BaMgF4 is a ferroelectric fluoride which shows a very wide transparency range extending from 125 nm to 13 µm. The conjunction of these properties confers to BaMgF4 a unique chance for optical applications in the UV and mid-IR wavelength regions, where other nonlinear materials cannot be used. In particular its application as frequency converter in all solid-state lasers is considered. The wavelength dispersion of the refractive indices along the three optical principal axes is measured in the transparent region, and the Sellmeier coefficients for the three refractive indices are determined. The conditions for nonlinear optical processes are calculated for birefringent-matching and quasi phase-matching, with special emphasis in the UV and IR wavelength regions. Quasi phase-matching can be achieved in the whole transparent wavelength region, in contrast to birefringent-matching, which can be obtained in a limited range 573-5634 nm. First demonstration of second harmonic generation by quasi phase-matching with a ferroelectric fluoride is shown by frequency-doubling the emissions of a 1064 nm Nd:YAG laser and a tunable Ti:sapphire laser. The shortest emission is obtained in the UV at 368 nm, indicating the potential of BaMgF4 as nonlinear medium for the fabrication of all solid-state lasers in the vacuum-UV/UV and mid-IR wavelength regions.
© 2009 Optical Society of America
All solid-state lasers (ASSLs) are preferred to dye and gas lasers because they can have a robust and compact setup, and a long lifetime. Till the development of GaN-based laser diodes, ASSLs emitting in the near UV and visible were realized by the use of nonlinear (NL) crystals, mainly KTiOPO4 (KTP), β-BaB2O4 (BBO), and LiB3O5 (LBO). By the birefringent-matching (BM) with these crystals second, third and even higher harmonic generations can be achieved. Although the borate crystal family shows a wide transparency in the UV-visible-IR range, the phase-matched directions are limitated, impeding the conversion in the vacuum-UV (VUV) region. Consequently, for the fabrication of ASSLs emitting in the VUV the development of new NL crystals is required. Further, BM becomes more criticaltowards shorter wavelengths: (a) the mismatch for small deviations from the phase-matched direction increases linearly with the frequency (i.e. the matching angle becomes more critical), and (b) the walk-off of the electro-magnetic wave from the polarization wave increases rapidly towards the pole of the refractive indices.
The quasi-phase-matching (QPM) technique has been developed as an alternative to the standard BM. This technique was already predicted in the early 60’s, but the experimental investigations were carried out at the early 90’s. In the recent years the commercialization of frequency converters based on this technique has started. By the periodical reversal of the polar axis of a ferroelectric material (i.e. by the reversal of the sign of the NL susceptibility), the phase mismatch between the interacting waves (caused by the dispersion of the refractive indices) can be compensated, so that non-critical phase matching can be obtained at the direction of maximum efficiency, i.e. with the largest NL coefficient. In particular, the QPM can be applied to ferroelectric NL crystals which cannot be birefrigently matched. This is the case of LiTaO3 (LT), which has a notable NL coefficient (d 33=25pm/V) but a very small birefringence ( ). LiNbO3 (LN) and LT are the main ferroelectric oxides that have yielded to the mature development of the QPM technique. These show notable NL coefficients, however, as the fundamental absorption edges of LN and LT are at 330 and 280 nm, respectively, these cannot be utilized in the VUV/UV region.
In the UV wavelength region mainly the ArF (193 nm) and KrF (248) excimer lasers are used. It is known that these lasers present several disadvantages such as fast degradation, toxicity and low beam quality. As an alternative UV source the use of periodically poled (PP) BaMgF4 (BMF) as frequency converter has been proposed in the recent years[3, 4]. This crystal belongs to the pyroelectric fluoride family BaMF4 (M=Mg, Co, Ni, Zn) with space group Cmc21. The transparency of BMF extends from ≈125 nm to 13 µm, which is very wide in comparison to the transparency of LN or LT with ≈300 nm to 5 µm. The remarkable contrast between both material systems is illustrated in Fig. 1. We have determined the ferroelectric properties of BMF: the coercive field Ec is as small as 4 kV/cm, and the spontaneous polarization 6.6 µC/cm2. This value of Ec is remarkably lower than the ones for stoichiometric or congruent LN and LT (≈20-200 kV/cm), what clearly facilitates the process of periodical poling. Some physical properties like piezoelectric coefficients, elastic constants and punctual refractive indices have been reported[6, 7, 8]. The orthorhombic structure of BMF indicates that it is optically biaxial, with the principal optical axes xyz coincident with crystallographic ones abc in some order. To date only the dispersion of the refractive indices along the b- and c-axis have been reported.
