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Abstract
We theoretically and experimentally researched on an intracavity frequency doubling red laser with walk-off compensation of bismuth borate (BIBO) for the first time, to the best of our knowledge. Through theoretical investigations, we described in detail the spatial walk-off characteristics of a BIBO crystal and discussed quantitatively the influence of different arrangements of a twin-BIBO-crystal on the output power of a second harmonic wave. Furthermore, the progress of walk-off compensation was revealed with the arrangement having the second BIBO 180° rotated along extraordinary axis. Experimentally, we found that the maximum average output power with walk-off compensation has been improved by 1.2 times compared to the uncompensated case, and the corresponding intensity profile restored from an oblique ellipse to an approximate circle.
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1. Introduction
Pulsed red laser sources with good beam quality have received considerable attention over the past few decades, owing to the growing number of promising applications in photoacoustic detection [1], skin tumor proliferation [2], photobiomodulation [3] and fluorescence imaging [4]. Intracavity frequency conversion using nonlinear optical (NLO) crystals is an important approach for the desired pulsed red laser generation. So far, potassium titanyl phosphate (KTP) [5] and lithium triborate (LBO) [6] have been reported to be capable of producing average output power of hundred watt level and high conversion efficiency of more than 14% for pulsed red laser, respectively. Recently, considerable researches have revealed that bismuth borate (BIBO) crystal features weak thermal effect, high effective nonlinear coefficient deff—up to 3.2 pm/V (higher than KTP and LBO) and high damage threshold (comparable with LBO) [7], which are highly desirable for acquiring efficient pulsed red laser output. For example, an actively Q-switched intracavity frequency doubled Nd:YVO4/BIBO red laser at 671 nm was demonstrated with the average output power of 4.38 W and the optical power conversion efficiency of 9.5% under the pulse repetition frequency (PRF) of 70 kHz [8]. However, the far-field intensity profile of red laser presented a very elliptic shape, and they attributed this phenomenon to the large difference in angular acceptance bands between the fundamental field and the second harmonic (SH) field along the orthogonal directions. Actually, this very elliptical intensity distribution can also be ascribed to the spatial separation between the fundamental field and the SH field in biaxial NLO crystal, which is called as the walk-off effect. The birefringence walk-off effect will limit the effective interaction length and the conversion efficiency, and distort the beam quality. Therefore, it is very necessary to eliminate the walk-off effect.
Considerable prior works focused on several common walk-off-reducing methods such as twin-crystal compensation method [9–12], noncollinear-frequency-mixing method [13–15], and external walk-off compensator method [16–18]. Particularly, for critical phase matching, the twin-crystal device has been recognized as a simple and efficient method for achieving high conversion efficiency and good beam quality second harmonic generation (SHG), which has been realized in several birefringent NLO crystals such as KTP and LBO. For instance, it has been proved experimentally by Bi et al. that exploiting the twin-KTP-crystal walk-off-compensated mode can achieve 30% improvement in conversion efficiency [19]. In another work, using a twin-LBO-crystal set, Jung et al. demonstrated the ultraviolet output power presented 1.4 times higher than that through a single long LBO crystal with the same whole length, while the SH beam shape was restored from an ellipse to a nearly circular [17]. However, the repair process of SH beam shape was not presented clearly. Notably, three BIBO crystals were applied to external cavity SHG and its conversion efficiency came up to 21% [20]. Nevertheless, such incomplete walk-off compensation arrangement did not possess the capacity to increase the effective interaction length sufficiently and improve the beam quality. To our knowledge, the BIBO crystal has not been investigated in twin-crystal walk-off compensation SHG. In theoretical studies, Armstrong et al. developed the amplitude theory of SHG with the plane wave model in twin-KTP-crystal [10]. In addition, the output power ratio of the compensated sum-frequency beam with respect to uncompensated one was deduced by Jung et al. based on the Gaussian model [16]. Overall, the above theoretical works mainly considered the influence of phases on the SH field, however, the effect of the walk-off angles on the SH field was not taken into account synchronously.
