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Abstract
Broadband second-harmonic-generation (SHG) in GdCOB crystals was demonstrated for the first time. Theoretical calculation and experiments for the type-I frequency doubling of GdCOB crystal was performed. The result revealed that the spectral retracing point of phase-matching angle was at around 1.65 µm. For broadband fundamental laser source tuning in the range of 1.55-1.7 µm, efficient SHG was realized, the highest conversion efficiency was 56%, and the output bandwidth reached 16 nm.
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1. Introduction
In past decades, GdCa4O(BO3)3 (GdCOB) has received significant attention as representative low symmetric nonlinear optical (NLO) crystal [1–2]. Large-sized GdCOB crystal with high optical quality can be obtained in a short time using the Czochralski pulling method. GdCOB possesses many advantages, including large nonlinearity, high laser damage threshold, as well as stable physicochemical properties. Therefore, GdCOB has been utilized in multiple NLO frequency conversions, such as second-harmonic-generation (SHG) and self-frequency doubling when doped with rare earth ions [3–5].
For birefringent NLO crystals, non-critical phase-matching (NCPM) is also called optimal phase-matching because of their high tolerance for operating conditions. According to the influence factors of phase mismatch, NCPM can be classified into three main categories, i.e., angular NCPM (A-NCPM), temperature NCPM (T-NCPM), and spectral NCPM (S-NCPM). In 2017, the A-NCPM SHG characteristics of RECOB (RE = Tm, Y, Gd, Sm, Nd and La) type crystals were systematically analyzed, which exhibited a broad tunable range (0.72–1.25 µm) and a large angular acceptance bandwidth (43–84 mrad·cm1/2) [6]. The earliest T-NCPM styles for GdCOB crystal were confined in its principal planes [7]. After investigation in the whole crystal space, the optimum T-NCPM SHG direction in GdCOB was determined to be (θ = 135°, ϕ = 47.3°) [8]. The corresponding temperature bandwidths measured from experiment was > 430 °C·cm, which was superior to the values of other NLO crystals, such as LN, LBO, KTP and BBO. To the best of our knowledge, as for S-NCPM, no work has been reported for GdCOB crystal.
Presently, the use of ultrashort pulse lasers has become increasingly popular in various fields, such as in biomedicine, spectroscopy, high speed communications, environment detection, and the investigation of ultrafast nonlinear phenomena. As a basic characteristic of ultrashort pulse lasers, their broad spectrum has special requirements for NLO crystals when frequency conversion is considered. To increase conversion efficiency, the group-velocity mismatch between the fundamental and newly generated harmonic pulses in the crystal needs to be as small as possible. That is, in the frequency domain, the spectral acceptance of the NLO crystal must be sufficiently large compared to the fundamental pulse bandwidth. When group-velocity mismatch is zero, the first-order wavelength sensitivity vanishes. This simultaneous phase-matching and group-velocity matching (PM-GVM) is the so-called S-NCPM, which is the most preferred frequency conversion style for ultrafast lasers because of its simplicity, reliability, and high efficiency. Some NLO crystals have been used for broadband SHG at certain wavelengths, such as BBO at 1.54 µm [9], BiBO at 1.56 µm [10], LBO at 1.3 µm [11], PPLN at 1.56 µm [12], PPKTP at 1.56 µm [13], PPKN at 1.62 µm [14], DKDP at 1.034 to 1.179 µm [15], and DADP at 1.027 to 1.161 µm [16]. In this paper, we report the S-NCPM of GdCOB crystal for the first time. In the wide 1.55–1.7 µm waveband range, high efficiency broadband type-I SHG can be performed.
2. Theoretical analyzing
Based on the Sellmeier equations of GdCOB crystal [17], the type-I SHG PM curve in the principal planes adjacent to the fifth octant (90° < θ < 180°, 0 < ϕ < 90°) was calculated and plotted as shown in Fig. 1. Usually, the samples processed along the PM directions in these planes are called principal plane samples, otherwise they are called spatial samples. The GdCOB crystal is an optical biaxial crystal. Its refractive index ellipsoid has mmm symmetry, so does its PM curve, which is completely symmetrical in all octants. That is to say, the PM curves do not depend on the used octant. The theoretical analysis shows that the S-NCPM wavelength, i.e., the wavelength when the group-velocity mismatch equals to 0, corresponds to the retracing point of the PM angle. As presented in Fig. 1, the S-NCPM wavelengths are 1.66 µm in the x-z plane (90° < θ < 180°, ϕ = 0°) and 1.63 µm in the y-x plane (θ = 90°, 0 < ϕ < 90°), and the corresponding phase matching angles are (146.4°, 0°) and (90°, 29.0°) respectively.
