New Physics: Sae Mulli, DOI: 10.3938/NPSM.65.1234 Vol. 65, No. 12, December 2015, pp. 1234∼1240 Optimizations of the Thickness and the Operating Temperature of LiB3O5, BaB2O4, and KTiOPO4 Crystals for Second Harmonic Generation Doo Jae Park Department of Physics, Hallym University, Chuncheon 24252, Korea Hong Chu Laseroptek Co. LTD, Sungnam 13212, Korea Won Bae Cho BioMed Research Section, Electronics and Telecommunications Research Institute (ETRI), Daejeon 34129, Korea Soo Bong Choi∗ Department of Physics, Incheon National University, Incheon 22012, Korea (Received 5 August 2015 : revised 27 August 2015 : accepted 27 August 2015) We demonstrate a theoretical study for determining the optimal crystal thickness and operating temperature when generating a second harmonic of a pulse laser with pulsewidths ranging from a few tens of femtosecond to a few nanosecond by using commonly-used nonlinear crystals of lithium barium borate, beta barium borate, and potassium titanyl phosphate. The optimal thicknesses of those crystals to avoid any pump pulse depletion for a fundamental-mode laser pulse having a high intensity and a long pulsewidth was calculated as a function of the intensity and the pulsewidth of the fundamental mode. Also, for short-pulse operation, thickness limits are calculated for conditions under which no pulse dispersion due to group velocity mismatch is observed. Finally, the fluctuation of second-harmonic yield due to temperature variations which introduce a refractive-index change is calculated, and the effective temperature ranges are demonstrated for room-temperature operation. PACS numbers: 42.65.Ky, 42.65.Re, 42.79.Nv Keywords: Harmonic generation, Ultrafast process, Optical frequency converter I. INTRODUCTION cal alignments. Considering that wavelengths of fre- quently used pulse lasers such as Ti:Sapphire laser and A virtue of pulse laser is its high peak intensity which q-switched Nd:YAG laser are centered at near-infrared is sufficient to introduce various nonlinear optical ef- region, SHG provides a handy method to push those to fect such as second harmonic generation (SHG), sum- visible frequency region, for application in biomedical frequency generation, difference frequency generation, imaging, curing, and therapy. electro-optic effect and etc. Specifically, SHG enables In those biomedical applications, supply of optimal us to double the frequency of fundamental pulse laser condition for highly efficient and stable generation of simply introducing a second-harmonic generating non- SHG in terms of choice of second-harmonic generating linear crystals as Lithium Barium Borate (LBO), beta- crystals and its thickness without disturbing pulseshape Barium Borate (BBO), and Potassium Titanyl Phos- of generated second harmonic pulse is important. Ad- phate (KTP), without requiring any complicated opti- ditionally, because properties of those nonlinear crys- tals are highly affected by ambient conditions (especially ∗E-mail: [email protected] temperature), it is also critical to suggest an optimal This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Optimizations of the Thickness and the Operating Temperature of ··· – Doo Jae Park et al. 1235 Fig. 1. (Color online) Calculated normalized SHG effi- Fig. 2. (Color online) Optimal thickness as function of ciency as a function of thickness for LBO (black curve), incident pump energy with fixed wavelength of 1064 nm KTP (red curve), and BBO (blue curve). and fixed pulsewidth of 750 ps for LBO (black curve), KTP (red curve), and BBO (blue curve). operating temperature. Even though there is a lot of of crystal, incident fundamental wavelength λ, and in- experimental, theoretical studies are performed through cident intensity of fundamental Iω (0). Here, nonlinear more than half of a century [1–7], surprisingly a system- interaction thickness can be given as [1] atic study for giving optimal thickness of SHG crystal s 2 2 for high intensity operation and temperature condition 1 2ε0nω n2ωcλ LNL = , (1) was not given so far. In this report, we demonstrate a 4πdeff Iω(0) theoretical research to give a proper choice of SHG crys- with ε0 being vacuum permittivity. Because of funda- tals for high intensity operation for medical therapy and mental depletion, SHG efficiency becomes reduced while surgery, including the thickness. Also, a specification for fundamental pulse travels inside crystal, so that the total temperature controller which assures a stable emission conversion efficiency η2ω can be given as [1] of second harmonic when operating SHG apparatus in 2 L near room temperature is suggested. η2ω = tan h . (2) LNL By using this formula and utilizing those optical con- stants of LBO, BBO, and KTP from literature [3, 8], II. OPTIMAL THICKNESS DUE TO SHG efficiency can be plotted as a function of crystal PUMP LASER DEPLETION thickness as depicted in Fig. 1. In