Degenerate Two-photon Absorption Research Articles

Degenerate and non-degenerate two-photon absorption of coumarin dyes.

Two-photon absorption (2PA) spectroscopy is a robust bioimaging tool that depends on the determined cross-sections (σ2PA). The absorption of both photons occurs simultaneously with equivalent (degenerate) or different (non-degenerate) photon energies, D-2PA and ND-2PA, respectively. The former has been investigated experimentally and computationally for many systems, while the latter remains relatively unexplored computationally and limited experimentally. In this study, response theory using time-dependent density functional theory (TD-DFT) and the 2-state model (2SM) have been utilized to investigate σD-2PA and σND-2PA for the excitation to the lowest energy singlet state (S1) of coumarin, coumarin 6, coumarin 120, coumarin 307, and coumarin 343. Solvents involved were methanol (MeOH), chloroform (ClForm), and dimethylsulfoxide (DMSO), where the latter leads to the largest σ2PA. Values of σ2PA are largest for coumarin 6 and lowest for coumarin, which illustrates the effect of substituents. The 2SM clarifies how the largest cross-sections correspond to molecules with the largest transition dipole moments, μ01. In general, σD-2SM computations agree with σD-2PA. Moreover, σND-2SM are in qualitative agreement with σND-2PA with comparable enhancement relative to σD-2PA. Overall, σND-2PA are larger than σD-2PA where the increase is in the range of 22% to 49%, depending on the coumarin as well as the relative energies of the two photons. This work aids in future investigations into various fluorophores to understand their photophysical properties for ND-2PA.

Research advances in nondegenerate two-photonabsorption and its applications

Nondegenerate two-photon absorption is a nonlinear optical effect in which two photons with different energy are absorbed by a medium simultaneously, resulting in a single electron transition from ground state to excited state through an intermediate virtual state. Compared with the degenerate two-photon absorption coefficient, the absorption coefficient of nondegenerate two-photon absorption is increased by tens or even hundreds of times due to the intermediate resonance effect, so it has great potentials in many nonlinear optical applications. Firstly, the basic principle of two-photon absorption is introduced and the enhancement mechanism of non-degenerate two-photon absorption is explained in this paper. Secondly, the basic method of measuring two-photon absorption is introduced in detail. Thirdly, the reports on nondegenerate two-photon absorption of three-dimensional semiconductor materials and two-dimensional materials are reviewed. Finally, the application progress of infrared detection and imaging, two-photon fluorescence microscope, all-optical switch and optical modulation is summarized, and the future research in this field is summarized and prospected.

Two-Photon Excitation Spectroscopy of Silicon Quantum Dots and Ramifications for Bio-Imaging.

Two-photon excitation in the near-infrared (NIR) of colloidal nanocrystalline silicon quantum dots (nc-SiQDs) with photoluminescence also in the NIR has potential opportunities in the field of deep biological imaging. Spectra of the degenerate two-photon absorption (2PA) cross section of colloidal nc-SiQDs are measured using two-photon excitation over a spectral range 1.46 < ℏω < 1.91 eV (wavelength 850 > λ > 650 nm) above the two-photon band gap Eg(QD)/2, and at a representative photon energy ℏω = 0.99 eV (λ = 1250 nm) below this gap. Two-photon excited photoluminescence (2PE-PL) spectra of nc-SiQDs with diameters d = 1.8 ± 0.2 nm and d = 2.3 ± 0.3 nm, each passivated with 1-dodecene and dispersed in toluene, are calibrated in strength against 2PE-PL from a known concentration of Rhodamine B dye in methanol. The 2PA cross section is observed to be smaller for the smaller diameter nanocrystals, and the onset of 2PA is observed to be blue shifted from the two-photon indirect band gap of bulk Si, as expected for quantum confinement of excitons. The efficiencies of nc-SiQDs for bioimaging using 2PE-PL are simulated in various biological tissues and compared to efficiencies of other quantum dots and molecular fluorophores and found to be comparable or superior at greater depths.

