Revealing photoluminescence and nonlinear optical absorption characteristics of PbMo0.75W0.25O4 single crystal for optical limiting applications

Nonlinear absorption properties of PbMo0.75W0.25O4 single crystal fabricated by the Czochralski method were studied. The band gap energy of the crystal was determined as 3.12 eV. Urbach energy which represents the defect states inside the band gap was found to be 0.106 eV. PbMo0.75W0.25O4 single crystal has a broad photoluminescence emission band between 376 and 700 nm, with the highest emission intensity occurring at 486 nm and the lowest intensity peak at 547 nm, depending on the defect states. Femtosecond transient absorption measurements reveal that the lifetime of localized defect states is found to be higher than the 4 ns pulse duration. Open aperture (OA) Z-scan results demonstrate that the PbMo0.75W0.25O4 single crystal exhibits nonlinear absorption (NA) that includes two-photon absorption (TPA) as the dominant mechanism at the 532 nm excitations corresponding to 2.32 eV energy. NA coefficient (β eff ) increased from 7.24 × 10−10 m W−1 to 8.81 × 10−10 m W−1 with increasing pump intensity. At higher intensities β eff tends to decrease with intensity increase. This decrease is an indication that saturable absorption (SA) occurred along with the TPA, called saturation of TPA. The lifetime of the defect states was measured by femtosecond transient absorption spectroscopy. Saturable absorption behavior was observed due to the long lifetime of the localized defect states. Closed aperture (CA) Z-scan trace shows the sign of a nonlinear refractive index. The optical limiting threshold of PbMo0.75W0.25O4 single crystal at the lowest intensity was determined as 3.45 mJ/cm2. Results show that the PbMo0.75W0.25O4 single crystal can be a suitable semiconductor material for optical limiting applications in the visible region.


Introduction
Fabrication and testing of new materials with combinations of various organic and inorganic elements to obtain better nonlinear optical properties (multiphoton absorption, inverse saturable absorption, saturable absorption, and self-focusing/defocusing effects) is a major goal of many disciplines.Molybdate (MoO 4 ) and tungstate (WO 4 ) compounds are good host materials for metals and rare earth elements and they have a wide range of uses such as supercapacitors [1,2], solid-state lighting [3], sensors [4], photocatalysis [5,6], wastewater treatment [6], smart filtering optical radiation [7], microwave imaging [8], energy conversion [9], electromagnetic interference (EMI) shielding [10], optical limiting [11,12], low temperature co-fired ceramic (LTCC) [13], and thermistor applications [14,15].Lead-doped crystal and thin film materials such as PbMoO 4 and PbWO 4 , which are inorganic semiconductor materials, attract attention due to their high density, high chemical stability, high radiation damage threshold, high thermal conductivity, high optical transmittance, short decay time and luminescence properties in the visible region [16,17].It has been reported that doping metal ions such as Zn and Mn can change the optical properties of host materials by providing efficient radiation channels [18,19].
Within the framework of light-matter interaction, various materials in crystal [30][31][32], thin film [33][34][35][36], nanostructure [37], and liquid [38] forms that exhibit nonlinear absorption properties at high light intensities are produced and examined.The nonlinear effect in the transmittance of a material can be observed in two different types, nonlinear absorption (NA) and saturable absorption (SA).SA indicates the increase in transmittance depending on the increasing light intensity.This relates to the fact that at relatively low light intensities the available energy levels are filled with excited electrons and no more electrons move these levels through the valence band [39,40].NA corresponds to the decrease in transmittance due to increasing light intensity and is determined by the NA coefficient.The well-known NA mechanisms are one-photon absorption (OPA), two-photon absorption (TPA), free-carrier absorption (FCA), and reverse saturable absorption (RSA).The NA feature offers materials in various usage areas such as optical switching [33], optical waveguide devices [41], ultrafast fiber lasers [42], self-defocusing lasing [43], self-frequency-doubling [44], and optical limiting [45,46] applications.
Studies examining the optical limiting properties of materials exhibiting NA behavior are common in the literature.An optical limiter can allow light to pass up to a certain intensity threshold while absorbing light at intensities above the threshold.High-intensity light can cause serious damage to the human eye and detectors.Therefore, it is desired that the limiting threshold of an optical limiting material be as low as possible for protecting eyes and detectors.Among the nonlinear optical materials, metal MoO 4 and WO 4 materials such as Sn 4+ doped BaMoO 4 [11], Cr 3+ doped La 2 (WO 4 ) 3 [12], PbMoO 4 [26], and Sn 4+ doped CdMoO 4 [47] showed that they have good NA properties and low optical limiting thresholds.
The present work represents the investigation of the photoluminescence and nonlinear absorption properties of PbMo 0.75 W 0.25 O 4 single crystal for optical limiting applications.Structural and optical characterization of PbMo 0.75 W 0.25 O 4 single crystal was performed in our previous study [48].

