Cu-engineered TiO₂ thin films: defect-driven nonlinear optical responses for ultrafast frequency conversion and optical limiting

Abstract

Cu-doped TiO₂ thin films with varying Cu concentrations were fabricated by spray pyrolysis to investigate the influence of Cu incorporation on their nonlinear optical (NLO) properties. XRD analysis confirms the formation of anatase TiO₂ with the emergence of Cu-related peaks at higher doping levels. XPS analysis verified the successful incorporation of Cu into the TiO₂ matrix. Z-scan measurements under continuous-wave laser revealed an intensity-dependent transition from saturable absorption to reverse saturable absorption in the 1 and 2 wt% Cu–TiO₂ films, with the 2 wt% film exhibiting the highest nonlinear absorption. Under nanosecond excitation, the 1 wt% Cu–TiO₂ film displayed the strongest second-harmonic generation response, while the pristine TiO₂ film showed the highest third-harmonic generation (THG) intensity. Maker fringe technique analysis under picosecond excitation demonstrated that the 2 wt% Cu–TiO₂ film possesses the highest third-order nonlinear susceptibility (χ⁽³⁾ = 3.85 × 10⁻²¹ m² V⁻²). Furthermore, the 1 and 2 wt% films exhibited superior THG performance under picosecond excitation, highlighting the role of ultrafast electronic nonlinearities. The enhanced NLO response is attributed to the synergistic effects of Cu-induced defect states, lattice distortion, and excitation-dependent nonlinear mechanisms. These findings establish Cu–TiO₂ thin films as promising candidates for applications in optical limiting and ultrafast frequency conversion devices.

Tunable nonlinear absorption and enhanced harmonic generation in Cu-doped TiO₂ thin films via Cu-induced defect engineering.

1. Introduction

Nonlinear optics (NLO) has turned out to be the most prominent field within the realm of photonics as it relies on materials whose parameters, such as refractive index and absorption coefficients, depend on the intensity of the incoming light.¹ NLO properties offer the foundation on which a number of advanced optical technologies are built, such as ultrafast signal processing, frequency conversion, optical switching, and optical computing systems.^2,3 The ideal materials are those that have large third-order nonlinearities, as they can be used to efficiently control light–matter interactions for the engineering of compact integrated photonic devices.^4,5 There has been widespread research involving NLO materials, such as inorganic crystals,^6,7 organic compounds,^8,9 metal oxides,^10–12 and polymers¹³ seeking variable systems that can support photonic applications. The nonlinear optical performance of a material is commonly assessed through parameters such as the nonlinear absorption coefficient (β), and nonlinear susceptibilities (χ⁽²⁾ and χ⁽³⁾). These parameters govern key phenomena including saturable absorption (SA), reverse saturable absorption (RSA), and harmonic generation processes. Materials exhibiting large nonlinear susceptibilities and efficient harmonic generation are highly desirable for applications such as optical limiting, all-optical switching, frequency conversion, and ultrafast photonic devices.^14,15 Consequently, significant efforts have been devoted to engineering material composition and defect states to enhance these nonlinear parameters and tailor the optical response.¹⁶

In recent years, metal oxide semiconductors have drawn attention owing to their chemical stability, low cost, and applicability for practical uses. Titanium dioxide (TiO₂) is preferred in this category. Anatase, brookite, and rutile are the three phases of TiO₂.¹⁷ It is one of the widely studied materials because of its high photochemical stability, high refractive index, nontoxicity, and strong catalytic activity.^18,19 TiO₂ thin films are widely utilized in photocatalysis,²⁰ photovoltaic devices,²¹ gas sensors,²² dielectric coatings,²³ and emerging nonlinear optical applications.²⁴

Yet the functional properties of TiO₂ can be improved by optimizing its inherent properties. Doping has been a proven route toward such modifications, as the introduction of foreign ions into the TiO₂ lattice can alter its electronic structure, create beneficial defect states, and influence crystallinity and charge carrier dynamics.^25,26 Transition metal dopants, in particular, have shown considerable results in improving the functional performance of TiO₂ based thin films.²⁷ Copper (Cu) is a suitable dopant for TiO₂ since its ionic radius being comparable to that of Ti⁴⁺, which permits substitution within the TiO₂ lattice.²⁸ Studies have reported that Cu doping can transform phase,²⁹ tune the bandgap³⁰ developing Cu–TiO₂ a promising material system for advanced applications.

Various techniques have been employed for the fabrication of TiO₂ thin films, including dip coating,³¹ spin coating,³² spray pyrolysis,³³ chemical vapor deposition,³⁴ and pulsed laser deposition.³⁵ In this study, spray pyrolysis was opted as the deposition method because of its cost-effectiveness, simple apparatus and scalability.³⁶ This technique permits one to have control over the composition of thin films, which can be achieved through the selection of solution concentration, spraying rate, and temperature of the substrate, which is particularly helpful when adding dopant ions into the TiO₂ matrix. The spray pyrolysis technique has the ability to produce films with high adhesion without necessitating vacuum systems or complicated steps.

Many studies have been dedicated to the modulation of structural and optical properties of TiO₂ by metal doping. Different fabrication methods and dopant species have been investigated to tailor microstructure and optical response. The following literature reports bring out the key advances in doped TiO₂ nanostructures, particularly in terms of structure–property correlations relevant to optical and nonlinear optical applications. Farzaneh et al.³⁷ published their research findings on the effect of doping with Al and Cu on TiO₂ thin films synthesized by the sol–gel technique. Single-phase anatase TiO₂ with no peaks related to dopants and their oxides was confirmed by the results of XRD analysis. Optical property analysis showed lower transmission and an enhanced absorption edge with doping with metals Al and Cu due to changes in the band structure. M. Rajabi et al.³⁸ found an enhanced NLO response in La–TiO₂ nanorod arrays when exposed to pulsed laser illumination. Nanorods were deposited on an FTO covered glass substrate. Single phase rutile TiO₂ with lower lattice distortion was confirmed by the results provided by XRD analysis upon lanthanum doping. Notably, La doping led to a major improvement in the nonlinear absorption coefficient. T. Raguram et al.³⁹ observed anatase phase of TiO₂ when the concentration of metal copper was lower. However, when the Cu amount was maximized, XRD peaks related to copper oxides were found, accompanied by a reduction in average crystallite size. Raman spectroscopy further ensured Cu incorporation through the detection of Cu-related lattice vibrational modes at increased dopant concentrations. M.A. Khan et al.⁴⁰ deposited Cu–TiO₂ nanoparticles by doping Cu at various concentrations using the hydrothermal method. XRD analyses revealed that the prepared nanoparticles were of pure anatase structure, although the size of the crystallites increased with the addition of Cu. Furthermore, the PL analyses revealed that the PL intensity significantly lowered in the doped sample, thereby confirming the retardation in the recombination of charge carriers. O. Zakir et al.⁴¹ fabricated Ag, Fe, and Cu-doped TiO₂ nanoparticles. XRD pattern of undoped TiO₂ revealed a mixed anatase, rutile, and brookite phase, whereas all doped samples showed anatase structure with enhanced crystallinity and structural quality. Dopant incorporation resulted in reduced grain and crystallite sizes, indicating effective modification of the TiO₂ lattice. F. Bensouici et al.⁴² examined Cu-doped TiO₂ thin films and reported that all samples crystallized in the anatase phase; however, at higher Cu concentrations (8–10%), CuO phases emerged. Because CuO and Cu₂O phases serve as sites where electron–hole pairs recombine, the efficiency of methylene blue degradation declined as the Cu²⁺ content increased. The role of Cu in the anatase to rutile phase transformation has been examined by Ciara Byrne et al.,⁴³ who found that Cu doping enhanced the thermal stability of anatase, shifting the transition to higher temperatures. Also, XPS analysis revealed that increasing the temperature caused the partial reduction of Cu²⁺ to Cu⁺. These were supported by the work done by S. A. Ahmed,⁴⁴ where he studied Cu–TiO₂ nano powders and observed predominantly rutile-type crystallinity with minor anatase traces, along with an increase in lattice parameters and unit cell volume, attributed to Cu ions substitution into Ti lattice sites. V. Krishnakumar et al.⁴⁵ reported that adding higher amounts of Cu reduced the crystallite size of TiO₂ nanoparticles. FESEM observations also showed smaller particle sizes in Cu incorporated samples relative to the pristine. Additionally, the optical band gap narrowed upon Cu incorporation. Together, these works demonstrate that copper incorporation significantly modifies the microstructure, phase stability, and functional efficiency of TiO₂.