Single-Photon Infrared Imaging With a Silicon Camera Based on Long-Wavelength-Pumping Two-Photon Absorption

We experimentally demonstrated an ultra-sensitive imaging system for telecom photons based on the non-degenerate two-photon absorption in a silicon-based electron multiplying charge-coupled device (EMCCD). The proposed long-wavelength-pumping scheme with mid-infrared pulsed excitation could not only effectively increase the two-photon absorption coefficient, but also significantly suppress the background noise caused by the harmonic absorption of the strong pumping field. In comparison to the photoelectric response via the degenerate two-photon absorption, the implemented configuration could offer over 30-folded enhancement of the photon-counting rate in the infrared imaging. The resulting detection sensitivity up to 1 photon/pixel/pulse was unprecedentedly approached, thus facilitating the single-photon operation. The elimination of the stringent phase matching as typically required in the optical parametric conversion has led to a high spatial resolution of 13 μm. Moreover, the on-chip nonlinearity of the optical imager would enable a broadband spectral window and an enlarged field of view. In combination with the 5-ps temporal resolution due to the coincident optical gating, the presented imaging system would find various promising applications, such as low-light fluorescence lifetime microscopy and photon counting time-of-flight 3D imaging.

Resonance-Enhanced Two-Photon Absorption and Optical Power Limiting Properties of Three-Dimensional Perylene Bisimide Derivatives.

Push-pull organic structures characterized by an intramolecular charge transfer (ICT) process and π-electron delocalization are potentially interesting luminescent materials. A series of three-dimensional o-carborane-containing perylene bisimide derivatives (PBIs) were synthesized, and their optical properties were systematically investigated to illustrate the stereo effect, especially on the two-photon absorption (2PA) and optical power limiting (OPL) properties. Open-aperture Z-scan curves showed that all four PBIs displayed strong and broad two-photon absorptivities based on the resonance-enhanced phenomenon. The maximum degenerate two-photon absorption cross section (δ2PA) increased with the number of PBI substituents. The derivative CB-PBI possessed a δ2PA value of ∼2400 GM at 650 nm, a significant enhancement in comparison with that of the parent PBI (∼719 GM), ascribed to the present stereo effect. When the aromatic-donating units changed from naphthyl and pyrenyl to PBI, the generated multidimensional intramolecular charge transfer (ICT) from the aromatic units to the o-carborane cage contributed to the 2PA processes. All of the fluorophores exhibited excellent optical power limiting (OPL) performances as well as a minimum limiting threshold of ∼4.98 mJ/cm2 for CB-PBI. These significant results not only allow us to get deep insight into the nature of the fundamental stereo effect and nonlinear optical (NLO) response involved but also guide us toward the design of new multifunctional luminescent materials.

Tunable nonlinear optical responses of few-layer graphene through lithium intercalation

Abstract Intercalation has been demonstrated to be a powerful tool for tuning the physical and chemical properties of two-dimensional (2D) materials, providing the highest possible doping level and an ideal system to study various electronic states. In this work, we demonstrate that the nonlinear absorption effect of few-layer graphene (about 6–8 layers) is changed from saturable absorption (SA) to reverse saturable absorption (RSA) after lithium intercalation. This is attributed to the increase of Fermi energy owing to the charge transfer from Li to graphene layers in intercalated compounds (LiC6). And the change of nonlinear absorption effect is revisable after deintercalation. In addition, the modulation depth of RSA in lithiated graphene is found to rise with the decrease of incident laser wavelength, different from that of pristine graphene. Besides, the dispersion relationships of degenerate and nondegenerate two-photon absorption are analyzed from the results of nonlinear absorption and transient dynamics of lithiated graphene, indicating the 1.91–2.21 eV upshift of the Fermi surface. Our findings of the intercalation-tunable nonlinear optical absorption effect pave the way for the construction of nonlinear optical devices based on 2D intercalation compounds.

Im{χ(3)} spectra of 110-cut GaAs, GaP, and Si near the two-photon absorption band edge

Spectra of the degenerate two-photon absorption coefficient β(ω), anisotropy parameter σ(ω), and dichroism parameter δ(ω)=[σ(ω)+2η(ω)]/2 of crystalline 110-cut GaAs, GaP, and Si, at 300 K were measured using femtosecond pump–probe modulation spectroscopy over an excitation range in the vicinity of each material’s half-bandgap Eg/2 (overall 0.62&amp;lt;ℏω&amp;lt;1.91 eV or 2000&amp;gt;λ&amp;gt;650 nm). Together, these three parameters completely characterize the three independent components of the imaginary part of the degenerate third-order nonlinear optical susceptibility tensor Im{χabcd(3)(ω)}. In direct-gap GaAs, these components peak at ℏω≈0.78Eg, which is close to the peak at ℏω=0.71Eg predicted by the Jones–Reiss phenomenological model. The dispersion is comparable with ab initio calculations. In indirect-gap GaP and Si, these components tend to increase with ℏω over our tuning range. In Si, the dispersion differs significantly from predictions of semi-empirical models, and ab initio calculations do not account for transitions below the two-photon direct bandgap, motivating further investigation. Kleinman symmetry was observed to be broken in all three materials. We also note anomalies observed and their possible origins, emphasizing the advantages of a 2-beam experiment in identifying the contribution of various nonlinear effects.

