1. Introduction

In the emerging age of mid-infrared (mid-IR) science and technology much interest has centered on finding materials that have suitable nonlinear optical (NLO) properties for use in diverse applications [1–6]. Several classes of materials for this goal include organic- and oxide-based systems [7–10]. On the other hand, a current consensus points to chalcogenides as the best choice of materials owing to their typical properties such as high refractive indices and optical transparency [11]. Numerous noncentrosymmetric chalcogenide crystals have been investigated for tunable coherent mid-IR generation involving the second-order NLO processes [12–16]. Amorphous chalcogenide materials are also important for mid-IR optical switching and signal amplification, which are based on third-order NLO processes [17, 18].

Of particular interest is the polar alkali chalcogenide compound KPSe₆ that crystallizes in a noncentrosymmetric one-dimensional (1-D) polymeric structure (see Fig. 1). KPSe₆ has a remarkable set of properties in a single material; it i) undergoes a reversible crystal-glass phase transition, ii) exhibits significant second-order NLO responses in both crystalline and amorphous phases, iii) is soluble in organic solvents and thus processible into thin films, and iv) melts congruently to give honey-like viscous melts from which long fibers can be drawn [16, 19, 20]. We recently demonstrated that this multifaceted feature of the material could lead to a new design principle of highly-efficient NLO devices of fiber and film forms [19, 20]. Previous NLO studies on this unique compound, however, were focused on the second-order processes only within a limited fundamental wavelength λ in the range of 1.2 – 1.6 μm. Therefore, the fundamental NLO aspect and the potential of the compound in a broader mid-IR range were far from fully understood. Here we report on strong second- and third-order NLO properties of both crystalline and glassy KPSe₆ powders over an extended spectral range (λ = 1.0 – 3.0 μm). We note that broadband THG studies on newly discovered chalcogenides are rare and our wavelength-dependent THG study offers a unique opportunity to evaluate the mid-IR third-order nonlinearity of KPSe₆.

 

Fig. 1 Crystal structure of KPSe₆ viewed down the b-axis.

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This paper is organized as follows: Section. 2 describes KPSe₆ sample preparation followed by several key characterizations of the compound. The experimental method for the powder NLO measurements is described in Sec. 3. In Sec. 4 we characterize the NLO properties of KPSe₆ based on broadband second harmonic generation (SHG) and third harmonic generation (THG). Section 5 gives our summary and conclusions.

2. Sample preparation and characterization

For the synthesis of crystalline KPSe₆, stoichiometric amounts of K₂Se (144 mg, 0.919 mmol), P (57.0 mg, 1.84 mmol), and Se (799 mg, 10.1 mmol) were placed in a fused silica tube (9 mm in diameter) inside a nitrogen-filled glovebox. The tube was evacuated to ∼ 3×10⁻⁴ mbar then flame sealed. The sealed tube was about 15 cm long, and the starting materials occupied about 1/6 of the total tube volume. The tube was placed in a programmable furnace at an angle 30° from the floor then heated to 460 C in 5 hours and dwelled at this temperature for 12 hours to form a homogeneous melt. The sample was cooled to 210 C in 8 hours, heated to 280 C over the course of 2 days to crystallize the product, which annealed at 280 C for 36 hours then cooled to room temperature in 6 hours. This novel heating profile was employed to form highly crystalline product of KPSe₆, which uniquely only crystallizes on heating, but the general principles of this synthesis follow already well-established general procedures for crystal growth [21–23]. The same stoichiometric mixture in a flame-sealed tube of the same proportions was prepared for glassy KPSe₆ but the sample was heated to 800 C over the course of 8 hours and was immediately quenched in ice water. The final product was an ingot for both syntheses. The apparent colors of crystalline and glassy KPSe₆ were orange and red, respectively. We confirmed the phase purity of the samples using powder X-ray diffraction (PXRD) [see Fig. 2(a)]. The material is air and moisture sensitive and all samples were stored in an evacuated desiccator to prevent decomposition.

 

Fig. 2 (a) Experimental PXRD patterns of crystalline KPSe₆ (blue) and glassy KPSe₆ (red) compared to the simulated pattern (black). Each trace is vertically translated for clarity. (b) Solid-state UV-VIS absorption spectra of crystalline (blue) and amorphous (red) KPSe₆ superimposed by the theoretical fits (solid lines).

