Two-dimensional red phosphorus: Emerging nonlinear optical material with solvent effect

doi:10.21203/rs.3.rs-3787432/v1

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Two-dimensional red phosphorus: Emerging nonlinear optical material with solvent effect

https://doi.org/10.21203/rs.3.rs-3787432/v1

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Currently, the existing third-order nonlinear optical research about phosphorus-based two-dimensional materials mainly focuses on black phosphorus, while the study on red phosphorus is still insufficient. Here, the third-order nonlinear optical properties of two-dimensional red phosphorus are reported for the first time. Interestingly, the nonlinear optical solvent effect is observed in several solvents including 1,2-propylene glycol and 1,2,3-glycerol. Ultrafast carrier dynamics and time-dependent density functional theory calculations jointly reveal that this solvent-dependent nonlinear optical behavior is attributed to different absorption capacities between the ground and excited states, which are influenced by the dielectric polarizations of the solvents. These results endow two-dimensional red phosphorus with promising prospects in nonlinear optical applications.

Physical sciences/Optics and photonics/Lasers, LEDs and light sources/Ultrafast lasers

Physical sciences/Optics and photonics/Optical physics/Ultrafast photonics

With the discovery of graphene in 2004, two-dimensional (2D) materials took a giant leap forward¹. Since then, thousands of 2D materials have been discovered, such as h-BN², graphdiyne³, silicene⁴, and borophene⁵. Among them, red phosphorus (RP) has attracted increasing attention in many fields due to its excellent optical and chemical properties^6,7. The RP can be categorized into crystalline and amorphous structures. Especially, the amorphous RP is a kind of chain-like linear polymer, arranged in the space through intermolecular force⁸. The growth on one orientation can be restricted, making it easy to form a 2D structure. Compared with the allotrope black phosphorus (BP), the commercial amorphous RP is low-cost and non-toxic, facilitating its widespread availability for large-scale productions and practical applications such as flame retardant⁹, semiconductor dopant¹⁰, and biological therapy¹¹. More importantly, RP shows advantages in strong visible light responses and tunable bandwidths (~ 1.5–2.4 eV)^12,13, making it suitable for optical modulation¹⁴. Nonetheless, whether the 2D RP has a third-order nonlinear optical (NLO) response and what is the mechanism have not been studied yet.

Third-order NLO effect is a phenomenon where the refraction or absorption of the medium changes with the intensity of the incident light. It has permeated into various professions and become the key theory in numerous modern techniques¹⁵. The NLO mechanisms employed in these techniques are diverse, including the two-photon absorption^16,17, the optical Kerr effect^18,19, and the excited state absorption (ESA)^17,20. ESA is one of the most important mechanisms that can exert significant influence on the NLO absorption types. When the cross section of ESA is smaller than that of ground state absorption (GSA), a saturable absorption (SA) will be observed. When larger, a reverse saturable absorption (RSA) occurs²¹. For example, Wu et al. explained the RSA phenomenon of 2D BP under strong pump fluence by the ESA theory²². These absorption cross sections can be regulated by the interaction between the solvent environments and the materials. Lim et al. observed that the sub-stoichiometric graphene oxide exhibits SA or RSA depending notably on the solvent interaction²³. The interaction can be divided into long-range dielectric polarization and short-range bonding interaction²⁴. As stated by Roberto et al., solvents can induce charge separation and geometric distortion, which can further affect the linear and nonlinear electro-optical properties of molecules²⁵. For a new NLO material, the mechanism of its NLO response is unknown. Revealing the NLO mechanisms of the material is conducive to guiding its development in the NLO field.

Transient absorption spectroscopy (TAS) and time-dependent density functional theory (TD-DFT) are effective means for studying the NLO mechanisms. TAS is a technique that utilizes the pump light to excite electrons in the medium to the excited state and employs the probe light to observe the time-resolved absorption changes²⁶. This method is effective in investigating the ESA of materials. For example, Zhang et al. took advantage of TAS to study the size-dependent ESA performance of antimony nanosheets²⁰. TD-DFT is a computational theory that expands the density functional eigen solution to the time domain, which can solve problems related to the properties and behavior of a system in the excited state²⁷. For the NLO effect, this method can make reasonable design and systematic prediction²⁸. By using the TD-DFT, Cocchi et al. explained the primary mechanism behind the optical limiting phenomena in a metal-free phthalocyanine as dipole-forbidden excitations promoted by ESA²⁸. These two methods are essential for exploring the NLO properties of materials from both theoretical calculations and practical experiments to verify the NLO theories and enrich the NLO applications.