Despite these advancements, the precise correlation between Cu concentration and the resulting nonlinear optical (NLO) properties in TiO₂ thin films synthesized via spray pyrolysis remains largely unexplored. To address this gap, the present study focuses on the fabrication and systematic analysis of copper-doped TiO₂ (Cu–TiO₂) thin films with varying dopant levels. The objective is to elucidate how Cu incorporation modulates the structural, morphological, and linear optical characteristics, and how these changes dictate the NLO response. Uniquely, this work investigates nonlinear absorption (NLA) under continuous-wave (CW) excitation, while the second- and third-harmonic generation (SHG and THG) responses are analyzed in the nanosecond (ns) regime. Furthermore, picosecond (ps) laser excitation is employed to probe the angle-dependent THG response, providing insights into the ultrafast electronic contributions. Building upon our previous investigation into the effects of precursor concentration,⁴⁶ this research aims to provide a comprehensive understanding of defect-engineered TiO₂ nanostructures for advanced optoelectronic and photonic applications.

2. Experimental details

2.1. Synthesis of Cu–TiO₂ thin films

In this study, copper-doped TiO₂ (Cu–TiO₂) thin films were deposited via the spray pyrolysis technique with varying dopant concentrations using a HOLMARC spray pyrolysis equipment (Model No: HO-TH-04). For the deposition of pristine films, a 0.2 M solution of titanium(iv) isopropoxide (Ti [OCH(CH₃)₂]₄, Sigma-Aldrich) was prepared using ethanol (CH₃CH₂OH) as the solvent, and acetylacetone (CH₃COCH₂COCH₃, Sigma-Aldrich) was added as a stabilizing agent. The dopant solution was obtained by dissolving copper (ii) chloride dihydrate (CuCl₂·2H₂O, MERCK) in ethanol to obtain a 0.2 M CuCl₂ solution. Both the TiO₂ precursor and the Cu dopant solutions were magnetically stirred for 30 min. With a speed of 2000 rpm at room temperature to ensure complete dissolution and homogeneity. Cu doping was performed by incorporating appropriate amounts of the dopant solution into the host solution to obtain final precursor solution with 1, 2, and 3 wt% Cu. The resulting mixtures were further stirred for an additional 30 min. To ensure uniform mixing. Prior to deposition, glass substrates were cleaned sequentially using soap solution, acetone, and isopropyl alcohol (IPA) in an ultrasonic cleaner to remove surface contaminants. The deposition was performed via spray pyrolysis by introducing the precursor solution at a controlled flow rate of 2 mL min⁻¹. The thin films were coated onto the preheated substrates maintained at 400 °C under a working pressure of 0.5 bar. The thin films were synthesized following the same experimental parameters for all compositions. A flow diagram depicting the complete thin film synthesis route is provided in Fig. 1. The atomic arrangement in TiO₂ and Cu–TiO₂ crystals were visualized using the VESTA software. The obtained structural models are depicted in Fig. 2.

Fig. 1. Schematic illustration of the thin film synthesis process.

Fig. 2. Structural models of pristine and Cu–TiO₂.

2.2. Material characterization

X-ray diffraction (XRD) experiments were conducted to assess the impact of Cu addition on the microstructural parameters of TiO₂ using Rigaku SmartLab diffractometer operated at 100 mA and 45 kV with Cu Kα radiation (λ = 1.5406 Å) as source. The measurements were performed in Bragg–Brentano geometry with a step size of 0.05° and a scan rate of 2° min⁻¹. Microstructural characteristics and defect-related features of the nanostructured Cu–TiO₂ films were evaluated using Raman spectroscopy (Horiba LabRAM HR Evolution Raman spectrometer with an excitation source of 532 nm). Raman spectra were recorded using a neutral density filter with 10% transmission with an acquisition time of 10 s. Surface morphology was investigated using a field-emission scanning electron microscope (Apreo 2 SEM, Thermo Fisher Scientific) operated at an accelerating voltage of 2.0 kV and a working distance of 10 mm. Energy-dispersive X-ray spectroscopy (EDX) was employed for elemental composition analysis. The linear optical behavior of the Cu–TiO₂ thin films was examined by employing a UV-vis spectrophotometer (Shimadzu UV-1900i). Absorbance and transmission spectra were acquired across the 190–1100 nm range to estimate the optical band gap and evaluate the films' absorption characteristics. The influence of Cu addition on the defect levels and radiative recombination in TiO₂ matrix was evaluated by Photoluminescence (PL) spectrofluorometer (JASCO FP-8500) with an excitation source of 280 nm at room temperature. The oxidation states of the elements in the pristine and Cu–TiO₂ thin films were analyzed by utilizing X-ray photoelectron spectroscopy (Thermo Scientific K-Alpha) with Al Kα X-ray source.

2.3. Nonlinear optical measurements

2.3.1. Z-scan measurements

The influence of addition of Cu on the NLO behavior of the Cu–TiO₂ thin films was assessed by employing the open-aperture (OA) configuration of Z-scan method. The experiments were conducted on a system equipped with a translation stage (Thorlabs HRP350-EC-1) and a CW He–Ne laser (λ = 632.8 nm). To focus the beam on thin film, a convex lens (f = 5 cm) was used, and an aperture of 1.1 mm diameter was aligned in front of the lens. In order to adjust the beam power, neutral-density filters were applied. During data collection, the sample was programmed to move along the Z-axis, and the transmitted signal was captured using a photo detector linked to the data-logging unit of system. A schematic diagram of Z-scan experiment is presented in Fig. 3.

Fig. 3. Schematic representation of Z-scan experiment.

2.3.2. Harmonic generations measurement

SHG and THG experiments were conducted to measure the harmonic generation in pristine and Cu–TiO₂ thin films. The experimental arrangement incorporated ns laser source, reflective optics, a rotating stage, a silicon photo detector, a Glan–Taylor polarizer, a PMT, interference filters, an oscilloscope, and a computer-controlled data acquisition unit.

A nanosecond (ns) Nd: YAG laser (λ = 1064 nm) delivered radiation with a repetition rate of 10 Hz, pulse width of 8 ns, and an energy density close to 150 J m⁻². Laser intensity and linear polarization were regulated by a Glan–Taylor polarizer positioned along the beam direction; its orientation was varied in 5° steps to achieve optimal THG signal detection at low input power. A semi-reflective mirror divided the incident beam, channeling one fraction to the silicon detector for timing reference while the remaining portion propagated toward the thin film.

Nonlinear interaction between the ns laser and the material produced harmonic emissions: the second harmonic, when generated, appeared around 532 nm, and the third harmonic emerged near 355 nm. These emitted wavelengths were isolated using appropriate interference filters and captured by the PMT, with detailed waveform acquisition accomplished on a Tektronix MSO 3054 oscilloscope. The entire optical system was enclosed within a dark, sealed chamber to suppress ambient light and guarantee accurate, noise-free SHG and THG measurements. A schematic diagram of harmonic generation experiment is presented in Fig. 4.

