Third-order non-linear optical switching and threshold limiting of NiO thin films

Abstract

This study discusses the nonlinear optical properties of as-grown and annealed NiO thin films using the Z-scan technique utilizing the femtosecond laser pulses at a repetition rate of 100 kHz of wavelength 1030 nm with a pulse duration of 370 fs. In open aperture measurements, pristine reveal saturable absorption (SA) with a negative sign of nonlinearity, while annealed samples exhibit reverse saturable absorption (RSA) with a positive sign of nonlinearity. In closed aperture conditions, all samples show prefocal minima and postfocal maxima, indicating self-focusing behavior. The observed RSA phenomena are attributed to the indirect two-photon absorption (TPA) process. The influence of surface plasmon resonance on nonlinear absorption is successfully ruled out due to insufficient excitation energy (1.20 eV) to induce resonance in the samples. The increase in bandgap with annealing temperature, associated with indirect TPA, is elucidated with the shifting of Ni-$d_{x^2-y^2}$ and Ni-$d_{z^2}$ orbitals in the conduction band, under the framework of Density Functional Theory (DFT). The DFT results are correlated with the observed nonlinear SA and RSA processes. The Ni d-d and Ni-d to O-p transitions contribute to the modulation of nonlinearity in the indirect TPA process. The study suggests that the sample annealed at 400 °C exhibits superior optical limiting properties with the highest nonlinear absorption coefficients compared to the other annealed sample, while the as-grown sample is suitable for passive Q-switching applications.

Introduction

The transparent conductive oxide (TCO) thin films, which have a meticulous combination of optical transparency and optical conductivity, attracted researchers due to low-cost optoelectronic devices¹. Transparent semiconducting material has extensive application on architectural windows, solar cells, heat reflectors, light transparent electrodes, thin-film photovoltaics, etc. Among various TCO materials, NiO is one of the promising candidates for making optoelectronic devices due to (i) p-type semiconductor with transparent conductivity² and (ii) the modulation of conductivity by phase deviation from stoichiometry and/or adding a doping element in the material^3,4. Due to clear switching events, good reversibility, 3D staking compatibility, and simple structure, NiO can be used as a resistive random access memory device⁵. NiO also exhibits various excellent properties, such as catalytic⁶, magnetic⁷, electrochromic⁸, optical and electrochemical characteristics⁹, transparent p-type semiconducting layer for applications in smart windows¹⁰, electrochemical supercapacitors¹¹ and dye-sensitized photocathode¹². Controlling the intensity of laser light and lowering the optical losses are major challenges in optical technology. High and low power illumination on NiO thin films can provide various kinds of nonlinear applications. Intense lasers with optical nonlinearity can be useful for optical bistability-based memory elements, switches, saturable absorbers, etc applications. Positive and negative nonlinear absorption coefficient-associated materials have huge potential in optical limiting and saturable absorber device applications. Optical limiting material is transparent for low-input intensities and relatively opaque for high-level inputs. Optical limiters can provide safety to optical detectors, sensors, and human eyes. On the other hand, the saturable absorber is applied in passive mode-locking and Q-switching applications¹³. To achieve this, materials with nonlinear optical absorption behavior are required. Magnetically tuned absorptive nonlinear properties in NiO thin films and the consequence of sign reversal optical nonlinearity due to annealing in ion beam sputtered NiO films are observed^13,14. Chouhan et al. studied the effect of oxygen partial pressure (at 30$\%$ and 70$\%$) in the growing of NiO thin films and also in the closed aperture (CA) measurements for the nonlinearity of as-grown and annealed samples at a fixed temperature of 523 K¹⁴. They also reported the open aperture (OA) nonlinearity in as-deposited and 523 K annealing 523 K NiO thin films¹⁵. The impact of N doping and polarization patterns of femtosecond laser pulses on NiO to tune the nonlinear optical responses are investigated by Lei et al.¹⁶. The report explores that the undoped NiO exhibits overwhelmed nonlinear behavior such as RSA, self-focusing effect, and optical power limiting efficiency under radial polarization irradiation over linear polarization. However, the nonlinear responses become strong under linear polarization irradiance in N-doped NiO films with respect to the radial polarization beam. The large value of the nonlinear refractive index and negligible nonlinear absorption of NiO films has been observed at a laser wavelength of 800 nm using an eclipse Z-scan technique¹⁷. The Cr and Sb doping in NiO nanocomposite films plays a prominent role in enhancing the optical limiting threshold and nonlinear absorption coefficients compared to undoped samples¹⁸. Baraskar et al. reported on dispersive optical pathlength-related nonlinearities in NiO/Al-doped NiO films¹⁹. Chtouki et al. studied the third-order nonlinearity (TONL) in Tin-doped NiO films²⁰. Ganesh et al. reported TONL in spin-coated N doping NiO films using the Z-scan technique²¹. However, it has been observed that with thermal annealing temperature, the crystallinity of the NiO thin films changed systematically, which may affect the optical nonlinearity. To the best of our knowledge, the nonlinearity in OA and CA conditions for sputtered-grown NiO films with different annealing temperature has not been explored.