this plot, fundamen- tal (hereafter, pump) laser pulse was assumed to have In ideal case, while fundamental pulse is injected into 1064 nm center wavelength, 750 ps pulsewidth, and 300 SHG crystal, energy carried by pulse is either consumed mJ pulse energy with 5 mm beam diameter, which is a during second harmonic generation or dissipated by heat- typical value emitted from Nd:YAG q-switched laser. In ing or scattering, finally diminished inside crystal with a calculation, all crystals are assumed to have a cut for per- certain travel length, which is referred to as a nonlinear fect phase matching condition. As depicted in this plot, interaction thickness LNL. Consequently, of a nonlin- SHG efficiencies are saturated at thickness of about 3∼7 ear crystal L is thicker than LNL, some part of crystal mm for all crystals, which denotes that thicker crystals, never contributes in SHG. Hence, finding out the opti- i.e., >10 mm, is not needed to achieve maximal SHG. If mal thickness based on an exact determination of LNL we regards an optimal thickness Lopt as a thickness hav- is critical. It is well known that LNL is dependent on ing ∼90% conversion compared to maximum conversion nonlinear conversion efficiency deff , refractive index for when thickness is infinite, we can find that Lopt for LBO, fundamental (nω) and index for second harmonic (n2ω) BBO, and KTP is read as ∼2 mm, 4.5 mm, and 5.5 mm, 1236 New Physics: Sae Mulli, Vol. 65, No. 12, December 2015 Fig. 3. (Color online) Optimal thickness as function of pump puslewidth with fixed wavelength of 1064 nm and fixed pulse energy of 200 mJ for LBO (black curve), KTP (red curve), and BBO (blue curve). respectively. It is found that Lopt for LBO is remarkably smaller than other crystals, which originates from high nonlinear conversion efficiency of LBO, which suggests that LBO is the best candidates for high intensity SHG. Optimal thicknesses as a function of incident pump en- ergy is plotted in Fig. 2 with fixed wavelength of 1064 nm and pulsewidth of 750 ps. As expected, optimal thick- Fig. 4. (Color online) Bandwidth limit with no pulse ness was larger for smaller pump energy, and becomes broadening as a function of crystal thickness for various pump wavelength of 755 nm (black curve), 800 nm (red smaller while an increase of pump energy. However, in curve), and 1064 nm (blue curve) for (a) LBO crystal and our simulation energy region, optimal thickness was in a (b) BBO crystal. Upper dotted line denotes bandwidth corresponding to 100 fs and bottom dotted line denotes few mm range. Pulsewidth dependence was also moni- bandwidth corresponding to 10 fs pulsewidth. tored as plotted in Fig. 3. With increase of pulsewidth, optimal thicknesses are slowly grow, because of the peak second harmonic pulses generated at different site of intensity decrease. Here, pump wavelength and pulse crystal. This results in a decrease of total SHG intensity. energy was fixed as 1064 nm and 200 mJ, respectively. Additionally, such mismatch of refractive indices also in- troduce group velocity mismatch (GVM) between pump III. BANDWIDTH LIMIT WITHOUT pulse and second harmonic pulse, which introduces a de- INTRODUCING SECOND HARMONIC layed generation of second harmonic and finally cause a PULSE DISPERSION second harmonic pulse broadening. Hence, it is neces- sary to match refractive indices at the pump wavelength In wide bandwidth incidence (in other words, short and second harmonic wavelength, by using a birefrin- pulsewidth incidence), it is well known that a phase gence nature of crystal and corresponding cut of crystal. matching should be kept both to achieve maximal con- Even with this well-known phase matching techniques, version efficiency and minimal broadening of SHG pulse [1,3]. For almost every materials, refractive indices varies pulse dispersion still occurs in wide bandwidth opera- with wavelength, which introduces inequality of refrac- tion, because refractive index difference in spectral band tive index for pump and SHG. This introduces a phase of pump pulse and that in second harmonic pulse pre- mismatch between pump and SHG inside the crystal, fi- vents a perfect phase matching, resulting in introducing nally generates destructive interferences between those a second harmonic pulse dispersion. Hence, the only so- Optimizations of the Thickness and the Operating Temperature of ··· – Doo Jae Park et al. 1237 lution to avoid such dispersion is to use thinner crystals 50 µm, and 200 µm for 755 nm, 800 nm, and 1064 nm with sacrificing SHG intensity. pump wavelength, respectively for LBO, which suggests An amount of group velocity mismatch inside crystal quite a lot of SHG efficiency should be sacrificed to in phase-matched condition is given as follows: achieve short pulse SHG, regarding the optimal thick- c 1 ness for high-intensity operation obtained from previous GV M = (n(λ) − n(λ/2)).