Fig. 4. Schematic diagram of fluence dependent SHG and THG measurement.

2.3.3. Maker fringe technique

Maker fringe method was used to measure THG. The system consisted of a picosecond Nd:YVO₄ laser (EKSPLA PL2250) which served as the excitation source with following parameters: 1064 nm wavelength, 30 ps pulse duration, 95 mJ energy, and a repetition rate of 10 Hz. The output beam was initially incident on a beam splitter, where a fraction of the beam was reflected toward a photodiode to monitor the signal. The transmitted beam was traversed through a polarizer followed by a half-wave plate, enabling precise control over the polarization and pulse energy. A lens was used to focus the polarized beam. The film was placed on a motorized rotational platform to enable accurate control of the incidence angle in the range of −60° to +60°, with a step size of 0.5°. The beam emerging after traversing through thin film was directed through a KG3 optical filter to suppress the fundamental radiation. Subsequently, the third harmonic component was selectively transmitted by using a filter (355 nm) and was detected using a photomultiplier. An oscilloscope, a controller and a computer were connected to the PMT and photodiode to ensure the time aligned operation, signal acquisition and data analysis. Thus, the resulting Maker fringe pattern of the THG signal was measured. Fig. 5 depicts the schematic diagram of Maker fringe experiment.

Fig. 5. Schematic diagram of angle dependent THG measurement.

3. Results and discussion

3.1. XRD analysis

XRD analysis was conducted to assess the impact of Cu addition on the crystal structure, phase composition, and microcrystalline parameters of Cu–TiO₂ thin films. Fig. 6 presents the XRD patterns of pristine and Cu–TiO₂ thin films over a 2θ range of 20–80°. The XRD peaks are formed at 2θ ≈ 25°, 38°, 44°, 48°, 54°, 55°, and 62°. The dominant peak at 2θ ≈ 25° along (101) plane confirms the formation of tetragonal anatase TiO₂, in agreement with JCPDS card no. 01-083-2243. In 2 wt% and 3 wt% Cu–TiO₂ films, an additional peak at 2θ ≈ 44° corresponding to the (213) plane was observed, suggesting the occurrence of a secondary copper oxide phase in the doped thin films.^47–49 However, 1 wt% Cu–TiO₂ films did not exhibit any peaks related to copper, which confirms that lower Cu concentrations remain well incorporated into the host TiO₂ lattice.

Fig. 6. XRD pattern of pristine and Cu–TiO₂ at different doping levels.

An enhancement in the intensity of the prominent peak along (101) is observed in Cu–TiO₂ relative to the pristine, which reflects improvement in the crystalline structure with Cu doping.^50,51 At 3 wt% Cu doping, crystallinity of TiO₂ enhanced and a marginal reduction in the intensity of peak along (213) plane was observed. The crystallite size was estimated through Scherrer equation:⁵²

1

where θ is the Bragg's angle, λ = 0.15406 nm, β represents the FWHM of the TiO₂ XRD peak, and k is Scherrer coefficient. The dislocation density (δ) was estimated using the relation:⁵³

2

The strain (ε) in the films was determined using the formula:⁵⁴

3

An increase in crystallite size was observed with increasing Cu doping concentration. This may be attributed to the successful incorporation of Cu ions into the TiO₂ lattice, which can promote crystal growth and improve structural ordering during film formation, leading to a slight increase in crystallite size.⁵⁵

The dislocation density decreases with increasing Cu dopant concentration. This behavior may be attributed to the successful incorporation of Cu ions into the TiO₂ lattice, which promotes crystallite growth and improves atomic ordering, thereby reducing the density of lattice defects. Similarly, the lattice strain decreases with increasing Cu concentration. This reduction may be associated with improved structural relaxation and the effective accommodation of Cu ions within the TiO₂ lattice, resulting in enhanced structural ordering and reduced lattice distortions.⁵⁶

Lattice parameters and interplanar distance of films were estimated using the equation:⁵⁷

4

where hkl are miller indices.

A progressive lattice compression was observed with increasing Cu doping although Cu²⁺ (0.73 Å) has a larger ionic radius than Ti⁴⁺ (0.61 Å). This may be attributed to charge compensation through oxygen vacancy formation, which induces compressive strain in the TiO₂ lattice.⁵⁸ XPS results corroborate this by showing enhanced oxygen vacancy in 2 wt% Cu–TiO₂. Table 1 presents the microstructural parameters of pristine and Cu–TiO₂ thin films.

Table 1. Microstructural parameters of pristine and Cu–TiO₂ thin films.

Sample index	FWHM (deg.)	Crystallite size (nm)	Dislocation density (×1014 m−2)	Strain (×10−3)	Lattice parameter (Å)		Interplanar distance (Å)
					a = b	c
Pristine	0.365	23.27	18.46	7.10	3.779	9.553	3.514
1 wt% Cu–TiO2	0.309	27.53	13.20	6.00	3.781	9.508	3.514
2 wt% Cu–TiO2	0.295	28.83	12.03	5.73	3.782	9.488	3.513
3 wt% Cu–TiO2	0.281	30.28	10.91	5.45	3.780	9.489	3.511

3.2. Raman analysis

The Raman study was performed to analyze the vibrational modes of the Cu–TiO₂ thin films. Anatase TiO₂ exhibits 15 optical phonon modes, represented as 1A_1g + 1A_2u + 2B_1g + 1B_2u + 3E_g + 2E_u. Out of these, the E_g, A_1g, and B_1g are Raman active, while other modes are Raman inactive.⁵⁹Fig. 7 depicts the Raman spectral profile of pristine and Cu–TiO₂ films recorded over a range of 50–800 cm⁻¹. Pristine Raman peaks were found at ∼138, 419, 513, and 607 cm⁻¹. The peak at 138 cm⁻¹ can be assigned to the E_g mode of anatase TiO₂.⁶⁰ The peak at 419 cm⁻¹ can be assigned to B_1g Raman mode.⁶¹ Peak at 513 cm⁻¹ is associated with A_1g + B_1g mode⁶² and the peak around 607 cm⁻¹ is associated with the E_g mode.⁶³ E_g mode originates from the symmetric stretching vibration of O–Ti–O. B_1g mode is associated with the symmetric bending vibration and A_1g mode corresponds to antisymmetric bending vibration of O–Ti–O bonds.^64,65

Fig. 7. Raman spectra of pristine and Cu–TiO₂ thin films.

The intensity of characteristic anatase Raman mode of 138 cm⁻¹ gradually decreases as the Cu concentration increased up to 2 wt% Cu–TiO₂. At 3 wt% Cu doping, the peak becomes undetectable, indicating that Cu-induced oxygen vacancies and the resulting local structural distortion in the lattice suppress the Raman-active E_g vibrational mode of anatase TiO₂.³⁰

E_g and A_1g + B_1g modes exhibit a slight shift towards higher wavenumber with Cu addition. Changes in these modes are commonly linked to inherent defects, such as oxygen vacancies.⁶⁶ The addition of Cu induces oxygen vacancies in TiO₂. The generation of these oxygen vacancies leads to lattice contraction, which in turn results in the peak shifting to higher wavenumber.⁶⁷ In addition, the band near 607 cm⁻¹ broadens with Cu concentration, and spans over a range of 625–730 cm⁻¹ for 3 wt% Cu–TiO₂. Such shift and broadening occur when dopant ions substitute at Ti⁴⁺ lattice sites, disrupting the original O–Ti–O bonds and forming Cu–O–Ti or Cu–O–Cu bonds, thereby affecting Raman active modes.³⁰ Other than these peaks, other peaks appeared at ∼66 and 64 cm⁻¹ for pristine and 1 wt% Cu–TiO₂ are related to the Raman acoustic modes.⁶⁸Table 2 presents the list of Raman modes of Cu–TiO₂ thin films.