In this paper, we theoretically investigated the phase matching (PM) properties, effective nonlinear coefficients and spatial walk-off angles of BIBO crystal. The intensities of SH fields for different arrangements of twin-BIBO-crystal were modeled by considering the phase shifts, the spatial walk-off angles, and the relative signs of effective nonlinear coefficients in two BIBO crystals. The energy flow vector diagram of SH field was further established to reveal the repair process of SH beam shape intuitively. In addition, an intracavity frequency doubling nanosecond pulsed red laser was experimentally demonstrated with twin-BIBO-crystal walk-off compensation. Compared with uncompensated case, the maximum average output power grew from 4.1 to 4.93 W at the PRF of 4 kHz, and the corresponding beam qualities in the horizontal and vertical directions improved from $M_x^2 = 1.7$ and $M_y^2 = 1.5$ to $M_x^2 = 1.2$ and $M_y^2 = 1.4$, respectively, with the intensity profile restored from an oblique ellipse to approximate a circle. The experimental results verified the validity and feasibility of the theoretical analysis on twin-BIBO-crystal walk-off compensation method.
2. Theory
2.1 BIBO: relevant parameters
BIBO, as a positive biaxial crystal, crystallizes in the noncentrosymmetric monoclinic space group C2 with monoclinic angle β = 105.62° [21]. The relationship around crystallographic (abc), crystallophysical (XYZ) and dielectric (xyz) frames of BIBO is shown in Fig. 1, where φ = 47° and Ω = 25.1° corresponding to a wavelength of 1314 nm [22] and Ω is the angle between each of the two optic axes and the z axis, which is defined by:
Fig. 1. Crystallographic (abc), crystallophysical (XYZ) and dielectric (xyz) frames of BIBO. All frames right-handed (Ref. [21]).
The effective nonlinear coefficient deff is one of the important parameters in the SHG process. Following Tzankov and Yao’s method [23,24], there are three possibilities for phase matching in biaxial crystals in which slow (s) and fast (f) waves, corresponding to the eigenmodes with high and low refractive index, respectively, are involved. The effective second-order nonlinearities can be given by:
where the superscripts s and f of deff follow the sequence λ1, λ2, and λ3 of the three interacting wavelengths for which there is an established convention of assuming λ1 ≥ λ2 > λ3 and i, j, k = 1, 2, 3. $e_i^s$ and $e_i^f$ are the direction cosines of the s and f waves, respectively [23,24]:As a consequence of the Kleinman symmetry, the matrix of dijk for BIBO crystal can be transformed to the so-called contracted form of the dil tensor [24]:
Then, deff can be modelled by the general expressions:
Hence, using the obtained PM angles (θ, φ) and Eqs. (3a)–(3g), the expressions of deff in the principal planes can be acquired. Here, the “ordinary” (o) and “extraordinary” (e) waves represent the f and s waves, respectively. deff in the principal planes of BIBO for SHG as a function of fundamental wavelength λ is illustrated in Fig. 2, with the frame of the principal optical axes xyz. It can be found that the optimal deff (> 3.1 pm/V) lies in x-z plane over the fundamental wavelength region of 1.1-2.3 µm with PM type ooe (o + o→e).
Fig. 2. Effective nonlinearity deff versus fundamental wavelength λ for SHG in the principal planes of BIBO.
More concernedly, the spatial walk-off angle is defined by the intersection angle between the wave vector k and the Poynting vector s. It is more complicated for biaxial crystals to calculate the double-refraction walk-off angles, because walk-off occurs in two orthogonal planes with different angles. As is well known from crystal optics, the relation between the fundamental wave and the SH wave, with regard to the directions of electric field E, electric displacement D, wave vector k and Poynting vector (energy flow) s, are visualized in Fig. 3. For biaxial crystals, the electric displacements of the fundamental Dω,2 and SH D2ω,1 waves lie in the external and internal bisector planes, respectively. Correspondingly, the double-refraction angles ρω,2 and ρ2ω,1, between the directions of sω,2, s2ω,1 and k, respectively, can be expressed as [25,26]:
Fig. 3. Relation between the polarization directions of fundamental Dω,2 and SH D2ω,1 waves, and the directions of energy flow of sω,2 and s2ω,1, respectively, in a type I PM process (Ref. [25]).