Fig. 1. Type-I phase-matching curve in the principal planes adjacent to the fifth octant. x-z plane: 90° < θ < 180°, ϕ = 0°; z-y plane: 90° < θ < 180°, ϕ = 90°; y-x plane: θ = 90°, 0 < ϕ < 90°.
When the frequency has a small change of $\Delta \omega $ near the central frequency ${\mathrm{\omega }_0}$, Taylor series (accurate to second order) can be used to expand the phase mismatch $\mathrm{\Delta }k$ in the frequency domain:
Further, there is
Fig. 2. Inverse group-velocity mismatch curve of type-I phase-matching. a. x-z principal plane. b. y-x principal plane.
For GdCOB crystal, the PM direction with the largest effective NLO coefficient (deff) appears at θ = 114° around, which is close to the y-x plane (θ = 90°). So it can be deduced that the PM property at θ = 114° around will be similar with the property at θ = 90° (the y-x plane). Imitating the y-x plane in Fig. 1, we investigated the variation relationship of fundamental wavelength with the PM angle ϕ in the θ = 114° plane, i.e. fixing the PM angle θ as 114° in this calculation. The result shows that the S-NCPM wavelength in the θ = 114° plane is 1.64 µm. Referencing the Sellmeier equations [17] and the second-order NLO coefficients [18], the type-I SHG PM angles corresponding to 1.64 µm and the corresponding deff were calculated, as shown in Fig. 3. By comparing the first octant (0° < θ < 90°, 0° < ϕ < 90°) and the fifth octant (90° < θ < 180°, 0° < ϕ < 90°), we find that the PM curve is symmetric, while deff is non-symmetric. The value of deff in the x-z principal plane adjacent to the fifth octant (90° < θ < 180°, ϕ = 0°) is greater than that of deff in the x-z principal plane adjacent to the first octant (0° < θ < 90°, ϕ = 0°); and it is considerably greater than deff of the y-x principal plane between the first octant and the fifth octant (θ = 90°, 0 < ϕ < 90°). In the entire crystal space, the largest deff value was 1.52 pm/V, corresponding to the PM direction (114.1°, 32°). Through above analysis, we selected two directions to process GdCOB crystals for S-NCPM experiments: (114.1°, 32°) and (146.4°, 0°), as demonstrated in Fig. 3. The (114.1°, 32°) sample represents the spatial sample and the (146.4°, 0°) sample represents the principal plane sample.
3. Broadband SHG experiments
To examine the SHG performance for different central wavelengths, we used a tunable femtosecond laser (ORPHEUS-HP, Light Conversion Inc.) as the fundamental light source. Its repetition rate and pulse width are 100 kHz and 160 fs, respectively, and the beam diameter is 2.5 mm. The fundamental beam was focused into the crystal sample with a quartz plano-convex lens (f = 200 mm). Both samples were processed with a cross-sectional area of 6 mm×6 mm, and a transmission length of 10 mm. The transmittance surfaces of each sample were polished but uncoated. The crystal sample was mounted on a multiple-dimensional precision adjustment frame, which can move back and forth, and rotate horizontally and vertically. The focus diameter ϕ0 was calculated to be 163 µm, and the beam Rayleigh range was 13 mm, which was larger than the sample length of 10 mm. So it could be considered that the beam size in the crystal was basically unchanged. After the crystal sample, a filter which is high-reflective at 1400-1800nm and high-transmitted at 600-1000 nm was used to block the remaining fundamental wave, and the transmitted SHG wave was recorded by power meter and spectrometer. In this work, we used two spectrometers, one was for the near-infrared waveband to record the fundamental wave spectrum (AvaSpec-NIR256-2.5-HSC-EVO, Avantes, 1000–2500 nm), and the other was for the visible waveband to record the SHG spectrum (HR4000, Ocean Optics, 200–1100 nm). The resolution is 4.4 nm for AvaSpec-NIR256-2.5-HSC-EVO, and 0.75 nm for HR4000. The