Table 2. Raman modes of pristine and Cu–TiO₂ thin films.

Sample index	Raman shift (cm−1)
	Eg	B1g	A1g + B1g	Eg
Pristine	138.08	419.51	513.03	607.21
1 wt% Cu–TiO2	139.11	418.40	513.52	639.19
2 wt% Cu–TiO2	139.57	418.95	—	634.47
3 wt% Cu–TiO2	—	418.09	521.31	680.09

3.3. FESEM analysis

The morphological features of Cu–TiO₂ thin films was assessed by utilizing FESEM measurement. Micrographs recorded at high magnifications of 350 kX are presented in Fig. 8. The images reveal uniformly distributed nanoscale features without the presence of cracks, indicating the formation of dense and continuous films.

Fig. 8. FESEM micrograph of pristine and Cu–TiO₂ thin films.

The surface exhibits closely packed grains with relatively smooth topography. Cu doping does not lead to major morphological distortion, and there is no segregated Cu rich clusters in the thin films.

EDX verifies the purity of elemental composition and successful doping of Cu into the TiO₂ matrix. EDX spectra of pristine and Cu–TiO₂ thin films are presented in Fig. 9. The undoped films show only Ti and O in near stoichiometric amounts, whereas the doped thin films clearly display the presence of Cu, with its concentration progressively increasing with the dopant level. This indicates dopant incorporation without detectable phase segregation. The gradual rise in Cu signal with higher doping corroborates the controlled substitutional addition of Cu into the TiO₂ lattice.

Fig. 9. EDX spectra of pristine and Cu–TiO₂ thin films.

3.4. UV-vis analysis

The linear optical properties of the pristine and Cu–TiO₂ thin films were examined by UV-Visible characterization. Fig. 10 presents the optical transmission and absorption profiles of the Cu–TiO₂ thin films at various dopant levels. The maximum transparency is exhibited by the pristine, and a reduction in transparency is observed in the Cu–TiO₂ films. This decrease can be ascribed to enhanced light absorption and increased scattering induced by Cu related defects upon doping. The interference fringes observed in the transmittance and absorbance curves indicate that the deposited layers possess uniformity^42,69 reflecting a smooth and consistent film surface.

Fig. 10. Optical transmittance and absorbance profiles of pristine and Cu–TiO₂ thin films.

The optical band gap of Cu–TiO₂ films were calculated through Tauc's equation, given by:⁷⁰

(αhν) = A(hν − E_g)ⁿ 5

where α is absorption coefficient, E_g is optical bandgap, hν is the energy of incident photon, and A is the Tauc parameter, which is related to the degree of structural disorder within the material.⁷¹ And n takes the values of , 2, 3 and for allowed direct, allowed indirect, forbidden direct, and forbidden indirect transitions, respectively.

Fig. 11 depicts the plot for indirect bandgap energies of pristine and Cu–TiO₂ thin films.

Fig. 11. Tauc plots of pristine and Cu–TiO₂ thin films.

The refractive index (n) can be estimated from the optical bandgap energy (E_g) using empirical relations. The Moss relation was among the earliest proposed models correlating these two quantities, which is expressed as,⁶

n⁴E_g = 95 eV 6

In addition, Ravindra proposed a linear relationship between refractive index and optical bandgap energy, given by,⁶

n = 4.084–0.62 E_g 7

The Herve and Van–Damme equation,⁷²

8

where A = 13.6 eV and B = 3.4 eV represent empirical constants, was ultimately adopted in the present work as it is based on classical oscillator theory and has been reported to provide better agreement with experimental refractive-index values than earlier empirical models.⁸

Pristine exhibits a bandgap energy of 3.26 eV. With an increment in Cu concentration the bandgap progressively widens to 3.40 eV at 3 wt% Cu–TiO₂. This increase in bandgap energy is a result of the Burstein–Moss effect.^17,73 When Cu is introduced into the TiO₂ lattice, it can create donor-like states, which are electronic states located slightly below the conduction band that can donate electrons to the conduction band. As the concentration of these donor electrons increases, the lowest energy levels of the conduction band become progressively filled. Consequently, optical transitions from the valence band must occur to higher, unoccupied conduction-band states, effectively shifting the absorption edge toward higher energies, resulting in a blue shift in the bandgap energy. Refractive index was observed to decrease with an increment in Cu concentration. Overall, the opposite variation of refractive index with respect to bandgap is consistent with the Herve-Van Damme relation and reflects the interplay between impurity states and lattice restructuring upon Cu incorporation.

The thickness of the pristine and Cu–TiO₂ thin films was determined using Parav software based on the Swanepoel envelope approach applied to the UV-vis transmission data. In this method, the interference peaks and valleys are selected manually, after which the software generates the upper and lower envelope curves and evaluates the optical path variation between successive fringes to estimate the film thickness.⁷⁴ Film thickness decreased with Cu doping, likely due to Cu-induced modification of film growth kinetics, which reduced precursor utilization and altered nucleation and film growth behavior.

The extracted optical bandgap energies, corresponding refractive index values and film thickness for pristine and Cu–TiO₂ films are summarized in Table 3.

Table 3. Optical bandgap energies and refractive index of pristine and Cu–TiO₂ films.

Sample index	Bandgap energy (eV)	Linear refractive index	Thickness (nm)
Pristine	3.26 ± 0.03	2.268	855.1
1 wt% Cu–TiO2	3.31 ± 0.02	2.254	657.3
2 wt% Cu–TiO2	3.38 ± 0.03	2.244	651.4
3 wt% Cu–TiO2	3.40 ± 0.02	2.236	636.2

3.5. PL analysis

Photoluminescence measurements were conducted to study the defect states as well as radiative recombination mechanisms in pristine and Cu–TiO₂ thin films, as PL is very sensitive to dopant induced changes in electronic structure. Gaussian deconvoluted PL profiles of the Cu–TiO₂ films are depicted in Fig. 12, enabling the detection of individual peaks associated with defects. It is clear that Cu incorporation leads to an enhancement in the PL intensity of TiO₂, indicating the enhancement of radiative recombination channels. The addition of Cu improves the defect states' generation such as oxygen vacancies and Ti³⁺ centers, which act as trap levels that facilitate radiative carrier recombination. The strengthened emission clearly demonstrates an enhanced defect assisted recombination. The list of the emission peaks, corresponding energies, and defect assignments for the undoped and Cu–TiO₂ films are listed in Table 4.

Fig. 12. PL emission spectra of pristine and Cu–TiO₂ thin films.

Table 4. Summary of PL emission centers for pristine and Cu–TiO₂ thin films, including emission energies, and the associated defect states.