In this work, 2D RP nanosheets are successfully prepared by the decomposition of PI₃ at the interface. Interestingly, 2D RP exhibits obvious solvent-dependent NLO responses in different solvents. Among them, SA in 1,2-propylene glycol (PG) and RSA in 1,2,3-glycerol (GI) of 2D RP are selected for a focused study. From the experimental aspect, Z-scan results and laser spot images prove that this NLO phenomenon is mainly caused by nonlinear absorption. Ultrafast carrier dynamics analyses elucidate that the SA in PG is caused by a larger GSA cross section, and the RSA in GI is caused by a larger ESA cross section. From the theoretical aspect, TD-DFT is used to calculate the absorptions in different electronic populations and solvents, which not only well verifies the above experimental conclusions, but also points out that the dielectric constant of solvents is one of the essential factors influencing the NLO performance. This work highlights the considerable potential of 2D RP to apply to the optical modulation, all-optical switch, optical logic gate, and optical sensor.

A solid-state template method in Fig. 1a is used to prepare 2D RP. Firstly, the precursor PI₃ is coated on the surface of the L-ascorbic acid (L-ASA) template by solvent evaporation. A large amount of interface effectively limits the growth of materials in the two dimensions. In order to avoid reactions in the liquid phase, the evaporating temperature needs to be sufficiently low (~ 25°C), which can be estimated by the non-existence of purple iodine in the collection bottle. Afterwards, the coated mixture is heated at a relatively high temperature (~ 70°C) to bring about thermal decomposition on the interface. The reaction is controlled by temperature, as the color difference of reactants can be observed between the high-temperature reaction vessel edge and the low-temperature center (brown at the edge, orange at the center). Finally, the template and unreacted precursor are easily removed by dissolving and washing.

The morphology of 2D RP is characterized by transmission electron microscopy (TEM). The layered structure is detected, which is the distinct characteristic of 2D materials (Fig. 1b). The high-resolution TEM (HRTEM) image and selected area electron diffraction pattern in Fig. 1c give direct evidence of the amorphous structure and disordered atomic arrangement of 2D RP. As shown in Fig. 1d, the homogeneous morphologies and size uniformities are observed from the scanning electron microscopy (SEM) images. The size of 2D RP is about 115 nm (Fig. S4). The atomic force microscopy (AFM) result proves the average height of 2D RP is 1.62 ± 0.09 nm (Fig. 1e). Elemental mapping of energy dispersive spectroscopy (EDS) is used to study the chemical composition of 2D RP (Fig. 1f). Three kinds of elements of P, O, and C are detected, among which P is the most significant. The existence of O is due to the oxidation of the surface to stabilize the edge structure of 2D RP.

To figure out the molecular vibration of 2D RP, the sample is characterized by Raman spectroscopy in Fig. 2a. These three characteristic peaks of 2D RP at 356.7, 385.0, and 445.0 cm^− 1, which are also observed in commercial amorphous RP, are attributed to B1 fundamental mode, A1 symmetric stretching modes, and E1 degenerate mode, respectively²⁹. In the group theory analysis, B1, A1, and E1 modes are the irreducible symmetric types of point groups. X-ray diffraction (XRD) spectra are presented in Fig. 2b. The sharp diffraction peak at 2θ = 15.5° can be ascribed to a medium-range ordered structure matching with commercial amorphous RP. The wide diffraction peak from 20.0 to 39.0° suggests a long-range disordered structure³⁰. Taking use of Fourier transform infrared (FT-IR) spectroscopy, functional groups in 2D RP are detected in Fig. 2c. The peaks located at 1637, 1158, and 1042 cm^− 1 can be ascribed to P = O, P-O, and P-P-O stretching vibration, respectively³¹. In addition, the peaks at 3440 and 1644 cm^− 1 can be attributed to the stretching vibration and the bending vibration of the hydroxyl group of water absorbed on the surface of the sample. The peak at 2364 cm^− 1 is caused by the bending vibration of the attached CO₂. X-ray photoelectron spectroscopy (XPS) is used to probe the surface chemical composition and state of 2D RP. As shown in Fig. 2d, the strong peaks in XPS survey spectra from left to right are O 1s, N 1s, C 1s, P 1s, and P 2p of 2D RP and commercial amorphous RP. For comparison, the O content in 2D RP is lower than that in commercial RP. The high-resolution XPS spectra at the binding energy of the P element are differentiated and fitted to analyze the chemical states (Fig. 2e). The peaks centered at 134, 133, 132, 131, and 130 eV can be assigned to P₂O₅, O-P = O, P-O-P, P 2p_1/2, and P 2p_3/2, respectively. The peaks of O can be divided into oxidation states of P and C (Fig. 2f). Compared with commercial RP, the oxidation state of 2D RP is lower.