In the present study, we demonstrated the variation in Nonlinear Optical Properties (NLOP) of as-grown and 300–500 °C annealed NiO thin films using the Z-scan technique. We successfully showed that SPR has no contribution to change in nonlinearity. The pristine NiO sample shows SA. On the other hand, the RSA has been observed in the case of annealed samples and understood on the basis of Ni d-d and Ni-d to O-p transition in the TPA process. The shifting of Ni-$d_{x^2-y^2}$ and Ni-$d_{z^2}$ orbitals obtained from DFT calculations is correlated with the experimental observations.

Methodology

Experimental method

The RF sputtering technique was utilized to grow the 150 nm thick NiO thin films on the cleaned glass substrate at room temperature. The 2-inch diameter of NiO target of purity 99.99$\%$ was used for sputtering. The substrate was kept fixed at a distance of 7.5 cm from the target. The base pressure, working pressure, RF power, and reflectance were 6.57 $\times {10}^{-6}$ mbar, 5 $\times {10}^{-3}$ mbar, 80 W, and 0 W, respectively. High-purity Ar gas (99.99$\%$) was used as Sputtered gas to react with the target at a flow rate of 15 sccm. Then, the sputtered grown NiO thin films were annealed at the temperature of 300, 350, 400, 450, and 500 °C (annealed samples) in a vacuum of pressure 2.13 $\times {10}^{-2}$ mbar using the Plasma Enhanced Chemical Vapor Deposition (PECVD) system. The surface morphology of as-grown and annealed samples were examined using the Zeiss sigma model Field Emission Scanning Electron Microscopy (FESEM) system. The crystal structure and phases of the thin films were investigated by analyzing the X-Ray Diffraction (XRD) spectra, taken using the Rigaku Smartlab X-ray diffractometer with Cu $K_{\alpha }$ source ($\lambda =1.5418$ Å). The optical absorbance spectra for the as-grown and annealed samples were taken using the Cary 5000 UV-Vis-NIR spectrometer. The spectra were taken at room temperature in transmission mode in the 300–800 nm wavelength range. The photoluminescence (PL) spectra were taken at room temperature by He-Cd laser excited at 325 nm in the wavelength range of 330–700 nm. The steady-state spectra were collected through the 40 $\times$ objective lens. The cathodoluminescence (CL) measurements were carried out at room temperature using the Monarc-P (GATAN) high-resolution CL detector integrated with the FESEM system. The scanning over the 1 $\times$ 1 $\mathrm{\mu }$m area of NiO thin film was done with an accelerating voltage of 15 kV during CL measurements. The third-order non-linear optical properties of the thin films were investigated using the Z-scan technique. The schematic of the standard Z-scan experimental setup utilized for the measurement is shown in Fig. 1. In our case, we used the Calmar fiber femtosecond laser at a repetition rate of 100 kHz of wavelength 1030 nm with a pulse duration of 370 fs. The laser beam is brought to focus on the sample by a converging lens, which has a spot size of $w_0$ = 32 $\mathrm{\mu }$m with a power of 5 mW. The path length of the sample is much lower than the Rayleigh length, which is a crucial prerequisite for Z-scan measurements. The spectra were taken in two conditions: OA and CA. In OA conditions, the photodetector directly collected the total transmitted power. The partial transmittance from the films was detected in CA measurements because, this time, the aperture was inserted in front of the photodetector. The non-linear absorption coefficient and refractive index were calculated in OA and CA conditions, respectively. The sample was translated across the focal point of the converging lens along the z-axis during the beam exposure by a motorized translation stage.

Figure 1.

The experimental setup of Z-scan technique.

Theoretical method

The DFT calculation of bandstructure and Density of States (DOS) of NiO is carried out with the Vienna Ab Initio Simulation Package (VASP) code²² using the Projector-Augmented-Waves (PAW) potentials²³ and the semi-local Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional²⁴. In our case, we implemented the Generalized Gradient Approximation (GGA) along with onsite Coulomb repulsion corrections (Hubbard U correction) in Ni-d orbitals for all the calculations²⁵. NiO is a rocksalt cubic structure with a space group of Fm$\overline{3}$m. A supercell containing 64-atom for the antiferromagnetic arrangement of NiO along the (111) plane was taken for the calculation, as shown in Fig. 2. The experimentally found lattice parameter was utilized to calculate band structure and DOS for pristine and annealed samples. In our case, the lattice constant varies with the variation of annealing temperature. Hence, the annealing aspect is considered by taking the annealing temperature associated lattice constant value introduced in the structure in the calculations. The atomic configuration of NiO was optimized under a conjugate gradient scheme, and the only atomic position relaxation without changing cell shape and cell volume was completed when the force for each atom was less than 1$\times {10}^{-4}$ eV/Å. The relaxed structure was employed for the self-consistent calculation to attain the convergence result using the plane-wave basis set with a cutoff energy of 500 eV and a Monkhorst k-point mesh of $7\times 7\times 7$. The convergence was accomplished when the total energy approached the threshold of 1$\times {10}^{-7}$ eV. The tetrahedron method with Blochl corrections was applied for DOS calculations²⁶.