Sample index	Peaks	PL emission centers (eV)	Proposed defect states/mechanisms
Pristine	1	3.41	Intrinsic emission of anatase TiO2 thin film75
	2	3.20	Excitonic emission76
	3	2.97	Strong excitonic emission77
	4	2.64	Radiative recombination involving electrons at F/F+ or F++ states,78 oxygen vacancy related trap states77,79,80
	5	2.16	Oxygen vacancies81
	6	2.06	Defects of under coordinated Ti3+ ions82
1 wt% Cu–TiO2	1	3.26	Band edge emission83
	2	3.13	Near band edge emission84
	3	3.00	Strong excitonic emission77
	4	2.65	Radiative recombination from F/F+, or F++ defect centers78 oxygen vacancy related trap states77,79,80
	5	2.20	Radiative recombination involving electrons at F/F+ or F++ states78
	6	2.14	Additional electron states in the band gap85
2 wt% Cu–TiO2	1	3.28	Near band edge emission83,86
	2	3.13	Near band edge emission84,86
	3	3.00	Strong excitonic emission77
	4	2.64	Radiative recombination of electrons from F/F+ or F++ defect centers,78 oxygen vacancy related trap states77,79,80
	5	2.19	Radiative recombination from F/F+, or F++ defect centers78
	6	2.12	Additional electron states in the band gap85
3 wt% Cu–TiO2	1	3.35	Near band edge emission86
	2	3.14	Near band edge emission84
	3	2.98	Strong excitonic emission77
	4	2.63	Recombination from F/F+ or F++ states,78 oxygen vacancy related trap states77,79,80
	5	2.19	Recombination of electrons involving F/F+ or F++ states78
	6	2.12	Additional electron states in the band gap85

In the undoped TiO₂, the high energy emissions observed around 3.41 eV results from intrinsic transitions of anatase TiO₂ and peaks around 3.20 eV to 2.97 eV correspond to strong excitonic recombination processes. The broad blue emission originated at ∼2.64 eV is attributed to radiative recombination involving oxygen vacancy related defect levels, represented as F, F⁺, and F⁺⁺ centers. These centers are related to oxygen vacancies with two, one, and zero trapped electrons, respectively,⁶⁴ which introduce shallow donor levels below the conduction band. Electrons trapped in these sub-band gaps recombine with photogenerated holes, giving rise to the characteristic blue luminescence. In the longer wavelength regions, the visible emission at ∼2.16 eV band is associated with transitions from donor states of oxygen vacancies to acceptor levels. The emission peak at ∼2.06 eV is assigned to under coordinated Ti³⁺ sites, which form due to partial reduction of Ti⁴⁺ ions and act as deep level traps that facilitate radiative recombination.

Cu addition leads to changes in the emission pattern because of the Cu induced modifications of the local electronic structure of TiO₂. There is an increased PL emission around ∼3.35 to 3.13 eV, which suggests enhanced band edge and excitonic recombination facilitated by electronic coupling between Cu states and the TiO₂ lattice. The blue emission assigned to oxygen vacancies at ∼2.65–2.63 eV persists across all dopant concentrations, indicating that Cu incorporation does not hinder the creation of oxygen vacancies. The visible emissions in the 2.19–2.12 eV range are assigned to recombination through deeper level defect states. In particular, the rise of bands at ∼2.14 to 2.12 eV reflects the introduction of Cu induced electronic states within the band gap, which acts as intermediate recombination centers. These states are likely generated from Cu²⁺/Cu⁺ redox couples or Cu–O–Ti localized states, which influence charge localization and deepen trap mediated radiative pathways.

3.6. XPS analysis

The elemental composition of the pristine and 2 wt% Cu–TiO₂ were examined by employing the XPS experiment. The XPS spectrum reveals signals corresponding to titanium and oxygen, along with a contribution from copper in the 2 wt% Cu–TiO₂. The binding energy scale was calibrated by referencing the C 1s peak positioned at 284.8 eV. The survey spectra of pristine and 2 wt% Cu–TiO₂ are presented in Fig. 13a.

Fig. 13. (a) XPS Survey spectra, core level spectra of (b) Ti 2p and (c) O 1s in pristine and 2 wt% Cu–TiO₂ thin film.

3.6.1. Core level Ti 2p spectra

The core level spectra of Ti 2p are presented in Fig. 13b. In pristine, Ti 2p core spectrum exhibited characteristic doublet peaks Ti 2p_3/2 and Ti 2p_1/2 at 458.63 eV 464.33 eV respectively, confirming the existence of Ti⁴⁺ in the anatase TiO₂ lattice.^87,88 In 2 wt% Cu–TiO₂, these peaks shift slightly toward lower binding energies 458.43 and 464.13 eV, respectively. This shift towards lower Ti 2p_3/2 and Ti 2p_1/2 binding energies in Cu–TiO₂ can be attributed to Cu²⁺ ion incorporation into TiO₂ lattice. This changes electronic environment near Ti⁴⁺ ions, increasing oxygen vacancies.⁸⁹ Despite the binding energy shift, the spin–orbit splitting (5.7 eV) remains unchanged in both pristine and 2 wt% Cu–TiO₂ films, indicating the preservation of the Ti⁴⁺ state.⁹⁰

3.6.2. Core level O 1s spectra

The core level spectra of O 1s are presented in Fig. 13c. Two peaks were identified within O 1s core spectra: lattice oxygen (O_L) and oxygen vacancies (V_O). In pristine, the peak related to lattice oxygen appears at 530.13 eV, while the peak related to oxygen vacancies is found at 531.75 eV. For the 2 wt% Cu–TiO₂, O_L is shifted to 529.92 eV, and the V_O peak is shifted to 531.52 eV. This shift along with shift in Ti 2p peak observed in 2 wt% Cu–TiO₂ indicates that Cu incorporation changes the local structure and electronic states in TiO₂ matrix.⁸⁹ Additionally, a minor peak was observed at ∼533 eV in both pristine and 2 wt% Cu–TiO₂ which corresponds to chemisorbed water species.⁹¹

The oxygen vacancy concentration was calculated using the area ratio. The area ratio increases from 21.6% in pristine to 23.9% in 2 wt% Cu–TiO₂. The enhancement in oxygen vacancy is caused by the ionic radii mismatch between Ti and Cu, which induces lattice distortion and promotes oxygen vacancy formation.⁹²

3.6.3. Core level Cu 2p spectrum

The core level spectrum of Cu 2p is presented in Fig. 14, confirming the presence of Cu in the 2 wt% Cu–TiO₂ film. In Cu 2p core spectrum, Cu 2p_3/2 and Cu 2p_1/2 peaks appear at 932.28 and 952.36 eV respectively, indicating the presence of Cu²⁺.^93,94

Fig. 14. Core level spectrum of Cu 2p in 2 wt% Cu–TiO₂ thin film.

Table 5 lists the summary of binding energies, FWHM, and peak areas obtained from the deconvolution of O 1s, Ti 2p and Cu 2p core level spectra of pristine and 2 wt% Cu–TiO₂ thin films. The XPS results confirm Cu incorporation and reveal doping induced modifications to the chemical environment, including enhanced oxygen vacancy concentration and altered Ti–O electronic interactions.

Table 5. List of binding energies, FWHM and peak areas obtained from the deconvolution of Ti 2p, O 1s and Cu 2p spectra of pristine and 2 wt% Cu–TiO₂ thin films.

