Self-organized nonlinear gratings for ultrafast nanophotonics


As devices utilizing femtosecond-duration laser pulses become more commonplace, there is a need for next-generation nonlinear-photonics technologies that enable low-energy femtosecond pulses to be converted from one wavelength to another with high efficiency. However, designing nonlinear materials to operate with femtosecond pulses is challenging, because it is necessary to match both the phase velocities and group velocities of the light. Here, we show that femtosecond laser pulses can generate self-organized nonlinear gratings in nanophotonic waveguides, thereby providing a nonlinear optical device with both quasi-phase-matching and group-velocity matching for second-harmonic generation. We use nonlinear microscopy to uniquely characterize the self-organized nonlinear gratings and demonstrate that these waveguides enable simultaneous χ(2) and χ(3) nonlinear processes for laser-frequency-comb stabilization. Finally, we derive the equations that govern self-organized grating formation for femtosecond pulses and uncover the crucial role of group-velocity matching. In the future, nanophotonics with self-organized gratings could enable scalable, reconfigurable nonlinear photonics.

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Fig. 1: SONG formation in nanophotonic waveguide.
Fig. 2: SHG in amorphous SiN waveguides using femtosecond pulses.
Fig. 3: Theoretical estimate of SHG with SiN waveguides.
Fig. 4: Frequency comb stabilization through one-step f–2f self-referencing.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


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The authors thank G. Moille, N. Sanford and the National Institute of Standards and Technology (NIST) Boulder Editorial Review Board for providing helpful feedback on this manuscript, and K. Dorney, J. Ellis, H. Kapteyn and M. Murnane for the timely loan of a polarizer. This work is supported by AFOSR under award no. FA9550-16-1-0016, DARPA (DODOS and ACES programmes), NIST and NRC. Nonlinear optical imaging instrumentation at CU-Boulder was supported by the National Science Foundation Grant DMR-1420736. Certain commercial equipment, instruments or materials are identified here in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by NIST, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

Author information




D.D.H. and D.R.C. conducted the SHG experiments. D.D.H., H.M. and I.I.S. conceived and conducted the microscopy experiment. K.S. and D.W. designed, fabricated and characterized the SiN waveguides. D.D.H., D.R.C., S.B.P., S.A.D. and A.K. analysed and interpreted the data. J.B.K. developed the theoretical models.

Corresponding authors

Correspondence to Daniel D. Hickstein or Scott B. Papp.

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Competing interests

D.D.H. is currently employed by KMLabs, Inc., a company that manufactures femtosecond lasers. D.R.C. is an owner of Octave Photonics, a company specializing in nonlinear nanophotonics.

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Hickstein, D.D., Carlson, D.R., Mundoor, H. et al. Self-organized nonlinear gratings for ultrafast nanophotonics. Nat. Photonics 13, 494–499 (2019).

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