Optical interferometry

Wave interference is a common phenomenon that everybody has probably experienced in everyday life. For example, you might have noticed that two waves colliding in the sea can either build up in a bigger one or suddenly annihilate each other. These two opposite events correspond to constructive or destructive interference, respectively. You can witness such interference phenomena by throwing two stones in a lake and observing the surface ripples created where the waves produced by each stone cross each other. Interference can also be observed when sunlight is reflected by a soap bubble. In fact, its typical iridescent coloration is caused by the fact that some colors of the solar spectrum are enhanced while others cancelled due to constructive or destructive interference between the multiple reflections within the thin bubble film. From a more technological point of view, interference is employed in the active noise-cancelling of modern high-hand headphones. Here, the same drive delivering the music concurrently produces a replica of the surrounding noise sound waves and feeds it to your ear with a delay to effectively cancel the noise through destructive interference.

A paramount property required to observe either constructive or destructive interference is that the two overlapping waves possess the same ‘pitch’ – i.e. wavelength or frequency – and a well-defined phase relation. For this reason, some of the most advanced applications that make use of interference have been realized in the optical domain and exploit laser sources that feature a high degree of spatial and temporal coherence. Optical interference, first reported by Thomas Young at the beginning of the 19^th century, is nowadays employed in optical interferometers. Mach-Zehnder interferometers are used to realize light routing and switching in integrated photonics, while a Michelson interferometer is the main device operating at the LIGO-Virgo observatories, which allow to detect gravitational waves. The space deformation imparted by the arrival of these waves produces a unidirectional variation of space hence varying the relative paths – and hence the relative phase – of two light beams propagating in the two orthogonal arms of the interferometer. This is ultimately detected by monitoring an intensity change in the light beam produced by constructive/destructive interference, with a sensitivity to variations in the length in the two arms of less than one ten-thousandth the diameter of a proton.

A nonlinear twist to optical interferometry

While the impact of optical interference on both technology development and society is therefore indisputable, the field of nonlinear optics – established shortly after the invention of the laser in the early 1960s – is still craving impact. We believe that the results of this paper [1], which merges the basic concept of interference with nonlinear optics at the nanoscale, open a yet unexplored path of nonlinear optics. The main innovation here is the implementation of optical interference between two coherent and wavelength-degenerate beams originating from two simultaneously-generated nonlinear optical processes having different parities – specifically third-harmonic generation (THG) and sum-frequency generation (SFG). While the first is a third-order four-photon-based process, where the output photon preserves the parity of the input photons, the latter is a second-order three-photon-based process, where the parity of the output photon strictly depend on the symmetry of the material that mediates the process. In our experimental realization a periodic nonlinear metasurfaces composed by subwavelength meta-atoms (an array of nanopillars) of aluminum gallium arsenide (AlGaAs) supports both the THG of an ultrafast light pulse (w) at telecom wavelengths (l = 1550 nm) as well as the SFG between the w pulse and its frequency-doubled replica at 2w. In this way, it is possible to attain marked constructive/destructive interference in well-designed directions (namely the ones corresponding to the main diffraction orders of the metasurface), thanks to the opposite parity and the frequency degeneracy at 3w of the two underlying processes (see Figure 1). In addition, by controlling the relative phase delay between the two pump pulses with a resolution n better than π⁄10 (equivalent to a time delay of about 150 attoseconds), we can switch between constructive or destructive interference in those specific directions, hence effectively realizing all-optical interferometric routing of the upconverted light among different metasurface diffraction orders with a modulation amplitude up to 90% (see Figure 1b).

The phase control over the process allows envisioning free-space all-optical signal routing at frequencies up to the THz, provided that the absolute conversion efficiency of the nonlinear processes is high enough. Interestingly, the proposed concept is also particularly appealing for sensing. Indeed, given that the two employed pump frequencies feature a different refractive index dispersion relation, the presence of an analyte can be effectively sensed via phase changes, which results in the steering of the upconverted light. In addition, the presence of multiple output ports offered by the different diffraction orders of the metasurface is ideal for differential measurements, which compensate for intensity fluctuations and enhance the platform sensitivity. Indeed, by collecting the intensities at two opposite diffraction orders with a balanced photodiode will thus de facto realize a homodyne amplification scheme for the SHG signal with effective rejection of common-mode laser noise, without the need to equalize the pump beam intensities. We stress that this approach is not limited to the nonlinear processes described here but it can be expanded to all processes with opposite parity. For example, by combining the linear scattering of the 2w pump with the second harmonic of the w one, hence exploiting the sole extremely large χ⁽²⁾ of AlGaAs. Moreover, the extreme phase sensitivity of the upconverted light in these platforms can also be thought for future LiDAR applications where compact telecom ultrafast laser sources are employed.