The walk-off angle w, as the angle between the unit vectors sω,2 and s2ω,1 for the type I PM process, can be calculated by the relation [25]:
By virtue of Eqs. (4) and (5), the spatial walk-off angles varying with fundamental wavelength are numerically exhibited in Fig. 4. One may find that BIBO crystal has large walk-off angles for allowable fundamental waves in all three principal planes. Exploiting type ooe has the larger walk-off angles than type eeo in x-z plane.
Fig. 4. Spatial walk-off angles as a function of fundamental wavelength for type I PM: (a) x-z plane and (b) x-y, y-z planes.
Particularly, deff with respect to the PM angle at the fundamental wavelength of 1314 nm is depicted in Fig. 5. It can be clearly seen that there are two kinds of type I PM (ooe and eeo). For the PM angle of θ = 8.4° and φ = 0° (in x-z plane), deff reaches the maximum value of 3.16 pm/V as to type ooe. However, even with the maximum deff at this PM direction, the large spatial walk-off angle w is still a concern. As shown in Fig. 4(a), the corresponding double-refraction angles of ρω and ρ2ω are modeled as 6.3° and 1.3°, respectively, leading to the walk-off angle w of 6.5°. The large disparity between ρω and ρ2ω in two orthogonal directions will induce the intensity profile of SH wave to deviate from the circle.
Fig. 5. Effective nonlinearity deff as a function of PM angle at the fundamental wavelength of 1314 nm (295 K).
2.2 Intensity of SHG with a twin-BIBO-crystal
In order to eliminate the walk-off effect, we established a twin-crystal device consisting of two identical type I (ooe) PM BIBO crystals for which deff is to be 3.2cosθ pm/V. In order to achieve the right arrangement of two segment BIBO crystals, the nonlinear-coefficients matching as well as spatial walk-off angle should be considered. Assuming the orientation of the first segment is fixed and that of the second one is changed, there should be two arrangements having the opposite-direction walk-offs, and thus having internal walk-off compensations, as illustrated in Fig. 6. In first segment, the direction cosines of the s and f waves are ${e^{s,1}} = ({\cos \theta ,0, - \sin \theta } )$ and ${e^{f,1}} = ({0,1,0} )$, respectively. If the second segment is 180° rotated along the propagation axis, the direction cosines of the s and f waves in the second one will turn to be ${e^{s,2}} = ({ - \cos \theta ,0,\sin \theta } )={-} {e^{s,1}}$ and ${e^{f,2}} = ({0, - 1,0} )={-} {e^{f,1}}$, respectively, resulting in the sign of deff,2 is opposite to deff,1, as shown in Fig. 6(a). Figure 6(b) denotes that the second segment is 180° rotated along the extraordinary axis (${e^s}$). In this case, ${e^{f,2}} = ({0, - 1,0} )$ is the inverse of ${e^{f,1}}$, but ${e^{s,2}}$ is consistent with ${e^{s,1}}$, which signifies that the sign of deff does not change for type ooe according to Eq. (3g). The change in the sign of deff is equivalent to formulating a phase mismatch of π between the two segments. For a qualitative description of this phenomenon, the SHG coupling wave equation can be expressed as:
Fig. 6. Arrangements of twin-BIBO-crystal. (a) One having the second segment 180° rotated along propagation axis; (b) One having the second segment 180° along extraordinary axis.
When the second segment is not rotated or 180° rotated along the extraordinary axis, the deff of the two segments are equal. Under the slow-varying amplitude approximation, the plane-wave approximation and ignoring the walk-off effect, the complex amplitude of SH wave at the exit plane of the second segment can be expressed as:
Equation (6d) shows that I2 is proportional to the cosine of δ. Supposing Δk = 0, in order to maximize I2, ΔkaLa must be zero (i.e. La = 0), which could be realized by adjusting two segments as close as possible. Similar equations were derived by Pack et al. [20] except that the phase difference caused by anti-reflection (AR) coating on the crystal surfaces is neglected in our work.
