Nonlinear optical frequency conversion is an important enabling technology for a variety of applications, especially laser spectroscopy. Molecular spectroscopy experiments typically require light in the UV/VIS or mid-infrared (MIR) regions of the electromagnetic spectrum, in order to probe strong electronic and rotational-vibrational transitions of molecules, respectively. Laser light with narrow linewidth and broad wavelength tunability - as required in high-resolution gas spectroscopy - is difficult to produce directly at these wavelength regions, but can be generated by nonlinear optics, which allows for the efficient conversion of near-infrared laser light to other wavelengths. These nonlinear processes are usually called parametric up- and down-conversion depending on whether the working wavelength decreases or increases, respectively.
- Invention of a new method for optical frequency comb generation, based on CW-pumped cascaded quadratic nonlinerities. Opt. Lett. 38, 4281 (2013), Opt. Express 22, 10535 (2014)
- Generation of fully stabilized mid-infrared frequency combs by synch-pumped femtosecond optical parametric oscillators. Opt. Express 25, 4190 (2017)
- Observation of CW-pumped cascaded quadratic comb generation in a lithium-niobate waveguide resonator. Phys. Rev. A 98, 053850 (2018)
One of the most common uses of nonlinear optics in spectroscopy is parametric down-conversion to the 3 to 5 µm molecular fingerprint region. High efficiency and broad wavelength coverage can be obtained by using an Optical Parametric Oscillator (OPO) for the down-conversion process. When pumped with a single-frequency continuous-wave (CW) laser, a narrow-linewidth OPO instrument for high-resolution molecular spectroscopy can be realized. We have developed several high-power mid-infrared CW OPO instruments with enhanced wavelength tuning characteristics and high stability [1-4].
In addition to single-frequency light generation in the mid-infrared region, we investigate the use of nonlinear optics for optical frequency comb (OFC) generation. Our work on mid-infrared OFC generation by synchronously pumped femtosecond OPOs is briefly descibed on the Frequency-comb spectroscopy page. While the femtosecond combs based on mode-locked lasers are excellent light sources for laboratory experiments, they are generally too bulky and expensive for field applications. This has motivated us to investigate the possibility of generating mid-infrared OFCs by simple continuous-wave laser pumping.
OFC generation by CW-pumped cascaded quadratic nonlinearities
Our approach for CW-pumped comb generation is based on cascaded quadratic nonlinearities (CQN). The basic idea of this method, which we discovered in 2013 , can be understood as follows: In the simpliest case, single-frequency CW light from the pump laser is coupled into an optical resonator, which contains a nonlinear crystal that is designed for second harmonic generation (SHG) of the pump light; see the figure below and references [5-9] for more details. If the second-harmonic power builds up sufficiently high, efficient back conversion to the pump spectral region takes place. This back-conversion process can be understood as a doubly-resonant OPO, which is pumped by the SH light and fills cavity modes adjacent to the initial pump frequency. As the cascaded process (SHG & sum-frequency generation (SFG) followed by back-conversion) continues, it transfers energy to a large number of cavity modes around the intial pump frequency. In favorable conditions, these several oscillating modes can be stabilized by mutual injection locking.
Another way of qualitatively understanding the CQN comb formation process is by analogy to Kerr comb generation: A CQN process essentially mimics cubic nonlinearity, which can lead to comb generation by four-wave mixing. An advantage of the CQN method is that the effective cubic nonlinearity arising from cascaded quadratic nonlinearity is often several orders of magnitude stronger than the inherent cubic nonlinearities of typical materials suitable for Kerr comb generation. Furthermore, the sign and magnitude of self phase modulation caused by CQN can be adjusted, which makes it possible to compensate for both normal and anomalous dispersion.
Our first proof-of-principle experiments on CQN frequency comb generation were carried out using bulk crystals in free-space optical resonators [5-7]. Instead of using the implementation schematically depicted above, we typically place the CQN crystal inside a CW OPO. This approach simplifies resonant pumping of the CQN process and enables direct mid-infrared comb generation with very high output powers of several watts . Our ongoing work in this field focuses on miniaturization and optimization of the CQN comb generator by using nonlinear optical waveguide resonators and whispering-gallery mode resonators .
 M. Vainio, J. Peltola, S. Persijn, F. J. M. Harren, and L. Halonen, "Singly resonant cw OPO with simple wavelength tuning," Opt. Express 16, 11141 (2008)
 M. Vainio, M. Siltanen, J. Peltola, and L. Halonen, "Grating-cavity continuous-wave optical parametric oscillators for high-resolution mid-infrared spectroscopy," Appl. Opt. 50, A1-A10 (2011)
 M. Siltanen, M. Vainio, and L. Halonen, "Pump-tunable continuous-wave singly resonant optical parametric oscillator from 2.5 to 4.4 µm," Opt. Express 18, 14087 (2010)
 V. Ulvila, M. Vainio, "Diode-laser-pumped continuous-wave optical parametric oscillator with a large mid-infrared tuning range," Opt. Commun. 439, 99 (2019)
 V. Ulvila, C. R. Phillips, L. Halonen, and M. Vainio, "Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities," Opt. Lett. 38, 4281 (2013)
 V. Ulvila, C. R. Phillips, L. Halonen, and M. Vainio, "High-power mid-infrared frequency comb from a continuous-wave-pumped bulk optical parametric oscillator," Opt. Express 22, 10535 (2014)
 V. Ulvila, C. R. Phillips, L. Halonen, and M. Vainio, "Spectral characterization of a frequency comb based on cascaded quadratic nonlinearities inside an optical parametric oscillator," Phys. Review A 92, 033816 (2015)
 M. Stefszky, V. Ulvila, Z. Abdallah, C. Silberhorn, M. Vainio, "Towards optical-frequency-comb generation in continuous-wave-pumped titanium-indiffused lithium-niobate waveguide resonators," Phys. Review A 98, 053850 (2018)
 M. Vainio, V. Ulvila, L. Halonen, "Infrared Laser Frequency Combs for Multispecies Gas Detection," in THz for CBRN and Explosives Detection and Diagnosis, 151-158 (2017), NATO Science for Peace and Security Series - B: Physics and Biophysics, Springer (Eds. Mauro F. Pereira and Oleksiy Shulika).