• Infrared and Laser Engineering
  • Vol. 49, Issue 6, 20190423 (2020)
Kong Hui1、2, Bian Jintian1、2、*, Ye Qing1、2, Yao Jiyong3, Wu Chang1、2, and Sun Xiaoquan1、2
Author Affiliations
  • 1[in Chinese]
  • 2[in Chinese]
  • 3[in Chinese]
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    DOI: 10.3788/irla20190423 Cite this Article
    Kong Hui, Bian Jintian, Ye Qing, Yao Jiyong, Wu Chang, Sun Xiaoquan. Comparison of mid-infrared laser generated by optical parametric oscillation of BaGa4Se7 and KTiAsO4[J]. Infrared and Laser Engineering, 2020, 49(6): 20190423 Copy Citation Text show less

    Abstract

    Both BaGa4Se7 (BGSe) and KTiAsO4 (KTA) can generate mid-infrared lasers pumped by 1.06 μm laser. Firstly, the phase matching curves of two kinds of non-linear crystals were simulated and calculated. The results show that BGSe with cutting angles of (56.3°, 0°) and KTA with cutting angle of (90°, 0°) can generate idle frequency light of ~3.5 micron under phase matching conditions of type I and type II-A, respectively. Then through theoretical calculation, the effective non-linear coefficients of BGSe (56.3°, 0°, type-I) is ?11.9 pm/V, and that of KTA (90°, 0°, type II-A) is ?3.2 pm/V. The OPO oscillation threshold of 15 mm long BGSe (56.3°, 0°, type-I) is 35.11% of that of 20 mm long KTA (90°, 0°, type II-A). Then, the experimental results show that the oscillation threshold of BGSe-OPO (56.3°, 0°, type-I, 15 mm) is smaller than that of KTA-OPO (90°, 0°, type-II-A, 20 mm). The output energy of BGSe (56.3°, 0°, type-I) is larger than that of KTA (90°, 0°, type II-A). Therefore, BGSe is a promising mid-infrared non-linear crystal.
    $ \left\{\begin{aligned} & {{{n}}}_{{{x}}}^{2}=6.724\;31+\frac{0.263\;75}{{{{\lambda}}}^{2}-0.042\;48}+\frac{602.97}{{{{\lambda}}}^{2}-749.87}\\ & {{{n}}}_{{{y}}}^{2}=6.866\;03+\frac{0.268\;16}{{{{\lambda}}}^{2}-0.042\;59}+\frac{682.97}{{{{\lambda}}}^{2}-781.78}\\ & {{{n}}}_{{{z}}}^{2}=7.167\;09+\frac{0.326\;81}{{{{\lambda}}}^{2}-0.069\;73}+\frac{731.86}{{{{\lambda}}}^{2}-790.16}\\ & 0.901\leqslant \lambda \leqslant 10.591\end{aligned}\right. $(1)

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    $ {{{n}}}_{i}^{2}={{{A}}}_{i}+\frac{{{{B}}}_{i}{{{\lambda}}}^{{p}_{i}}}{{{{\lambda}}}^{{p}_{i}}-{{{C}}}_{i}}+\frac{{{{D}}}_{i}{{{\lambda}}}^{{q}_{i}}}{{{{\lambda}}}^{{q}_{i}}-{{{E}}}_{i}} $(2)

