Detection and quantification of analytes such as proteins, nucleic acids, and small molecules in minute quantities provide important information for monitoring human health, food safety, and environmental pollution [1]. One of the most accurate and sensitive techniques to detect these chemicals is using the collective oscillations of free electrons coupled to photons, known as surface plasmon polaritons [2–4]. Surface plasmons shrink the light into the sub-wavelength scale, enabling the sensor to be sensitive to nanometric perturbations [5]. Traditionally, prism-based techniques such as the Kretschmann and Otto [6] configurations are used to implement surface-plasmon-based sensing, providing a highly sensitive platform for label-free monitoring of molecular kinetics such as antibody-antigen interactions [7,8]. However, these setups require free-space optics and are inevitably bulky [9]. Photonic integrated circuits (PICs) provide a versatile platform to transfer bulky free-space optical systems into compact centimeter-scale chips [10,11]. Surface-plasmon-based sensing has been integrated by fabricating metallic waveguides [12,13].

Together with these planar surface plasmon systems, metallic nanoparticles have been used extensively to boost the sensitivity of molecular sensors via the localized surface plasmon resonance (LSPR) effect [14–18]. In these systems, metallic nanoparticles such as gold act as nanoantennas with a resonant frequency that depends on factors such as the size, shape, and orientation of the plasmonic nanoparticle and the material properties of both the particle and the surrounding medium [14]. Localized sensing using plasmonic nanoantennas has been shown using dark-field microscopy [19] and nanoantennas coupled to PIC resonators [20–22]. However, while surface plasmon polaritons provide enhanced sensitivity due to light-field localization, they suffer from inherent loss, causing resonant broadening and decreased sensitivity [23] compared to dielectric sensors with small mode volumes [24,25]. To circumvent this shortcoming in plasmonic sensors, the idea of using non-trivial topological modes has emerged recently, showing exceptional points (EPs) in the double-layer plasmonic metasurface [26]. This modifies the topology of the system around EP and skews it, reducing the system’s dimensionality [26,27]. EP is defined as a singularity in a non-Hermitian system where two or more eigenmodes coalesce into a single degenerate mode in a complex space [28]. Around EP, the sensitivity is modified from a trivial linear response into a non-trivial square root response, leading to larger enhancements [26,29]. Interferometric measurements [26,30–32] enable the extraction of the eigenmodes regardless of the sharpness of the resonances, unlike sensing based on only intensity measurement that needs high-Q resonances [24,25]. It is worth noting that EPs have been used for many applications including sensing [26,30–33], asymmetric mode switching [34,35], light stopping [36], enhanced non-reciprocity [37,38], and parametric instability [39].

A systematic technique to implement EP is to use parity-time (PT) symmetric resonators, which has restricted the sensor to diffraction-limited scales [40]. However, a recently presented symmetry-breaking method [26] introduces a robust technique to achieve EP in plasmonic systems, which were challenging to implement due to the nanofabrication limits [41]. In the symmetry-breaking technique, the general Hamiltonian of the system is considered, and by shifting distinguished lossy resonating modes, a complex critical coupling is achieved [26]. We show in this article that it is possible to achieve comparable performance by changing the parameter space [see Fig. 1(b)]. We also demonstrate EP for single coupled resonator nanoantennas and a new platform to measure its response by efficiently coupling the nanoantenna to an integrated Mach–Zehnder interferometer (MZI) [42] capable of recording its amplitude and phase in real-time [see Fig. 1(a)]. While there are a few papers about integrated EP sensing [43–45], to our best knowledge, this is the first time showing a single nanoantenna integrated plasmonic EP CMOS-compatible design, with the potential for co-integration with micro/nanofluidics to monitor molecular kinetics in real-time by recording small refractive index perturbations through specific chemical interactions around the plasmonic nanoantenna [see Figs. 1(a), 1(c), and 1(d)].

To analyze the complex eigenmodes of the system, we consider two electromagnetically coupled resonators, 1 and 2, representing gold nanobars with lengths L0 and L0+ΔL, having complex resonances due to the intrinsic loss of plasmonic materials. The Hamiltonian of the system can be written as Eq. (1): H=(ω˜1κ˜κ˜ω˜2),(1)where ω˜1 and ω˜2 are complex resonant modes of resonators 1 and 2, and κ˜ is the complex coupling between them [46]. From the Hamiltonian of the system, eigenvalues, ω˜A and ω˜B [see Fig. 1(b)], can be extracted as Eq. (2): ω˜A,B=ω˜2+ω˜12±(ω˜2−ω˜12)2+κ˜2.(2)

The term under square root defines the state of the coupled system. At particular κ˜ value, this term equals zero, causing both complex eigenmodes to coalesce into a single degenerate mode, an EP. It should be noted that, for a general plasmonic system [Fig. 1(b)] the eigenvalues of the coupled system are complex-valued before and after EP. The corresponding κ˜ is the critical complex coupling, κ˜c, as written in Eq. (3): κ˜c=i(ω˜2−ω˜12)2.(3)

Equation (3) makes it clear that achieving an EP is possible if and only if resonators 1 and 2 are different, at least in real or imaginary parts. Parity-time symmetric systems simplify this process by imposing the constraint that both resonant frequencies are the same, while having balanced gain and loss [40,41]. However, in the general case of two different lossy resonators, this condition is not necessary, and the coupling should be controlled to reach the critical value. In a system with two complex resonators, two parameters are needed to achieve κ˜c [see Fig. 1(b)]. Original design parameters, described in the first realization of plasmonic EP [26], were lateral displacement between resonators along the electric dipole direction, ΔX, and lattice periodicity in the direction perpendicular to the electrical dipole of the antennas, Py. We present a new parameter space that is ΔX and the length difference between coupled resonators, ΔL, which opens the possibility of designing single meta-atom plasmonic EP.