Experimental methods
A single crystal of PbMo 0.75 W 0.25 O 4 was grown using the Czochralski technique.The requisite melts, composed of PbO, MoO 3 , and WO 3 oxides, were precisely combined in stoichiometric proportions within a Pt crucible for the purpose of crystal growth.This growth process involved maintaining specific rates: a pulling rate of 2 mm h −1 , a rotation rate of 20 rpm, and a cooling rate of 30 °C h −1 .Subsequently, the elongated bulk crystal obtained underwent cutting and meticulous polishing of both of its surfaces to achieve a high level of optical quality.The photograph of the crystal examined in the present paper, the x-ray diffraction pattern, and detailed information about the crystalline parameters were reported in our previous study [48].The findings indicated that the grown compound is in single crystal form and exhibits a favorable crystalline structure.A Shimadzu-1800 model UVvis spectrophotometer was used to examine the linear optical absorption features of PbMo 0.75 W 0.25 O 4 single crystal.Photoluminescence measurement was performed by Pelkin Elmer LS 55 Fluorescence Spectrometer.The nonlinear optical responses of PbMo 0.75 W 0.25 O 4 single crystal to intense laser light were investigated with the OA and CA Z-scan experiments at 532 nm wavelength excitations of Quantel Brilliant model Q-switched Nd:YAG laser source with 4 ns pulse duration, and 10 Hz repetition rate.
Ultrafast pump probe spectroscopy measurements were performed using a Ti:Sapphire laser amplifier and an optical parametric amplifier system with 52 fs pulse duration and 1 kHz repetition rate (Spectra Physics, Spitfire Pro XP, TOPAS) with a white light continuum probe a commercial pump probe experimental setup from Spectra Physics, Helios to reveal the charge transfer dynamics of PbMo 0.75 W 0.25 O 4 single crystal.Pulse duration was measured as 120 fs by cross-correlation inside the pump probe setup.The pump wavelengths were chosen based on the maximum linear absorption wavelength of the crystal.The excited state dynamics were measured between 0.1 ps and 3.2 ns timescale.Experimental data was analyzed by using Surface Xplorer software that is provided by Ultrafast Systems.

Linear optical properties
The linear absorption spectrum of PbMo 0.75 W 0.25 O 4 single crystal was given in figure 1(a).there is no explicit absorption in the 500-1100 nm range.However, the absorption band corresponding to smaller wavelengths than 500 nm is close to perfect but not sharp due to the defect states localized below the conduction band.As a result, defect states are responsible for narrowing the band gap.
The band gap energy of the crystal is expressed by the equation (1) [49], given as where α is the linear absorption coefficient defined from the absorption spectra, hν is the photon energy, A is a constant, E g is the energy of band gap, and n equals 1/2 for direct transitions and 2 for indirect transitions, respectively.The direct band gap energy of the PbMo 0.75 W 0.25 O 4 single crystal was found to be 3.11 eV from the point where the linear fit line intersects the hν axis in the Tauc plot given in figure 1(b).Electronic transitions to the defect states within the band gap and close to the conduction band contribute to the NA of the PbMo 0.75 W 0.25 O 4 single crystal.The Urbach energy of the crystal identifies the distribution of the defect states localized within the band gap and it can be obtained by the following equation [50], where a 0 is a constant, and E U is the Urbach energy.The E U value is proportional to the defect states distributed between the valance and conduction bands.The Urbach energy of the PbMo 0.75 W 0.25 O 4 single crystal was determined as 0.106 eV from the inverse slope of the ln (α) versus hν curve illustrated in figure 2. This result points out that the defect states are distributed below 0.106 eV of the conduction band.
The photoluminescence (PL) spectrum of the PbMo 0.75 W 0.25 O 4 single crystal was obtained under 350 nm wavelength excitation and given in figure 3.As seen in the figure, the PbMo 0.75 W 0.25 O 4 single crystal has a wide PL emission band between 376 and 700 nm.The highest emission intensity occurred at 486 nm.The lower intensity peak at 547 nm is based on the defect states.The transitions of trapped electrons from defect states localized below the conduction band to the valance band caused the emissions with lower energy.Details and a discussion of decay kinetics are given in section 2.3 Femtosecond Transient Absorption Spectroscopy.The peaks observed in the photoluminescence spectrum can be attributed to the ordered lattice defects of [WO 4