The NLO performance of 2D RP is measured by an Nd: YAG laser with a wavelength of 532 nm, a repetition frequency of 10 Hz, and a pulse duration of 6 ns. The open-aperture (OA), closed-aperture (CA), and nonlinear scattering Z-scan are equipped with the optical settings in Fig. 3a and b. The waist radius of the lens is 13.55 µm. The transmittance of all samples in different solvents are ~ 60% (at 532 nm). The OA Z-scan results of the blank samples (without the 2D RP) are shown in Fig. S16. By using the OA Z-scan, the solvent-dependent NLO phenomenon of 2D RP is observed at the same waist power density of incident light (I₀, 1.132 GW/cm²) in Fig. 3c. The SA signals are detected in a part of these solvents and RSA signals are in the other part. It is discovered that the imaginary parts of third-order NLO susceptibilities (Imχ⁽³⁾, calculated by expression 18, obtained by fitting the OA Z-scan curves) of 2D RP show linear correlation with the relative dielectric constants of solvents (Fig. 3g). Among these solvents, PG and GI were selected as the focus of this research. SA and RSA signals of 2D RP are observed in PG and in GI, respectively (Fig. 3d and e). Both their absolute values of modulation depth (MD, defined as the transmittance at Z = 0) increase with the increase of incident light power density. The absorption coefficients (obtained by fitting the OA Z-scan curves) are related to light intensities as well as the susceptibilities and the quality factors (FOM, calculated by expression 19) in Fig. S5 and Table S3. The OA Z-scan curves in Fig. 3f reveal that 2D RP can convert between SA and RSA by adjusting the volume ratios of PG and GI in the mixed solvents. The Imχ⁽³⁾ and FOM of 2D RP in mixed solvents are calculated in Fig. 3h and Table 1. The Imχ⁽³⁾ increases with the increase of GI content. When the volume ratio is 1:1, the FOM of 2D RP decreases to the bottom value. By comparing the FOM, the NLO performance of 2D RP in PG is better than that in GI. To demonstrate that the conversion from SA in PG to RSA in GI is not caused by the higher viscosity of GI (800 mPa·s) than PG (61 mPa·s), 2D RP in dimethyl silicone oils with different viscosities is detected by OA Z-scan (Fig. S6). Even when the viscosity of silicone oil (60000 mPa·s) is much higher than that of GI (800 mPa·s), there is no conversion between SA and RSA, indicating that the viscosity is not the reason for the different signals in PG and in GI. Besides, CA Z-scan properties of 2D RP in PG and in GI are investigated in Fig. S7a. No self-focusing or self-defocusing signal (up-to-down or down-to-up oriented centrosymmetric shape) is found. With the sample placed in focus, laser power densities at both front and rear of the sample are detected and converted into the laser transmittance spectra (Fig. S7c and d). The transmittance of 2D RP in PG increases with the increase of incident power density, as opposed to GI.

