Journal of the Korean Physical Society, Vol. 56, No. 1, January 2010, pp. 325∼328 Optimization of the Input Fundamental Beam by Using a Spatial Filter Consisting of Two Apertures Bonghoon Kang∗ Department of Visual Optics, Far East University, Chungbuk Eumseong-gun 369-700 Gi-Tae Joo Materials Science and Technology Division, Korea Institute of Science and Technology, Seoul 136-791 Bum Ku Rhee Department of Physics, Sogang University, Seoul 121-742 (Received 17 August 2009) The primary importance of the power efficiency of second-harmonic generation (SHG) is deter- mined by using the spatial shape of the fundamental input beam, its confocal parameter. The improvement of the fundamental input beam by using a spatial filter consisting of two apertures. The beam quality factor M2 of the improved fundamental beam was about 2.3. PACS numbers: 42.62.-b, 42.79.Nv, 42.25.Bs Keywords: Second-harmonic generation (SHG), Spatial filter, Beam quality factor, Confocal parameter DOI: 10.3938/jkps.56.325 I. INTRODUCTION Beam shaping requires a specific input beam. In order for the shaping to create an undistorted flat top beam or Gaussian-like beam, the input beam must be Gaus- Second harmonic generation (SHG) is widely used in sian. If the input beam does not have the proper profile, nonlinear optical spectroscopy. The optimization of the then measurements will tell the user that adjustments power efficiency of SHG is of primary importance in a to the source beam must be made before attempting to number of applications, especially when continuous wave perform the laser beam shaping. Therefore, a beam pro- (cw) beams with relatively low peak power are frequency file analysis becomes an essential part of effective beam doubled. If the input light field is a Gaussian beam, shaping. Also, the significance of the beam profile is that the dynamics of SHG is determined by the power of the the energy density, the concentration, and the collima- input beam, the spatial shape of the input beam, its tion of the light are all affected by it [6, 7]. The aim confocal parameter, the Poynting vector walk-off length, of this work is to investigate, for a given thin crystal (; the phase matching condition, and so on [1,2]. periodically poled LiNbO3 crystal), the optimum beam The existence of an optimum for the beam waist is the conditions for maximum second harmonic power. result of the best compromise between the beam focal- ization, which tends to increase the efficiency, and the diffractive spread, which tends to reduce the efficiency. In some previous paper, a Bessel beam could generate the II. EXPERIMENTS second harmonic more efficiently than Gaussian beams because they propagate without any modification of the The experimental setup for a non-critical phase- transverse intensity profile and, in this respect, they are matched SHG is shown in Fig. 1. At a fundamental ‘non-diffracting’ [3–5] . wavelength of 1064 nm, the period of the grating (2 times Beam shaping is a process whereby the irradiance of the coherence length) for SHG in LiNbO3 (periodically- the laser beam is changed along its cross section. In order poled lithium niobate, PPLN) is about 6.5 µm [8] . If for beam shaping to be effective, it is necessary to be able the largest nonlinear optical coefficient d33 of LiNbO3 is to measure the degree to which the irradiance pattern or used the polarization direction of the fundamental beam beam profile has been modified by the shaping medium. must be parallel to the z-axis. The thin film polarizer (a) and the polarizer (c) in Fig. 1 were used for a non- ∗E-mail: [email protected] critical phase matching. The half-wave plate (b) adjusts -325- -326- Journal of the Korean Physical Society, Vol. 56, No. 1, January 2010 Table 1. Spatial filtering condition.