Determination of the contributions of degenerate and non-degenerate two-photon absorption response in silicon avalanche photodiode for infrared photon detection

The study of non-linear interactions in semiconductor photo-electronic devices to achieve effective and fast photon identification is an ongoing and important task. We investigated the specific contribution of degenerate and non-degenerate two-photon absorption (D-TPA and ND-TPA) response in silicon avalanche photodiode (Si-APD) for infrared photon detection at room temperature. We experimentally demonstrated that when the two laser pulses overlapped, the average D-TPA quantum detection efficiencies at 1800 nm, and that at 1550 nm were measured as 3.3 × 10−16 counts•pulse/photon2, 4.3 × 10−15 counts•pulse/photon2, respectively. And the ND-TPA quantum detection efficiency of 1800 nm and 1550 nm was measured to be 7.9 × 10−16 counts•pulse/photon2. This study provides a solution for the practical infrared photon detection devices based on TPA effect in Si-APDs.

The two-photon absorption coefficient in a wide spectral range of Cd1-0.45Mn0.45Te

Abstract We are reporting, for the first time to our knowledge, measurement of the degenerate two-photon absorption (TPA) coefficient in Cd1-xMnxTe (x = 0.45) in a wide spectral range (690–1040 nm), with a 5 nm resolution. The spectral dependence of the TPA is modeled as a combination of a-a and f-f transitions. The time response is ultrafast at 780 nm with a relaxation time on the order of 14.1 ps and a large TPA coefficient on the order of 60 cm/GW at 690 nm.

Revisiting the temporal dispersion and broadening impact on degenerate two-photon absorption

A method to calibrate the peak power spectral density (PSD) for white light continuum (WLC) has been proposed. It is applied to measure degenerate two-photon absorption (TPA) coefficients β for continuous spectral range at 550–750 nm and obtains consistent results with the previous work. Via this method, it has been proved that different spectral components can be appropriately dispersed by adding an adequate chirp so that degenerate TPA coefficients can be extracted. Two factors are demonstrated to impact the extraction of nondegenerate absorption contribution using Z-scan setup. One is the co-effect of the band width (line width) of incident pulses and the nonlinear absorption (NLA) band width of the material on the nondegenerate absorption. The other one is the balance between chirp effect caused by the dispersion and nonlinearity. As a consequence, in order to obtain degenerate NLA information, the chirp of WLC pulses should be set to be an appropriate value especially for materials with broad NLA coefficients.

2D Perovskites with Giant Excitonic Optical Nonlinearities for High-Performance Sub-Bandgap Photodetection.

Two-dimensional (2D) perovskites have proved to be promising semiconductors for photovoltaics, photonics, and optoelectronics. Here, a strategy is presented toward the realization of highly efficient, sub-bandgap photodetection by employing excitonic effects in 2D Ruddlesden-Popper-type halide perovskites (RPPs). On near resonance with 2D excitons, layered RPPs exhibit degenerate two-photon absorption (D-2PA) coefficients as giant as 0.2-0.64 cm MW- 1 . 2D RPP-based sub-bandgap photodetectors show excellent detection performance in the near-infrared (NIR): a two-photon-generated current responsivity up to 1.2 × 104 cm2 W-2 s-1 , two orders of magnitude greater than InAsSbP-pin photodiodes; and a dark current as low as 2 pA at room temperature. More intriguingly, layered-RPP detectors are highly sensitive to the light polarization of incoming photons, showing a considerable anisotropy in their D-2PA coefficients (β[001] /β[011] = 2.4, 70% larger than the ratios reported for zinc-blende semiconductors). By controlling the thickness of the inorganic quantum well, it is found that layered RPPs of (C4 H9 NH3 )2 (CH3 NH3 )Pb2 I7 can be utilized for three-photon photodetection in the NIR region.

Efficient non-degenerate two-photon excitation for fluorescence microscopy.

Non-degenerate two-photon excitation (ND-TPE) has been explored in two-photon excitation microscopy. However, a systematic study of the efficiency of ND-TPE to guide the selection of fluorophore excitation wavelengths is missing. We measured the relative non-degenerate two-photon absorption cross-section (ND-TPACS) of several commonly used fluorophores (two fluorescent proteins and three small-molecule dyes) and generated 2-dimensional ND-TPACS spectra. We observed that the shape of a ND-TPACS spectrum follows that of the corresponding degenerate two-photon absorption cross-section (D-TPACS) spectrum, but is higher in magnitude. We found that the observed enhancements are higher than theoretical predictions.