To confirm whether nonlinear scattering is the main reason for the convertible orientation of OA Z-scan curves in PG and in GI, the optical devices behind the sample are rotated by 10 degrees around the focus to receive the scattering signals (Fig. 3b). As shown in Fig. S7b, nonlinear scattering Z-scan results of 2D RP in different solvents are both downward signals. Additionally, the intensities of the nonlinear scattering signals are smaller than those of the OA signals by about two orders of magnitude. Therefore, the nonlinear scattering just slightly influences the intensity of the OA Z-scan curves and does not change the curve orientations. According to the laser spot images in Fig. 3i and j, these downward nonlinear scattering signals are caused by the expansion of scattered laser spots and the decrease of light intensity received by the detector. Because the light expands outside the detector when the sample is near Z = 0. This is reflected in the nonlinear scattering Z-scan curve as a decrease in transmittance (i.e. the signals are both downward signals) because the transmittance is obtained by the ratio of light intensity value received by detector A to B. However, the OA Z-scan curves of 2D RP are upward in PG and downward in GI (Fig. 3d and e). Even if the nonlinear scattering can slightly influence the OA Z-scan signals due to the range of scattering spots exceeding the size of the detector, the intensities of nonlinear scattering signals are too weak to dominate the orientations of these curves. At the waist (Z = 0) and the Gaussian laser center parts, the light intensity of 2D RP in GI is weak. While in PG, it is strong. Together with the fact that the sizes of the Gaussian light spots are not visibly reduced or enlarged, the difference at the center part of the Gaussian laser can be explained by the nonlinear absorption.

In order to evaluate the NLO performance of 2D RP, the OA Z-scan of 2D BP is examined and the nonlinear absorption coefficients of other materials are investigated. Similar to 2D RP, SA and RSA are also observed on 2D BP in PG and in GI, respectively (Fig. S9). Compared with 2D BP, 2D RP has much better RSA performance, whether in terms of the starting NLO threshold (${F}_{on}^{5\%}$, defined as the power density when the linear transmittance is increased or decreased by 5%, Fig. S10b) or MD (Fig. S11b). For SA performance, the RP also exhibits a better MD and FOM (Fig. S11a and 13a) despite the lager ${F}_{on}^{5\%}$ (Fig. S10a). Consequently, the significance lies in the point that RP is more capable and suitable for the practical application scenario of a wider-ranged NLO modulation. Table 2 compares other materials with 2D RP on the nonlinear absorption coefficients^32–39. It can be concluded that 2D RP has excellent NLO performance.

Ultraviolet-visible-near infrared (UV-vis-NIR) diffuse reflectance spectra (DRS) are obtained to explore the intrinsic absorption properties and band gap of 2D RP (Fig. 4b). Compared with bulk commercial RP, the absorption band of 2D RP is blue-shifted. Based on the Kubelka–Munk theory^40,41 $[F\left(R\right)={\left(1-R\right)}^{2}/2R]$ and the Tauc plot Eq. 4^2,43 $\left[{\left(ah\nu \right)}^{2}=A\left(h\nu -{E}_{g}\right)\right]$, the band gap of 2D RP is confirmed to be about 1.93 eV, as shown in the inset of Fig. 4b. UV-vis-NIR absorption spectra in Fig. 4c show that the GSA of 2D RP in PG is slightly stronger than that in GI at 532 nm. Femtosecond ultrafast carrier dynamics of 2D RP are pumped at 320 nm and probed from 420 nm to 620 nm. Their optical setting is shown in Fig. S14. The laser generated by the resonant cavity is divided into two beams through a splitter. One of the 800 nm lasers is converted to a 320 nm pump light through the optical parametric amplifier. The other is converted into a supercontinuum white light (350~800 nm) through a CaF₂ crystal. The ground state electrons of the sample absorb the pump light energy and rise to the excited state. The excited state electrons absorb the probe light energy and the detector collects the absorption spectra. The TAS at different time scales are obtained by an optical delay device. 2D mapping of TAS in Fig. 4d and g provide direct and visible proof of the stronger ESA of 2D RP in GI. The positive absorption peaks centered at 580 nm decrease with the increase of probe delay time in Fig. 4e and h. Excited electrons at 580 nm have the largest number of transition electrons and the slowest de-excitation velocity, indicating that the upper-level bandwidth matches the corresponding energy of this wavelength (Fig. 4f and i). Therefore, the simplified two- and three-level models of 2D RP in PG and in GI are established to explain its SA and RSA in OA Z-scan results (Fig. 4a). In addition, the characteristic of the intermolecular energy or charge transfer on TAS is that the positive absorption signal must be accompanied proportionally by a bleaching signal nearby. No intermolecular charge transfer signal (the positive absorption signal accompanied proportionally by a negative bleaching signal nearby) is found in the TAS (Fig. 4e and h), indicating that the dielectric polarizations of the solvents affect the nonlinear absorption.