Figure 2.

The NiO crystal structure of pristine, used for computational calculation.

Surface morphology and structural analysis

SEM study

The surface morphology of as-grown (pristine) NiO and annealed samples is shown in Fig. 3a–f, respectively. The film thickness of the pristine sample was 150 nm, shown in the inset of Fig. 3a. A uniform surface was observed for all the samples. There is a small black patchy circle in the annealed sample, which is not present in pristine.

Figure 3.

The surface morphology of (a) pristine and the sample annealed at (b) 300, (c) 350, (d) 400, (e) 450 (f) 500 °C. The inset of (a) shows the thickness of the pristine film.

XRD analysis

The XRD pattern of the pristine and thermally annealed samples at 300, 350, 400, 450, and 500 °C are shown in Fig. 4a. The peak shift of the XRD pattern in the annealed samples with respect to the pristine is observed. The dashed line guides the eyes. The peaks observed for 500 °C annealed sample at 37.24, 43.28, 62.84, 75.38, 79.46° matches well with the JCPDS number 780429. These peaks correspond to the 111, 200, 220, 311, and 222 planes with the face-centered cubic structure of NiO with a space group of Fm$\overline{3}$m. The corresponding peak position of these planes for pristine is identified at 36.41, 42.37, 61.50, 73.82, $77.{71}^{\circ }$. The shifting of the XRD peak position with the increasing annealing temperature may happen due to the release of stress and strain in the system. Figure 4b shows the variation of crystallite size and microstrain with temperature. The temperature for the pristine sample is considered as the room temperature (25 °C) throughout the paper. The crystallite size is calculated utilizing the Scherrer formula²⁷ by fitting the XRD peak using the Gaussian function.

$$\begin{array}{c}\hfill D=\frac{K\lambda }{\beta cos\theta }\end{array}$$ 1

where, K = Scherrer constant (0.9), $\lambda$ = Cu $K_{\alpha }$ radiation wavelength (0.154 Å), $\beta$ = FWHM of the diffracted peak in radians, $\theta$ = Bragg’s diffraction angle in radians. The strain ($ϵ$) is calculated using the following formula:

$$\begin{array}{c}\hfill \epsilon =\frac{\beta }{4tan\theta }\end{array}$$ 2

The crystallite size increases with the increase in temperature while the strain decreases. The increment of crystallite size and decrement of strain affect in shifting the peak position toward the exactitude XRD peak position of NiO than the pristine. Since the strain decreases with temperature, it is expected that the vacancy defects will decrease significantly at the highest annealing temperature²⁸. The lattice constant (a) is evaluated by the following equation:

$$\begin{array}{c}\hfill a=d_{\mathit{hkl}}\times {(h^2+K^2+l^2)}^{\frac{1}{2}}\end{array}$$ 3

where $d_{\mathit{hkl}}$ is the inter-planner distance, and h, k, l are the Miller indices. $d_{\mathit{hkl}}$ is calculated using Bragg’s equation²⁹. The variation of lattice constant with temperature is presented in Fig. 4c. The lattice constant decreases monotonically with the increase of temperature. There is a drastic change in lattice constant from pristine (4.26 Å) to 300 °C annealed sample (4.21 Å), which is also noticed in the shifting of the XRD peak position. The lattice constant for the 500 °C annealed sample is 4.17 Å, matching exactly with the reported JCPDS file (number 780429). The phase, peak position, and lattice parameters improved greatly with the increase in the annealing temperature of the grown films, which concurred with the standard JCPDS. So, the amelioration of these parameters can affect the optical and nonlinear properties of NiO thin films.

Figure 4.

(a) The XRD patterns of the pristine and annealed NiO thin film at 300, 350, 400, 450, and 500 °C, (b) the variation of crystallite size and microstrain with annealing temperature, (c) the decrement of lattice constant with annealing temperature.