Layer-modulated two-photon absorption in MoS2: probing the shift of the excitonic dark state and band-edge

Questions hovering over the modulation of bandgap size and excitonic effect on nonlinear absorption in two-dimensional transition metal dichalcogenides (TMDCs) have restricted their application in micro/nano optical modulator, optical switching, and beam shaping devices. Here, degenerate two-photon absorption (TPA) in the near-infrared region was studied experimentally in mechanically exfoliated MoS2 from single layer to multilayer. The layer-dependent TPA coefficients were significantly modulated by the detuning of the excitonic dark state (2p). The shift of the quasiparticle bandgap and the decreasing of exciton binding energy with layers were deduced, combined with the non-hydrogen model of excitons in TMDCs and the scaling rule of semiconductors. Our work clearly demonstrates the layer modulation of nonlinear absorption in TMDCs and provides support for layer-dependent nonlinear optical devices, such as optical limiters and optical switches.

Nondegenerate and degenerate two-photon absorption in cuprous oxide thin film

A cuprous oxide (Cu2O) thin film was prepared by radio-frequency (RF) magnetron sputtering. The crystal structure, linear transmission spectrum and film thickness were characterized by X-ray diffraction (XRD), ultraviolet–visible–near infrared (UV–Vis–NIR) absorption spectroscopy and ellipsometry. By performing the pump-probe and [Formula: see text]-scan technique, respectively, nondegenerate and degenerate two-photon absorption (D-TPA) coefficients of the Cu2O thin film at several different excitation wavelengths were experimentally determined. The nondegenerate two-photon absorption (ND-TPA) coefficient always exhibits larger magnitude than the corresponding D-TPA coefficient. In particular, the ND-TPA coefficient shows a maximum value of [Formula: see text][Formula: see text]cm/GW. This study indicates that the cuprous oxide could be a potential material for ultrafast nonlinear photonic devices based on two-photon absorption due to its large ND-TPA coefficient.

Temporally Resolving Synchronous Degenerate and Nondegenerate Two‐Photon Absorption in 2D Semiconducting Monolayers

AbstractDegenerate and nondegenerate two‐photon absorption (TPA) in WS2 and MoSe2 monolayers are synchronously induced and temporally resolved by femtosecond laser pump‐probe. Differential transmission signals in the first 500 fs consist of negative and positive components, that originate from direct probe depletion via nondegenerate TPA and carrier accumulation via degenerate TPA, respectively. Temporal cross‐correlation of pump and probe pulses allows us to fully decouple the ultrafast nondegenerate and degenerate TPA signals. Subsequently, degenerate and nondegenerate TPA coefficients are calculated as a function of pump irradiance. Under nonresonant pumping, 100 ± 10 and 250 ± 25 cm GW−1 are obtained for degenerate and nondegenerate TPA coefficients of monolayer WS2, respectively, which both present linearly decreasing trends as increasing pump irradiances. However, under resonant pumping of 2p excitonic states in monolayer MoSe2, degenerate TPA coefficients exponentially decrease from 800 to 80 cm GW−1 as increasing pump irradiances, due to the interplay between band‐renormalization and band‐filling effects, while nondegenerate TPA coefficient is about 650 ± 50 cm GW−1. For comparison, a trilayer MoSe2 is also investigated. These results set a foundation for precisely measuring TPA coefficients and actively controlling nonlinear excitonic dynamics via TPA in 2D semiconducting monolayers.

Investigation of nondegenerate two-photon absorption in common fluorescent dyes

The nondegenerate two-photon excited fluorescence (ND-TPEF) and nondegenerate two-photon absorption (ND-TPA) cross-sections of two common fluorescent dyes were investigated using the femtosecond pump-probe technique at several wavelength combinations. Time-resolved and laser intensity dependent fluorescence revealed that the fluorescence was originated from the ND-TPA effect. Experimental ND-TPA cross-section exhibited larger values than corresponding degenerate two-photon absorption case. Additionally, an improved essential-state model involving multiple TPA excited states was proposed to evaluate the TPA cross-section of organic molecules, which showed good agreement with experimental results. This study indicates that the investigated fluorescent dyes would play important roles in multicolor two-photon imaging.