If the second segment is 180° rotated along the propagation axis, Eq. (6c) transforms into
By comparing Eqs. (6c) and (6f), a phase mismatch of π between the two segments will be formed if the second one is 180° rotated along the propagation axis. Hence, the output intensity of SH beam can be expressed as follows:
It can be known from Eqs. (6f–6h) that ${\hat{I}_2}$ will be zero if Δk and La are both set to be zero, which has been experimentally verified by Yanagawa et al. [28]. There are two common methods to compensate for the increase in π phase. One is to insert a wave plate between the two segments making $\hat{\delta } = \mathrm{\Delta }k{L_c} + \mathrm{\Delta }{k_a}{L_a} + \mathrm{\Delta }{K_p} + \pi $, where ΔKp is the phase delay between the fundamental beam and the SH beam in wave plate. In this case, assuming Δk = 0, ${\hat{I}_2}$ will be maximized if ΔKp + ΔkaLa is an odd multiple of π. Nevertheless, this method will introduce insertion loss in the laser cavity to some extent, which will hinder the efficient generation of SH wave. The second method is to take advantage of air dispersion to make ΔkaLa an odd multiple of π. However, in order to meet this condition, La should be at least ∼6.5 cm with regard to Δka = 0.48 rad/cm, which will restrict the design of resonator. As a result, the extraordinary-axis-rotated arrangement is more suitable for walk-off compensation SHG, compared to the propagation-axis-rotated arrangement. Therefore, we only investigate the two cases of extraordinary-axis-rotated arrangement and unrotated arrangement in the following sections, which are defined as compensated case and uncompensated case, respectively.
In addition, in order to analyze the influence of the walk-off angle on I2, a power reduction factor G(t) should be introduced [29]:
By means of the internal compensation, the influence of the reduction factor G(t) on the SH output power can be reduced.
2.3 Walk-off-compensating process
In order to intuitively understand the process of walk-off-compensation, the energy flow vector diagram in twin-BIBO-crystal with extraordinary-axis-rotated arrangement is plotted in Fig. 7. In the first segment, the nxonz plane in the principal axis system is parallel to the horizontal plane, while the propagation direction of wave vector k is perpendicular to the crystal end face (XOY) with the PM angle of θ = 8.4° and φ = 0°. As described in section 2.2, the directions of Dω,2 and D2ω,1 are along the positive Y-axis and the negative X-axis, respectively. When the fundamental wave passes through the first segment, the direction of the energy flow sω,2 is separated from k about 6.3° along the Y-axis, which leads to the energy distribution of the generated SH wave to extend in the same direction. Meanwhile, the direction of s2ω,1 splits away from k about 1.3° along the positive X-axis in the horizontal plane. The large energy disparity of SH wave in two orthogonal directions results in the intensity distribution of the output beam in first segment to spread from circular to oblique ellipse in which the angle between the long axis and the Y-axis is about 12.2°, as illustrated in Fig. 7. Similarly, for uncompensated case, the energy flow vector will continue to propagate in the same form in the second segment, and the elliptical beam size will expand further.
Fig. 7. The energy flow vector diagram of twin-BIBO-crystal with extraordinary-axis-rotated arrangement.
But as for compensated case, when the fundamental wave enters into the second one, the directions of sω,2 and s2ω,1 flow in the opposite direction compared to the first segment. As shown in the deep red region of Fig. 7, the energy distribution of SH wave spreads further in the opposite direction along the same double-refraction angle, which will enlarge the beam overlap between the fundamental field and the SH field as well as between the SH fields produced by two segment crystals. Thus, the SH beam shape at the exit plane of the second segment reverts back to a circular but with a larger horizontal size than uncompensated case.
