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Abstract
The angle-dependent poling properties of 0.5-mm-thick BaMgF4 (BMF) crystals are investigated by means of calligraphically poled, radially oriented domains. We present a fanout periodic poling pattern for quasi-phase matching (QPM) applications, which covers an angular spectrum of about 14°. Within this range there is no angle-dependent degradation of the domain quality. This is the first realization of non-parallel domains for QPM in BMF-crystals.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
BaMgF$_4$ (BMF) is an ultra-transparent, ferroelectric, nonlinear-optical crystal [1–4] which bears the potential for mid-IR and vacuum-UV (VUV) frequency conversion – spectral ranges where frequently used nonlinear optical crystals like lithium niobate (LN), lithium tantalate (LT), potassium titanyl phosphate (KTP) and its isomorphs or borate crystals cannot be used due to their limited transparency range or due to light-induced crystal degradation. BMF is transparent from around 130 nm to 13 µm wavelength and shows no photo-darkening even under intense VUV-illumination [5,6]. As BMF is ferroelectric, quasi-phase matching (QPM) can be achieved via electric-field poling, which makes the entire transparency range accessible for parametric frequency conversion processes. Relevant nonlinear-optical coefficients of BMF are $d_{31} \approx$ 0.15 pm/V, $d_{32} \approx$ 0.36 pm/V and $d_{33} \approx$ 0.12 pm/V [4]. Especially the short wavelength transmission and its related potential for parametric VUV-generation has attracted much interest in the past – BMF-crystals could be key to all-solid-state VUV-laser systems [3–10]. Moreover, BMF is non-toxic, non-hygroscopic and has a rather low coercive field strength of about 4 kV/cm [8] facilitating handling and processing considerably. Nowadays, potassium beryllium fluoroborate (KBBF) is used in sub-200-nm laser systems [11,12]. However, it contains toxic Beryllium and requires a prism-coupling device to achieve birefringent phase matching. The latter is limited to a second-harmonic output wavelength not shorter than $\approx$ 161 nm [13].
In previous poling experiments of BMF it has been observed that dot-like domains tend to grow in a hexagonal shape, regardless of the applied poling technique [10,14–16]. This indicates that the domain growth in BMF is strongly anisotropic, which is particularly relevant for poling of elongated domains. The latter is typically necessary for QPM-patterns. It is known from electric-field poling of crystals like LN, LT or KTP, that an intrinsic, crystal-dependent anisotropic poling behaviour renders one (or several) preferred orientation(s) for elongated domains with respect to the crystallographic $a$- and $b$- (or $x$- and $y$-) axes. In analogy to LN, which shows a hexagonal domain growth characteristic as well, we can expect that preferred domain orientations are parallel to the edges of the intrinsically formed hexagons in BMF, i.e. parallel, $\pm$ 60$^{\circ }$ and $\pm$ 120$^{\circ }$ to the crystallographic $b$-axis. This assumption is consistent with the good quality of the reported $b$-parallel QPM-patterns [5,6]. Due to the aniotropic poling behaviour, it can be expected that poling of elongated domains which are not parallel to one of the preferred orientations, will be hampered. However, non-parallel poling is required for non-parallel QPM-structures like fanouts, which play a key role for widely and continuously tunable frequency converters [17]. Thus, non-parallel poling of BMF is highly relevant for widely and continuously tunable all-solid-state VUV-sources. Despite the need for non-parallel poling, the severeness of the angle-dependent influence on the poling properties in BMF is not yet investigated.
In this article, we investigate the influence of the domain orientation on the domain dimensions by means of a radial poling structure in 0.5-mm-thick, $c$-cut BMF-crystals. Based on the radial poling experiment, we deduce an angular bandwidth in which unperturbed poling can be achieved. The latter is confirmed by the presentation of a high-quality fanout QPM-structure, which does not show any angle-dependent quality degradation. The presented fanout is suited to access the largest nonlinear optical coefficient $d_{32}$ of BMF. In this work, we make use of the calligraphic poling technique, which was originally developed to periodically pole undoped congruent and stoichiometric bulk LN crystals in a pioneering work [18]. Meanwhile, calligraphic poling of non-parallel domains in bulk crystals could be demonstrated in MgO-doped stoichiometric LN [19] and LT [20], MgO-doped congruent LN [21] and even in Nd- and MgO-codoped congruent LN [22]. This work is the first demonstration of calligraphic and non-parallel poling of bulk BMF-crystals.