In this work we present a comprehensive study of the NL optical properties of BMF single crystals. After the precise measurement of the three refractive indices as a function of the wavelength in the whole transparent range, VUV-visible-IR, the matching conditions for NL three-wave mixing processes are calculated and analyzed: BM for second harmonic generation (SHG), and QPM for (a) sum-frequency generation (SFG), (b) difference-frequency generation (DFG) and (c) optical parametric oscillation (OPO). We demonstrate for the first time the emission from a ferroelectric fluoride by the QPM technique.
BMF single crystals were grown by the Czochralski technique with a 30 kW R.F.-generator. High purity powders (⊱99.99%) of commercially available BaF2 and MgF2 powders were weighted in stoichiometric ratio and grown under CF4 (⊱99.99%) atmosphere at about 920°C . The crystal rotation and pulling rates were fixed at 10 rpm and 1 mm/h, respectively. A detailed description of the growth characteristics is reported in a separate paper.
Transmission spectra were measured at three different wavelength regions: (a) in the VUV with a KV-201 spectrometer from Bunkoh-Keiki Co., Ltd., (b) in the visible with a PerkinElmer Lambda 900, and (c) in the IR with a JASCO FT/IR-8000. Selectively etched domains on PP c-plane surfaces were visualized with an Olympus BX51 microscope. The dispersion of the refractive indices in the VUV-visible region was measured by the minimum deviation technique using two oriented prisms and a goniometer-spectrometer model 1 UV-VIS-IR made by Möller-Wedel. The precision of the measured values is ± 0.00001. Instead, ellipsometry analysis was utilized in the IR region in a c-cut sample of 1 mm thickness. For it an Infrared Variable Angle Spectroscopic Ellipsometer from J.A. Woolam Co. Inc. was used. As fundamental laser sources for the testing of the PP-BMF frequency converters we used (a) a pulsed Nd:YAG laser YAG 5000 series from B.M. Industries Co., Ltd (10 ns pulse width at a repetition rate of 10 Hz), and (b) a pulsed Ti:sapphire Mira Optima 900-P from Coherent (3 ps pulse width at a repetition rate of 76 MHz).
3. Results and discussion
The refractive indices along the crystallographic axes (na, nb, and nc) are shown in Fig. 2 as a function of the wavelength from the VUV to the IR region. For any wavelength the inequality nb<nc<na is satisfied. The equivalence between crystallographic and optical axes is bca≡xyz in the ascending frame, i.e. nx<ny<nz. The measured refractive indices are fitted according to the Sellmeier equation given in Eq. (1), and the resulting Sellmeier coefficients are given in Table1. The accuracy of the fittings in the can be appreciated in Fig.3, which shows in detail the VUV and visible wavelength regions. In the visible and near-IR the refractive indices vary between 1.44 and 1.48, na and nc being relatively close. Below 200 nm the indices increase rapidly and become very similar.
The wavelength dependence of the angle Ω between the optical axis and the a-axis, calculated by the Eq. (2), is shown in Fig. 4. The angle Ω decreases continuously from the VUV to the IR region. BMF changes from negative biaxial (Ω>45°) to positive biaxial (Ω<45°) at the wavelength 7850 nm.
This complete set of refractive indices allows us the calculation of the matching conditions for NL optical processes with BMF crystals. In the next two sections the conditions for BM and for QPM are described in detail.
3.1. Birefringent matching
Any NL crystal splits an incident electromagnetic wave of given direction and polarization into two waves with perpendicular polarizations. The two associated refractive indices ns and nf for the ”slow” and ”fast” waves, respectively, are obtained by the two solutions of the Fresnel’s equation:
The propagation direction is indicated relative to the optical axes xyz in spherical coordinates (Θ, Φ), where Θ is the polar angle (z→x) and Φ the azimuthal one (x→y). The solutions for any general propagation direction are two index surfaces, which vary with the wave wavelength due to the dispersion of the refractive indices.
