Optimizations of the Thickness and the Operating Temperature of Lib3o5, Bab2o4, and Ktiopo4 Crystals for Second Harmonic Generation

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 crystals 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, fundamental (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 energy 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 introduce 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)). (3) λ 2 chapter. However, when pulsewidth exceeds 100 fs Applying this relation to broadband laser pulse, band- (<10 nm bandwidth), crystal thickness without pulse width limit for a crystal having thickness of L can be broadening is larger than 500 µm which becomes much given as follows: closer to the optimal thickness without pump depletion, which denotes that such pulse dispersion phenomena is 0.44λ/L δλFWHM = 1 , (4) not a major concern in long pulse, high intensity SHG. n(λ) − 2 n(λ/2) In case of BBO, crystal thicknesses for 10 fs operation with an assumptions of Fourier-limited pulse and Gaus- without pulsewidth broadening were obtained as shorter sian distribution of pulse spectrum [1]. Based on this, than LBO as ∼25 µm, ∼32 µm, and 150 µm for 755 bandwidth limit in various pump wavelengths for LBO nm, 800 nm, and 1064 nm operation. This comparison and BBO crystals are plotted in Fig. 4. In obtaining suggests that LBO is better choice for SHG for short refractive indices, a Sellmeier equation was utilized pulse operation, compared to BBO. for ordinary axis. A calculation for KTP was omitted because phase matching condition cannot be found for this crystal due to inappropriate index contrasts IV. TEMPERATURE DEPENDENT YIELD between ordinary axis and extraordinary axis in near-IR FLUCTUATION region. In figures, upper dotted line near 100 nm denotes Since GVM and corresponding phase matching condi- bandwidth of Fourier-limited pulse corresponding to 10 fs pulsewidth, and lower dotted line near 10 nm denotes tion critically determined by refractive indices of SHG 100 fs pulsewidth. As can be seen in figure, bandwidth crystals, a small changes of indices due to variation of limits for different wavelengths rapidly decrease with ambient condition such as vapor pressure and temper- increasing thickness of crystal, which denotes that pulse ature induces a considerable fluctuation of SHG yields. broadening is highly sensitive to the thickness of crystal. For example, index variation ∆n(x,y,z) for crystal axes Specifically, for short pulse operation reaching 10 fs, x, y, and z with temperature variation ∆T is expressed crystal thickness should be relatively small as 40 µm, as follows for LBO [5]:

−6 −3 2 ∆nx = (−3.76λ + 2.30) × 10 × (∆T + 29.13 × 10 (∆T ) ) (5) −6 −4 2 ∆ny = (6.01λ − 9.70) × 10 × (∆T − 32.89 × 10 (∆T ) ) (6) −6 −3 2 ∆nz = (1.50λ − 9.70) × 10 × (∆T − 74.49 × 10 (∆T ) ) (7)

When applying this relation, it is found that the refrac- Such variation of phase matching angle introduces a tive index for crystal axis x varies from ∼1.55 to ∼1.57 in wavevector mismatch between fundamental and second temperature range of 0 to 300 degree Celcius at a fixed harmonic, even a crystal having perfect phase matching wavelength of 1000 nm. This rather small changes of condition at fixed temperature. Traditionally to mini- refractive index introduces variation of phase matching mize the amount of such wavevector mismatch due to angle as amount of ∼0.5 degree, as depicted in Fig. 5. temperature fluctuation, phase matching cut of LBO 1238 New Physics: Sae Mulli, Vol. 65, No. 12, December 2015