Optical studies

UV–Vis analysis

The UV-Vis absorption spectra are investigated in the wavelength range of 300–800 nm, shown in Fig. 5a. The spectra show that the absorption edge for the bandgap of NiO is in the UV region. Another broad absorption peak was observed at 447 nm (described later). The change in the Urbach energy with temperature is shown in Fig. 5b. The Urbach energy is characterized using the following empirical formula³⁰:

$$\begin{array}{c}\hfill ln(\alpha )=\frac{h\nu }{E_u}+ln({\alpha }_0)\end{array}$$ 4

where $\alpha$ is the absorption coefficient, $h\nu$ is the incident photon energy, $E_u$ is Urbach energy, and ${\alpha }_0$ is a constant. The reciprocal of the slope of the linear fitting of $ln(\alpha )$ vs energy will give the Urbach energy. The Urbach energy decreases with the increment of annealing temperature. The reduction of Urbach energy signifies that the lattice defects and disorders decrease with temperature. The $E_u$ value changes drastically from the pristine to 300 °C annealed sample. This means that pristine contains a lot of defects and disordered states. The lower value of $E_u$ proposed the narrowing band tails and localized states within the conduction and valance band, predicting the increment of the bandgap. Furthermore, the lower value of Urbach energy signifies the lower dislocation density within the system and vice versa. The decreasing of dislocation density can also be noticed from the increasing trend of crystallite size, calculated from XRD spectra. The variation of bandgap with annealing temperature is presented in Fig. 5c. The bandgap increases with the increment of temperature, as predicted. The bandgap is calculated using the Tauc equation as follows^31,32:

$$\begin{array}{c}\hfill {(\alpha h\nu )}^n=A(h\nu -E_g)\end{array}$$ 5

where, $h\nu$ = incident photon energy. n determines the nature of electron transition. For the indirect transition of the electron, n = $\frac{1}{2}$. A is a constant. $E_g$ = bandgap of the material. The intersection on the x-axis of the extension of linear fitting of Tauc plot gives the bandgap value of NiO. The typical Tauc plotting for pristine is shown in the inset of Fig. 5c. The indirect bandgap (IB) of pristine NiO is evaluated to 2.82 eV, which is increased to 3.24 eV for 500 °C annealed sample. The decrease of defect, disorder, and dislocation density with the increment of annealing temperature may be responsible for the increment of bandgap. The increase of crystallite size and reduction of lattice constant toward the standard value of NiO also play a crucial role in the increment of the bandgap of NiO.

Figure 5.

(a) The UV–Vis absorbance spectra for pristine and annealed samples, the variation of (b) Urbach energy, and (c) indirect bandgap of NiO with temperature. Inset of (c) shows the typical Tauc plot of pristine.

PL analysis

PL emission is very sensitive and depends on film quality and the presence of defects in the system. The PL spectra for pristine and thermally annealed samples are shown in Fig. 6a. The typical deconvoluted spectra for pristine can be observed in Fig. 6b. The spectra are deconvoluted into three peaks at 413, 524, and 572 nm. The peak at 413 nm (3.00 eV) can be attributed to the defect-related deep-level emission due to oxygen vacancy³³. The insignificant shifting of this emission is observed, and the disorder and defects reduce gradually with the annealing temperature associated with this peak, as seen in Fig. 6c. The visible emission at 524 nm can correspond to the inter-band transition surface states due to oxygen vacancy, Ni interstitial defects, and incomplete bond formation³⁴. The 572 nm peak also originated due to the presence of oxygen vacancies in NiO thin films³⁵. The variation of the integrated intensity for the emission of 413, 524, and 572 nm are shown in Fig. 6c–e, respectively. The integrated intensity decreases with annealing temperature for visible and blue emissions, signifying that the defect states reduce with temperature. This also concurs with the variation of Urbach energy evaluated from UV-Vis spectra. The drastic change in the integrated intensity from pristine to annealed samples occurred due to the rapid change in lattice parameters and Urbach energy.

Figure 6.

(a) The PL spectra of pristine and annealed samples, (b) The typical deconvoluted spectra of pristine, The integrated intensity variation with temperature for (c) 413 nm, (d) 524 nm and (e) 572 nm, respectively.

CL analysis

Fewer studies on CL signals have been done to analyze the defect-related properties of annealed NiO samples. Luminescence in NiO is correlated to different defects and impurities present between the Conduction Band (CB) and Valence Band (VB). The CL spectra of pristine and the sample annealing at 300, 350, 400, 450, and 500 °C are shown in Fig. 7a. The CL spectra are deconvoluted into three peaks at 403, 485, and 744 nm. The typical deconvoluted spectra for pristine are shown in Fig. 7b. There is a blue shift of the 403 nm peak position with annealing temperature with respect to the pristine sample, as observed in Fig. 7a. The blue shifting of this peak position with temperature is shown in Fig. 7c. The CL emission at 403 nm (3.07 eV) is attributed to the near-band emission due to the transition of electrons from CB to VB. The energy gap doesn’t match exactly with the gap found from UV-Vis spectra. The peak position shifted to 385 nm (3.22 eV) for 500 °C annealed samples. This value is quite close to the energy gap for this sample. The blue shift of this peak position agrees well with the increasing trend of the energy gap found from UV-Vis spectra. The visible emission at the 485 nm (2.55 eV) peak corresponds to the formation or lowering of the lattice defects with annealing temperature. Local noncubic distortion, which breaks the crystal symmetry, and also the change in the native and surface-induced defects in NiO can be responsible for changes in emission intensity³⁶. Ni vacancies, which act as shallow acceptors in NiO, can vary with annealing temperature³⁷. The crystal field d-d transition, Ni vacancies, and ${\text{Ni}}^{2+}$ defect states can also be attributed to the visible emission peak at 485 nm of NiO sample^38–40. The near-IR emission at 744 nm (1.66 eV) can be associated with oxygen vacancies that formed during annealing in a vacuum due to the limitation of oxygen supply³⁵.