(The fundamental beam power at the front of pinhole#1 is 4 W.) Pinhole#1 Pinhole#2 dsf Power diameter diameter 2mm 0.7W 3mm 3mm 1.5W 50cm 4mm 2.8W 2mm 0.6W 2mm 3mm 1.5W 4mm 2.5W 2mm 0.3W 3mm 3mm 0.8W 4mm 1.1W Fig. 1. (color online) Experimental setup for a non-critical 100cm phase-matched SHG: (a) thin film polarizer, (b) half-wave 2mm 0.2W plate, (c) polarizer, (d) 1064-nm R, and (e) 532-nm T. 2mm 3mm 0.7W 4mm 1.2W pinhole#1 is 4 W. The beam quality factor M2 of the improved fundamental beam after spatial filtering was about 2.3. The PPLN crystal was located in the middle of a ± 0.1 ◦C controlled mini furnace. III. RESULTS AND DISCUSSION Figure 3 shows the beam profile behind the focal point to 2.0 cm. In case of (a), a 150 µm focused beam was made by using a 10 cm-focal-length lens (L1). However, in order to obtain the same beam width in case (b), a 12.5 Fig. 2. (color online) Profile of the fundamental beam. cm-focal-length lens (L1) was used. As is well-known, 2 the relation between the beam width and the lens can The beam width, w0, is 3.0 mm (M ∼ 3). be represented by λf πnw2 w = , 2z = f (1) the power of the fundamental beam. Figure 2 shows the f πw 0 λ profile of the fundamental beam. The relation of beam 0 2 quality factor M to the beam diameter-divergence prod- where wf is the beam width of the beam focused by lens 2 uct DΘ is defined by M = DΘ/(4λ/π), where D is the L1, w0 is the beam width of the fundamental beam, f beam diameter and Θ is the full beam angle. The beam is the focal length of lens L1, λ is the wavelength of the 2 quality factor M in our experiment was about 3. fundamental beam, n is the refractive index, and 2z0 is In order to propagate through 0.5-mm-thick PPLN the confocal length. with a 10- or 20-mm crystal length, a tight beam is nec- The beam divergence behind lens L1 with the funda- essary, and the beam quality of the beam focused by mental beam through the spatial filter consisting of two the lens L1 is related to the beam quality of the input apertures is smaller than the fundamental beam of the fundamental beam. To obtain an improved fundamen- normal setup. Generally, the wavefront of a laser beam tal input beam, we performed spatial filtering by using through an aperture is described by diffraction and is two apertures (below setup in Fig. 1). We measured the known as an Airy disk. The energy distribution of this beam quality factors for the conditions shown in Table diffraction shows a central spot in which 84% of the total 1. In our experiments, the optimized conditions of the energy through the aperture is contained [9, 10]. fundamental beam were 50 cm (dsf ): the distance be- In case of the SHG, the factors of efficient second- tween pinhole#1 and pinhole#2), 3 mm (the diameter harmonic power were the power of the input beam, the of pinhole#2), and 4 mm (the diameter of pinhole #2). spatial shape of the input beam, its confocal parameter, The measured power in Table 1 is the power behind pin- the Poynting vector walk-off length, the phase-matching hole#2. The fundamental beam power at the front of condition and so on. The primary importance of the Optimization of the Input Fundamental Beam··· – Bonghoon Kang et al. -327- Fig. 4. Beam profile behind the focal point to 2.0 cm: (a) the focal length of L1 is 10 cm and (b) the focal length of L1 is 12.5 cm. In all cases, the beam width of the focused Fig. 3. (color online) Beam profile behind the focal point fundamental beam was 150 µm to 2.0 cm: (a) the focal length of L1 is 10 cm and (b) the focal length of L1 is 12.5 cm. In all cases, the beam width of the focused fundamental beam was 150µm IV. CONCLUSION power efficiency of SHG is the quality of the fundamental The beam divergence of the fundamental beam input beam with a low beam divergence. through a spatial filter consisting of two apertures is We performed a non-critical phase-matched SHG with smaller than that of the fundamental beam in a normal the improved fundamental beam. Figure 4 shows the setup. The beam quality factor, M2, of the improved SHG intensity as a function of temperature. The phase- fundamental beam was about 2.3. The primary impor- matching temperature of 10-mm / 20-mm-long PPLN tance of the power efficiency of SHG is the quality of the was measured to be around 193.7 ◦C The full widths fundamental input beam with a low beam divergence. at half maximum (FWHMs) of the SH curve were 1.7 In comparison with theoretical prediction, the measured ◦C(10-mm-long PPLN) and 0.8 ◦C (20-mm-long PPLN). power reached about 73%. With a focused beam width of 150µm the SH powers before and after the spatial filtering at a pump power of 1 W were 0.5 mW and 0.8 mW in 10-mm-long PPLN ACKNOWLEDGMENTS and 1.1 mW and 2.2 mW in 20-mm-long PPLN, respec- tively. The pump power was measured behind lens L1. The second-harmonic power P2ω for a focused beam of This work was supported by a Korea Research Foun- waist spot size w0 and second-harmonic intensity I2ω was dation(KRF) grant funded by the Korean Government 1 2 calculated by using P2ω = 2 I2ωπw0).