3. Experimental equipment
The experimental configuration is presented in Fig. 8. The pump source was a 50 W continuous wave (CW) fiber-coupled laser diode with a numerical aperture of 0.22 and a core radius of 200 µm, which worked at the weak absorption peak (880 nm) of Nd:YLF crystal. The pump beam was re-imaged into the gain medium with a spot radius of approximately 400 µm utilizing a pair of coupling lenses (F1 and F2, 1:4 magnification). The laser gain medium was an a-cut 1at.% Nd:YLF crystal sized by 3×3×40 mm3, which was coated for high transmission (HT) at 880 nm (T > 99.8%) and 1047–1321 nm (T > 99.5%) on the entrance facet, and HT at 1047–1321 nm (T > 99%) on the rear facet. Benefiting from the long upper-laser-level lifetime and weak thermal lensing, Nd:YLF has enabled to achieve high pulse energy and good beam quality fundamental laser output. A 46-mm-long acousto-optic Q-switcher (Gooch & Housego) had an AR coating around 1.3 µm (R < 0.2%) on both surfaces, driven at a 27.12 MHz ultrasonic frequency and a 100 W radio-frequency power. Two identical type I PM (o + o → e) BIBO crystals were exploited for frequency doubling the Nd:YLF laser. These two BIBO crystals with the same dimension of 3×3×6 mm3 were cut along θ = 8.4°, φ = 0°, and AR coated at 657 nm (R < 3%) and 1314 nm (R < 0.1%) on both ends. During the experiment, all of crystals were wrapped with indium foils and clamped into water-cooled copper holders with a constant temperature of 16°C.
Fig. 8. Experimental layout of an actively Q-switched intracavity frequency doubling red laser with twin-BIBO-crystal walk-off compensation.
As depicted in Fig. 8, the fundamental resonator was composed of a concave input mirror M1 with a radius-of-curvature of 300 mm and a flat dichroic mirror M3 acted as output coupler. M1 was coated to be high reflection (HR) at 1314 nm (R > 99.9%), and HT at 880 nm (T ≈ 97%) as well as 1047-1053 nm (T ≈ 98%). M3 had HR coated at 1314 nm (R > 99.9%), and HT coated at 657 nm (T ≈ 99.3%). Besides, to collect the red light in the backward propagation, another flat dichroic mirror M2 having HT coated at 1314 nm (T > 99.7%) and HR coated at 657 nm (R > 99.2%) was inserted between Nd:YLF and BIBO. The physical lengths of the fundamental and frequency doubling resonators were approximately 200 and 30 mm, respectively. The superiority for this long fundamental resonator was reflected in the high losses for the π-polarization due to the stronger negative thermal lensing, and thus the fundamental laser will operate on the σ-polarization at 1314 nm [30,31]. Based on the calculated thermal lens focal length of ∼1.1 m for σ polarization under the maximum pump power of 40 W, the average spot radii of the 1314 nm TEM00 mode at the Nd:YLF crystal and two BIBO crystals were estimated to approximately 360 and 200 µm, respectively. A short-wavelength pass filter (Thorlabs, FES0800) was employed to accurately measure the average power of red laser. The lasing spectral information was registered by means of an optical spectrum analyzer (Yokogawa, AQ6374) with a resolution of 0.05 nm. The pulse temporal characterizations were recorded by a digital oscilloscope (Agilent, DSO90604A) with a fast InGaAs photodiode (Thorlabs, DET08CL/M).
4. Results and discussions
Initially, the central wavelength of fundamental beam was measured to be 1313.4 nm with the full width at half-maximum (FWHM) of ∼0.51 nm under the full incident pump power. On account of the large wavelength acceptance Δλl (@3.71 nm·cm) of BIBO, the energy of fundamental field can be expected to be extracted efficiently. For ease of comparison, the output characteristics of the red lasers were evaluated for both uncompensated and compensated cases. The central wavelengths of the red lasers were determined to be 656.7 nm for both cases with the FWHM of ∼ 0.14 nm under the maximum pump power of 40.3 W. Based on the theoretical analysis mentioned above, the second BIBO crystal was set as close as possible to the first one in both cases to maximize the intensity of SH wave. The power transfers of the red lasers with respect to the pump power are plotted in Fig. 9. Under the pump power of 40.3 W, the measured highest average output powers amounted to 4.1 and 4.93 W at the PRF of 4 kHz for uncompensated and compensated cases, respectively, resulting in the optical-to-optical conversion efficiencies of 10.1% and 12.2%. Meanwhile, the corresponding power fluctuations were measured to be less than 5.2% and 4.1% over one hour, respectively. In addition, the pulse durations of the red lasers were determined to 150.7 and 127.9 ns under the full pump power of 40.3 W and the PRF of 4 kHz, respectively.