2-
] in the crystalline structure (responsible for blue emission), charge transfer transitions within [MoO 4 ] clusters (electrons are excited from 2p states of oxygen to 4d states of Mo localized within the band gap and they emit light at different energies as they pass to different lower states during the relaxation process), and oxygen-related defect centers (responsible for green emission) [51,52].Photoluminescence properties can be adjusted by doping metal or rare earth elements.Shifts in the photoluminescence wavelengths were observed in molybdate and tungstate crystals doped with different alkali metals such as Ca, Cd, and Sr [53].The emission band of the PbMo 0.75 W 0.25 O 4 single crystal is narrower than that of these crystals.It can be due to the PbMo 0.75 W 0.25 O 4 single crystal having a less defective structure than these crystals.

Nonlinear absorption properties
OA Z-scan measurements under 532 nm wavelength excitations at 4 ns pulse duration were carried out and NA behaviors of the PbMo 0.75 W 0.25 O 4 single crystal at various intensities were given in figure 4. It can be seen in the figure that the normalized transmittance decreased with increasing input intensity.On account of the energies of defect states and excitation wavelength (532 nm) corresponding to ∼3.0 eV and 2.32 eV, respectively, the electrons in the valance band do not reach defect states close to the conduction band via OPA in PbMo 0.75 W 0.25 O 4 single crystal.On the other hand, the possibility of OPA occurring requires deep defect states, excitonic states, or thermally induced free carriers [54].Since the energy of excitation light is higher than the half of band gap energy (E g /2), the TPA condition is satisfied.Therefore, the dominant NA mechanism is TPA in PbMo 0.75 W 0.25 O 4 single crystal.Additionally, the defect states prohibit the recombination of electron-hole pairs and contribute to NA by trapping carriers excited by TPA.Besides, the electrons carried to the upper parts of the conduction band by TPA transfer their energies to the electrons occupying lower energy levels, and therefore, ESA contributes to NA.Another result from OA Z-scan experiments at higher input intensity excitations indicated the saturation of TPA, as seen in figure 5.This can be explained by the fact that as higher intensities are increased, defect levels and upper excited levels begin to fill.For this reason, NA coefficients begin to decrease.
A theoretical model given in equation (3) was used for analyzing the Z-scan results.This model represents the OPA, TPA, and free carrier absorption (FCA) and their saturations [55], is the linear aperture transmittance, r a is the radius of the aperture and ω a is the beam waist on the aperture.S is defined as 0.3 for this study.The nonlinear refractive index is found by the following equation.
/ is the effective thickness of the sample and I 0 is the intensity at the focus.The pure n 2 was obtained by dividing the CA into OA data.Therefore, the CA Z-scan trace was taken into account, as shown in figure 6.The normalized CA Z-scan trace shows prefocal transmittance valley and postfocal transmittance peak, of the self-focusing ( > n 0 2 ) behavior of the PbMo 0.75 W 0.25 O 4 single crystal.The n 2 value was calculated to be 4.68 × 10 -13 cm 2 /W at 54.1 MW cm −2 input intensity.
The obtained NA coefficients (b eff ) and saturation intensities (I SAT ) at various input intensities (I 0 ) from the theoretical fits of Z-scan data are listed and compared with PbMoO 4 and rare earth elements doped PbWO 4 crystals in table 1.The b eff increased from 7.24 × 10 −10 m W −1 to 8.81 × 10 −10 m W −1 with increasing pump intensity.At higher intensities, the b eff values tended to decrease from 1.51 × 10 −9 m W −1 to 1.36 × 10 −9 m W −1 with increasing input intensity.I SAT is the input intensity value required for saturable absorption (SA) to occur.Unlike PbMoO 4 and PbWO 4 crystals, the decrease in the b eff values of PbMo 0.75 W 0.25 O 4 single crystal with increasing input intensity is a consequence of the fact that SA also occurred along with TPA, called saturation of TPA.The PbMo 0.75 W 0.25 O 4 single crystal we studied has lower nonlinear absorption coefficients than that of the other crystals as referenced in table 1.The reason for this is the less defective structure of the PbMo 0.75 W 0.25 O 4 single crystal than the others, and then the nonlinear effect occurs at relatively higher laser intensities and initiates saturation.At low intensities, the PbMo 0.75 W 0.25 O 4 single crystal did not show nonlinear properties.The nonlinear effects were observed in molybdate and tungstate crystals at relatively lower laser intensities as seen in table 1. Accordingly, it is seen that the alkaline metal contribution, Mo and W ratios, and their combinations affect the nonlinear absorption and optical limiting properties, and these effects can be adjusted.However, since the band gap energies of these crystals are in 3-5 eV range, optical limiting cannot be achieved for the near-infrared region.
The optical limiting threshold of PbMo 0.75 W 0.25 O 4 single crystal was defined from the normalized transmission curve as a function of fluence, as seen in figure 7. The decrease in the normalized transmittance