Sample index	Core level	Peak name	Peak position	FWHM	Area
Pristine	Ti 2p	Ti 2p3/2	458.63	1.25	346 889.76
		Ti 2p1/2	464.33	2.11	164 735.65
	O 1s	OL	530.13	1.23	391 454.70
		VO	531.75	2.00	108 214.64
		Chem. water	533.56	1.21	6933.10
2 wt% Cu–TiO2	Ti 2p	Ti 2p3/2	458.43	1.24	332 925.39
		Ti 2p1/2	464.13	2.13	158 643.85
	O 1s	OL	529.92	1.24	370 208.72
		VO	531.52	2.04	116 050.06
		Chem. water	533.34	1.76	13 764.81
	Cu 2p	Cu 2p3/2	932.28	2.31	10 735.76
		Cu 2p1/2	952.36	2.60	5311.22

3.7. Nonlinear optical studies

3.7.1. Z-scan analysis

The NLA properties of Cu–TiO₂ thin films were analyzed using the Z-scan technique.⁹⁵ This single-beam experimental approach is a well-established and widely adopted method for characterizing NLO properties of materials.¹ In this study, measurements were carried out in the OA configuration, in which the total transmitted laser beam is detected without any aperture filtering.⁹⁶ Such a configuration directly probes the NLA response of the material. Typically, OA Z-scan measurements exhibit two characteristic absorption signatures: Saturable absorption (SA) takes place when absorption decreases with an increase in intensity, producing a transmission peak at focus, whereas reverse saturable absorption (RSA) results from intensity-enhanced absorption mechanisms, leading to a transmission dip at the focal position.^96,97 The absorption coefficient as a function of intensity I, is expressed as⁹⁸

α(I) = α + β_eff 9

where α is the linear absorption coefficient, β_eff is the effective NLA coefficient. In an OA Z-scan experiment, the variation in normalized transmittance (T) with the position of sample (z) is obtained by curve-fitting using:^78,99

10

where z_R represents the Rayleigh length, q₀ is the dimensionless NLA parameter, expressed as⁹⁹

q₀ = β_effI₀L_eff 11

where L_eff is the effective length and I₀ represents the maximum intensity of the laser at focal point. Finally, the imaginary part of the third-order nonlinear susceptibility (Imχ⁽³⁾) is given by:¹⁰⁰

12

where n₀ is the material's refractive index, c is the speed of light, and ε₀ is the permittivity of free space.

The OA Z-scan technique was employed to systematically investigate the NLA characteristics of pristine and Cu–TiO₂ thin films under varying laser input intensities (8.27, 9.82, and 11.40 MW m⁻²), as shown in Fig. 15. The plain glass substrate exhibited a flat OA Z-scan trace with no variation around the focus confirming that it does not induce the NLO response of Cu–TiO₂ films. Pristine and 3 wt% Cu–TiO₂ thin films exhibit RSA nature, while 1 and 2 wt% Cu–TiO₂ thin films exhibit both SA and RSA behavior. RSA may originate from mechanisms such as two photon absorption (TPA), multiphoton absorption (MPA), or excited state absorption (ESA).¹⁰¹

Fig. 15. OA Z-scan curves of pristine and Cu–TiO₂ thin films recorded at different incident laser intensities.

Pristine films exhibited only RSA behaviour which can be attributed to TPA process. In this study, the Cu–TiO₂ thin films have bandgap energy of ∼3.3 eV, while the photon energy of the excitation source used is 1.96 eV. With such excitation, TPA can occur since the photon energy satisfies the criterion.¹⁰² So TPA is the primary NLA mechanism contributing to the observed NLO behavior of the Cu–TiO₂ thin films. In TPA process, an electron in the valence band simultaneously absorbs two photons within a single optical cycle, enabling its transition to the conduction band through a virtual intermediate state.^103,104 Alongside TPA, ESA may also contribute to the NLO response of the material, wherein charge carriers that are already promoted to excited or defect-related states undergo further photon absorption to reach higher energy levels, leading to an overall increase in absorption with increasing excitation intensity.¹⁰⁵ In pristine, the highest β_eff value was observed at an incident intensity of 8.27 MW m⁻², declined at 9.82 MW m⁻² and increased at 11.40 MW m⁻².

1 wt% Cu–TiO₂ showed SA behavior at an incident intensity of 8.27 MW m⁻². The observed SA behavior arises from the progressive depletion of ground-state carriers under low-intensity excitation, which reduces the probability of further photon absorption.¹⁰⁶ With increasing laser intensity (9.82 and 11.40 MW m⁻²), a transition from SA to RSA was observed. This transition can be attributed to the competition between the ground state bleaching and thermally induced non-linearities. At higher intensities (11.40 MW m⁻²), the cumulative thermal effect, potentially coupled with ESA and TPA, dominates the optical response, leading to the observed RSA behaviour. β_eff value showed a progressive increment from −5.40 × 10⁻¹ m W⁻¹ at an intensity of 8.27 MW m⁻² to 3.53 × 10⁻¹ m W⁻¹ at 11.40 MW m⁻². This increment can be attributed to dominance of ESA mechanism induced by TPA process.¹⁰⁷

Similarly, 2 wt% Cu–TiO₂ showed SA behavior at an incident intensity of 8.27 MW m⁻² and transitioned from SA to RSA with increasing laser intensity, showing a similar intensity-dependent switching mechanism. A significant enhancement in β_eff value was observed, increasing from −8.00 × 10⁻¹ m W⁻¹ at an excitation intensity of 8.27 MW m⁻² to 5.90 × 10⁻¹ m W⁻¹ at 11.40 MW m⁻², making the 2 wt% Cu–TiO₂ exhibit the highest β_eff value among all the Cu–TiO₂ thin films in this study.

However, the 3 wt% Cu–TiO₂ film exhibited a stable RSA dominated response across all the excitation intensities and the β_eff value gradually decreased from 4.12 × 10⁻¹ m W⁻¹ to 3.22 × 10⁻¹ m W⁻¹ with increasing laser intensity. The calculated Imχ⁽³⁾ values follow a similar trend to that of β_eff values and are listed in Table 6.

Table 6. NLA coefficient and Im χ⁽³⁾ values of pristine and Cu–TiO₂ thin films calculated for different laser intensities.

Sample index	I 0 (MW m−2)	β eff (×10−1 m W−1)	Im χ(3) (×10−10 m2 V−2)
Pristine	8.27	4.51	6.40
	9.82	1.33	1.89
	11.40	3.08	4.37
1 wt% Cu–TiO2	8.27	−5.40	−7.53
	9.82	2.43	3.38
	11.40	3.53	4.92
2 wt% Cu–TiO2	8.27	−8.00	−11.0
	9.82	3.70	5.10
	11.40	5.90	8.14
3 wt% Cu–TiO2	8.27	4.12	5.65
	9.82	3.28	4.49
	11.40	3.22	4.41

The highest value of Imχ⁽³⁾ value was observed for the 2 wt% Cu–TiO₂. At an excitation intensity of 9.82 MW m⁻², Imχ⁽³⁾ value increased from 1.89 ×10⁻¹⁰ m² V⁻² (pristine) to 5.10 ×10⁻¹⁰ m² V⁻² (2 wt% Cu–TiO₂), representing a 2.7-fold increase relative to pristine. This enhancement can be attributed to optimal Cu incorporation, which introduces defect states and oxygen vacancies that modify the band structure and promote additional electronic transition pathways under laser excitation. However, 3 wt% Cu–TiO₂ showed relatively lower Imχ⁽³⁾ values compared to the 2 wt% Cu–TiO₂. This behavior may be attributed to dopant-induced defect clustering or increased non-radiative recombination, which can limit the effective population of excited states contributing to NLA. A comparison of the effective nonlinear absorption coefficient of the present Cu-doped TiO₂ thin film with previously reported TiO₂-derived materials is presented in Table 7.

Table 7. Comparison of nonlinear absorption coefficients (β_eff) reported for TiO₂-derived materials under different laser excitation conditions.