Figure 7.

(a) The CL spectra of pristine and annealed samples, (b) the typical deconvoluted spectra of pristine, (c) the shifting of the 403 nm peak position with annealing temperature.

Theoretical analysis

The DFT band structure for pristine and 300, 350, 400, 450, and 500 °C annealed samples are shown in Fig. 8a–f, respectively. The spin-polarised magnetic calculation for the stable antiferromagnetic arrangement of NiO (along (111) plane) with the experimentally found lattice parameter value was accomplished for all the samples. The band structure in Fig. 8 shows that the up and down spin overlap with each other to make the total moment zero, as expected for the antiferromagnet NiO system. The calculated bandgap is found to be 2.83 eV for pristine by taking the Hubbered U value to 4.7 eV, which closely matches our experimental results (2.82 eV). As seen in Fig. 8a and Table 1. that, the transition did not occur along the same gamma point. Rather, we found that the transition of electron happens from $\mathrm{\Gamma }$ (CB minimum) to L (VB maximum) for pristine. The transition for other samples is listed in Table 1. This justifies the taking of n = 1/2 in the Tauc plot to get the experimental indirect bandgap of NiO. It is noticed that the transition point differs after the 300 °C annealed samples. The reason for this is that there is a shifting in the CB band along $\mathrm{\Gamma }$ points in annealed samples than the pristine, as highlighted by the red square. The magnified view (in red square) of CB around the $\mathrm{\Gamma }$ point for pristine and 500 °C annealed samples is shown in the inset for clear vision. This shifting may happen due to the changing of the lattice parameter in the system. The theoretically calculated bandgap values with their corresponding U value are listed in Table 1. It is observed that the calculated bandgap increases with the increase of the U value and matches with the experimental value quite well. For further verification, we fixed the U value (taking the pristine one, U = 4.7 eV) and calculated with the varying experimental lattice parameters. We observed that the bandgap also increases (calculated values are listed in Table 1). So, we can conclude that the gradually decreasing lattice parameter and the increase of the onsite Coulomb repulsion correction between the electrons in the Ni-d orbital influence the increase of the bandgap in annealed samples.

Figure 8.

The electronic band structure for (a) pristine, (b) 300, (c) 350, (d) 400, (e) 450, and (f) 500 °C annealed samples. The black dashed line along zero indicates the Fermi level.

Table 1.

The DFT calculated IB values (with experimental lattice constant value) for different values of U, matching with experimental values.

Samples (°C)	IB (eV) (Exp.)	IB (eV) (Th.)	U value (eV)	IB (eV) (Th.), U = 4.7 eV (fixed)	Lattice constant (Å)
Pristine (25)	2.82	2.83, CB min = $\mathrm{\Gamma }$, VB max = L	4.7	2.83, CB min = $\mathrm{\Gamma }$, VB max = L	4.26
300	3.10	3.10, CB min = $\mathrm{\Gamma }$, VB max = L	5.0	2.99, CB min = $\mathrm{\Gamma }$, VB max = L	4.21
350	3.15	3.15, CB min = $\mathrm{\Gamma }$-X, VB max = L	5.08	3.00, CB min = $\mathrm{\Gamma }$-X, VB max = L	4.20
400	3.19	3.19, CB min = $\mathrm{\Gamma }$-X, VB max = L	5.15	3.01, CB min = $\mathrm{\Gamma }$-X, VB max = L	4.19
450	3.21	3.21, CB min = $\mathrm{\Gamma }$-X, VB max = L	5.18	3.02, CB min = $\mathrm{\Gamma }$-X, VB max = L	4.18
500	3.24	3.24, CB min = $\mathrm{\Gamma }$-X, VB max = L	5.23	3.03, CB min = $\mathrm{\Gamma }$-X, VB max = L	4.17

The variation of calculated IB values for fixed U value along with calculated lattice constant.