Fig. 9. Measured (symbols) and modelled (lines) average power with respect to the pump power at the PRF of 4 kHz.
It can be also seen from Fig. 9 that there is only a nominal improvement in the power with this walk-off compensation scheme, which could be mainly attributed to the serious walk-off effect in single BIBO crystal. In our experiment, the effective interaction length $L = \sqrt \pi r/w\; $ can be calculated to about 3.1 mm by considering the walk-off angle of w = 6.5°, which is much smaller than the 6 mm length of single BIBO crystal. Therefore, the influence of the power reduction factor G(t) cannot be efficiently eliminated for current walk-off compensation scheme. Based on Eqs. (7a) and 7, the power reduction factors G(t) were calculated to about 0.24 and 0.45 for uncompensated and compensated cases, respectively. Furthermore, by taking Eq. (7c) into the framework of the full-fledged rate equation theory [32], the output behaviors of SH waves in both cases were modeled, as visualized in Fig. 9. As we can see, after considering the power reduction factor, the theoretical results are highly coincided with the experimental data for both cases. According to the theoretical prediction, the substantial improvement of SH output power might be anticipated by enhancing the power reduction factor G(t), which can be realized by use of multiple-crystal walk-off-compensating method [33]. For instance, an even number of identical BIBO crystals with the length of 3 mm are placed close to each other, in which the odd segments are aligned in the same optical axis, and the even segments are 180° rotated along the extraordinary axis. In this scheme, the overlapping efficiency of the fundamental and SH beams can be maintained at a high level, thus extending the effective interaction length and increasing the SH conversion efficiency.
More intuitively, the beam qualities of the red lasers were measured by a laser beam analyzer (Spiricon, Inc. M2 − 200s), and the far field intensity profiles were recorded by a CCD camera placed 175 cm away from the output coupler, as shown in Fig. 10. For uncompensated case, the beam quality factors in the X and Y directions were measured to be $M_x^2 = 1.7$ and $M_y^2 = 1.5$ under the full pump power, respectively. As can be seen from the inset of Fig. 10(a), the SH beam has an oblique ellipse shape with the ellipticity of ∼0.63, while the horizontal and vertical FWHM diameters are about 0.6 and 0.95 cm, respectively. Besides, the angle between the long axis and the Y-axis was about 13°, which highly coincided with our theoretical analysis. Interestingly, for compensated case, it can be seen from the inset of Fig. 10(b) that the beam shape of the SH wave is a nearly circular with the ellipticity greater than 0.9, corresponding to the horizontal and vertical FWHM diameters of approximately 0.91 and 1.0 cm, respectively. Accordingly, the beam quality factors in the X and Y directions improved to $M_x^2 = 1.2$ and $M_y^2 = 1.4$ under the same pump power, respectively. The beam quality and beam shape were significantly ameliorated by using the twin-crystal walk-off compensation method, which is in good agreement with our theoretical prediction.
Fig. 10. Beam quality measurements of the red lasers for (a) uncompensated case and (b) compensated case. The insets show the corresponding beam profiles recorded in far-field.
5. Conclusion
In summary, we have obtained the mathematical expressions of the SH intensities for different arrangements of twin-BIBO-crystal by taking the nonlinear-coefficients matching and the spatial walk-off angle into account. Moreover, the repair process of SH beam shape was presented intuitively with aid of the energy flow vector diagram. The theoretical analysis showed that the output power as well as the beam quality can be enhanced by using the twin-BIBO-crystal set with extraordinary-axis-rotated arrangement. Additionally, we have experimentally performed the first demonstration of intracavity frequency doubling red laser with walk-off compensation of BIBO crystal. The experimental results indicated that 1.2-times-higher output power and a nearly circular beam shape were achieved through the twin-BIBO-crystal walk-off compensation, which were consistent with the theoretical predictions. We believe that the proposed twin-BIBO-crystal walk-off compensation structure and its theoretical analysis can be applied to other nonlinear crystals. The development of high-average-power and high-beam-quality red laser sources can be anticipated with the twin-BIBO-crystal walk-off compensation method.