experimental results measured from the two samples are plotted as discrete points in Figs. 4(a), 4(b), which were obtained from (146.4°, 0°)-cut GdCOB and (114.1°, 32°)-cut GdCOB, respectively. The sampling range is 1.5–1.8 µm, and the sampling interval is 10 nm. For NLO experiment with femtosecond laser as light source, the spectral influence to the data accuracy usually needs to be considered [19]. In this experiment, the spectral bandwidth of the femtosecond laser is about 22 nm, which will bring an angular measuring inaccuracy of ± 0.05° for the (146.4°, 0°) sample, and ± 0.1° for the (114.1°, 32°) sample. In addition, the experimental error caused by the precision of the adjustment frame is ± 0.1°. The calculated type-I SHG PM curve in the ϕ = 0° plane (i.e. x-z plane) was shown in Fig. 4(a), for the variation of fundamental wavelength with θ angle; the calculated type-I SHG PM curve in the θ = 114.1° plane was shown in Fig. 4(b), for the variation of fundamental wavelength with ϕ angle. The corresponding wavelengths of retracing points are 1.66 µm, 1.64 µm, respectively. The further calculations for (146.4°, 0°) and (114.1°, 32°) manifest that the Fig. 4(a) does not depend on ϕ value and the Fig. 4(b) does not depend on θ value. Altogether, the experimental results are in good agreement with the theoretical calculations. Thus, the theoretical calculations and experimental results show that the GdCOB crystal can realize type-I S-NCPM SHG for a fundamental laser with a wavelength around 1.65 µm.
Fig. 4. Variation of the fundamental wavelength with the PM angle for type-I SHG. The curves are theoretically calculated results in different planes, and the discrete points represent experimentally measured data of different crystals. a. ϕ = 0° plane (i.e. x-z plane) of GdCOB, (146.4°, 0°)-cut GdCOB sample; b. θ = 114.1° plane of GdCOB, (114.1°, 32°)-cut GdCOB sample.
The typical spectra measured from the SHG experiments are presented in Fig. 5. Fig. 5(a) shows the fundamental spectra at different central wavelengths of the pump source, where the full width at half maximum (FWHM) at 1550, 1600, 1650, and 1700nm is 22, 21, 23, and 23 nm, respectively. The corresponding frequency bandwidth at these four wavelengths is 2.81, 2.53, 2.54, 2.41 THz, respectively. Besides the two GdCOB samples for S-NCPM SHG experiments, a 10 mm long, (19.8°, 30°)-cut BBO crystal which could realize type-I S-NCPM SHG at 1550 nm was set as the reference sample. For the fundamental wavelengths shown in Fig. 5(a), the SHG spectra obtained from three samples are shown in Figs. 5(b)–5(d). In Fig. 5(b), the FWHMs of SHG spectral lines with central wavelengths at 775, 800, 825, and 850 nm are 15 nm, 14 nm, 15 nm, and 14 nm, respectively, attributed to the (146.4°, 0°)-cut GdCOB crystal. In Fig. 5(c), the FWHMs of SHG spectral lines with central wavelengths at 775, 800, 825, and 850 nm are 13 nm, 13 nm, 16 nm, and 14 nm, respectively, attributed to the (114.1°, 32°)-cut GdCOB crystal. For above wavelength bandwidth data, the corresponding frequency bandwidth of the SHG output is calculated to be 5.70-7.52 THz. In Fig. 5(d), the 775 nm spectral line has a FWHM of 6 nm (3.1 THz), which is attributed to the (19.8°, 30°)-cut BBO crystal. Here we define a parameter named spectral bandwidth ratio, which is the ratio of SHG spectrum bandwidth (FWHM) to the fundamental spectrum bandwidth (FWHM). For the (19.8°, 30°)-cut BBO crystal, the spectral bandwidth ratio is 27% (22 nm → 6 nm) in the SHG of 1550 nm; while for the (146.4°, 0°)-cut, (114.1°, 32°)-cut GdCOB crystals, the spectral bandwidth ratios can reach 64 ± 4% (22 ± 1 nm → 14-15 nm) and 65 ± 5% (22 ± 1 nm → 13-16 nm) respectively in the SHG of 1.55–1.7 µm. These results manifest the advantage and application value of GdCOB crystal in S-NCPM field.