To further understand the band structure, we calculated total, partial, and orbital DOS for pristine and 500 °C annealed samples, shown in Fig. 9. The total and partial DOS for pristine and 500 °C annealed samples in Fig. 9a,d shows that the CB is mainly formed by Ni-d orbital and VB by O-p and Ni-d orbitals. It is seen clearly from Fig. 9a,d that the O-p has no contribution near the minimum of CB but rather Ni-d. So, the shifting in the CB minimum in the band structure mainly occurs due to the shifting of Ni-d orbitals. The decomposed DOS of Ni-d and O-p orbital for these samples (Fig. 9b,e and c,f, respectively) clearly identified that the shifting of CB minimum happens due to the shifting of Ni-$d_{x^2-y^2}$ and Ni-$d_{z^2}$ orbitals by increasing U values which leads to the enhancement of the bandgap in the annealed samples.

Figure 9.

The total and partial (a,d), the Ni-d (b,e), and O-p (c,f) orbital decomposed DOS for pristine and 500 °C annealed samples. The black dashed line along zero denotes the Fermi level.

Non-linear optical properties

The normalized transmittance in OA and CA conditions as a function of distance in Z-scan measurements for pristine and annealed samples are shown in Figs. 10 and 11, respectively. The OA and CA normalized transmittance are governed by⁴¹,

$$\begin{array}{cc}\hfill T(z,S=1)=& 1-\frac{\beta I_0{L}_{\mathit{eff}}}{2^{3/2}{(1+x)}^2}\hfill \end{array}$$ 6

$$\begin{array}{cc}\hfill T(z,\mathrm{\Delta }{\varphi }_0)=& 1-\frac{4\mathrm{\Delta }{\varphi }_{0}x}{(x^2+9)(x^2+1)}-\frac{2(x^2+3)\mathrm{\Delta }{\psi }_0}{(x^2+9)(x^2+1)}\hfill \end{array}$$ 7

where $\beta$ = nonlinear absorption coefficient, $I_0$ = peak intensity at the focal point (z = 0), x = Z/$Z_0$, and $L_{\mathit{eff}}$ = $\frac{1-e^{-\alpha L}}{\alpha }$, effective length of the sample, where $\alpha$ = absorption coefficient, and L = sample thickness. S = 1 for OA configuration measurements. $\mathrm{\Delta }{\varphi }_0=k{n}_2{I}_0{L}_{\mathit{eff}}$ and $\mathrm{\Delta }{\psi }_0=\beta I_0{L}_{\mathit{eff}}/2$ = phase-change terms due to nonlinear refraction and nonlinear absorption, respectively, and k = $2\pi /\lambda$.

Figure 10.

Open aperture normalized transmittance curve of (a) pristine and annealed samples at (b) 300, (c) 350, (d) 400, (e) 450, and (f) 500 °C, respectively. Inset of (b) shows the indirect two-photon absorption process.

Figure 11.

Closed aperture normalized transmittance curve of (a) pristine and annealed samples at (b) 300, (c) 350, (d) 400, (e) 450, and (f) 500 °C, respectively.

The $\beta$ and $n_2$ values are evaluated after fitting the OA transmittance by Eq. (6) and CA by 7, listed in Table 2. The threshold value of annealing for enhancing the nonlinear coefficient is found to the 400 °C annealed sample, and after that, the nonlinearity decreases.

Table 2.

The comparison table of the evaluated $\beta$ and $n_2$ values of the present study and previous reports on other oxide and NiO.

Sample	$\beta$ (cm ${\text{W}}^{-1}$)	$n_2$ (${\text{cm}}^2$ ${\text{W}}^{-1}$)	Parameters	References
Ni-doped ZnO thin film	$2.80-4.28\times$ ${10}^{-7}$	$4.04-4.78\times$ ${10}^{-11}$	$\lambda =750$ nm	42
170 nm thick ITO thin film	–	$9.0\times$ ${10}^{-12}$	$\lambda =820$ nm	43
As deposited NiO films	–	$9.4-8.8\times$ ${10}^{-7}$	$\lambda =632.8$ nm	14
250 °C annealed NiO films	–	$2.3-3.3\times$ ${10}^{-5}$	$\lambda =632.8$ nm	14
NiO microrods	$3.5\times$ ${10}^{-9}$	–	$\lambda =532$ nm	44
NiO-PVA composite film	$1.30-3.39\times$ ${10}^{-6}$	–	$\lambda =532$ nm	45
Undoped NiO films	$0.92\times$ ${10}^{-5}$	$2.2\times$ ${10}^{-12}$	$\lambda =532$ nm	16
N-doped (20% Ar, 80% N$_2^{}$) NiO films	$4.55\times$ ${10}^{-5}$	$6.5\times$ ${10}^{-12}$	$\lambda =532$ nm	16
Undoped NiO films	$9.01\times$ ${10}^{-2}$	$8.36\times$ ${10}^{-9}$	$\lambda =632.8$ nm	21
15% N in NiO films	$5.32\times$ ${10}^{-2}$	$6.35\times$ ${10}^{-7}$	$\lambda =632.8$ nm	21
NiO films	$6.60\times$ ${10}^{-7}$	$0.2\times$ ${10}^{-10}$	$\lambda =800$ nm	17
Pristine NiO	$-6.66\times$ ${10}^{-6}$	$2.68\times$ ${10}^{-10}$	$\lambda =1030$ nm	This work
300 °C annealed	$9.23\times$ ${10}^{-6}$	$1.99\times$ ${10}^{-10}$	$\lambda =1030$ nm	This work
350 °C annealed	$9.86\times$ ${10}^{-6}$	$1.64\times$ ${10}^{-10}$	$\lambda =1030$ nm	This work
400 °C annealed	$19.08\times$ ${10}^{-6}$	$4.21\times$ ${10}^{-10}$	$\lambda =1030$ nm	This work
450 °C annealed	$17.08\times$ ${10}^{-6}$	$4.11\times$ ${10}^{-10}$	$\lambda =1030$ nm	This work
500 °C annealed	$0.89\times$ ${10}^{-6}$	$0.92\times$ ${10}^{-10}$	$\lambda =1030$ nm	This work