Funding
Science and Technology Planning Project of Guangdong Province (2018B010114002); National Natural Science Foundation of China (11974146, 51872307, 51972149, 61935010, 62175091, 62175093); Basic and Applied Basic Research Foundation of Guangdong Province (2020A1515110001); Special Project for Research and Development in Key areas of Guangdong Province (2020B090922006); Guangzhou Municipal Science and Technology Project (201904010294, 202102020949).
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.
References
1. K. Keeratirawee and P. C. Hauser, “Photoacoustic detection of ozone with a red laser diode,” Talanta 223(Pt 2), 121890 (2021). [CrossRef]
2. H. Goo, S. J. Mo, H. J. Park, M. Y. Lee, and J. C. Ahn, “Treatment with LEDs at a wavelength of 642 nm enhances skin tumor proliferation in a mouse model,” Opt. Express 12(9), 5583–5596 (2021). [CrossRef]
3. A. El-Hussein, M. R. Hamblin, A. Saad, and M. A. Harith, “Photobiomodulation of avian embryos by red laser,” Lasers Med. Sci. 36, 1177–1189 (2021). [CrossRef]
4. M. Heilemann, S. V. D. Linde, M. Schüttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem., Int. Ed. 47(33), 6172–6176 (2008). [CrossRef]
5. T. Yang, J. J. Wang, D. S. Jiang, H. Zhao, and L. G. Yuan, “All-solid-state red laser with 83 W output power at 659.5 nm,” Chin. J. Lasers 34(9), 1178–1181 (2007).
6. Q. Wan, C. Du, and Y. Wang, “Double-end-pumped acoustic-optically q-switched intracavity-frequency-doubling red laser,” Proc. SPIE 6279, 627911 (2007). [CrossRef]
7. M. Peltz, J. Bartschke, A. Borsutzky, R. Wallenstein, S. Vernay, T. Salva, and D. Rytz, “Harmonic generation in bismuth triborate (BiB3O6),” Appl. Phys. B 81(4), 487–495 (2005). [CrossRef]
8. C. L. Du, S. C. Ruan, and Y. Q. Yu, “High-power intracavity second-harmonic generation of 1.34 microm in BiB3O6 crystal,” Opt. Express 13(21), 8591–8595 (2005). [CrossRef]
9. J. J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walk-off-compensated type-II second-harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11(12), 2368–2379 (1994). [CrossRef]
10. D. J. Armstrong, W. J. Alford, T. D. Raymond, and A. V. Smith, “Parametric amplification and oscillation with walkoff-compensating crystals,” J. Opt. Soc. Am. B 14(2), 460–474 (1997). [CrossRef]
11. E. Roissé, F. Louradour, O. Guy, V. Couderc, and A. Barthélémy, “Walk-off and phase-compensated resonantly enhanced frequency-doubling of picosecond pulses using type II nonlinear crystal,” Appl. Phys. B 69(1), 25–27 (1999). [CrossRef]
12. J. Friebe, K. Moldenhauer, E. M. Rasel, W. Ertmer, L. Isaenko, A. Yelisseyev, and J. J. Zondy, “β-BaB2O4 deep UV monolithic walk-off compensating tandem,” Opt. Commun. 261(2), 300–309 (2006). [CrossRef]
13. B. Ruffing, A. Nebel, and R. Wallenstein, “High-power picosecond LiB3O5 optical parametric oscillators tunable in the blue spectral range,” Appl. Phys. B 72(2), 137–149 (2001). [CrossRef]
14. H. Chen, Q. Liu, P. Yan, Q. Xiao, and M. Gong, “High-repetition-rate, single-pass third-harmonic of 354 nm ultraviolet laser with 51.5% efficiency,” Appl. Phys. Express 5(9), 092702 (2012). [CrossRef]
15. X. Yan, Q. Liu, C. Pei, D. Wang, and M. Gong, “High-power 355 nm third-harmonic generation with effective walk-off compensation of LBO,” J. Opt. 16(4), 045201 (2014). [CrossRef]
16. C. Jung, W. Shin, B. A. Yu, Y. L. Lee, and Y.-C. Noh, “Enhanced 355-nm generation using a simple method to compensate for walk-off loss,” Opt. Express 20(2), 941–948 (2012). [CrossRef]
17. C. Jung, K. K. Kim, B. A. Yu, Y. L. Lee, W. Shin, H. Kang, and Y. C. Noh, “Enhancement of ultraviolet-beam generation through a double walk-off compensation,” Appl. Opt. 54(27), 8043–8048 (2015). [CrossRef]
18. P. Heist, “Device for the frequency conversion of a fundamental laser frequency to other frequencies,” U.S. patent 0043452 A1 (3 June 2003).