Depending on the NL interacion between the mixing waves, two different types of SHG by BM are distinguished, so-called type I and II. Both types satisfy the energy- and momentum-conservation laws according to the Table2, i.e. ∑i Ei=0 and ∑iKi=0 (i=1,2,3: 1 and 2 input waves, 3 output wave), respectively. In the case of Type I two ”slow” waves yield to a frequency-doubled ”fast” wave, and the respective refractive indices have to be equal (n 3, f=n 1,s=n 2,s). On the contrary, in the case of Type II the two incident waves are perpendicularly polarized (”slow” and ”fast” waves), and the refractive index corresponding to the frequency-doubled ”fast” wave has to be an average of the initial ones (n 3, f=(n 1,s+n 2, f)/2). The matching loci Θ(Φ) for Type I and II have been analyzed with a computer program that calculates the crossing lines of the corresponding index surfaces.
The wavelength dependence of the loci for Type I and Type II BM is shown in Fig.5. From the 13 theoretically possible loci-diagrams 5 are found in the case of BMF SHG. The loci shown in Fig. 5 correspond to directions for critical phase-matching (CPM), and therefore ”walk-off” between fundamental and second-harmonic waves occurs. Non-CPM directions are at the transitions between two diagrams, when the refractive indices match along the principal axes x, y or z. In order to find these conditions for non-CPM it is convenient to overview the wavelength dependence of the angles Θ and Φ at the extreme positions. This is shown in Fig. 6 for Φ(Θ=90°), Θ(Φ=0°), and Θ(Φ=90°). From this graph the conditions for non-CPM are obtained, and the corresponding axes and wavelengths are summarized in Table3 together with the analogous in LBO. The fundamental wavelength interval for BM is very wide, namely 573–5634 nm (SHG 287-2817 nm), in contrast to the ones for KTP (497–3300 nm), BBO (410–3500 nm), LBO (553–2600 nm), and LN (1075–3715 nm).
In order to gain more insight into the conditions for BMF BM, a direct comparison with LBO is presented. Both crystals have the same point group, namely mm2, and therefore the non-vanishing NL coefficients are d 31, d 32, d 33, d 24, and d 15. The values for BMF and LBO are listed in Table4[12, 13]. Although the ones of BMF may need some revision, it is seen that these are over one order of magnitude smaller than those of LBO. The matching directions at the fundamental wavelength λ=1064 nm are shown in Fig. 7 together with the effective NL coefficients and the ”walk-off” angles. The loci are similar for both BMF and LBO, except for the case of SHG Type II. It should be noticed that the BMF loci are in very good agreement with the only ones reported so far. The directions with the largest effective NL coefficient differ from one crystal to the another, however in both crystals tend to correlate with relatively large ”walk-off” angles. From these considerations, we find that BM with BMF does not overcome the properties of other standard crystals in the visible wavelength region. In order to obtain the maximum benefit from the BMF transparency and the NL coefficients, the matching by the QPM-technique needs to be considered. This is analyzed in the next section 3.2.
3.2. Quasi phase-matching
The advantages of QPM versus BM are several:
(a) the matching is engineerable within the transparency range. Therefore, in contrast to the limited wavelength interval for BM SHG (573–5634 nm), the VUV and mid-IR wavelength regions can be approached with QPM BMF,
(b) the largest NL coefficient can be used by selecting the matching along a convenient direction,
(c) the matching is non-critical at any wavelength, so that phase-matching can be maintained over a longer crystal length.
In the following we will consider not only the especial cases of SHG and THG, like in the previous section 3.1, but a more general three-wave mixing scheme: SFG, DFG, and OPO. The latter is equivalent to optical-parametric amplification (OPA), where the ”signal wave” appears in the input and is amplified within the NL crystal. The QPM conditions are summarized in Table 5. The energy conservation has to be satisfied like in the case of BM (Table 2), while the momentum mismatch requires the engineering of the NL response of the device. The difference in the refractive indices causes a phase shift between the waves, which is periodically reseted by the reversal of the sign of the NL susceptibility with a period Λ. Although SFG, DFG and OPO are equal from the mathematical point of view, for the sake of clarity we consider them separately. The frequency restrictions for DFG and OPO are w 1>w 2 and wp>ws>wi, respectively. OPO ”pump”, ”signal”, and ”idler” waves are equivalent to DFG ”wave1”, ”wave2”, and ”wave3”, respectively, if w 2>w 3.