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KPSe₆ crystallizes in the noncentrosymmetric polar orthorhombic space group Pca2₁ with a = 11.491(12) Å, b = 6.791(7) Å, c = 11.289(12) Å, and Z = 4 at room temperature [24]. It is composed of infinite 1-D chains of $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\infty $}\right.\left[{\text{PSe}}_6^{-}\right]$ along the a-axis and separated by K⁺ cation as schematically illustrated in Fig. 1. Short-range intra- and inter-layer Se-Se interactions play an important role in the crystal structure together with alkali-metal ionic interactions between the chains. The corresponding band structure is shown in Ref. [25] in which the pivotal dependence of the second-order NLO tensor χ⁽²⁾ on the bandgap energy, optical matrix elements, and joint density of states is also extensively discussed.

Figure 2(a) plots the PXRD patterns of crystalline KPSe₆ (blue) and glassy KPSe₆ (red), respectively, collected using a computer-controlled INEL CPS 120 powder diffractometer (Cu Kα radiation operating at 40 kV and 20 mA) equipped with a positive-sensitive detector with flat sample geometry. The simulated pattern (black) was generated using the CIF file of the refined structure and the Visualizer program within FindIt. Our PXRD analysis shows that crystalline KPSe₆ matches the simulated pattern, although a minor amount of the glassy phase is present (slight background). PXRD measurements of glassy KPSe₆ reveal no crystalline peaks, signifying the material is completely amorphous.

Optical diffuse reflective measurements were performed in the range of 0.2–2.0 μm at room temperature using a Shimadzu UV-3101 PC double-beam, double-monochromator spectrophotometer. BaSO₄ was used as the standard and set to 100% reflectance. Samples were prepared by pressing well-ground powders on a surface of compressed BaSO₄. The collected reflectance data were converted to absorbance via the Kubelka-Munk equation: α/S = (1 − R)²/2R, where R is reflectance, α is the absorption coefficient, and S is the scattering coefficient [26]. The converted data are plotted in Fig. 2(b) and used to estimate the fundamental absorption edges by linearly fitting the absorbance spectra. Analysis of these data shows that crystalline and glassy KPSe₆ have bandgaps of 2.11 eV (0.587 μm) and 2.03 eV (0.610 μm), respectively. The tail end in absorbance of crystalline KPSe₆ is due to the presence of some of the glassy phase.

The thermal properties of crystalline KPSe₆ were investigated by differential thermal analysis (DTA) performed on a Shimadzu DTA-50 thermal analyzer. Ground crystalline samples (∼ 90 mg) were sealed under vacuum in a fused silica ampoule. A similar mass of α-Al₂O₃ sealed in a separate ampoule was used as the standard. The sample and reference were heated and cooled at rate of 5 C/min, with a maximum temperature of 400 C. The crystallization and melting points were measured at the maximum of the exothermic peak and the minimum of the endothermic peak, respectively. Figure 3(a) shows that KPSe₆ only crystallizes on heating at 261 C and melts at 300 C. No exothermic peak was observed in the first DTA cycle because the material was already crystalline. The reproducible exotherm in the second and third cycles demonstrates that the recrystallization of KPSe₆ is reversible. The DTA residue was examined by PXRD and reveals amorphous KPSe₆ because this compound only crystallizes on heating.

 

Fig. 3 (a) DTA of crystalline KPSe₆ from 50 C to 400 C, displaying three cycles to demonstrate its reversible crystal-glass phase-change properties; first cycle (black), second cycle (red), and third cycle (blue). (b) Raman spectra of crystalline (blue) and glassy (red) KPSe₆. Each trace is vertically translated for clarity.

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Raman spectra were recorded from 100 – 1000 cm⁻¹ on a DeltaNU Advantage NIR spectrometer equipped with a charge-coupled device (CCD) camera using 0.785 μm radiation from a diode laser [see Fig. 3(b)]. The samples were ground into powders and loaded into borosilicate glass capillaries for measurement. The spectra were collected using an integration time of 5 s. The Raman spectrum of crystalline KPSe₆ (blue) shows major shifts at 220 cm⁻¹, 228 cm⁻¹, and 245 cm⁻¹. The shift at 220 cm⁻¹ corresponds to the PSe₄ stretching mode determined by comparison with the A_g stretching mode of the T_d symmetry of the [PSe₄]³⁻ ligand. The shifts at 228 cm⁻¹ and 243 cm⁻¹ are assigned to the antisymmetric and symmetric Se-Se stretching modes of the diselenide group, respectively. The Raman spectrum of glassy KPSe₆ (red) shows major shifts at 219 cm⁻¹ and 252 cm⁻¹. The overall pattern of the glassy Raman spectrum is similar to crystalline KPSe₆ although slightly broader. Generally, the Raman spectra of chalcogenide glasses are broad and featureless because of a larger variation in the structural building units in the glass [27, 28]. The fact that the overall Raman pattern of the glass is similar to the crystalline phase suggests that the local structure and the [PSe₄] building block and Se-Se bonds are mostly preserved in the glassy phase [19, 29]. This essentially leads to an “intrinsic” SHG response with no poling treatment as described in Sec. 4.