Materials	Excitation source	β eff (m W−1)	Ref.
CNT/TiO2–Pt composite	Q-switched Nd:YAG nanosecond laser with 4 ns pulse duration, and 10 Hz repetition rate	1.54 × 10−6	108
TiO2 thin film grown in an oxygen partial pressure of 16%	Continuous-wave He–Ne laser source operating at a wavelength 632.8 nm	−13.41 × 10−2	109
Bismuth-doped TiO2 colloids	Femtosecond laser with 150 fs pulse duration, and 76 MHz repetition rate	5.7 × 10−9	110
Gold-doped TiO2 colloids	Femtosecond laser with 150 fs pulse duration, and 76 MHz repetition rate	6.5 × 10−9	111
TiO2 nanoparticle colloids	Femtosecond laser with 100 fs pulse duration, and 80 MHz repetition rate	2.12 × 10−11	112
Cr-doped NiO nanopowder	Continuous-wave Nd: YAG laser operating at a wavelength of 532 nm	1.21 × 10−2	113
Mn-doped ZnO	Continuous-wave He–Ne laser source operating at a wavelength 633 nm	5.26 × 10−2	114
2 wt% Cu-doped TiO2 thin film	Continuous-wave He–Ne laser source operating at a wavelength 632.8 nm	5.90 × 10−1	Present work

3.7.2. Fluence-dependent SHG under nanosecond laser

SHG is a second-order NLO process in which two photons at a fundamental frequency interact within a nonlinear medium to generate a single photon at twice the frequency.¹¹⁵ SHG is allowed only in non-centrosymmetric materials, as centrosymmetric media possess inversion symmetry that cancels the second-order nonlinear response under the electric dipole approximation.¹¹⁶ Consequently, SHG is highly sensitive to crystal symmetry and structural order. At interfaces between materials or at surfaces, inversion symmetry is naturally broken, making reflection-based SHG highly sensitive to surface-induced non-centrosymmetry and interface-related defects.¹¹⁷ In this study, SHG measurements were performed in reflection mode using a nanosecond (ns) Nd: YAG laser (λ = 1064 nm) to assess the second-order NLO behavior and the associated electronic polarization behavior of the Cu–TiO₂ thin films. The reflection geometry was specifically chosen to enhance sensitivity to surface-induced non-centrosymmetry and interface-related defects, as transmission-based SHG (Maker fringe) under picosecond excitation yielded negligible signals due to the bulk centrosymmetric nature of the films. This is consistent with the centrosymmetric crystal structure of TiO₂, where the bulk second-order susceptibility χ⁽²⁾ vanishes by symmetry,¹¹⁸ and any local symmetry-breaking contributions from randomly oriented grains do not accumulate coherently along the transmission path due to the lack of net crystallographic texture in the polycrystalline films. In contrast, reflection-mode SHG captures the interface-localized response arising from surface/interface symmetry breaking.¹¹⁷ SHG experiments were carried out by varying the laser fluence ranging between 80–155 J m⁻² as depicted in Fig. 16.

Fig. 16. SHG intensity for pristine and Cu–TiO₂ thin films.

The SHG intensity showed minimal variation for all the thin films up to a fluence of 128 J m⁻², followed by a sharp increase beyond 143 J m⁻². The intensity of SHG signals initially increases with Cu doping, attaining a maximum value for the 1 wt% Cu–TiO₂ film. This enhancement can be attributed to the introduction of an optimal density of Cu-related defects and oxygen vacancies. These defects induce local lattice distortions and break the centrosymmetric nature of the TiO₂ matrix, thereby enhancing the effective second-order nonlinear polarization.¹¹⁹ However, with further increase in the dopant concentration SHG intensity decreases, becoming a minimum for the 3 wt% Cu–TiO₂. This decline is likely due to excessive structural disorder and the potential formation of secondary phases that may restore a higher degree of centrosymmetry or increase scattering, thereby diminishing the coherent SHG response.

In addition to defect-induced distortions, the dense distribution of grain boundaries observed in FESEM contributes to local symmetry breaking at the film's surface, further facilitating the SHG process under reflection.

3.7.3. Fluence-dependent THG under nanosecond laser

THG studies were performed to analyze the NLO response in Cu–TiO₂ thin films. THG is a third-order nonlinear optical process arising from the interaction of three photons within a nonlinear medium to produce radiation at triple the fundamental frequency.¹¹⁵ THG is allowed in all materials irrespective of symmetry, since the third-order susceptibility (χ⁽³⁾) remains non-zero even in centrosymmetric media.¹²⁰Fig. 17 depicts the dependence of THG intensity with the laser fluence in the range of 125–155 J m⁻². The 2 wt% Cu–TiO₂ film shows superior THG performance compared to pristine at lower fluences (130–147 J m⁻²). However, at higher fluences, the pristine thin film shows the highest THG intensity, surpassing the Cu-doped TiO₂ films. The 3 wt% Cu–TiO₂ film displays the lowest THG intensity overall. This crossover suggests that while Cu-doping enhances χ⁽³⁾ at low excitation levels, higher intensities may trigger excited-state quenching or saturation of the available electronic pathways in the doped matrix. The 3 wt% film consistently shows the lowest THG response, which can be attributed to the formation of impurity bands and increased structural disorder; these factors likely introduce significant non-radiative decay channels that suppress the coherent light–matter interaction required for efficient THG.

Fig. 17. THG intensity for pristine and Cu–TiO₂ thin films.

3.7.4. Maker fringe technique analysis

Maker fringe technique was employed using P- and S-polarized fundamental beams to study the impact of Cu introduction on the THG intensity of TiO₂ thin films. Fig. 18 and 19 show dependence of intensity of THG signal with the incidence angle for Cu–TiO₂ thin films under P and S polarization configurations, respectively. In both P- and S- configurations, the angular dependence of THG intensity exhibits a symmetric profile about normal incidence for the pristine film, indicating good film quality and accurate optical alignment.¹²¹ The Maker fringe patterns for the 2 wt% Cu–TiO₂ film display a high degree of symmetry in both polarization configurations, indicating superior structural homogeneity and uniform film thickness. In contrast, the 1 wt% sample exhibits a less symmetric profile, which may be attributed to local variations in thickness or surface non-uniformity inherent to the spray pyrolysis process. To accurately determine the third-order nonlinear susceptibility (χ⁽³⁾), the linear absorption at the third-harmonic wavelength (355 nm) was taken into account. Since TiO₂ possesses significant absorption in the UV range, the model proposed by K. Kubodera and H. Kobayashi model¹²² was employed. This approach allows for a precise estimation of χ⁽³⁾ by incorporating the absorption coefficient (α) and the integration of the nonlinear interaction length within the Cu–TiO₂ thin films.¹²³

13

where χ_s⁽³⁾ is the χ⁽³⁾ value of reference material (fused silica) with known value of 2.0 × 10⁻²² m² V⁻², α is the linear absorption coefficient at the third-harmonic wavelength, l is the thickness of sample and l_C,S is coherence length. I^3w and I_S^3w represent the highest intensities of the THG signals exhibited by the Cu–TiO₂ thin films and the reference respectively.

Fig. 18. THG intensity of pristine and Cu–TiO₂ thin films under P-polarization at an input laser energy of 129 µJ.

Fig. 19. THG intensity of pristine and Cu–TiO₂ thin films under S-polarization at an input laser energy of 129 µJ.

In P-polarization configuration, the maximum χ⁽³⁾ value was exhibited by 2 wt% Cu–TiO₂, followed by pristine and then 1 wt% Cu–TiO₂ and the lowest for 3 wt% Cu–TiO₂. However, under S-polarization configuration χ⁽³⁾ values exhibit a different trend, with 1 wt% Cu–TiO₂ showing the maximum χ⁽³⁾ response, followed by 2 wt% Cu–TiO₂, pristine, and the lowest for 1 wt% Cu–TiO₂. Notably, the variation in χ⁽³⁾ values in the case of P- and S- polarization configurations is very small. The difference in optimal Cu concentration under P- and S-polarization configurations may be attributed to variations in the intrinsic material properties.