Dispersive white light continuum single Z-scan for rapid determination of degenerate two-photon absorption spectra

We present an experimental technique to determine the degenerate two-photon absorption (2PA) spectra by performing a single Z-scan using a high-spectral-irradiance white light continuum (WLC) generated by a hollow core fiber. The hollow fiber was filled with Argon (Ar) gas at a pressure of 0.6 bar and was pumped with 500 mJ, 30 fs, and 800 nm pulses. The broadband WLC pulses with 350 nm bandwidth in the range of 600–950 nm were compressed to sub-8 fs pulses. To characterize and interpret the data obtained from this method, the spectral, temporal and spatial characteristics of the WLC were first analyzed. The WLC emerging from the compressor was dispersed using a prism pair and then focused into the sample by a cylindrical lens. Since different spectral components are spatially separated, any part of the sample in the beam cross section is irradiated with almost single wavelength pulses leading to only a degenerate 2PA process. The nonlinear transmittance was then measured by a charge-coupled-device (CCD) line camera as a function of the sample position while the sample was moved along the beam direction by a motorized translation stage. In this way the Z-scans at different wavelengths in the WLC spectral range can be measured and thus the wavelength-resolved degenerate 2PA spectra can be obtained by performing a single scan using dispersive WLC. This method was verified on a well-characterized dye Rhodamine B and yield a reasonable agreement with the data found in the literature. We used this method to determine the 2PA spectra of some two-photon initiators (2PIs) developed for two-photon polymerization (2PP) based 3D micro-structuring.

Dual Emissive Multinuclear Iridium(III) Complexes in Solutions: Linear Photophysical Properties, Two-Photon Absorption Spectra, and Photostability

Linear steady-state and time-resolved spectroscopic properties, degenerate two-photon absorption (2PA) spectra, and photochemical stability of IrIII complexes TCQ[IrIII(ppz)2]n, (TCQ = tricycloquinazoline; ppz = 1-phenylpyrazole; n = 1 (1), n = 2 (2), and n = 3 (3)) are presented for liquid solutions. The analysis of the linear photophysical properties revealed the nature of the observed dual-component fluorescence–phosphorescence emission of 1–3 at room temperature. The values of 2PA cross sections were determined by open aperture Z-scans using a 1 kHz femtosecond laser system. The specific dependence of the 2PA efficiency on the number of ppz ligand units in 1–3 was determined. The quantum yields, Φph, for photochemical decomposition of TCQ[IrIII(ppz)2]n complexes were obtained for the first time using the absorption method [Corredor, C. C.; J. Photoch. Photobio. A 2006, 184, 105−112] with continuous wave laser irradiation, and the highest stability of Φph ≈ 4 × 10–6 was shown for 2 in toluene.

Mid-infrared two-photon absorption in an extended-wavelength InGaAs photodetector

We investigate the nonlinear optical response of a commercial extended-wavelength In0.81Ga0.19As uncooled photodetector. Degenerate two-photon absorption in the mid-infrared range is observed using a quantum cascade laser emitting at λ = 4.5 μm as the excitation source. From the measured two-photon photocurrent signal, we extract a two-photon absorption coefficient β(2) = 0.6 ± 0.2 cm/MW, in agreement with the theoretical value obtained from the Eg−3 scaling law. Considering the wide spectral range covered by extended-wavelength InxGa1–xAs alloys, this result holds promise for applications based on two-photon absorption for this family of materials at wavelengths between 1.8 and 5.6 μm.

Measurement of degenerate two-photon absorption spectra of a series of developed two-photon initiators using a dispersive white light continuum Z-scan

To achieve efficient micro- and nanostructuring based on two-photon polymerization (2PP), the development and evaluation of specialized two-photon initiators (2PIs) are essential. Hence, a reliable method to determine the two-photon absorption (2PA) spectra of the synthesized 2PIs used for 2PP structuring is crucial. A technique by which absolute visible-to-near-infrared 2PA spectra of degenerate nature can be determined via performing a single dispersive white-light continuum (WLC) Z-scan has been realized. Using a dispersed white light beam containing 8 fs pulses at wavelengths ranging from 650 nm to 950 nm, the nonlinear transmittance as a function of the sample position can be measured for all spectral components by performing a single scan along the laser beam propagation direction. In this work, the 2PA spectrum of three different 2PIs was determined using this technique. 2PP structuring was also accomplished using the developed 2PIs at different wavelengths. Tuning the wavelength of the laser to match the peak of the 2PA spectra of the developed 2PIs resulted in lower intensity thresholds and facilitated higher structuring speeds. As an example, using M2CMK 2PI for 2PP, the scanning speed can be increased up to 5 folds when the laser wavelength is tuned to 760 nm (i.e., 2PA maximum) instead of the conventionally used 800 nm.