The OA curve in Fig. 10a shows that pristine exhibits the peak at the focal point. This indicates the signature of SA and is attributed to the negative sign of nonlinearity. The annealed samples exhibit a dip in the transmittance at the focus, revealing the RSA behavior with the positive sign of nonlinear absorption. When intense laser light is incident on a pristine sample, the atoms become excited. When the pristine sample is positioned at the focal point of a converging lens, there are insufficient atoms remaining in the ground state to further absorb the light. As a result, most of the atoms are found in an excited state, leading to high transmission of light through the sample. This phenomenon results in SA in the pristine sample. In contrast, annealed samples exhibit a transformation from SA to RSA. The RSA is associated with an indirect TPA process, which will be discussed later. One can notice that there is a rapid change in the sign reversibility between pristine and annealed samples in the nonlinear curve. The positive nonlinear absorption can be used for optical limiting applications. So, in this case, the annealed samples can be applied in optical limiting devices, which can provide safety to optical detectors, sensors, and even to human eyes, acting as transparent for low-level input intensity and relatively opaque to high-level inputs. Good optical limiting materials exhibit potential response in large nonlinearity, broad-band spectral response, fast response time, low limiting threshold, high linear transmittance, stability, etc. The negative nonlinear absorption is beneficial for Q switching. The RSA of nonlinear properties in semiconductor thin films can be assigned to TPA, Three-Photon Absorption (ThPA), Excited State Absorption (ESA), nonlinear scattering or free carrier absorption, etc.⁴⁶. On the other hand, the SA can be associated with the bleaching of the electronic ground state originated due to the effect of efficient plasmon adsorption⁴⁷. The direct TPA is possible when the energy bandgap of the sample satisfies the following condition: $E_g<2h\nu <2E_g$. The indirect TPA can also occur in the sample via intermediate energy level due to vacancy defect states⁴⁸. In our case, $E_g$ of NiO (2.82–3.24 eV) is larger than twice the excitation energy ($2h\nu$ = 2.40 eV), which signifies the possibility of occurring the indirect TPA. The room temperature PL shows that oxygen vacancy states can form inside the bandgap, suggesting the probability of indirect TPA. Deng et al. and Li et al. reported such indirect TPA process occurring due to defects and trap states in semiconducting materials^49,50. Since the indirect TPA condition is satisfied, as shown in the inset of Fig. 10b, it also occurs indirectly via the intermediate levels formed by vacancy. The RSA and SA are further examined by analyzing the UV-Vis spectra carefully. Figure 5a shows that there is a clear broad hump centered at 447 nm (2.77 eV) appeared in annealed samples. This hump is not prominent in the pristine. This peak can be attributed to the partially filled d-band of Ni. The other possible reason for arising this hump may be surface plasmon resonance (SPR) which is predicted to appear at 2.8 eV due to Ni nanoparticles⁵¹. It has been observed from XRD spectra that the crystallite size varies from 7.48 nm to 12.49 nm. In order to verify the contribution of the surface plasmon effect to the optical nonlinearity due to the crystallinity of NiO crystallites, it is found that at the resonance frequency (${\omega }_p=\sqrt{2}\omega$), the surface plasmon significantly affects the nonlinear polarization¹³. In this present study, the excitation energy of the laser is 1.20 eV. The resonance energy to occur with this laser intensity ($\sqrt{2}ħ\omega$) is 1.70 eV, which is far lower than the energy required for the SPR (2.77eV). This justifies that, in our case, SPR has an almost insignificant role in optical nonlinearity. So, indirect TPA is mainly responsible for the RSA process.

