1. Introduction

Ultraviolet (UV) diode-pumped solid-state lasers that have high average power and high repetition rates are useful in precision material processing fields such as marking, drilling, cutting, and welding [1]. Recently, material processing requires larger areas and higher speeds; thus, higher average power UV lasers are in greater demand. In general, UV lasers for material processing are developed through frequency tripling of neodymium-based infrared (IR) lasers. Therefore, in order to develop high-power UV lasers, high-power IR lasers and efficient UV conversion are important.

Frequency tripling of IR lasers has two nonlinear-optical processes. First, the IR beam is converted to a green beam. Then, the generated green beam and the residual IR beam are mixed to generate the UV beam. Although there are many nonlinear crystals that can be for these two processes, lithium triborate (LBO) crystals are the most common for IR lasers that have a peak power below 1 MW [1–9], owing to their deep UV transparency, large nonlinearity, relatively small walk-off loss, and high growth yield. The LBO crystal for the IR-to-green conversion can have noncritical phase matching (NCPM) condition, while the one used to mix the IR and green to UV cannot. This results in beam walk-off which lowers the conversion efficiency. Walk-off loss can be a serious problem in the UV conversion of low peak-power IR lasers, which is common in the development of material-processing sources where the IR lasers having high repetition rates and thus low pulse energy are used. For high conversion the low peak-power beams should be focused in small size, which makes the walk-off loss serious. Several methods to compensate for the walk-off loss have been suggested. The first one [10] is to slightly shift the green beam at the green-generation step in advance by using the critical phase matching (CPM) interaction instead of NCPM interaction. However, the CPM interaction lowers the green-generation efficiency and worsens the green-beam quality, which can make the UV-beam poorer in the end. The second one [2, 11-12] is to make the UV-generation interaction noncollinear. This method can increase the efficiency. However, complexity is its disadvantage. In 2003, P. Heist has suggested a simple method for reducing the UV-generation loss due to walk-off in his patent [13]. According to his suggestion, the walk-off loss can be reduced using a single birefringent crystal as compensator. However, Heist’s suggestion has been described very simply and has not been experimentally investigated until now.

In this paper, we theoretically described in detail how the power of a generated UV beam can be increased using Heist’s method, and we experimentally proved the proposition. In Heist’s proposal, calcite crystals are used as the typical material for walk-off compensation. However, calcite crystals are not good for high-power UV generation because of their low damage threshold. Alpha barium borate crystals are thought to be the best material for walk-off compensation. We performed an UV-generation experiment using an alpha barium borate crystal as the walk-off compensator and observed that the power of the UV beam was 1.9 times higher owing to walk-off compensation. In addition, we found through theoretical analysis that the beam quality as well as the power can be improved using this method.

2. Theoretical description

In the situation that the ordinary fundamental beam interacts with the extraordinary second harmonic beam in the nonlinear-optical material for generation of the ordinary sum-frequency beam, the second harmonic beam experiences the walk-off effect while the fundamental beam does not. Hence, the two beams spatially split more and more as they pass the nonlinear medium, as shown in Fig. 1(a) , which reduces the overlapped interaction area of the two beams and thus deteriorates the sum-frequency generation (SFG). This can be a serious problem in the case of narrow beams and long material. However, this problem can be diminished just by using a birefringent crystal as a walk-off compensator [13]. If the walk-off compensator is placed before the SFG material so that the second harmonic beam deviates opposite of that in the SFG material in advance, as shown in Fig. 1(b), the walk-off loss mentioned above can be diminished. In addition, it can be intuitively predicted that the walk-off compensation can be optimized when the walk-off deviation during the whole length of the compensator, l_com, is the same as that during half of the length of the SFG material, l_SFG, as follows:

 

Fig. 1 Scheme of walk-off compensation: (a) uncompensation case, (b) compensation case.

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For a qualitative description of this phenomenon, first, the electric fields of the beams should be mathematically expressed. If the fundamental beam has a Gaussian spatial profile and the conversion of the fundamental to the second harmonic is low enough, it can be said that the second harmonic beam also has a Gaussian profile. Assuming that their radii are large enough, electric-field amplitudes of the two beams are uniform over the propagation axis, z, and can be expressed in the region before the walk-off compensator as follows:

These two beams can interact together in the SFG material to generate the sum-frequency beam. Assuming that the sum-frequency conversion is low enough, the electric-field amplitude of the ordinary fundamental beam in the SFG material still keeps uniformity over z and can be expressed as follows:

However, the amplitude of the extraordinary second harmonic that has experienced the compensational walk-off in the compensator medium and experiences other walk-off also in the SFG medium does not have uniformity over z any longer and can be expressed as follows:

The electric-field amplitude of the sum-frequency beam emitted out of the SFG material having a nonlinear coefficient, d_eff, can be expressed as follows:

Thus, the output intensity of the sum-frequency beam can be expressed as follows:

Then, the output power of the sum-frequency beam can be expressed as follows:

From the above equation, the output power ratio of the compensated sum-frequency beam with respect to uncompensated one, $P_{3,out}^{un}$, i.e., $P_{3,out}^{}$with x₀ = 0, can be expressed as follows:

Analysis of the above equation helps us grasp the walk-off compensation effect on the output-power enhancement. Taking a sum-frequency generation of 1064 nm and 532 nm into 355 nm using a 20-mm-thick type-II LBO crystal as an example, two material parameters, ${\gamma }_{2,SFG}$and $l_{SFG}$, equal 9.3 mrad and 20 mm, respectively. For w₁ values of 50 μm, 100 μm, 150 μm, and 500 μm, the output-power ratio, $P_{3,out}^{}/P_{3,out}^{un}$ can be obtained as a function of the compensation amount normalized by the walk-off deviation in the SFG material, i.e., $x_0^{}/({\gamma }_{2,SFG}{l}_{SFG})$, as shown in Fig. 2 . Figure 2 shows that the sum-frequency output power can be enhanced through appropriate walk-off compensation, which is clearer for the narrower beams and that the power enhancement by compensation is optimized at $x_0^{}/({\gamma }_{2,SFG}{l}_{SFG})=\frac{1}{2}$, i.e., when Eq. (1) holds, as expected.

 

Fig. 2 Output-power ratio as function of walk-off compensation amount.

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Looking at Fig. 1, which shows beam overlap in SFG material, gives us another prediction that is the spatial beam profile of the output beam can be also enhanced through walk-off compensation. Since the spatial overlap of the fundamental beam and the harmonic beam, that is not symmetric in the non-compensation scheme becomes symmetric in the optimum-compensation scheme, it can be predicted that the spatial beam shape of the generated beam can be also enhanced by walk-off compensation. This prediction can be proven through analysis of the expression for the intensity of the output beam, Eq. (6). When w₁ = 50 μm, the intensity profiles of the two cases can be calculated, as shown in Fig. 3 . The solid curves in Fig. 3 denote the calculated profiles. First, it can be seen that the profile in the uncompensated case is not centered at the x = 0 point, while the one in optimally-compensated case is centered exactly, which is the natural result of walk-off compensation. Gaussian fitting to two calculated profiles makes it possible to understand the qualities of the two beams. The dotted curves in Fig. 3 denote the fitting results. Figure 3 clearly shows that the uncompensated output beam doesn’t have a symmetric or Gaussian profile; the compensated beam has a perfectly-symmetric and an almost-Gaussian profile.

 

Fig. 3 Spatial beam profiles of output beam in uncompensated and compensated case.

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3. Experimental setup

Experimental setup for 532-nm and then 355-nm generation is shown in Fig. 4 . A diode-pumped solid-state laser (DPSSL) having the wavelength of 1064 nm was used as the fundamental source. At a repetition rate of 20 kHz, the laser has a pulsewidth of 10 ns and an average power of up to 6 W. The output beam was polarized to be perpendicular to the optical table. To increase the 532-nm-generation efficiency, a lens pair AR-coated at 1064 nm, i.e., a plano-convex lens with 50-mm focal length and a plano-concave lens with 20-mm focal length was used to reduce the size of the fundamental beam. At the focus, an LBO crystal mounted in an oven was placed for 532-nm generation. The crystal has the interaction type of type I and the cut direction for non-critical phase matching (NCPM) at about 150°C. It has surfaces AR-coated at 1064 nm and 532 nm. It has a surface area of 5*5 mm² and length of 20 mm. The oven used for controlling the temperature of the LBO crystal has a precision of 0.1°C. The generated 532-nm beam and the residual 1064-nm beam were focused for 355-nm generation using a bi-convex lens of 50-mm focal length, which is AR-coated at 1064 nm and 532 nm.

 

Fig. 4 Setup for green and UV generation.