2. Experiments
2.1 Crystal growth
We grew a BMF single crystal by the Czochralski method. UV-grade crystalline pieces of BaF$_2$ and MgF$_2$ (Korth Kristalle GmbH) were used as the starting materials. They are weighed for the composition with a slight excess of BaF$_2$ from the stoichiometry, and inductively heated and melted in a pyrolytic-carbon-coated graphite crucible. For seeding we used a BMF crystalline rod oriented to its crystallographic $c$-axis prepared from another as-grown BMF-crystal. The seed crystal was pulled along +$c$-direction at 0.3 mm/h with a rotation speed of 10 RPM. During the entire growth period, nitrogen gas mixed with 5 vol.% CF$_4$ (99.999% purity) had been continuously purged into the furnace. Figure 1(a) shows a photograph of the as-grown BMF-crystal. The bottom part of the boule exhibits inclusions which we attribute to the BaF$_2$-phase due to the BaF$_2$-enriched melt. The X-ray fluorescence spectroscopy (Bruker, M4 TORNADO) confirmed that the entire crystal had the stoichiometric composition of BaMgF$_4$, i.e., 50 mol% BaF$_2$ : 50 mol% MgF$_2$. As seen in Fig. 1(a), the crystal shows flat facets corresponding to the crystallographic $b$-planes. Figure 1(b) shows the transmission spectrum for unpolarized light under vacuum (< 10$^{-4}$ mbar) propagating for $\approx$ 12.5 mm through these planes which was measured using a vacuum-UV spectrometer (Laser Zentrum Hannover e.V.). We obtained a transmission higher than 50% at 200 nm wavelength. The uniform surfaces after chemical-mechanical polishing and the polarity of the piezoelectric signal suggested that the crystal had a single ferroelectric domain. We prepared 0.5-mm-thick samples by cutting the crystalline boule perpendicular to the $c$-axis and polished the $\pm c$-planes for the poling experiments.
Fig. 1. (a) Photograph of the as-grown BMF-crystal. Scale bar: 10 mm. (b) Transmission spectrum of the BMF-crystal through the unpolished $b$-planes with a thickness of $\approx$ 12.5 mm.
2.2 Calligraphic poling
Calligraphic electric-field poling is achieved by moving a metal tip over the -$c$-plane of the BMF-crystal. A high voltage between the metal tip and a planar bottom electrode on the +$c$-plane inverts the orientation of the spontaneous polarization, as illustrated in Fig. 2. The inverted domains are directly written into the crystal, determined by the trajectory of the metal tip and the on-time of the high-voltage supply. During the poling process, two computer-controlled translation stages move the tip along a predefined trajectory with a velocity $v$. The metal tip is made of tungsten carbide with a nominal tip radius of about 10 µm. It is brought into gentle contact with the surface of the 0.5-mm-thick BMF-crystal without scratching the same. A 90-M$\Omega$-resistor between the tip and the high-voltage supply limits the maximum current. An 150-nm-thick, sputtered chromium layer serves as planar bottom electrode ensuring good electrical contact to the crystal’s bottom side. Silver conductive paste between the sample and the grounded aluminum chuck holds the BMF-crystal in position. The chuck is temperature-stabilized to a temperature $T$. After domain inversion, the Cr-layer is wet-chemically etched with a standard Cr-etchant, which also acts as a domain-selective etchant. Poling quality assessment is done by means of a standard bright field optical microscope.
Fig. 2. (a) Illustration of the calligraphic poling setup. A high voltage between a metal tip and a planar chromium bottom electrode leads to a well localized domain inversion below the tip. Moving the metal tip over the crystal surface leads to elongated domains. The sample is mounted onto a grounded aluminum chuck. The dark arrows indicate the orientation of the spontaneous polarization of the crystal. The grey arrow indicates the movement direction of the tip. (b) Illustration of the crystallographic structure of BMF. The semi-transparent image represents the structure after domain inversion [23].
3. Results and discussion
In order to reveal the angular dependence of the poling quality, we poled a radial structure, covering the full angular spectrum of $\pm$ 180$^{\circ }$ with respect to the crystallographic $b$-axis. For domain inversion we applied a constant voltage of $-$0.5 kV between the tip and the sample chuck. Neglecting the electric field enhancement close to the tip, this corresponds to an electric field of 10 kV/cm, which is well above the reported coercive field of BMF of 4 kV/cm [8]. The moving velocity of the tip was set to 0.5 mm/s. The crystal temperature was about 25 $^{\circ }$C during poling.