Two-level model⁴⁴ is developed to facilitate the fitting of SA signals. The rate equations can be expressed as:

$\frac{d{N}_{0}}{dt}=-\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }+\frac{{N}_{1}}{{\tau }_{10}}$	(1)
$\frac{d{N}_{1}}{dt}=\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }-\frac{{N}_{1}}{{\tau }_{10}}$	(2)
$N={N}_{0}+{N}_{1}$	(3)

where $N={N}_{0}+{N}_{1}$ is the total population density. ${N}_{i}$ are the population densities of levels ${S}_{i}$. ${\sigma }_{ij}$ are the absorption cross sections of level ${S}_{i}$. ${\tau }_{ji}$ are the lifetimes of electrons relaxing from level ${S}_{j}$ to level ${S}_{i}$.

Because the width of the incident laser pulse is much longer than the lifetimes (${\tau }_{L}\gg {\tau }_{ji}$), the steady-state approximation can be brought into the rate equations to calculate the population densities of each level, i.e., $d{N}_{i}/dt=0$. This results in:

$${N}_{0}=\frac{N}{1+I/{I}_{s}}$$

Where ${I}_{s}$ is the saturated absorption intensity, ${I}_{s}=h\nu /\left({\sigma }_{01}\bullet {\tau }_{10}\right)$.

Therefore, the absorption coefficient of the medium is:

$$\alpha ={\sigma }_{0}{\bullet N}_{0}=\frac{{\sigma }_{0}\bullet N}{1+I/{I}_{s}}=\frac{{\alpha }_{0}}{1+I/{I}_{s}}$$

Where ${\alpha }_{0}$ is the linear absorption coefficient of the medium.

Three-level model⁴⁵ is developed to facilitate the fitting of RSA signals. The rate equations can be expressed as:

$\frac{d{N}_{0}}{dt}=-\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }+\frac{{N}_{1}}{{\tau }_{10}}$	(6)
$\frac{d{N}_{1}}{dt}=\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }-\frac{{\sigma }_{12}\bullet I\bullet {N}_{1}}{h\nu }-\frac{{N}_{1}}{{\tau }_{10}}+\frac{{N}_{2}}{{\tau }_{21}}$	(7)
$\frac{d{N}_{2}}{dt}=\frac{{\sigma }_{12}\bullet I\bullet {N}_{1}}{h\nu }-\frac{{N}_{2}}{{\tau }_{21}}$	(8)
$\frac{d{N}_{0}}{dt}=-\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }+\frac{{N}_{1}}{{\tau }_{10}}$	(9)

The steady-state approximation can be brought into the rate equations to calculate the population densities of each level, i.e., $d{N}_{i}/dt=0$. This results in:

$${N}_{0}=\frac{N\bullet {h}^{2}\bullet {\nu }^{2}}{{I}^{2}\bullet {\sigma }_{01}\bullet {\sigma }_{12}\bullet {\tau }_{10}\bullet {\tau }_{21}+{I\bullet \sigma }_{01}\bullet {\tau }_{10}\bullet h\nu +{h}^{2}\bullet {\nu }^{2}}$$

$${N}_{1}=\frac{N\bullet {\sigma }_{01}\bullet {\tau }_{10}\bullet h\nu \bullet I}{{I}^{2}\bullet {\sigma }_{01}\bullet {\sigma }_{12}\bullet {\tau }_{10}\bullet {\tau }_{21}+{I\bullet \sigma }_{01}\bullet {\tau }_{10}\bullet h\nu +{h}^{2}\bullet {\nu }^{2}}$$