Fig. 5. (Color online) Bandwidth limit with no pulse broadening as a function of crystal thickness for various pump wavelength of 755 nm (black curve), 800 nm (red curve), and 1064 nm (blue curve) for (a) LBO crystal and (b) BBO crystal. Upper dotted line denotes bandwidth corresponding to 100 fs and bottom dotted line denotes bandwidth corresponding to 10 fs pulsewidth. crystal is given at a certain temperature where refractive index variation is minimized. This temperature is found as 104. 5 ◦C, 141 ◦C, and 148 ◦C at wavelength of 1064 nm, 800 nm, and 755 nm, respectively, by finding local maximum of Eq. (5). Fig. 6(a) depicts wavevector Fig. 6. (Color online) (a) Wavevector mismatch as a function of temperature for those crystals optimized for mismatch of those optimally prepared crystals for differ- 1064 nm pump wavelength and 104 degree temperature ent operating wavelength as a function of temperature. (black curve), 800 nm pump wavelength and 141 degree temperature (red curve), 755 nm pump wavelength and As can be seen in this figure, the amount of wavevector 148 degree temperature (blue curve). (b) Wavevector −1 mismatch as a function of temperature for those crystals mismatch is ∼30 cm within the temperature span of optimized in 40 degree Celcius. ∼200 ◦C. However, those optimal temperature is relatively higher than room temperature, hence necessitates with fixed crystal thickness of 2 mm. As depicted in heating device for crystal which may introduce an in- Fig. 7(a), SHG yield almost vanishes when temperature crease of cost and complexity of SHG apparatus. To exclude such heating device, an operating temperature changes more than 100 degree from optimal temperature, −1 may be about 40 degree Celcius regarding natural heat- where wavevector mismatch is about 30 cm . However, ing of crystal due to pump laser irradiation. To answer a clear plateau are observed for every operation wave- such demand, same calculation was performed with as- length, which denotes that stable operation is available suming that the phase matching condition was met in 40 in those optimal temperature region. The span of tem- degree temperature and depicted in Fig. 6(b). Unlike to perature range ∆Topt allowing 5% yield fluctuation is the case depicted in Fig. 6(a), the amounts of wavevec- read as ∼60 degree Celcius at 1064 nm pump wavelength. tor mismatch are quite different between different oper- However, as depicted in Fig. 7(b), ∆Topt becomes much ating wavelength having ∼20 cm−1 to ∼40 cm−1, which narrower as ∼32 ◦C for 1064 nm and ∼10 ◦C for 755 nm implies SHG yield fluctuation should be larger at this and 800 nm pump wavelength in 40 degree operation temperature. temperature. This suggests that quite precise temper- SHG yields fluctuations due to such wavevector mis- ature controller is require for stable operation of SHG match were calculated and depicted in Fig. 7(a) and (b), device when trying to use in room temperature. Optimizations of the Thickness and the Operating Temperature of ··· – Doo Jae Park et al. 1239

Fig. 7. (Color online) (a) SHG yield fluctuation as a func- Fig. 8. (Color online) (a) Wavevector mismatch as a tion of temperature for those LBO crystals optimized for function of temperature for BBO crystals optimized in 40 1064 nm pump wavelength and 104 degree temperature degree Celcius. (b) SHG yield fluctuation as a function (black curve), 800 nm pump wavelength and 141 degree of temperature for BBO crystals optimized in 40 degree temperature (red curve), 755 nm pump wavelength and Celcius. 148 degree temperature (blue curve). (b) SHG yield fluctuation as a function of temperature for those LBO crystals optimized in 40 degree Celcius. for 1064 nm pump incident as expected, while halved ◦ for other wavelength i.e., ∆Topt ∼25 C. However, com- In case of BBO application, scenario becomes quite pare to the case of LBO application at 40 ◦C operation, different because of different response of refractive index ∆Topt is larger for all operating wavelength, which sug- to temperature variation [2]. In BBO, refractive index gests that BBO is better choice for stable operation than change as a function of temperature variation is given LBO in room temperature operation. as a linear function in the temperature range from -10 to 300 degree, hence no optimal temperature region is available. Consequently, wavevector mismatch is also lin- V. CONCLUSION early dependent to the temperature for every observed operating wavelength, as can be seen Fig. 8(a). The In conclusion, we have demonstrated a series of cal- only difference is its slope, which is smallest for 1064 culation to supply optimal choice of crystal and optimal nm wavelength. This implies that the stable operation condition in second harmonic generation. We found that may possible for 1064 nm pump wavelength. Fig. 8(b) optimal thickness which is given from pump depletion is depicts SHG yield as a function of temperature when order of few millimeter, and most efficient crystal was phase matching condition is fixed as 40 degree operation. found as LBO. Also, we found that the maximum thick- ◦ Here, it is clearly seen that ∆Topt is largest having 50 C ness of SHG crystals without introducing dispersion was 1240 New Physics: Sae Mulli, Vol. 65, No. 12, December 2015 order of few tens of microns in 10 fs operation condi- REFERENCES tion, however, this thickness becomes acceptably larger having few millimeter when pulsewidth becomes larger [1] R. L. Sutherland, Handbook of Nonlinear Optics than 100 fs. Finally, for stable frequency doubled-pulse (Marcel Dekker, Inc., 2003). generation free from temperature fluctuation BBO which [2] D. Eimerl, L. Davis, S. Velsko, E. K. Graham and A. has relatively big ∆Topt can be the best choice in room Zalkin, J. Appl. Phys. 62, 1968 (1987). temperature operation. We believe our study helps in [3] R. W. Boyd, Nonlinear Optics (Academic Press, optimizing SHG devices for various applications. 1992). [4] S. P. Velsko, M. Webb, L. Davis and C. Huang, IEEE J. Quantum Electron. 27, 2182 (1991). ACKNOWLEDGEMENTS [5] K. Kato, IEEE J. Quantum Electron. 30, 2950 (1994). This research is supported by the Industrial Strategic [6] K. Kato and E. Takaoka, Appl. Opt. 41, 5040 (2002). technology development program (No. 10048690) funded [7] D. N. Nikogosyan, Appl. Phys. A 58, 181 (1994). By the Ministry of Trade, industry & Energy (MI, Ko- [8] R. Eckardt, H. Masuda, Y. X. Fan and R. L. Byer, rea). IEEE J. Quantum Electron. 26, 922 (1990).