3. Wavelength-dependent NLO experimental methods

Both crystalline and amorphous samples for NLO measurements in powder form were prepared under dry nitrogen conditions. The powders were sieved with size ranges of 20 – 32 μm, 32 – 45 μm, 45–53 μm, 53–63 μm, 63–90 μm, 90–106 μm, 106–125 μm, and 125–150 μm to examine the phase-matching behavior [30] of KPSe₆. The specific particle sizes were then placed in borosilicate capillary tubes. Each tube was loaded into a homemade sample holder that was mounted on a Z-scan translation stage. All capillary tubes were capped in dry nitrogen environment then flame sealed to keep all materials from being exposed to air and moisture during the measurement.

Broadband SHG and THG experiments were conducted at room temperature. In order to generate tunable pulses, coherent light of wavelength 1.064 μm was first produced using an EKSPLA PL-2250 series diode-pumped picosecond Nd:YAG laser with a pulse width of 30 ps and a repetition rate of 50 Hz. The Nd:YAG laser pumped an EKSPLA Harmonics Unit (HU) H400 where the input beam can be frequency tripled by successive NLO wave mixing. The 1.064 μm and frequency-tripled radiation from the HU entered an EKSPLA PG403-SH-DFG Optical Parametric Oscillator (OPO) composed of four main parts; a double-pass parametric generator, a single-pass parametric amplifier, a second harmonic generator (SH), and a difference frequency generation (DFG) scheme. The output wavelengths of the OPO used in our experiments were from 1.0 μm to 3.0 μm at increments of 0.1 μm.

The incident pulse energy was tuned to 20 μJ before being mildly focused onto samples with a spot size of 0.5 mm in diameter by a convex lens or a concave gold mirror, far away from the Z-scan focus. Here we deliberately determined the beam spot size in order to i) properly average the NLO signals from powders of random orientations and ii) to minimize the change in the spot size when we swept λ over a broad range of 1.0–3.0 μm; the beam waist w₀ at the Z-scan focus undergoes a significant λ-dependent variation via w₀ = (λ/π)(f/σ), where f and σ are the focal length and the Gaussian width of the incident beam, respectively. For the fundamental wavelengths inaccessible with 20 μJ, the NLO counts were properly scaled in accordance with the measured SHG and THG power dependence. However, the data at λ = 2.2 μm were omitted because the pulse energy was too low to be measured by a Gentec energy meter. The NLO signals from the samples were collected using reflection geometry by a fiber-optic bundle, which was coupled to a selective-grating (1800, 600, and 300 grooves/mm) spectrometer equipped with a CCD camera (Synapse) as well as an extended InGaAs (Symphony) detector. The overall detection range obtained from the combination of the two detectors was 0.3–2.0 μm. We confirmed that any surface-induced effect as well as NLO signals from other optical components were negligible. Any thermal load on the samples by the laser pulses tuned below the bandgap was negligible due to its slow repetition rate of 50 Hz. The relative NLO signals recorded in a broad wavelength range were precisely calibrated with the known and measured efficiencies of all optical components.

4. Broadband NLO properties of KPSe₆

Prior to observing SHG and THG from KPSe₆, the NLO responses were measured from our reference materials, AgGaS₂ and AgGaSe₂, prepared by a similar method as described in Sec. 2. Figure 4(a) plots the series of SHG spectra as a function of SHG wavelength, λ_SHG = λ/2, from AgGaS₂ for the particle size d in the range of 125 – 150 μm, when λ was varied from 1.0 μm to 3.0 μm. AgGaS₂ is type-I phase-matchable in our experimental range as we also confirmed based on its particle-size dependence [19,31]. The SHG signals decrease when λ_SHG approaches the bandgap wavelength of AgGaS₂ (λ_g ∼ 0.5 μm at room temperature) because of strong absorption of the SHG light and/or two-photon absorption of the fundamental light near the band edge. However, the mid-IR SHG response is essentially flat as λ approaches the static limit (λ → ∞) [25]. AgGaS₂ was used to estimate the absolute value of χ⁽²⁾ of crystalline KPSe₆ as explained later.

 

Fig. 4 Wavelength-dependent (a) SHG from AgGaS₂ and (b) THG from AgGaSe₂.