Define the parameters of saturated absorption intensities of ground and excited states as:

$${I}_{{s}_{0}}=\frac{h\nu }{{\sigma }_{01}\bullet {\tau }_{10}}$$

$${I}_{{s}_{1}}=\frac{h\nu }{{\sigma }_{12}\bullet {\tau }_{21}}$$

Hence:

$${N}_{0}=\frac{N\bullet {I}_{{s}_{0}}\bullet {I}_{{s}_{1}}}{{I}^{2}+I\bullet {I}_{{s}_{1}}+{I}_{{s}_{0}}\bullet {I}_{{s}_{1}}}$$

$${N}_{1}=\frac{N\bullet {I}_{{s}_{1}}\bullet I}{{I}^{2}+I\bullet {I}_{{s}_{1}}+{I}_{{s}_{0}}\bullet {I}_{{s}_{1}}}$$

Therefore, the absorption coefficient of the medium is:

$$\alpha ={\sigma }_{01}\bullet {N}_{0}+{\sigma }_{12}\bullet {N}_{1}=\frac{{\alpha }_{0}\bullet {I}_{{s}_{1}}\bullet \left({I}_{{s}_{0}}+{\sigma }_{12}/{\sigma }_{01}\bullet I\right)}{{I}^{2}+I\bullet {I}_{{s}_{1}}+{I}_{{s}_{0}}\bullet {I}_{{s}_{1}}}$$

Adding a perturbation ${\eta }_{NLS}$ caused by nonlinear scattering, its normalized transmittance can be approximated as:

$$T=\frac{1-\alpha \bullet l-{\eta }_{NLS}\bullet l}{1-{\alpha }_{0}\bullet l}$$

Where $l$ is the sample thickness.

Table 1

NLO parameters of 2D RP in mixed solvents.
Mixed solvents V_PG:V_GI	I₀ (GW/cm²)	I_S0 (GW/cm²)	I_S1 (GW/cm²)	σ₁₂/σ₀₁	MD	α_NL (cm/GW)	Imχ⁽³⁾ (10^− 11 esu)	FOM (10^− 12 esu cm)
1:0	1.132	0.270	-	-	1.620	-524.822	-3.536	5.440
3:1	1.132	0.541	-	-	1.328	-439.809	-2.963	4.559
1:1	1.132	15.296	-	-	1.074	-44.789	-0.302	0.464
1:3	1.132	1.922	27.354	1.594	0.701	131.130	0.884	1.359
0:1	1.132	0.230	58.010	1.600	0.453	308.594	2.079	3.199

The rate equations are used to solve the transmittance expressions in different solvents. The transmittance expressions are then used to fit the OA Z-scan curves to further obtain the nonlinear absorption coefficients ${\alpha }_{NL}$ and other relevant NLO parameters. The expression for the imaginary part of the third-order nonlinear susceptibility is as follows:

$$Im{\chi }^{\left(3\right)}=\frac{{c}^{2}\bullet {n}_{0}^{2}}{240\bullet {\pi }^{2}\bullet \omega }\bullet {\alpha }_{NL}$$

Where $c$ is the light velocity, ${n}_{0}$ is the linear refraction, $\omega$ is the angular frequency of light, and ${\alpha }_{NL}$ is the nonlinear absorption coefficient, $\alpha ={\alpha }_{0}+{\alpha }_{NL}$.

The FOM is the abbreviation of figures of merit for evaluating the NLO performance of materials, and is expressed as follows:

$$FOM=\left|\frac{Im{\chi }^{\left(3\right)}}{{\alpha }_{0}}\right|$$

Table 2

Nonlinear absorption coefficients of different materials at 532 nm.
Sample	Wavelength (nm)	Pulse width	α (cm/GW)	References
GO (DMF)	532	6 ns	30.22	32
GO–PcZn (DMF)	532	6 ns	51.16	32
TiS₂	532	7 ns	62	33
MoSe₂/GO	532	5 ns	580	34
GDY	532	6 ns	1.7	35
PDPP-TTzPt	532	6 ns	36	36
Carboxyl-GO	532	30 ps	0.17	37
Cd_0.5Zn_0.5S	532	40 ps	120	38
2D Cr	532	230 ps	3.12	39
2D RP (PG)	532	6–7 ns	328.8	This work
2D RP (GI)	532	6–7 ns	578.5	This work

