Nonlinear optics

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.



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 MIR region, we investigate the use of nonlinear optics for mid-infrared optical frequency comb (OFC) generation. Our work on mid-infrared OFC generation by synchronously pumped femtosecond OPOs is briefly described on the Frequency-comb spectroscopy page. Along with various difference-frequency generation approaches, the SP-OPOs are currently the workhorse techniques for MIR OFC spectroscopy in many laboratories, including ours. Because of the optical resonator, which is an essential part of all OPOs, these techniques are however rather complicated to implement, especially when full stabilization, traceable frequency and tunability of the comb offset are required. We have developed a mid-infrared comb generation approach that is free from optical resonators, is easy to implement and inherently provides us with an accurate and versatile control of the comb parameters, including the carrier-envelope offset frequency. This new approach is based on femtosecond optical parametric generation (OPG) seeded by a CW laser [5].

Mid-infrared OFC by CW-seeded optical parametric generation

The basic principle of mid-infrared comb generation by femtosecond (fs) optical parametric generation is shown below in Fig. 1. Femtosecond pulses from the fs pump laser are passed through a second-order nonlinear crystal. Once the threshold for OPG is reached, the pump pulses are converted into signal and idler pulses with high efficiency. In our case, the generated MIR wavelength (idler) is typically between 3 and 4 µm.

As a consequence of the law of energy conservation, the pulse repetition frequencies of the signal and idler combs are inherited from the pump comb. However, in the case of simple fs OPG, pulse-to-pulse coherence is lost, because the process starts from noise upon each pump pulse. This means that the carrier-envelope offset (CEO) frequency of the generated signal and idler combs randomly vary from pulse to pulse. In order to stabilize the offset frequency, we synchronize the OPG processes of subsequent pulses by seeding the signal comb with a narrow-linewidth CW laser. The seeding determines the frequency of one of the signal comb lines and thus controls the signal comb offset frequency (Fig. 1). Furthermore, we lock the CW-laser phase to a supercontinuum created from the pump comb, such that the CW laser faithfully follows the offset frequency fluctuations of the pump. This procedure stabilizes the idler comb offset frequency, since CEOidler = CEOpump – CEOsignal. The idler comb offset can therefore be accurately controlled by adjusting the phase-lock offset.

Fig. 1. Left: Simplified illustration of an experimental setup for MIR comb generation by CW-seeded femtosecond OPG. Right: The basic idea of the method shown in frequency domain.

The CW-seeded OPG method offers several benefits in MIR comb generation. First, a fully stabilized MIR can be generated from a near-infrared pump comb without stabilizing the pump CEO; only the pump repetition frequency needs to be stabilized. (This is a significant advantage because stabilization of the offset frequency is typically challenging, while the repetition frequency is easy to stabilize). Second, the CEO of the idler comb is inherently known with high accuracy without measuring it – the CEOidler is determined by the radiofrequency signal generator used for CW laser phase locking. This also allows us to accurately control CEOidler by simply adjusting the signal generator frequency. Finally, the output power of the generated MIR comb is high (several 100 mW) and exceptionally stable.

For more details, see

OFC generation by CW-pumped cascaded quadratic nonlinearities

While the femtosecond combs based on mode-locked lasers are excellent light sources for laboratory experiments, they are currently too bulky and expensive for field applications. This has motivated us to investigate the possibility of generating mid-infrared OFCs by simple continuous-wave (CW) laser pumping.

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 [6], 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 [6-11] 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.

Fig. 2. (a) Schematic of OFC generation by CW-pumped quadratic nonlinearities and (b) the basic principle of a cascaded quadratic nonlinear process leading to comb generation in such system.

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 [6-8]. 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 [7]. 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 [9].


[1] 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)

[2] 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)

[3] 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)

[4] V. Ulvila, M. Vainio, "Diode-laser-pumped continuous-wave optical parametric oscillator with a large mid-infrared tuning range," Opt. Commun. 439, 99 (2019)

[5] M. Roiz, K. Kumar, J. Karhu, M. Vainio, "Simple method for mid-infrared optical frequency comb generation with dynamic offset frequency tuning," APL Photonics 6, 026103 (2021)

[6] 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)

[7] 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)

[8] 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)

[9] 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)

[10] 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).

[11] V. Ulvila, M. Vainio, "Experimental study of the effect of phase mismatch on a CW-pumped cascaded quadratic nonlinear frequency comb," J. Phys. Photonics 2, 034006 (2020)