We consider from now a practical device, where the mixing waves pass collinearly through the crystal along the a or b axis, while the c axis is periodically reversed. Depending on the NL coefficient (d 31, d 32, or d 33) and the polarization of the three mixing waves (electric field vectors relative to the crystallographic axes Ē1,abc, Ē2,abc, and Ē3,abc) the matching conditions vary. The possible mixing configurations are shown in Table 6. The grating period Λ has been calculated as a function of the mixing wavelengths λ1 and λ2 (λ3 is fixed by the other two), and the corresponding contour plots are shown in Figs. 8 and 9. For simplicity, the notations for the polarization vectors are shortened, e.g. Ē1,a Ē2,c Ē3,a to aca. SFG QPM covers the whole BMF transparency region in the configurations d 31-caa, d 32-bbc, and d 33-ccc, with maximum periods Λ in the order of 140, 70 and 210 µm, respectively. The other two configurations, d 31-aac and d 32-cbb, present poles or singularities, and therefore only contour periods up to 1000 µm are shown. In general we observed that to generate light with a wavelength of <200 nm periods Λ in the order of 1–3 µm are necessary for first order matching. In the case of DFG poles are found in d 31-caa, d 32-bbc, and d 32-bcb. Although the contour plots of Figs.8 and 9 contain complete matching conditions for three-wave mixing, the grating period dependence on the wavelength can be better viewed at particular wavelengths.
The grating periods for frequency- and wavelength-doubling (SFG and OPO with λ1=λ2 and
λs=λi, respectively) are shown in Fig. 10 as a function of the wavelength. Apart from the fact that BMF can be used in a much wider wavelength region than LN, we find that the periods for BMF are notably larger than the one for LN-d 33. It should be noticed that the period Λ is a critical parameter for practical periodical poling of the devices, as it will be seen in the next section. Concerning this particular, the semi-logarithmic plot in the UV-visible region shows that towards short wavelengths (200 nm SHG) all configurations tend to a period of about 3 µm for the first order matching: for Type I matching (Ē1‖Ē2) Λd 31-aac>Λd 33-ccc> Λd 32-bbc, and for Type II (Ē1⊥Ē2) Λd 32-bcb> Λd 31-aca.
As we have seen, the main advantage of BMF is its wide transparency in the UV and IR. It is therefore interesting to analyze in more detail which are the matching conditions in these two regions, where there is a demand for ASSL sources. In the UV region we consider the SFG, while in the IR the OPO. The grating periods necessary to obtain SFG at the emission wavelengths of the excimer lasers (157 nm F2, 193 nm ArF, and 248 nm KrF) are illustrated in Fig.11. The wavelength dependence of the periods is relatively small in all three cases, with values for first order matching ranging between 1–2, 2–5 and 4–14 µm, respectively, in the visible and near-IR range. The shortest periods correspond to SHG. On the opposite side, ”signal/idler” wavelengths as a function of the grating period are shown in Fig. 12 for two pumping wavelengths, 1064 nm (Nd:YAG laser) and 2.0 µm (eye-safe laser). For both lasers the configuration OPO-d 32-cbb (i.e. ”pump” c-polarized, ”signal” and ”idler” b-polarized, all collinear along a) provides emission in the whole IR wavelength region with very convenient periods, ranging between 35–50 and 50–75 µm for 1.064 and 2.0 µm lasers, respectively. Further, it is noteworthy that d 32 is the largest NL coefficient (see Talbe4), and therefore yields to the largest conversion efficiencies.