Femtosecond transient absorption spectroscopy
In an attempt to understand photoluminescence and nonlinear absorption mechanism and decay kinetics of PbMo 0.75 W 0.25 O 4 single crystal femtosecond transient absorption spectroscopy measurements were carried out.
The pump wavelength was determined as 400 nm corresponding to the edge of the energy band gap of the crystal.Thus, the defect states localized under the conduction band were also excited.In transient absorption spectra of PbMo 0.75 W 0.25 O 4 single crystal, it was observed that there is a broad and continuous excited state absorption (ESA) band in the range of 400-800 nm as expected nature of the semiconductors (figure 8).The strong ESA signal around 450 nm can be originated from the localized defect state.It was also observed that the maxima of the ESA signal red shifted with time delay due to filling of the defect states.Possible transitions between the energy states are shown in figure 9.  Saturable absorption property occurs only if the lifetime of the localized defect states is longer than the pulse duration of the laser.To get deep insight into the dynamics of the defect states, the decay kinetics were fitted using Surface Xplorer software with the function as given [58], where I t ( ) is the time-resolved intensity, R t ( ) is the instrument response function and S t ( ) is the response from the crystal, respectively.
The salient features of nonlinear dynamics in semiconductors under optical excitation have been studied in the literature [59][60][61].The understanding of the transient processes occurring in photo-generated carrier populations is of great relevance because it would allow a deeper physical insight on the dynamical effects of interaction mechanisms upon observable properties of the system.The first of them, commonly called the thermalization process, is mainly governed by the rapid interactions, namely, the electron-electron and the electron-optical phonon interactions.In this stage the carrier distribution function is far from equilibrium.Once thermalized, the electronic system relaxes by dissipating the energy in excess into the lattice.This stage ends when the interaction mechanisms randomize the energy and momentum in the carrier population.The second stage of the relaxation is the so called, cooling process, and is mainly ruled by the slow interactions in the system, namely, electron-phonon scattering and recombination.Associated to each one of the stages of the relaxation process, there is a characteristic time.The first one, the thermalization time, is an effective time determined by the intrinsic characteristic times of the rapid interaction mechanisms within the system and the second one is a characteristic time determined by the interaction mechanisms of the system with the surroundings.Carrier thermalization is a relatively fast process, typically in the range of 10 fs to 1 ps.Semiconductors typically have some shallow or deep sub-bandgap defect states.Carriers from the band-edge quickly get trapped into these states within a short span of 10-100 ps.More the number of traps faster is the trapping rate [62].Further decay of excess carriers take place through band-to-band or excitonic radiative recombination.The radiative recombination lifetime of typical compound semiconductors is in the range of 0.1-100 ns [62].
The decay traces of PbMo 0.75 W 0.25 O 4 single crystal by probing 450 nm and 600 nm are given in figure 10.The transient absorption signal caused by the excited carrier absorption in the PbMo 0.75 W 0.25 O 4 single crystal immediately appears after the pump excitation.The fast component around 100 fs indicates that the photoexcited carriers complete the thermalization through carrier-carrier scattering in PbMo 0.75 W 0.25 O 4 single crystal.The second component in the order of a few picoseconds can be attributed to the charge recombination with getting trapped by the localized defect states.The time components are about 9 ps and 11 ps for 450 nm and 600 nm probe wavelengths, respectively.Finally, the slow component (out of the time scale range in pumpprobe setup) is attributed to the carrier vanishing from localized defect states to valence band for electron-hole recombination.This time scale is compatible with the radiative recombination lifetime of typical compound semiconductors, as the results also prove that PL signals originate from defect states [62].Since the trapping lifetime of the crystal is higher than the laser pulse duration (4 ns), the SA properties were observed under high intensities.

