spontaneously breaking into two fragments. Numerical simulations based on the nonlinear Schrödinger equation including the three-photon absorption and nonpolynomial …
Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons…
Passive mode-locking critically relies on a saturable loss mechanism to form ultrashort pulses. However, in Kerr-lens mode-locking (KLM), no actual absorption takes place, but rather losses appear due to diffraction, and actual light must escape the cavity. The Kerr-lens effect works to generate through diffraction an effective instantaneous saturable absorber that delicately depends on the interplay between the spatial and temporal profiles of the pulse. Despite the importance of KLM as a technique for generating ultrafast pulses and the fundamental role of the diffraction losses in its opera…
Saturable absorption in defect-rich diamond nanophotonics
Institute for Quantum Science and Technology, University of Calgary（卡尔加里大学量子科学与技术研究所）；Department of Physics, University of Alberta（阿尔伯塔大学物理系）；National Research Council of Canada, Quantum and Nanotechnology Research Centre（加拿大国家研究委员会量子与纳米技术研究中心）
A comparative analysis of two approaches to description of the light modulation pulse delay in a saturable absorber is presented. According to the simplest model, the delay of the optical pulse is a result of distortion of its shape due to absorption self-modulation in the nonlinear medium. The second model of the effect, proposed at the beginning of our century, connects the pulse delay with the so-called "slow light" resulting from the group velocity reduction under conditions of the coherent population oscillations. It is shown that all the known experimental data on the light pulse delay i…
We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons. Because the setting does not requi…
It is shown that the effect of hole-burning under conditions of coherent population oscillations as well as the light pulse delay in a saturable absorber (a modification of the "slow light" effect) can be interpreted, in a comprehensive way, in terms of {\it intensity spectrum} of the light and {\it intensity-related susceptibility} of the non-linear medium. The physical content of these effects is illustrated by a simple electric circuit with a non-linear resistor which realizes a full analog of the saturable absorber. In this case the effect of hole-burning in the absorption spectrum of the …
The interaction of intense light with matter gives rise to competing nonlinear responses that can dynamically change material properties. Prominent examples are saturable absorption (SA) and two-photon absorption (TPA), which dynamically increase and decrease the transmission of a sample depending on pulse intensity, respectively. The availability of intense soft X-ray pulses from free-electron lasers (FEL) has led to observations of SA and TPA in separate experiments, leaving open questions about the possible interplay between and relative strength of the two phenomena. Here, we systematicall…
The optical conductance of monolayer graphene is defined solely by the fine structure constant. The absorbance has been predicted to be independent of frequency. In principle, the interband optical absorption in zero-gap graphene could be saturated readily under strong excitation due to Pauli blocking. Here, we demonstrate the use of atomic layer graphene as saturable absorber in a mode-locked fiber laser for the generation of ultrashort soliton pulses (756 fs) at the telecommunication band. The modulation depth can be tuned in a wide range from 66.5% to 6.2% by varying the thickness of graphe…
We propose to achieve a strong bistable response of a thin layer of a saturable absorption medium by involving a planar metamaterial specially designed to bear a high-Q trapped-mode resonance in the infrared region.
We introduce a system of two component two-dimensional (2D) complex Ginzburg-Landau equations (CGLEs) with spin-orbit-coupling (SOC) describing a wide-aperture microcavity laser with saturable gain and absorption. We report families of two-component self-trapped dissipative laser solitons in this system. The SOC terms are represented by the second-order differential operators, which sets the difference, $|ΔS|=2$, between the vorticities of the two components. We have found stable solitons of two types: vortex-antivortex (VAV) and semi-vortex (SV) bound states, featuring vorticities $\left( -1,…
The question is raised about whether the pulse delay in a saturable absorber has anything to do with the "slow light" and group velocity reduction. We also wonder why the 40-years-old trivial interpretation of the effect remains so far ignored.
The observations reported by Franke-Arnold et al (SCIENCE Reports, 1 July 2011 p. 65) do not provide evidence of slow light enhanced rotary photon drag as claimed, but arise from well-known saturable absorption phenomena consistent with the use of a spectrally broad light source, as described in their theoretical analysis (supporting online material)
Nonlinear optical (NLO) response in terms of reverse saturable absorption (RSA) has been exploited extensively for optical limiting. Here, we experimentally demonstrate that flower-like hybrid nanostructures of NiCo2O4 and Multiwall Carbon Nanotubes (NCO@MWCNT) exhibit a strong non-linearity in their absorption, specifically an excited state absorption (ESA) induced RSA, when exposed to nanosecond laser pulses. We obtain strong nonlinear absorption coefficient (\b{eta}) and nonlinear refractive index (n2) in hybrid NCO@MWCNT, the values that are 2-times and 2-orders of magnitude higher, respec…
Atomic layer graphene possesses wavelength-insensitive ultrafast saturable absorption, which can be exploited as a full-band mode locker. Taking advantage of the wide band saturable absorption of the graphene, we demonstrate experimentally that wide range (1570 nm - 1600nm) continuous wavelength tunable dissipative solitons could be formed in an erbium doped fiber laser mode locked with few layer graphene.