3.3. Periodical poling and UV SHG
The theoretically predicted matching conditions for SHG QPM have been tested. Devices with different periods have been processed and checked. With an initial period of 70 µm we succeeded to frequency-doubling the emission from a 1064 nm Nd:YAG laser using the d 33 NL coefficient. A photograph of the emitting device is shown in Fig. 13. As a next step we reduced the period to match the tunable range of a Ti:sapphire laser. Periods between 24 and 40 µ were used to obtain SHG in the visible and near-UV wavelength regions. The photograph of Fig.14 shows as an example the 396 nm SHG visualized on a phosphorescent paper. The shortest emission obtained so far is 368 nm, which is close to the limit of the pulsed Ti:sapphire laser. In order to achieve emission at shorter wavelengths similar to those of the gas excimer lasers, the grating period needs to be considerably shortened, as seen in Fig. 11. The realization of these periods gets towards the limit of standard photo-lithographical processes, which use contact masks and a minimum pitch of ≈1µm. The shortest period achieved so far is shown in Fig. 15. This photograph shows a c-cut BMF sample after the poling process. The ferroelectric domain structure is visualized by a selective etching process of +c and -c surfaces. The obtained period is 6.6 µm, just about double of the one necessary for 193 nm emission.
Present work studies the NL properties of the biaxial BaMgF4 crystal. The optical principal axes are coincident with the crystallographic ones (xyz≡bca). The wavelength dispersion of the refractive index along the three optical principal axes has been determined in the whole transparency range. On this basis the matching conditions for BM and QPM have been calculated. BM is possible in the wavelength range 573–5634 nm. The IR limit lies at a larger wavelength than that of standard NL crystals like KTP, BBO, LBO, and LN. On the other side, the QPM makes possible to take advantage of the wide transparency of BMF in the UV wavelength region. Periods in the order of 2–3 and 5–10 µm are necessary for first order SHG of 193 and 248 nm, respectively. Experimental results confirmed the accuracy of the estimated grating periods. SHG QPM has been obtained for Nd:YAG and Ti:sapphire lasers. This is the first report on QPM using a PP ferroelectric fluoride, moreover, emitting in the ultraviolet wavelength region. The shortest period realized so far is 6.6 µm, indicating the potential of BMF as NL medium for VUV-UV and mid-IR ASSLs.
This work has been partially supported by the Industrial Technology Researach Grant Program in 2007 from New Energy and Industrial Technology Development Organization (NEDO) of Japan.
References and links
1. J. A. Armstrong, N. Bloembergen, J. Duncan, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
2. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
3. K. Shimamura, E. G. Víllora, K. Muramatsu, and N. Ichinose, “Advantageous growth characteristics and properties of SrAlF5 compared with BaMgF4 for UV/VUV nonlinear optical applications,” J. Cryst. Growth 275, 128–134 (2005).
4. K. Shimamura, E. G. Víllora, K. Takekawa, and K. Kitamura, “Ferroelectric properties and poling of BaMgF4 for ultraviolet all solid-state lasers,” Appl. Phys. Lett. 89, 232,911 (2006).
5. M. Eibschuetz, H. J. Guggenheim, S. H. Wemple, I. Camlibel, and M. DiDomenico, “Ferroelectricity in BaM2+F4,” Phys. Lett. A 29, 409–410 (1969).
6. K. Recker, F. Wallrafen, and S. Haussühl, “Single crystal growth and optical, elastic, and piezoelectric properties of polar magnesium barium fluoride,” J. Cryst. Growth 26, 97–100 (1974).
7. F. S. Bechthold and S. Haussühl, “Nonlinear optical properties of orthorhombic barium formate and magnesium barium fluoride,” Appl. Phys. A 14, 403–410 (1977).
8. S. C. Buchter, T. Y. Fan, V. Liberman, J. J. Zayhowski, M. Rothschild, E. J. Mason, A. Cassanho, H. P. Jenssen, and J. H. Burnett, “Periodically poled BaMgF4 for ultraviolet frequency generation,” Opt. Lett. 26, 1693–1695 (2001).
9. M. Rolin and M. Clausier, “Le systeme fluorure de calcium fluorure de baryum - fluroure de magnesium,” Rev. Int. Hautes Temp. Refract. 4, 39–42 (1967).
10. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
11. M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967).
12. J. G. Berman, G. R. Crane, and H. Guggenheim, “Linear and nonlinear optical properties of ferroelectric BaMgF4 and BaZnF4,” J. Appl. Phys. 46, 4645–4646 (1975).
13. M. Kaschke and C. Koch, “Calculation of nonlinear optical polarization and phase matching in biaxial crystals,” Appl. Phys. B 49, 419–423 (1989).