Figure 3(a) and (b) show microscope images of the inverted domains after domain selective etching from the top (-$c$) and bottom (+$c$) side, respectively. The radial structure consists of about 200 200-µm-long, radially oriented domains which cover the full angular spectrum. It can be seen that poling along any direction was successful and that all domains grew through the full crystal without merging with adjacent domains. However, the domain width orthogonal to the writing direction shows a strong dependence of the writing angle with respect to the crystallographic axes as illustrated in Fig. 3(c) and (d) for top and bottom side, respectively. Interestingly, the overall structure of the this angle-dependency shows the same symmetry as expected from the $mm2$ point group of BMF. When comparing the top and bottom side it can be seen, that the domain width can vary considerably: Poling along the $b$-axis (i.e. 0$^{\circ }$ or $\pm$180$^{\circ }$-poling) leads to wider domains on the top side, and thinner domains on the bottom side. Poling parallel to the $a$-axis (i.e. $\pm$90$^{\circ }$-poling) renders very thin domains on the top side, and broader domains on the bottom side. From other ferroelectric media like lithium niobate, it is known, that domain growth starts with a nucleus from either side, propagating as cone-shaped domain through the crystal [24]. Having this in mind, the latter observation could be an indication that domain growth starts at different sides of the crystal for different writing directions. Further research is needed to understand this phenomena. From a technological point of view, 0$^{\circ }$-poling is most relevant, as it allows to access the largest nonlinear optical coefficient $d_{32}$ of BMF. Hence, a technologically-useful fanout structure covers a certain angular bandwidth centered around 0$^{\circ }$. From Fig. 3(c) and (d) we can deduce that an angular bandwidth of about $\pm$ 7$^{\circ }$ should be acceptable without experiencing any negative influence on the poling quality, which is by far enough for the realization of reasonable fanout structures. Based on this prediction, we poled a fanout structure, covering an angular spectrum of about $\pm$ 7$^{\circ }$ with respect to the $b$-axis. Without changing the process parameters, we poled 50 2-mm-long domains as a fanout structure, as presented in Fig. 4. All domains have grown through the full crystal. Within the covered angular spectrum of about $\pm$ 7$^{\circ }$, we could not see any degradation of the poling quality, which is consistent to the previous experiment and confirms our prediction. When comparing Fig. 4(c) and (d) one can see that the domain width on the top side (c) is systematically slightly larger than on the bottom side (d), which is consistent with the first experiment.
Fig. 3. Bright field microscope images of top (a) and bottom side (b) of a radial poling patterns in a BMF-crystal. The poling pattern consists of about 200 200-µm-long radially oriented domains. Scale bars: 200 µm. The polar plots in (c) and (d) present the measured domain width orthogonal to the writing direction versus the writing direction with respect to the crystallographic $b$-axis. The shaded range covers $\pm$ 7$^{\circ }$.
Fig. 4. Bright field microscope images of a fanout periodically poled BMF crystal after domain selective etching from top (a) and bottom (b) view. The pattern consists of 50 2-mm-long domains. The period ranges from 30 to 40 µm. Scale bars: 200 µm. (c) and (d) show a closeup of the marked sections in (a) and (b), respectively.
For fanout poling of QPM-structures with a larger angular spectrum than $\pm$ 7$^{\circ }$, we suggest to apply an angle-dependent bias voltage, in order to compensate the observed angle-dependent domain growth behavior.
As frequency conversion in the VUV spectral range requires (sub)-µm QPM-periods, it is worth discussing possible approaches for writing thinner domains: A smaller tip diameter is expected to be beneficial, as it will help to confine the electric field lines. Moreover, reducing the bias voltage will reduce the area below the tip, in which the externally applied electric field exceeds the coercive field strength. Besides those measures for spatial confinement of the applied electric field, temporal confinement is another promising approach: Writing faster, or the application of voltage pulses is expected to allow for smaller domains as well, as this reduces the time in which the domains can grow.
4. Conclusion
We have presented the application of the calligraphic poling technique to 0.5-mm-thick BMF crystals to investigate the direction-dependent poling properties of the same. We identified an angular bandwidth for which fanout poling is expected to work without degradation of the poling quality and confirmed this successfully with a fanout QPM-structure. The orienetation of this QPM-structure is suited to access the largest nonlinear optical coefficient of BMF. Our results mark an important step towards technological exploitation of BMF as converter crystal, bringing continuously-tunable all-solid-state VUV-laser sources a step closer into reach. In order to harness the full potential of BMF in the VUV spectral range, further research is needed to realize (sub)-µm QPM-periods and an improved VUV-transmission.
Funding
Fraunhofer-Gesellschaft.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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