Conclusion
For understanding the nonlinear absorption and the nonlinear refraction properties of PbMo 0.75 W 0.25 O 4 single crystal, the open aperture (OA) and closed aperture (CA) Z-scan methods were used at 532 nm laser excitations with 4 ns pulse duration and 10 Hz repetition rate.Femtosecond transition absorption spectroscopy experiments were carried out to understand the photoluminescence and nonlinear absorption mechanism of PbMo 0.75 W 0.25 O 4 .The decay kinetics of PbMo 0.75 W 0.25 O 4 single crystal are discussed in detail.

Figure 4 .
Figure 4. OA Z-scan curves of PbMo 0.75 W 0.25 O 4 single crystal with different input intensities.

Figure 6 .
Figure 6.CA Z-scan curves of PbMo 0.75 W 0.25 O 4 single crystal at various intensities.
PbMo 0.75 W 0.25 O 4 single crystal fabricated by the Czochralski technique and nonlinear absorption properties were investigated.The band gap and Urbach energies of PbMo 0.75 W 0.25 O 4 single crystal were calculated as 3.12 and 0.106 eV.PbMo 0.75 W 0.25 O 4 single crystal has a broad PL emission band from 376 to 700 nm depending on defect states.Results of the OA Z-scan experiment at 532 nm excitations with 4 ns pulse duration indicate that the PbMo 0.75 W 0.25 O 4 single crystal has NA and SA behavior.Based on the femtosecond transient absorption measurements, the lifetime of the localized defect states was found higher than 4 ns pulse duration.This explains why open aperture Z-scan experiments exhibit saturable absorption characteristics with high intensities.TPA is the dominant mechanism of NA at 532 nm excitations corresponding to 2.32 eV.Since the defect states close to the conduction band, OPA does not contribute to NA. β eff increased from 7.24 × 10 -10 m W −1 to 8.81 × 10 -10 m W −1 with increasing pump intensity.At higher intensities, β eff indicated a decreasing trend due to the saturation of TPA.The higher nonlinear refractive index was found to be 4.68 × 10 -13 cm 2 /W at 54.1 MW cm −2 input intensity.The optical limiting threshold of PbMo 0.75 W 0.25 O 4 single crystal was found as 3.45 mJ/cm 2 .As a result, PbMo 0.75 W 0.25 O 4 single crystal can be a promising optical limiter material in the visible region.

Table 1 .
Comparison of I SAT and b eff values of PbMo 0.75 W 0.25 O 4 single crystal with different studies on PbMoO 4 and PbWO 4 crystals with excitation wavelengths and pulse durations (τ).PbWO 4 : (0.3%) Cr 3+ 1.78 × 10 −6 PbWO 4 : (0.5%) Cr 3+ 1.83 × 10 −6 PbWO 4 : (0.7%) Cr 3+ 2.31 × 10 −6 input intensity.In the previous study, the optical limiting threshold was found as 4.91 mJ/cm 2 at 2.16 MW/cm 2 for PbMoO 4 single crystal [26].This result shows that the PbMo 0.75 W 0.25 O 4 single crystal exhibits better optical limiting performance at greater input intensities compared to the previous study.Besides, the optical limiting threshold of PbMo 0.75 W 0.25 O 4 was compared with MoO 4 and WO 4 based materials with various components in the literature and listed in table 2.

Table 2 .
Comparison of the optical limiting thresholds of PbMo 0.75 W 0.25 O 4 single crystal and MoO 4 and WO 4 based materials in the literature.