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    $ \left\{\begin{aligned} &{{{n}}}_{{{{e}}}_{1}}(\theta ,\phi )=\sqrt{2}{[{{d}}+{{A}}-{({{{b}}}^{2}-2{{b}}{{B}}+{{{A}}}^{2})}^{1/2}]}^{-\frac{1}{2}}\\ &{{{n}}}_{{{{e}}}_{2}}\left({{\theta}},\phi\right)=\sqrt{2}{[{{d}}+{{A}}+{({{{b}}}^{2}-2{{b}}{{B}}+{{{A}}}^{2})}^{1/2}]}^{-\frac{1}{2}}\\ & A={{{k}}}_{{{z}}}^{2} \cdot c-{{{k}}}_{{{x}}}^{2} \cdot a,B={{{k}}}_{{{z}}}^{2} \cdot c+{{{k}}}_{{{x}}}^{2} \cdot a\\ &a=\frac{1}{{{{n}}}_{{{x}}}^{2}}-\frac{1}{{{{n}}}_{{{y}}}^{2}},b=\frac{1}{{{{n}}}_{{{x}}}^{2}}-\frac{1}{{{{n}}}_{{{z}}}^{2}},c=\frac{1}{{{{n}}}_{{{y}}}^{2}}-\frac{1}{{{{n}}}_{{{z}}}^{2}},d=\frac{1}{{{{n}}}_{{{x}}}^{2}}+\frac{1}{{{{n}}}_{{{z}}}^{2}}\\ &{{{k}}}_{{{x}}}={{\sin\theta \cos}}\theta ,{{{k}}}_{{{y}}}={{\sin\theta \sin}}\theta ,{{{k}}}_{{{z}}}={{\cos\theta}} \end{aligned}\right. $(3)

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    $ \left\{\!\!\!\begin{array}{c}{\rm{type-I}}\\ \dfrac{{{{n}}}_{{{{e}}}_{2}}^{{{{\omega }}}_{3}}}{{{{\lambda}}}_{3}}=\dfrac{{{{n}}}_{{{{e}}}_{1}}^{{{{\omega }}}_{1}}}{{{{\lambda}}}_{1}}+\dfrac{{{{n}}}_{{{{e}}}_{1}}^{{{{\omega }}}_{2}}}{{{{\lambda}}}_{2}}\\ \dfrac{1}{{{{\lambda}}}_{3}}=\dfrac{1}{{{{\lambda}}}_{1}}+\dfrac{1}{{{{\lambda}}}_{2}}\end{array}\right.\left\{\!\!\!\begin{array}{c}{{{\rm type-II}-A}}\\ \dfrac{1}{{{{\lambda}}}_{3}}=\dfrac{1}{{{{\lambda}}}_{1}}+\dfrac{1}{{{{\lambda}}}_{2}}\\ \dfrac{{{{n}}}_{{{{e}}}_{2}}^{{{{\omega }}}_{3}}}{{{{\lambda}}}_{3}}=\dfrac{{{{n}}}_{{{{e}}}_{2}}^{{{{\omega }}}_{1}}}{{{{\lambda}}}_{1}}+\dfrac{{{{n}}}_{{{{e}}}_{1}}^{{{{\omega }}}_{2}}}{{{{\lambda}}}_{2}}\end{array}\right.\left\{\!\!\!\begin{array}{c}{{{\rm type-II}-B}}\\ \dfrac{1}{{{{\lambda}}}_{3}}=\dfrac{1}{{{{\lambda}}}_{1}}+\dfrac{1}{{{{\lambda}}}_{2}}\\ \dfrac{{{{n}}}_{{{{e}}}_{2}}^{{{{\omega }}}_{3}}}{{{{\lambda}}}_{3}}=\dfrac{{{{n}}}_{{{{e}}}_{1}}^{{{{\omega }}}_{1}}}{{{{\lambda}}}_{1}}+\dfrac{{{{n}}}_{{{{e}}}_{2}}^{{{{\omega }}}_{2}}}{{{{\lambda}}}_{2}}\end{array}\right. $(4)