TD-DFT is used to calculate the GSA and ESA of 2D RP in PG and in GI. So far, the exact structure of amorphous RP is still unclear, and we only know it is composed of the possible linear-chain polymer⁸. In many researches, calculations have chosen a section of the structure proposed by Pauling in 1952, which is formed by P₄ molecules after opening a covalent bond and bond-connecting each other^46–48. Therefore, the structure in Fig. S17a is taken as the input configuration. Geometric optimization is performed to minimize the energy. In PG, the GSA of 2D RP at 532 nm is larger than the ESA (Fig. 5a). It is the reason for the SA of 2D RP in PG. In GI, the absorption property is just the opposite, which leads to the RSA (Fig. 5b). Compared with the experimental results, the positions of the absorption lines in theoretical molar extinction coefficient spectra show a blue-shift to some degrees, which may be caused by the inadequate size of the atomic system or the uncertainty of the optimized configuration. Non-electrostatic terms are not considered in the implicit solvent model, and the solvent environments are simply treated as the polarizable continuous medium because the sample does not have strong bonding or hydrogen bonding with the solvents. With the static and dynamic dielectric constants of solvents as variables, the ESA of 2D RP exhibits a significant change in these two solvents.

Amorphous 2D RP nanosheets, with a thickness of 1.62 ± 0.09 nm, a size of ~ 115 nm, and a band gap of ~ 1.93 eV, are prepared by interfacial thermal decomposition of PI₃ on the surface of solid-state L-ASA. Under 532 nm nanosecond-pulsed laser excitation, 2D RP exhibits solvent-dependent third-order NLO responses. Proved by experiments, this NLO response of 2D RP is mainly dominated by nonlinear absorption, slightly affected by nonlinear scattering, and not affected by nonlinear refraction. SA and RSA of 2D RP are observed in PG and in GI, respectively (with the Imχ⁽³⁾ of -3.536×10^− 11 esu in PG and 2.079×10^− 11 esu in GI). TAS and TD-DFT results indicate that the SA in PG is due to a larger GSA cross section and the RSA in GI is due to a larger ESA cross section. The dielectric polarization of solvents plays an important role in influencing these absorptive capacities. Consequently, two- and three-level models are proposed to explain this NLO behavior. Although the chemical stability of 2D RP requires further improvement (Fig. S2b and c), 2D RP shows advantages in the solidification of NLO devices by doping it into methyltriethoxysilane gel glass (Fig. S15). This work exhibits the excellent third-order NLO properties of 2D RP and paves the way for future applications in NLO devices.

Raw materials

Phosphorus triiodide (PI₃, 99%) was purchased from Sigma-Aldrich Co., LLC. (Shanghai, China). L-ascorbic acid (L-ASA, 99%), cyclohexane (CYH, 99.5+%, extra dry with molecular sieves), red phosphorus (RP, 98.5%), 1,2-propylene glycol (PG, 99%) and 1,2,3-glycerol (GI, 99.5%), ethylene glycol (EG, 99%), ethanol (EtOH, 99.9%), 1,2,4-Butanetriol (BT, 98+%), and methyltriethoxysilane (MTES, 98%) were purchased from InnoChem Science & Technology Co., Ltd. Silicone oil PMX-200 (100, 1000 and 60000 mPa·s, neat 25°C) were purchased from Aladdin Biochemical Technology Co., Ltd. Two-dimensional black phosphorus (2D BP, 99.9%) was purchased from Zhongke Experimental Materials Co., Ltd. All the above chemicals were purchased and used without further purification.

Preparation

2D RP was prepared by a solid-state template method (Fig. S1). Specifically, 0.5 g of PI₃ was dissolved in cyclohexane (CYH). Under nitrogen protection, 15 g of L-ascorbic acid (L-ASA) and CYH solution of PI₃ were added into a three-necked flask in sequence. Subsequently, vacuum distillation and nitrogen were alternately used at 25°C for 120 min under magnetic stirring. After CYH was completely removed, the temperature was raised to 70°C and kept for 20 min. After the system was cooled down to room temperature naturally, ethanol and deionized water were added in the three-necked flask to remove unreacted PI₃, dissolve L-ASA and disperse 2D RP. Then, the sample was washed and purified by centrifugation using ethanol and deionized water. Finally, 2D RP was obtained by a freeze-drying process.