Fig. 5. a. Fundamental spectra with different wavelengths. b. SHG spectra of (146.4°, 0°)-cut GdCOB crystal with different wavelengths. c. SHG spectra of (114.1°, 32°)-cut GdCOB crystal with different wavelengths. d. SHG spectrum of (19.8°, 30°)-cut BBO crystal at 775 nm.
For the fundamental wavelengths in Fig. 5(a), different crystal samples were adjusted to their optimum SHG PM directions during the experiment; and the results of SHG conversion efficiencies are shown in Fig. 6. Because the beam Rayleigh range is larger than the sample length, the focused beam size in the crystal can be seemed as basically unchanged, which has an average diameter of 184 µm (1.13ϕ0). Reference other experimental parameters, the optical intensity corresponding to the pump power can be determined, which is plotted as the top horizontal ordinate of Fig. 6. Both GdCOB crystals can perform efficient S-NCPM SHG with 1550, 1600, 1650, and 1700nm fundamental lasers. The most significant difference appears in the results of the 1550 nm fundamental laser. For the samples cut along principal plane, i.e., the (146.4°, 0°)-cut GdCOB, the results for 1550 nm are almost the same as those of the other three wavelengths (Fig. 6(a)). While for the sample cut in spatial direction, i.e., (114.1°, 32°)-cut GdCOB, results for the 1550 nm fundamental laser are lower than those of lasers with the other three wavelengths (Fig. 6(b)). This phenomenon can be attributed to its smaller angular acceptance and greater beam walk-off than those of the sample cut in the principal plane, in addition to the deviation from S-NCPM condition. In most of the fundamental power range (< 120 mW), the spatial sample is more efficient than the principal plane sample because its deff value is larger (as shown in Fig. 3). Taking 1650 nm as an example, when the fundamental power is fixed at 80 mW, the SHG conversion efficiencies is 25.9% for (146.4°, 0°)-cut GdCOB, while 35.6% for (114.1°, 32°)-cut GdCOB, as demonstrated in Fig. 6(a), (b). When the average power of fundamental laser is greater than 120 mW (28.13GW/cm2), both samples exhibit conversion-efficiency saturation at most fundamental wavelengths. Nevertheless, compared with the (114.1°, 32°) sample, the saturation phenomenon of the (146.4°, 0°) sample appears at higher fundamental power (∼ 140 mW). It leads that at the highest fundamental power of 160 mW, the SHG conversion efficiency of (146.4°, 0°) sample is higher than that of (114.1°, 32°) sample, although the deff of the (146.4°, 0°) sample is lower. This is because the conversion efficiency is not only dependent on deff, but also related to other factors like angular acceptance bandwidth and beam walk-off angle. For the (146.4°, 0°) GdCOB sample, the angular acceptance bandwidth and beam walk-off angle are 46.3 mrad·cm, 20.2 mrad respectively; For the (114.1°, 32°) GdCOB sample, the corresponding parameters are 13.8 mrad·cm and 16.6 mrad. Under focusing experimental condition, the larger angular acceptance bandwidth of the (146.4°, 0°) sample corresponds larger effective crystal length, which means the SHG output is more difficult to saturate for the same crystal length. As a result, its conversion efficiency reaches a higher level than the (114.1°, 32°) sample when the fundamental power is elevated constantly. Previously, this phenomenon was also observed in some SHG experiments [20–22], where at the same sample length the NLO crystal with smaller deff presented higher conversion efficiency ultimately.
Fig. 6. SHG conversion efficiency vs. fundamental power (optical intensity) for different samples at different fundamental laser wavelengths. a. (146.4°, 0°) -cut GdCOB crystal. b. (114.1°, 32°) -cut GdCOB crystal. c. (19.8°, 30°) -cut BBO crystal.