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For 355-nm generation, a type-II LBO crystal in which 532-nm light is extraordinary was used. The LBO crystal used in the 355-nm generation experiment has a surface area of 5*5 mm², a length of 20 mm, and cut direction of θ = 43° and ϕ = 90°. Therefore, the 532-nm beam has a walk-off angle of 9.3 mrad [14] and thus the walk-off deviation during the half length of the LBO crystal equals 93 μm. As a walk-off compensator we chose an alpha–barium borate crystal having moderate birefringence and a high UV damage threshold. Since alpha–barium borate crystals has birefringence of n_o = 1.6776 and n_e = 1.5534 at 532 nm [15], the optimum length of the compensator which is made out of 45°-cut alpha–barium borate crystal was calculated to be 1.21 mm. The LBO crystal was mounted in an oven having precision of less than 0.1°C for phase matching. When measuring the generated 355-nm beam, two dichroic filters were used to filter out the 1064-nm and 532-nm beams. Although not contained in Fig. 4, dichroic filters to filter out the 1064 nm beam were used when measuring the 532-nm beam.

4. Experimental results and discussions

By moving the convex lens of a 532-nm generation lens pair, the beam size could be set to about 65 μm in w-radius. Then, we measured the power of the generated 532-nm beam as we changed the LBO-crystal temperature from 146.0°C to 154.4°C under a fundamental-beam power of 6.0 W and thus obtained the result shown in Fig. 5 .

 

Fig. 5 Power of 532-nm beam versus temperature of 532-nm-generation crystal.

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From Fig. 5, it can be seen that the maximum power of the second harmonic was 3.11 W, resulting in a conversion efficiency of 52%. The crystal temperature at which the maximum occurred and the FWHM temperature bandwidth were 150.7°C and 1.4°C, respectively, which are in agreement to previously-presented values [14].

When the focusing lens with 50-mm focal length was placed 100 mm away from the center of 532-nm-generation LBO crystal, a new focal point was made near a position that was about 100 mm away from the lens. At the point, the w-radius of the 1064-nm beam was measured to be about 65 μm. We placed the LBO crystal for 355-nm generation at the focal point and then observed the 355-nm generation. First, we measured the power of the generated 355-nm beam as we varied the temperature of the 355-nm generation crystal while keeping that of the 532-nm-generation LBO crystal at 150.7°C, which was the temperature for maximum second harmonic generation. The maximum occurred at 42.7°C. Next, we repeated the same procedure varying the temperature of the 532-nm generation crystal while keeping that of the 355-nm generation LBO crystal at the 42.7°C; thus we obtained the results shown in Fig. 6 . Figure 5 and Fig. 6 show that efficiency of 355-nm conversion can be lower when 532-nm conversion is too high. Maximum 355-nm conversion occurred not at 150.7°C where maximum 532-nm-conversion showing 52% efficiency occurred, but at temperatures displaced about 0.35°C from the temperature. From Fig. 5, it can be seen that at the temperatures displaced 0.35°C from the center the 532-nm conversion efficiency was 39-45%.

 

Fig. 6 Power of 355-nm beam versus temperature of 532-nm-generation crystal.

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Subsequently, we repeated the experiment varying the temperature of the 355-nm generation crystal while keeping that of the 532-nm generation LBO crystal at 151.1°C and thus obtained the filled-symbol curve results in Fig. 7 . Next, in order to confirm the effect of walk-off compensation, we performed the same experiment with the walk-off compensator removed in the setup; thus we obtained the empty-symbol curve results in Fig. 7. Figure 7 clearly shows the effect of the walk-off compensator. It can be seen that the maximum power of the 355-nm beam was enhanced from 0.63 W to 1.20 W, i.e., 1.9 times just by using a single walk-off compensator. The experimental value of power enhancement is somewhat different from the theoretically-predicted one of 2.75 times. This demonstrates a 31% error in our theoretical prediction. The difference between the two values is attributed to the approximations assumed in theoretical description, i.e., wide-beam and low-conversion approximation.

 

Fig. 7 Power of 355-nm beam versus temperature of 355-nm-generation crystal.

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5. Conclusion

We theoretically described in detail how the output power in sum-frequency generation can be raised by using a walk-off compensator; thus we obtained a brief expression for the output power that has a prediction error of about 30%. Through an experiment of sum-frequency generation of a 1064-nm and a 532-nm beam into a 355-nm beam using a type II LBO crystal, we experimentally demonstrated that UV output power can be significantly increased using a single birefringent walk-off compensator. We saw that the generated 355-nm beam power was enhanced 1.9 times by using a walk-off compensator made out of alpha-barium-borate crystal. In addition, we found through theoretical analysis that the beam quality as well as the output beam power can be enhanced using this method. Although the beam-quality enhancement was not experimentally demonstrated in our experiment due to the fact that the IR laser used as the fundamental source lacked the necessary quality, we can say that the beam-quality enhancement will be shown in the case using high-beam-quality IR lasers like fiber lasers as the fundamental source.

We expect that this method will be useful in the development of high-power and high-beam-quality UV lasers, especially in the serious walk-off case of narrow beams and long crystal.