Characterization

TEM was investigated by a HT7700 (Hitachi, Japan). HRTEM images and EDS elemental mappings were characterized by a JEM-F200 (Japan Electronics, Japan). SEM was investigated by a S-4800 (Hitachi, Japan). AFM was characterized by a Multimode 8 (Bruker, USA). Raman spectra were generated from an inVia-Qontor (Renishaw, UK). XRD spectra were measured by a D8 focus (Bruker, Germany). FT-IR spectra were obtained from an Excalibur 3100 (Varian, USA). XPS spectra were profiled on an Escalib 250Xi (ThermoFisher Scientific, UK). OA, CA, and nonlinear scattering Z-scan and laser spots images were performed by a Premiscan/240/MB-ULD (Spectra Physics, USA), with a wavelength doubling from 1064 to 532 nm, a pulse duration of 6–7 ns, a repetition rate of 10 Hz, and a Rayleigh length of 1.08 mm. UV-vis-NIR DRS spectra and UV-vis-NIR absorption spectra were detected on a Cary 7000 (Varian, USA). TAS was operated on a Vitara-Legend Elite (Coherent, USA).

Calculations

The density-functional theory (DFT) calculations were performed using the Gaussian 16 Software Package. For the form of the hybrid exchange-correlation functional, the functional B3LYP was used throughout. The van der Waals interaction was described using the DFT-D3 method proposed by Grimme. The excitation energy was calculated via the time-dependent density functional theory (TD-DFT) method. The solvation effect was described via the integral equation formalism polarizable continuum model (IEFPCM). The low-energy configuration was obtained by geometric optimization under empirical dispersion correction (GD3BJ). Keeping all other solvent parameters at the same level and taking the static and dynamic dielectric constants (EPS and EPSINF) of solvents as variables, molar extinction coefficients in different electron populations were then calculated. The discrete absorption lines were broadened by 0.67eV to form absorption peaks.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (22275202 and 21971250).

Author details

¹Key Laboratory of Photochemical Conversion and Optoelectronic Materials, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China. ²State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, 100083, China. ³College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China.

Author contributions

J. W. conducted the experiments and wrote the manuscript; C. W. and X. D. contributed to the testing of relevant materials; Y. L. put forward suggestions on the work design; F. L. offered assistance to the data analysis; Prof. H. Z., Prof. Y. C., Prof. Z. X., and Prof. H. Z. provided guidance on the project and revised the manuscript. All authors discussed the results and contributed to the improvement of the manuscript.

Conflict of interest

The authors declare no competing interests.

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Two-dimensional red phosphorus: Emerging nonlinear optical material with solvent effect

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\(\frac{d{N}_{0}}{dt}=-\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }+\frac{{N}_{1}}{{\tau }_{10}}\)	(1)
\(\frac{d{N}_{1}}{dt}=\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }-\frac{{N}_{1}}{{\tau }_{10}}\)	(2)
\(N={N}_{0}+{N}_{1}\)	(3)

\(\frac{d{N}_{0}}{dt}=-\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }+\frac{{N}_{1}}{{\tau }_{10}}\)	(6)
\(\frac{d{N}_{1}}{dt}=\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }-\frac{{\sigma }_{12}\bullet I\bullet {N}_{1}}{h\nu }-\frac{{N}_{1}}{{\tau }_{10}}+\frac{{N}_{2}}{{\tau }_{21}}\)	(7)
\(\frac{d{N}_{2}}{dt}=\frac{{\sigma }_{12}\bullet I\bullet {N}_{1}}{h\nu }-\frac{{N}_{2}}{{\tau }_{21}}\)	(8)
\(\frac{d{N}_{0}}{dt}=-\frac{{\sigma }_{01}\bullet I\bullet {N}_{0}}{h\nu }+\frac{{N}_{1}}{{\tau }_{10}}\)	(9)