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Figure 4(b) corresponds to the broadband THG spectra from AgGaSe₂ (d = 20 – 32 μm) obtained under the same experimental conditions. Bandgap absorption of THG is significant for λ_THG = λ/3 < λ_g ∼ 0.73 μm (bandgap wavelength of AgGaSe₂) but the THG response also converges into the static limit at mid-IR. The THG counts as a function of d indicated a non-phase-matching case, which is typical due to a large phase-mismatch between λ and λ_THG[33]. Although AgGaSe₂ is a good phase-matching SHG material for λ > 3 μm, the compound is not phase-matchable for λ used in our experiments [31, 32, 34]. Therefore, we used AgGaSe₂ as a standard for the non-phase-matching SHG and THG cases.

Unlike conventional glassy materials, the amorphous phase of KPSe₆ exhibits a substantial SHG response due to a partial preservation of the local crystallographic order as evidenced by Fig. 3(b) as well as the pair distribution function analysis [19]. Figure 5(a) plots the SHG counts as a function of d from the glassy compound at λ = 1.8 μm. The observed non-phase-matching behavior is indeed predicted for the macroscopically isotropic glassy phase due to lack of birefringence. The red dots in Fig. 5(b) correspond to the wavelength-dependent SHG counts from glassy KPSe₆ (d = 20 – 32 μm) in our experimental range. Those from AgGaSe₂ of the same particle size are also plotted for comparison (circles), yielding characteristic of bandgap absorption for shorter wavelengths and saturation to a static value for longer wavelengths except for a pronounced dip around λ_SHG ≃ 1.15 μm. The origin for the dip is twofold; i) linear absorption of the fundamental beam by the borosilicate tube [35] and ii) three-photon absorption of the fundamental beam by AgGaSe₂, which all in turn decrease the SHG efficiency observed. The latter process is viable considering that the corresponding λ is approximately resonant with the three-photon edge of AgGaSe₂ (3λ_g ≃ 2.2 μm). The former effect was seen from all of our SHG and THG measurements [see Figs. 6(b) and 6(c) near λ = 2.1 – 2.4 μm], but this does not affect our estimation of the NLO coefficients as explained later.

 

Fig. 5 (a) Non-phase-matching SHG from glassy KPSe₆ based on particle-size dependence at λ = 1.8 μm. Broadband (b) SHG counts and (c) THG counts from glassy KPSe₆ (red) and AgGaSe₂ (circles), respectively, plotted on a semi-log scale.

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Fig. 6 (a) Phase-matching SHG from crystalline KPSe₆ based on particle-size dependence at λ = 1.8 μm. (b) Broadband SHG counts from crystalline KPSe₆ (blue) and AgGaS₂ (black) at d = 125 – 150 μm. (c) Broadband THG counts from crystalline KPSe₆ (blue) and AgGaSe₂ (circles) at d = 20 – 32 μm.

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It is noteworthy that even glassy KPSe₆ shows a good SHG efficiency compared with the benchmark NLO material of AgGaSe₂ for λ < 2.0 μm. However, this innate SHG is highly suppressed for λ > 2.0 μm since the short-range noncentrosymmetric order partially intact in the glassy phase becomes averaged out for longer wavelengths. Though, we note that this unusual SHG occurs only in a few phase-change chalcogenide materials [29, 33, 34, 36]. More importantly, the SHG efficiency of the compound can be boosted by several orders of magnitude by simply exploiting its phase-change property as demonstrated by the blue dots in Fig. 6(b).

Figure 5(c) shows the broadband THG response (×100 magnified) from glassy KPSe₆ (red) under the same experimental conditions. Note that the measured THG counts are almost comparable with those from AgGaSe₂ (circles) and the response becomes most efficient at the mid-IR range. As the leading NLO process in an isotropic medium, THG becomes more efficient than the lower-order SHG process for λ > 2.0 μm due to the reason explained above. A considerable disparity between SHG and THG responses, therefore, proves that any contribution to frequency tripling by sum frequency generation of SHG and fundamental radiation (3ω = 2ω + ω) is negligible; this cascade process is unlikely in a powdered sample in which random scattering by powders prevents coherent overlap of both beams. As shown in Fig. 6(c), the THG response can be further enhanced by several times with simple annealing.

