Integrated induced-coherence spectroscopy in a single nonlinear waveguide

We present a generalized understanding of the induced-coherence (IC) effect, aiming to find new strategies for engineering and optimizing the IC response of nonlinear systems. We establish that sensing the cross density of states (CDOS) of the field lies at the core of IC and that it is the spatial profile of the nonlinearity that determines how this CDOS information is sampled. Based on our findings, we identify integrated nonlinear waveguides as a versatile and suitable platform for spectroscopy based on IC and show that our generalized treatment allows us to optimize the sensing performance. Our results open the way for the design of compact IC-based spectroscopic devices with customized responses.

Figure 1

(a) Sketch of induced coherence (IC) with two sequential photon-pair sources. (b) Schematic for the generalized description of IC based on Eq. (1). (c) Scheme for IC spectroscopy in a nonlinear waveguide. Pump, signal, and idler are denoted by p, s, and i, respectively. Different colors denote different materials, where striped regions indicate that several materials can be distributed inhomogeneously.

Figure 2

(a) Normalized signal spectral intensity $W_s\left({\omega }_s\right)$ from Eq. (11) for a single WG in the presence of an idler loss spectrally localized around ${\lambda }_i=2500$ nm as a function of different cw pump wavelengths. (b) Signal intensity with a cw pump at ${\lambda }_p=661.76$ nm for different idler loss magnitudes. (c) Signal intensity for a fixed idler wavelength ${\lambda }_i=2500$ nm. For each ${\lambda }_s$, ${\lambda }_p$ is varied to correspond to the fixed ${\lambda }_i$. (d) Comparison of single-WG IC spectroscopy (ICS) with linear absorption sensing or spectroscopy (LAS).

Figure 3

(a) Normalized signal intensity $W_s\left({\omega }_s\right)$ for a single WG with two phase-matched sections separated by a non-phase-matched one. (b) Signal intensity for a fixed idler wavelength of ${\lambda }_i^{*}=2500$ nm for the lossless and lossy idlers.

Figure 4

Sensitivity of IC spectroscopy using WG configurations with varying lengths of the linear section $L-2l$ and the nonlinear sections $2l$ in the presence of fixed idler loss ${\beta }_i^{″}=1{\text{mm}}^{-1}$. (a) The intensity sensitivity $S$ and (b) a cut through it for a constant total length $L=1.5\text{mm}$. (c) and (d) Similar data for the visibility sensitivity $Q$.

Figure 5

Waveguide design for investigating proposed induced-coherence spectroscopy. (a) Design for ridge waveguide in a $z$-cut ${\mathrm{LiNbO}}_3$ on an insulator sample. Considered (b) pump, (c) signal, and (d) idler fundamental quasi-TM modes of the waveguide.

Figure 6

Effective index $n_{\text{eff}}$ of the fundamental quasi-TM mode of the waveguide shown in Fig. 5 as a function of wavelength.

Figure 7

(a) Signal intensity fringes in the presence of pump and signal losses. These losses are taken as constant over the whole signal spectrum; that is, their dispersive nature is ignored here. Idler loss is taken to be ${\beta }_i^{″}L=2.0$ for all four cases shown. (b) Rescaled versions of the signal fringes shown in (a) reflect that the visibility of the fringes does not decrease substantially for moderate pump and signal losses.