In CA conditions, the on-axis beam intensity variation exhibits the pre-focal minima and post-focal maxima for all the samples. This valley-peak feature is the signature of the self-focusing effect and, hence, the positive value for the nonlinear refractive index ($n_2$). The real part of the non-linear susceptibility (${\chi }_R^{(3)}$) is related to the $n_2$ values, as follows¹⁴,

$$\begin{array}{c}\hfill {\chi }_R^{(3)}=\frac{1.4c{n}_0^2{n}_2}{480{\pi }^2}\times {10}^{-14}\end{array}$$ 8

where c = speed of light, $n_0$ = background refractive index. The susceptibility shows a similar variation with the third-order nonlinear refraction coefficient. The comparison of the nonlinear coefficient of the current study with the previously reported value of other oxide and NiO materials is listed in Table 2. Such a highly significant response in the nonlinear coefficient (see Table 2) of NiO with annealing temperature can be useful for various optoelectronic and electronic devices such as optical limiters, optical memory elements, etc. Various mechanisms have been proposed to explain the cause of the optical nonlinearity. Since the NiO samples are irradiated by the fs laser light with an energy of 1.20 eV, the following reasons may be responsible for the nonlinearity: (1) surface plasmon effect¹³, (2) the effect of thermal lensing⁵², and (3) the spin split d-d near resonant transition in sub-bandgap¹⁴. We have already explained that the SPR effect has no role in the nonlinear effect as the excitation energy is not sufficient to occur the plasmon resonance. Again, the change in the path length within the illumination region leads to the thermal lensing effect. The negative or positive value of the path length change is associated with photo densification (PD) or photo expansion (PE). The PD and PE are related to the disorderness of the film⁵³. The disorder reduces with thermal annealing, as observed from UV-Vis spectra. Since we are using the fs laser with low energy and the disorder of the annealed film reduces, we can say that the thermal lensing effect is negligible in this case. So, the spin split d-d transition can be the reason for the nonlinear behaviors in the present study. The Ni-d orbital decomposed DOS (Fig. 9b,e) showed that Ni-$d_{x^2-y^2}$ and Ni-$d_{z^2}$ orbitals are mainly forming the CB minimum, which shifts with the increasing U value. The electron in Ni-d or O-p orbital in VB absorbs the two-photon and reaches one of the two orbitals of the CB via the intermediate states. Hence, the d-d or d-p transition can give rise to changing the nonlinearity. Annealed samples are associated with indirect TPA processes governing the RSA, which can be used as an auto-correlator and optical power limiter. Since the bandgap increases in the annealed samples with temperature, the absorption in TPA is relatively low in the 300 °C annealed sample with respect to the higher annealed sample. So, the 400 °C annealed sample can be used as a better optical limiter than pristine and the lower annealed samples due to having a high nonlinear absorption coefficient. Further annealing of the NiO samples degrades the optical limiting properties. So, 400 °C annealing is the threshold temperature for better optical limiting applications. The SA observed in pristine is useful for passive Q switching and passive mode locking, which can be utilized in generating nanosecond and femtosecond pulses, respectively. The modulation depth, which is proportional to the nonlinear absorption coefficient, is the key parameter for passive mode-locking⁵⁴. Large modulation depth associated with SA can be used for generating short laser pulses and designing for self-starting mode-locked laser⁵⁵. Pristine and annealed NiO can show different potential applications according to their nonlinear properties.

Conclusion

In summary, we have analyzed the NLOP of as-grown and annealed NiO thin films using the Z-scan technique. The structural and other optical properties are also discussed and correlated to the NLOP. The DFT calculation of band structure and DOS explain the electronic reason for increasing the bandgap with annealing temperature. We investigated that the upward shifting of Ni-$d_{x^2-y^2}$ and Ni-$d_{z^2}$ orbitals in CB due to increasing U value with the decrease of lattice parameter causes the increase of bandgap. The theoretical calculation also gives the inner-sight reason for NLOP at the OA and CA measurements. In OA, SA and RSA are observed in pristine and annealed samples, respectively. The nonlinear absorption coefficient increases up to 400 °C annealed sample and then decreases, resulting in the 400 °C as the threshold temperature of NiO for achieving better optical limiter than the other annealed sample. In CA, the prefocal minima and postfocal maxima exhibit the signature of a self-focusing effect. The spin split d-d or d-p transition is responsible for nonlinear behavior. PL and CL confirm the probability of the formation of an intermediate state between CB and VB. So, RSA is explained on the basis of indirect TPA processes, taking into consideration the vacancy as intermediate states. The current study of SA to TPA process has technological applications for better optical limiting and passive Q-switching devices.

Author contributions

Sourav Bhakta: writing—original draft, analysis, investigation, methodology, validation, visualization, and performed the DFT calculations. Rudrashis Panda.: carried out the Z-scan measurements. Pratap Kumar Sahoo: Supervision, funding acquisition, Resources, project administration, review, editing. All authors reviewed the manuscript.

Data availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.