The crystalline KPSe₆ exhibits strong phase-matching SHG within our entire observation range. For example, Fig. 6(a) illustrates particle-size dependence of the SHG counts at λ = 1.8 μm, clearly showing a growing trend with increasing d (type-I phase-matchable). Figure 6(b) displays the semi-logarithmic (semi-log) plots of relative SHG counts from crystalline KPSe₆ (blue) and AgGaS₂ (black) at d = 125 – 150 μm as a function of λ for direct comparison. Although the SHG responses from both sample and reference show a similar tendency at mid-IR, they are noticeably different for lower λ due to distinct degree of bandgap absorption. From Fig. 6(b) we can estimate the absolute value of χ⁽²⁾ of the sample because AgGaS₂ is also phase-matchable with a well-established value of ${\chi }_{\mathit{ref}}^{\left(2\right)}=36$ pm/V [31]. Here the relative SHG counts must be compared in the static limit (plateau region), where bandgap absorption and multiphoton absorption are minimal. The χ⁽²⁾ value of crystalline KPSe₆ was calculated for the phase-matching case [30]:

The broadband THG response (×100 magnified) from crystalline KPSe₆ (d = 20 – 32 μm) is plotted as the blue dots in Fig. 6(c), which is noticeably higher than that from AgGaSe₂ (circles). We confirmed that THG is not phase-matchable. However, the majority of important third-order NLO applications do not involve beam mixing, and therefore, this stringent condition is not required. Estimation of the third-order NLO tensor χ⁽³⁾ based on the powder method is less straightforward because the corresponding THG coherence length l_c is much shorter than experimentally accessible particle sizes due to a large phase-mismatch. By simply assuming similar THG coherence lengths ( $l_c~l_c^{\mathit{ref}}$) and comparing with ${\chi }_{\mathit{ref}}^{\left(3\right)}=1.6\times {10}^5$ pm²/V² of AgGaSe₂[37], we estimated χ⁽³⁾ ≃ (4.7 ± 0.6) × 10⁵ pm²/V² using

Although KPSe₆ has a wide linear transparency window ranging from the fundamental bandgap in the visible regime to P-Se vibration modes in the far-IR (∼ 19.0 μm) [19, 20, 24], it is important to check the absence of multiphoton absorption for high-power NLO applications. The effect of multiphoton absorption can be probed by observing the power dependence of NLO harmonic signals [33, 34] that can noticeably deviate from the predicted power laws if multiphoton processes are significant. We found that this detrimental effect is insignificant in KPSe₆ up to the 30-ps pulse of 30 μJ, corresponding to a high irradiance of 1 GW/cm². For example, Figs. 7(a) and 7(b) display the measured SHG and THG spectra as a function of input pulse energies from 10 μJ to 30 μJ at λ = 1.55 μm, which corresponds to the major telecommunication wavelength. The corresponding power dependence is plotted by dots (SHG) and circles (THG) in Fig. 7(c) on a log-log scale. The solid lines are best fits to the data generated by simple square and cubic dependences, clearly indicating that multiphoton effects are negligible. Together with highly-efficient broadband NLO responses, this shows that KPSe₆ is a promising candidate for NLO applications especially in the mid-IR spectral range.

 

Fig. 7 (a) SHG spectra and (b) THG spectra at λ = 1.55 μm for several incident pulse energies (10 – 30 μJ), respectively. (c) Corresponding power dependence of SHG (dots) and THG (circles) superimposed by theoretical square and cubic fits (solid lines).

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5. Conclusions

We have investigated the NLO properties of a potential mid-IR NLO chalcogenide compound KPSe₆ in which a crystal-glass phase transition is reproducible as confirmed by DTA analysis. The phase-change aspects of the dual-phase material have been characterized in terms of PXRD and Raman experiments. The compound exhibits apparent optical contrast between the two phases as confirmed by optical absorption measurements. A series of NLO experiments has been conducted on both crystalline and armophous KPSe₆ over a broad wavelength range based on powder SHG and THG measurements. The observed NLO responses strongly depend on the fundamental wavelength but reach static ones in the mid-IR range without any signature of multiphoton absorption effects. Remarkably, the glassy phase of the compound yields an intrinsic but significant SHG response, which basically arises due to a partial retention of the local noncentrosymmetric order. The NLO efficiencies of the glassy compound can be further enhanced by converting into the crystalline counterpart with simple heat treatment. We have estimated the key NLO parameters of the crystalline compound; χ⁽²⁾ ≃ 142.8 ± 10.5 pm/V and χ⁽³⁾ ≃ (4.7 ± 0.6) × 10⁵ pm²/V². The observed strong optical nonlinearities are consistent with the theoretical calculation, which emphasizes the role of the low-dimensional structural anisotropy coupled with a strong covalent character in the KPSe₆ compound. The results of our study demonstrate that KPSe₆ can be utilized for both second- and third-order mid-IR NLO applications. Furthermore, due to its unique physical and chemical properties, optical fibers and thin films having strong NLO properties can be readily engineered. Further studies will focus on these forms of the material.