Chip-based self-referencing using integrated lithium niobate waveguides (2020)

The measurement and stabilization of the carrier–envelope offset frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>f</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math> via self-referencing is paramount for optical frequency comb generation, which has revolutionized precision frequency metrology, spectroscopy, and optical clocks. Over the past decade, the development of chip-scale platforms has enabled compact integrated waveguides for supercontinuum generation. However, there is a critical need for an on-chip self-referencing system that is adaptive to different pump wavelengths, requires low pulse energy, and does not require complicated processing. Here, we demonstrate efficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>f</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math> stabilization of a modelocked laser with only 107 pJ of pulse energy via self-referencing in an integrated lithium niobate waveguide. We realize an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mtext>-</mml:mtext><mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>2</mml:mn><mml:mspace width="negativethinmathspace"/><mml:mi>f</mml:mi></mml:mrow></mml:math> interferometer through second-harmonic generation and subsequent supercontinuum generation in a single dispersion-engineered waveguide with a stabilization performance equivalent to a conventional off-chip module. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>f</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math> beatnote is measured over a pump wavelength range of 70 nm. We theoretically investigate our system using a single nonlinear envelope equation with contributions from both second- and third-order nonlinearities. Our modeling reveals rich ultrabroadband nonlinear dynamics and confirms that the initial second-harmonic generation followed by supercontinuum generation with the remaining pump is responsible for the generation of a strong <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>f</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math> signal as compared to a traditional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mtext>-</mml:mtext><mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>2</mml:mn><mml:mspace width="negativethinmathspace"/><mml:mi>f</mml:mi></mml:mrow></mml:math> interferometer. Our technology provides a highly simplified system that is robust, low in cost, and adaptable for precision metrology for use outside a research laboratory.