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    $\begin{split} {{{d}}}_{\rm{eff}}=\; &\left[{{{b}}}_{1}\left({{{\omega }}}_{3}\right),{{{b}}}_{2}\left({{{\omega }}}_{3}\right),{{{b}}}_{3}\left({{{\omega }}}_{3}\right)\right]\times \\ & \left(\begin{array}{c}{{{d}}}_{11}\\ {{{d}}}_{21}\\ {{{d}}}_{31}\end{array}\begin{array}{c}{{{d}}}_{12}\\ {{{d}}}_{22}\\ {{{d}}}_{32}\end{array}\begin{array}{c}{{{d}}}_{13}\\ {{{d}}}_{23}\\ {{{d}}}_{33}\end{array}\begin{array}{c}{{{d}}}_{14}\\ {{{d}}}_{24}\\ {{{d}}}_{34}\end{array}\begin{array}{c}{{{d}}}_{15}\\ {{{d}}}_{25}\\ {{{d}}}_{35}\end{array}\begin{array}{c}{{{d}}}_{16}\\ {{{d}}}_{26}\\ {{{d}}}_{36}\end{array}\right)\times \\ & \left(\begin{array}{c}{{{a}}}_{1}\left({{{\omega }}}_{1}\right){{{a}}}_{1}\left({{{\omega }}}_{2}\right)\\ {{{a}}}_{2}{\left({{{\omega }}}_{1}\right){{a}}}_{2}\left({{{\omega }}}_{2}\right)\\ {{{a}}}_{3}{\left({{{\omega }}}_{1}\right){{a}}}_{3}\left({{{\omega }}}_{2}\right)\\ {{{a}}}_{2}\left({{{\omega }}}_{1}\right){{{a}}}_{3}\left({{{\omega }}}_{2}\right)+{{{a}}}_{3}\left({{{\omega }}}_{1}\right){{{a}}}_{2}\left({{{\omega }}}_{2}\right)\\ {{{a}}}_{1}{\left({{{\omega }}}_{1}\right){{a}}}_{3}\left({{{\omega }}}_{2}\right)+{{{a}}}_{3}\left({{{\omega }}}_{1}\right){{{a}}}_{1}\left({{{\omega }}}_{2}\right)\\ {{{a}}}_{1}\left({{{\omega }}}_{1}\right){{{a}}}_{2}\left({{{\omega }}}_{2}\right)+{{{a}}}_{2}\left({{{\omega }}}_{1}\right){{{a}}}_{1}\left({{{\omega }}}_{2}\right)\end{array}\right) \end{split} $ (5)

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    $\begin{split} & \left(\begin{array}{c}{b}_{1}\\ {b}_{2}\\ {b}_{3}\end{array}\right)=\left(\begin{array}{c}{b\_d}_{1}/{{{n}}}_{{{x}}}^{2}\\ {b\_d}_{2}/{{{n}}}_{{{y}}}^{2}\\ {b\_d}_{3}/{{{n}}}_{{{z}}}^{2}\end{array}\right)\dfrac{1}{\sqrt{{\left(\dfrac{{bd}_{1}}{{{{n}}}_{{{x}}}^{2}}\right)}^{2}+{\left(\dfrac{{bd}_{2}}{{{{n}}}_{{{y}}}^{2}}\right)}^{2}+{\left(\dfrac{{bd}_{3}}{{{{n}}}_{{{z}}}^{2}}\right)}^{2}}} , \\ & \left( {\begin{array}{*{20}{c}} {b\_{d_1}}\\ {b\_{d_2}}\\ {b\_{d_3}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} { - {{\cos\theta \cos}}\theta {{\sin\delta }} - {{\sin}}\theta {{\cos\delta }}}\\ { - {{\cos\theta \sin}}\theta {{\sin\delta }} + {{\cos}}\theta {{\cos\delta }}}\\ {{{\sin\theta \sin\delta }}} \end{array}} \right) \end{split} $ (6)

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    $\begin{split} & \left(\begin{array}{c}{{{a}}}_{1}\\ {{{a}}}_{2}\\ {{{a}}}_{3}\end{array}\right)=\left(\begin{array}{c}{{{a}}\_{{d}}}_{1}/{{{n}}}_{{{x}}}^{2}\\ {{{a}}\_{{d}}}_{2}/{{{n}}}_{{{y}}}^{2}\\ {{{a}}\_{{d}}}_{3}/{{{n}}}_{{{z}}}^{2}\end{array}\right)\dfrac{1}{\sqrt{{\left(\dfrac{{{{a}}{{d}}}_{1}}{{{{n}}}_{{{x}}}^{2}}\right)}^{2}+{\left(\dfrac{{{{a}}{{d}}}_{2}}{{{{n}}}_{{{y}}}^{2}}\right)}^{2}+{\left(\dfrac{{{{a}}{{d}}}_{3}}{{{{n}}}_{{{z}}}^{2}}\right)}^{2}}} , \\ & \left( {\begin{array}{*{20}{c}} {{{a}}\_{{{d}}_1}}\\ {{{a}}\_{{{d}}_2}}\\ {{{a}}\_{{{d}}_3}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {{\rm{cos\theta cos}}\theta {\rm{cos\delta }} - {\rm{sin}}\theta {\rm{sin\delta }}}\\ {{\rm{cos\theta sin}}\theta {\rm{cos\delta }} + {\rm{cos}}\theta {\rm{sin\delta }}}\\ {{\rm{ - sin\theta cos\delta }}} \end{array}} \right) \end{split} $ (7)