19. Y. Bi, R. N. Li, Y. Feng, X. C. Lin, D. F. Cui, and Z. Y. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controlled temperature,” Opt. Commun. 218(1-3), 183–187 (2003). [CrossRef]
20. Y. Bi, H. B. Zhang, Z. P. Sun, Z. Bao, H. Q. Li, Y. P. Kong, X. C. Lin, G. L. Wang, J. Zhang, W. Hou, R. N. Li, D. F. Cui, Z. Y. Xu, L. W. Song, P. Zhang, J. F. Cui, and Z. W. Fan, “High-power blue light generation by external frequency doubling of an optical parametric oscillator,” Chin. Phys. Lett. 20(11), 1957–1959 (2003). [CrossRef]
21. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser Photonics Rev. 4(1), 53–98 (2010). [CrossRef]
22. H. Hellwig, J. Liebertz, and L. Bohaty, “Linear optical properties of the monoclinic bismuth borate BiB3O6,” J. Appl. Phys. 88(1), 240–244 (2000). [CrossRef]
23. J. Yao, W. Shi, and W. Sheng, “Accurate calculation of the optimum phase-matching parameters in three-wave interactions with biaxial nonlinear-optical crystals,” J. Opt. Soc. Am. B 9(6), 891–902 (1992). [CrossRef]
24. P. Tzankov and V. Petrov, “Effective second-order nonlinearity in acentric optical crystals with low symmetry,” Appl. Opt. 44(32), 6971–6985 (2005). [CrossRef]
25. F. Brehat and B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B: At., Mol. Opt. Phys. 22(11), 1891–1898 (1989). [CrossRef]
26. G. Huo, T. Zhang, R. Wan, G. Cheng, and W. Zhao, “The factors of spontaneous parametric down conversion process in BiB3O6 crystal with a broadband pump,” Optik 124(24), 6627–6630 (2013). [CrossRef]
27. J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18(3), 70–73 (1971). [CrossRef]
28. T. Yanagawa and L. K. Samanta, “Increased second harmonic output power using walk-off compensation in birefringent crystals,” J. Phys.: Condens. Matter 3(38), 7421–7433 (1991). [CrossRef]
29. K. Asaumi, “Second-harmonic power of KTiOPO4 with double refraction,” Appl. Phys. B 54(4), 265–270 (1992). [CrossRef]
30. H. Zhao, K. Y. Li, S. B. Dai, Z. H. Tu, Q. G. Yang, S. Q. Zhu, H. Yin, Z. Li, and Z. Q. Chen, “Nanosecond pulsed deep-red laser source by intracavity frequency-doubled crystalline Raman laser,” Opt. Lett. 46(13), 3207–3210 (2021). [CrossRef]
31. H. Zhao, Z. H. Tu, S. B. Dai, S. Q. Zhu, H. Yin, Z. Li, and Z. Q. Chen, “Single-longitudinal-mode cascaded crystalline Raman laser at 1.7 µm,” Opt. Lett. 45(24), 6715–6718 (2020). [CrossRef]
32. K. J. Yang, S. Z. Zhao, G. Q. Li, and H. M. Zhao, “A new model of laser-diode end-pumped actively Q-switched intracavity frequency doubling laser,” IEEE J. Quantum Eletron. 40(9), 1252–1257 (2004). [CrossRef]
33. A. V. Smith, D. J. Armstrong, and W. J. Alford, “Increased acceptance bandwidths in optical frequency conversion by use of multiple walk-off-compensating nonlinear crystals,” J. Opt. Soc. Am. B 15(1), 122–141 (1998). [CrossRef]