The maximum χ⁽³⁾ value was exhibited by 2 wt% Cu–TiO₂ can also be ascribed to the optimal Cu incorporation, which increases defect density such as oxygen vacancies and induces local lattice distortion, thereby enhancing the nonlinear optical properties. These defects modify the electronic band structure, providing intermediate states that enhance the nonlinear polarization via resonance effects. However, for the 3 wt% film, the χ⁽³⁾ values fall below even those of the pristine TiO₂. This decline is likely due to excessive dopant-induced disorder and defect clustering, which disrupt the lattice periodicity and increase non-radiative recombination rates, thereby quenching the third-order nonlinear response. The obtained values of χ⁽³⁾ are listed in Table 8. Table 9 lists the reported χ⁽³⁾ values of various nanomaterials measured using the Maker fringe method under picosecond laser excitation. The variation in χ⁽³⁾ demonstrates that NLO behavior is strongly dependent on the material system and its microstructural and electronic characteristics.

Table 8. Estimated values of α and χ⁽³⁾ for Cu–TiO₂ thin films.

Sample index	α × 106 (m−1)	χ (3) × 10−21 m2 V−2
		P-polarization	S-polarization
Pristine	4.69	3.65	3.67
1 wt% Cu–TiO2	4.98	3.62	3.80
2 wt% Cu–TiO2	4.73	3.85	3.76
3 wt% Cu–TiO2	3.43	3.52	3.40

Table 9. Reported χ⁽³⁾ values of various nanomaterials.

Materials	χ (3) × 10−21 m2 V−2	Ref.
2% Ni-doped CdS	5.40	124
NiO	1.94	125
MgO	4.89	126

3.7.5. Input energy-dependent THG under picosecond laser

The THG intensity of pristine and Cu–TiO₂ thin films was further studied as a function of input laser energy using a picosecond Nd: YVO₄ laser (λ = 1064 nm). The use of picosecond pulses is crucial here, as it allows the nonlinear response to be dominated by ultrafast electronic polarization, while minimizing contributions from slower thermal effects. The variation of THG intensity in Cu–TiO₂ films against input energy in the range of 0–170 µJ is presented in Fig. 20. The pristine thin film exhibited a relatively weak THG signal. Upon Cu incorporation, a pronounced enhancement in THG response is observed. While the 1 wt% and 2 wt% Cu–TiO₂ films show the highest intensities, their profiles are remarkably similar; these minor differences are not statistically significant and can be attributed to experimental uncertainties, such as slight laser drift over time. This suggests that a doping range between 1 and 2 wt% represents an optimal window where Cu-induced defect states and lattice distortions effectively increase the electronic polarizability of the TiO₂ matrix. In contrast, the 3 wt% Cu–TiO₂ film exhibits a marked decrease in THG intensity, even lower than that of pristine. At higher Cu concentrations, increased structural disorders¹²⁷ can lead to enhanced carrier scattering and nonradiative recombination pathways. These effects suppress the coherent nonlinear polarization responsible for THG, resulting in a diminished third-order nonlinear response.

Fig. 20. Dependence of THG intensity with input energy in pristine and Cu–TiO₂ thin films.

3.7.6. Summary of NLO studies

In Z-scan technique under CW laser excitation, pristine and 3 wt% Cu–TiO₂ exhibited RSA behaviour while 2 and 3 wt% Cu–TiO₂ films showed a transition from SA to RSA with the increasing laser intensity. The 2 wt% Cu–TiO₂ film showed the highest β_eff and Imχ⁽³⁾ values of 5.90 × 10⁻¹ m W⁻¹ and 8.14 × 10⁻¹⁰ m² V⁻², respectively. This is attributed to an optimal balance between defect density and crystallinity in the 2 wt% Cu–TiO₂ film.

SHG measurements under ns laser excitation in reflection mode, with varying fluence showed maximum response for the 1 wt% Cu–TiO₂ film, arising from Cu-induced defects that introduce local lattice distortions and effectively break the centrosymmetric nature of the TiO₂ matrix. THG measurements under ns laser excitation in reflection mode, with varying fluence, showed maximum THG response for the pristine film.

The Maker fringe analysis under ps laser excitation further confirms that the 2 wt% Cu–TiO₂ film possesses the highest χ⁽³⁾ value of 3.85 × 10⁻²¹ m² V⁻², consistent with optimal Cu incorporation. Furthermore, THG studies with varying input energy show that the 1 wt% and 2 wt% films yield the strongest and most comparable THG responses. The variation in THG intensity under ns and ps-excitation is fundamentally governed by pulse duration-dependent nonlinear interaction and their sensitivity to defect states. Under ps excitation, the interaction is restricted to ultrafast timescales, effectively suppressing thermal and cumulative contributions and isolating the intrinsic electronic response of the material.¹²⁸ In this regime, the 1 and 2 wt% Cu doping range is optimal, as mid-gap levels and oxygen vacancies enhance electronic polarizability. Under ns excitation, the pristine film exhibits the highest THG response, as the longer pulse duration enables significant carrier generation, accumulation, and thermal and electrostrictive effects to the NLO response. This demonstrates that controlled defect engineering plays a decisive role in amplifying ultrafast NLO responses.

Overall, the 2 wt% Cu–TiO₂ film shows the most pronounced NLA response, and the observed SA-RSA switching behavior highlights its strong potential for optical-limiting, mode-locking, and Q-switching applications. In contrast, the strongest SHG response exhibited by the 1 wt% Cu–TiO₂ film highlights its suitability for frequency-doubling and wavelength-conversion applications, while the enhanced THG responses observed under picosecond excitation demonstrate the potential of Cu–TiO₂ films for ultrafast photonic devices.

4. Conclusion

Pristine and Cu-doped TiO₂ thin films (1–3 wt%) were successfully synthesized by spray pyrolysis technique and their structural, morphological, optical and NLO properties were systematically studied. XRD confirmed the anatase TiO₂ phase, with the appearance of Cu-related diffraction peaks in the 2 and 3 wt% Cu–TiO₂ films. The crystallite size increased from 23.27 to 30.28 nm upon Cu incorporation. The optical bandgap exhibited a blue shift from 3.26 to 3.40 eV upon Cu doping due to Burstein–Moss effect. The PL intensity increased with Cu doping, indicating enhanced radiative recombination in Cu–TiO₂ thin films. XPS analysis confirmed successful Cu incorporation and revealed an increased oxygen vacancy concentration in the Cu-doped film. Nonlinear optical studies revealed an intensity-dependent SA-RSA transition in the 1 and 2 wt% Cu–TiO₂ films. The 2 wt% Cu–TiO₂ film exhibited the strongest nonlinear response, with the highest β_eff value of 5.90 × 10⁻¹ m W⁻¹ and Imχ⁽³⁾ value of 8.14 × 10⁻¹⁰ m² V⁻², under CW laser excitation. Under picosecond laser excitation, the same film exhibited a maximum third-order nonlinear susceptibility (χ⁽³⁾) of 3.85 × 10⁻²¹ m² V⁻², confirming the significant enhancement of nonlinear optical performance at the optimum Cu doping concentration. Under nanosecond excitation, the maximum SHG signal was observed for the 1 wt% Cu–TiO₂ film, whereas the pristine thin film exhibited the strongest THG response. Collectively, these results demonstrate a relation between Cu-driven modifications in structural and electronic properties and the enhancement of NLO behavior. The optimized Cu–TiO₂ thin films therefore emerge as promising materials for next-generation photonic technologies, including optical limiting and ultrafast nonlinear devices. Further investigations could explore excitation under shorter pulse durations, particularly in the femtosecond regime, and translate these materials into scalable device architectures for next-generation nonlinear photonic technologies.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data sets supporting this article are not publicly available at the time of publication as they are not currently in a format suitable for broad distribution or reuse. However, the data can be provided by the authors upon reasonable request.