Thermal lensing effects and nonlinear refractive indices of fluoride crystals induced by high-power ultrafast lasers
Liam Andrus, Adela Ben‐Yakar
Abstract
Thermo-optical and nonlinear property characterization of refractive optical components is essential for endoscopic instrumentation that utilizes high-power, high-repetition-rate ultrafast lasers. For example, ytterbium-doped fiber lasers are well suited for ultrafast laser microsurgery applications; however, the thermo-optical responses of many common lens substrates are not well understood at 1035 nm wavelength. Using a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>z</mml:mi> </mml:mrow> </mml:math> -scan technique, we first measured the nonlinear refractive indices of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">C</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">g</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">B</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> at 1035 nm and found values that match well with those from the literature at 1064 nm. To elucidate effects of thermal lensing, we performed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>z</mml:mi> </mml:mrow> </mml:math> -scans at multiple laser repetition rates and multiple average powers. The results showed negligible thermal effects up to an average power of 1 W and at 10 W material-specific thermal lensing significantly altered <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>z</mml:mi> </mml:mrow> </mml:math> -scan measurements. Using a 2D temperature model, we could determine the source of the observed thermal lensing effects. Linear absorption was determined as the main source of heating in these crystals. On the other hand, inclusion of nonlinear absorption as an additional heat source in the simulations showed that thermal lensing in borosilicate glass was strongly influenced by nonlinear absorption. This method can potentially provide a sensitive method to measure small nonlinear absorption coefficients of transparent optical materials. These results can guide design of miniaturized optical systems for ultrafast laser surgery and deep-tissue imaging probes.