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    $ {{{d}}}_{{\rm{i}}{\rm{j}}}=\left(\begin{array}{c}0\\ 5.2\\ 1.2\end{array}\begin{array}{c}0\\ 24.3\\ -3.7\end{array}\begin{array}{c}0\\ -20.4\\ -2.2\end{array}\begin{array}{c}0\\ -3.7\\ -20.4\end{array}\begin{array}{c}1.2\\ 0\\ 0\end{array}\begin{array}{c}5.2\\ 0\\ 0\end{array}\right) $(8)

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    $\begin{split} {{{d}}}_{\rm eff}=\; &\left[{{{b}}}_{1}\left({{{\omega }}}_{3}\right),{{{b}}}_{2}\left({{{\omega }}}_{3}\right),{{{b}}}_{3}\left({{{\omega }}}_{3}\right)\right]\times \\ & \left(\begin{array}{c}{{{d}}}_{11}\\ {{{d}}}_{21}\\ {{{d}}}_{31}\end{array}\begin{array}{c}{{{d}}}_{12}\\ {{{d}}}_{22}\\ {{{d}}}_{32}\end{array}\begin{array}{c}{{{d}}}_{13}\\ {{{d}}}_{23}\\ {{{d}}}_{33}\end{array}\begin{array}{c}{{{d}}}_{14}\\ {{{d}}}_{24}\\ {{{d}}}_{34}\end{array}\begin{array}{c}{{{d}}}_{15}\\ {{{d}}}_{25}\\ {{{d}}}_{35}\end{array}\begin{array}{c}{{{d}}}_{16}\\ {{{d}}}_{26}\\ {{{d}}}_{36}\end{array}\right)\times \\ & \left(\begin{array}{c}{{{b}}}_{1}\left({{{\omega }}}_{1}\right){{{a}}}_{1}\left({{{\omega }}}_{2}\right)\\ {{{b}}}_{2}\left({{{\omega }}}_{1}\right){{{a}}}_{2}\left({{{\omega }}}_{2}\right)\\ {{{b}}}_{3}\left({{{\omega }}}_{1}\right){{{a}}}_{3}\left({{{\omega }}}_{2}\right)\\ {{{b}}}_{2}\left({{{\omega }}}_{1}\right){{{a}}}_{3}\left({{{\omega }}}_{2}\right)+{{{b}}}_{3}\left({{{\omega }}}_{1}\right){{{a}}}_{2}\left({{{\omega }}}_{2}\right)\\ {{{b}}}_{3}\left({{{\omega }}}_{1}\right){{{a}}}_{1}\left({{{\omega }}}_{2}\right)+{{{b}}}_{1}\left({{{\omega }}}_{1}\right){{{a}}}_{3}\left({{{\omega }}}_{2}\right)\\ {{{b}}}_{1}\left({{{\omega }}}_{1}\right){{{a}}}_{2}\left({{{\omega }}}_{2}\right)+{{{b}}}_{2}\left({{{\omega }}}_{1}\right){{{a}}}_{1}\left({{{\omega }}}_{2}\right)\end{array}\right) \end{split} $ (9)

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    $ {{{d}}_{{{ij}}}} = \left( {\begin{array}{*{20}{c}} 0&0&0\\ 0&0&0\\ {2.8}&{4.2}&{16.2} \end{array}{\rm{}}\begin{array}{*{20}{c}} 0&{2.3}&0\\ {3.2}&0&0\\ 0&0&0 \end{array}} \right) $ (10)