For the GdCOB crystals shown in Figs. 6(a), 6(b), the highest SHG conversion efficiencies are 56% (at 150 mW, 1600 nm), and 48% (at 122 mW, 1700nm), respectively. For the (19.8°, 30°)-cut BBO crystal, the highest conversion efficiency is 26% in the type-I S-NCPM SHG of 1550 nm (Fig. 6(c)), which can be attributed to its small angular acceptance bandwidth (1.9 mrad·cm) and large walk-off angle (42.6 mrad). Thus, the results of SHG conversion efficiency indicate the benefits of GdCOB crystal once again. For femto-seconds laser pulses, the damage threshold of GdCOB type crystals is larger than 100 GW/cm2 [23,24], which is much higher than the present pump power level (160 mW, 37.5 GW/cm2), as shown in Fig. 6. So, when pump power exceeded 160 mW, we have not observed the crystal damage, nor the generation of supercontinuum. In short, compared with BBO crystal, GdCOB produces broader SHG output spectra and higher SHG conversion efficiencies. At the same time, the experiments demonstrate that under medium and low pump power intensities (< 28 GW/cm2), the spatial GdCOB sample is more efficient than the principal plane GdCOB sample in S-NCPM SHG processes.
4. Conclusions
In Table 1, we listed the S-NCPM SHG performances of different NLO materials, including BBO, BIBO, LBO, PPLN, PPKTP, PPKN, DKDP, DADP, and GdCOB. The laser damage thresholds (LDTs) were under nano-seconds or pico-seconds laser pulses with a fixed wavelength of 1.064 µm [25]. It can be seen that the 56% conversion efficiency and 65% spectral bandwidth ratio of GdCOB crystal, which is obtained from this work, is the highest. Besides, among these NLO materials, GdCOB exhibits some notable characteristics, such as ease of growth and preparation, high laser-damage threshold, and wide operational waveband, which are very favorable for practical applications.
Table 1. S-NCPM SHG performances of different NLO crystalsa
Among RECOB type crystals, only three of them, i.e. YCOB, GdCOB, and LaCOB, are colorless, which can be applied to the visible and infrared optical frequency conversions conveniently. Because the radius of La3+ is larger than the one of Ca2+, large size, high quality LaCOB crystals without cleavage are hard to be obtained. As for YCOB and GdCOB crystals, no big property differences are found between them for visible and infrared nonlinear optical (NLO) applications, such as growth difficulty, nonlinearity and laser damage threshold. Nevertheless, GdCOB still shows some particularities compared with YCOB, such as smaller birefringence [6] and smaller thermo-optical coefficients [7,26], which represents high power/energy frequency conversion potentiality. In recent years, people pay much attention to the broadband optical parametric amplification (OPA) application (pump 800 nm, signal and idler 1600 nm) of YCOB crystal [23–28]. In these researches all of YCOB crystals were chosen from the PM direction in principle plane, which has large room for further optimization to elevate conversion efficiency. This research raises a powerful competitor, GdCOB crystal, as well as the optimization PM direction in whole crystal space, i.e. (114.1°, 32°) which has the largest deff and presents the most efficient conversion. Although its SHG output saturates faster than the principal plane PM direction (146.4°, 0°), we believe that this effect can be effectively alleviated by optimizing the experimental parameters like crystal length, beam waist radius, and focal length, just as the previous literatures [29,30] have ever performed.
In conclusion, we demonstrated efficient S-NCPM SHG in GdCOB crystal for the first time. For broadband fundamental lasers with central wavelengths at 1550-1700nm (Δλ = 22 ± 1 nm), the bandwidth of SHG waves is 13-16 nm, and the spectral bandwidth ratio of SHG pulse to fundamental pulse reaches 65 ± 5%. The highest SHG conversion efficiency is 56%, and the spatial sample is more efficient than the principal plane sample. Combined with Er-fiber laser technology, GdCOB crystal can be used to realize a novel, compact, convenient, and low-cost route to develop an ultrafast laser source at around 800 nm, which can have the potential for use as an alternative to existing fs Ti: Sapphire laser. In addition, GdCOB is also a promising competitor to YCOB crystal in broadband OPA application to generate high power near-infrared laser around 1.6 µm.
Funding
National Natural Science Foundation of China (61975096); Shenzhen Fundamental Research Program (JCYJ20180305164316517); Natural Science Foundation of Shandong Province (ZR2020QA072).
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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