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    ${{{J}}_{{\rm{th}}}} = \frac{{2.25{{\tau }}}}{{{{\kappa }}{{{g}}_{{s}}}{{L}}_{{\rm{eff}}}^2}}{\left[ {\frac{{{L}}}{{2{{c\tau }}}}{\rm{ln}}33 + 2{{\alpha l}} + \ln \frac{1}{{\sqrt {{R}} }} + {\rm{ln}}2} \right]^2}$(11)

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    $ \begin{split} {{{J}}_{{\rm{th}}}} =\; & \frac{{2.25{{{n}}_{{s}}}{{{n}}_{{i}}}{{{n}}_{{p}}}{{{\varepsilon }}_0}{{{c}}^3}\left( {{{w}}_{{p}}^2 + {{w}}_{{s}}^2} \right)}}{{2{{{\omega }}_{{s}}}{{{\omega }}_{{i}}}{{d}}_{{\rm{eff}}}^2{{w}}_{{p}}^2{{L}}_{{\rm{eff}}}^2}}{{\tau [}}\frac{{{L}}}{{2{{c\tau }}}}{\rm{ln}}33+\\ & 2{{\alpha l}} + \ln \frac{1}{{\sqrt {{R}} }} + {\rm{ln}}2]^2=\\ & \frac{{2.25{{{\lambda }}_{{s}}}{{{\lambda }}_{{i}}}{{{n}}_{{s}}}{{{n}}_{{i}}}{{{n}}_{{p}}}{{{\varepsilon }}_0}{{c}}}}{{2{{\left( {2{{{\text{π}}}}} \right)}^2}{{d}}_{{\rm{eff}}}^2{{L}}_{{\rm{eff}}}^2}} \cdot \frac{{\left( {{{w}}_{{p}}^2 + {{w}}_{{s}}^2} \right)}}{{{{w}}_{{p}}^2}} \cdot\\ & {{\tau }}[\frac{{{L}}}{{2{{c\tau }}}}{\rm{ln}}33 + 2{{\alpha l}} + \frac{1}{{\sqrt {{R}} }} + {\rm{ln}}2{]^2} \end{split} $ (12)

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    $\begin{split} &{{{J}}_{{\rm{th}}}}{\rm{BGSe}} = 1.992\;8 \times {10^{11}} \cdot \frac{{\left( {{{w}}_{\rm{p}}^2 + {{w}}_{\rm{s}}^2} \right)}}{{{{w}}_{\rm{p}}^2}} \cdot \\ &{\left[ {\frac{{\rm{L}}}{{2{{c\tau }}}}{\rm{ln}}33 + 2{{\alpha l}} + \ln \frac{1}{{\sqrt {{R}} }} + {\rm{ln}}2} \right]^2}\left( {{\rm{W}}/{{\rm{m}}^2}} \right) \end{split} $ (13)

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    $\begin{split} {{{J}}_{{\rm{th}}}}{\rm{KTA}} =\;& 5.676\;4{\rm{}} \times {10^{11}} \cdot \frac{{\left( {{{w}}_{\rm{p}}^2 + {{w}}_{\rm{s}}^2} \right)}}{{{{w}}_{\rm{p}}^2}} \cdot \left[\frac{{\rm{L}}}{{2{\rm{c\tau }}}}{\rm{ln}}33 +\right. \\ &\left. 2{{\alpha l}} + \ln \frac{1}{{\sqrt {{R}} }} + {\rm{ln}}2\right]^2\left( {{\rm{W}}/{{\rm{m}}^2}} \right) \end{split} $ (14)

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    $ \frac{{{{{I}}_{{\rm{th}}}}\left( {{\rm{BGSe}}} \right)}}{{{{{I}}_{{\rm{th}}}}\left( {{\rm{KTA}}} \right)}} = 0.351\;1 $ (15)

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    Kong Hui, Bian Jintian, Ye Qing, Yao Jiyong, Wu Chang, Sun Xiaoquan. Comparison of mid-infrared laser generated by optical parametric oscillation of BaGa4Se7 and KTiAsO4[J]. Infrared and Laser Engineering, 2020, 49(6): 20190423
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