Working at EP provides higher sensitivity to external perturbations due to the square root eigenvalue splitting behavior compared to the traditional linear splitting in the diabolic point (DP) systems where only the real parts of the eigen frequencies coalesce [26,28,29]. Without loss of generality, to show the square root behavior, a real perturbation can be virtually added to resonator 1 in the corresponding Hamiltonian of the system [Eq. (1)], resulting in the perturbed Hamiltonian, H′, as written in Eq. (4): H′=(ω˜1+εκ˜κ˜ω˜2).(4)

Considering ε≪1, the complex eigenfrequencies of the coupled system can be simplified as Eq. (5): ω˜A,B≅ω˜2+ω˜12+ε±(ω˜2−ω˜12)2+(ω˜2−ω˜1)ε+κ˜2.(5)

Then, the complex eigenvalue splitting, Δω˜, is defined as Eq. (6): Δω˜≅2(ω˜2−ω˜12)2+(ω˜2−ω˜1)ε+κ˜2.(6)

As the system works at EP, Eq. (6) can be simplified further by implementing the κ˜c definition from Eq. (3), resulting in Eq. (7): Δω˜∝κ˜cε.(7)

However, for a system working far from EP (κ˜≠κ˜c), Δω˜ turns into Eq. (8): Δω˜∝μ˜+κ˜cε≅μ˜(1+κ˜cε2μ˜),|μ˜|≫|κ˜cε|,(8)where μ˜ is equal to κ˜2−κ˜c22, showing that the splitting of the system far from EP behaves linearly in response to the applied perturbation, both in real and imaginary parts.

Therefore, perturbation analysis clearly shows that the complex splitting varies with the square root of applied perturbation such as variations of the surrounding medium refractive index and the stronger coupling between resonators makes the system more sensitive.

In an MZI, an input beam splits into two sensing and reference arms [see Fig. 1(a)] and then recombines, in order to measure the relative phase difference, Δϕ, applied on the sensing arm [42]. The proposed PIC design enables simultaneous measurements of the amplitude of the coupled nanobars [see Figs. 1(a) and 3(a)]. Subtracting the measured intensity at the reference port from the signal port gives the transmittance of the coupled nanobars system; however, the phase extraction requires more considerations. Starting with interfering the sensor and reference arms [phase port, see Fig. 3(aii)], the complex electric field at the phase port can be written as Eq. (9): EP=ESe−iϕS2+ERe−iϕR22,(9)where Ej and ϕj are the electric field amplitude and the phase of the propagating beam and j represents the signal, S, reference, R, and phase, P, ports. The measured intensity at the phase port can be described as Eq. (10): IP=IS+IR+2ISIRcos(Δϕ)4,(10)where Ij shows the measured intensity at port j, and Δϕ equals ϕS−ϕR. Hence, by rewriting Eq. (10), Δϕ can be expressed as Eq. (11): $$\begin{gathered} Δϕ=arccos(2γ′−η−12η), \\ η=ISIR,γ=IPIR,γ0=(IPIR)0,γ′=γγ0, \end{gathered}$$(11)where η and γ are the ratios of IS and IP to IR, and γ′ is the normalized γ with respect to its value for the chip without the coupled nanobars in the sensing arm to compensate for the different loss experienced by the phase port relative to the signal and the reference ports. Hence, using Eq. (11), the outputs of the designed PIC can be converted to the relative phase difference to monitor extremely small variations in Δϕ due to the very stable and less noisy phase signal [44,47].

The introduced parameter space [see Fig. 1(b)] enables reaching EP in single coupled resonators by relaxing the need for an array and periodicity manipulation. Our designed system consists of two optically coupled gold nanobars placed in proximity (e.g., 30 nm apart) with different lengths, providing two distinct resonating modes in an uncoupled system. In previously demonstrated plasmonic EP, light couples from free-space [26]; however, to achieve an integrated EP, we must couple the guided light to the resonating system. The most straightforward coupling method is to place the nanobars on top of the waveguide. However, the nanobars only interact with the evanescent tail of the guided mode leading to a negligible modulation of the waveguide transmission, both in amplitude and phase [48].

To solve this problem, we designed a new type of slot-waveguide, called junction-waveguide [see Fig. 1(a)], enabling direct coupling of the resonating system with the guided mode in the low-refractive-index region (e.g., 1.33 for water in this case [49]), leading to a more pronounced impact on the guided mode [see Fig. 2(a)].

The junction-waveguide is designed by cutting a ridge waveguide from the middle and tapering each end to focus the beam into a 200 nm gap, where coupled nanobars are located [see Fig. 1(a)]. The tapered ends of the junction-waveguide enable highly efficient beam propagation through a sub-wavelength gap and enhance the coupling efficiency with the inserted nanobars (parameters are given in Fig. 3 caption). The complex eigenvalues were analyzed in the parameter space (ΔX,ΔL) of the system, and the resonant frequencies and loss rates of modes A and B are plotted in Figs. 2(b) and 2(c). Note that we can only move towards EP, since reaching EP as a singularity is not possible. A crossing point representing the EP is clearly observed for ΔX=62nm and ΔL=26nm and is depicted by the star. To clearly show the system transition from resonant frequency crossing towards loss rate crossing, we present two cross-sections of the parameter sweep at ΔL=20nm and ΔL=30nm, before and after the EP [see Figs. 2(d), 2(e) and 2(g), 2(h)]. It is evident that modes A and B distributions switch after the crossing point in cases where the system encounters loss rate crossing, compared to the consistent mode shape for resonant frequency crossing situations [see Figs. 2(f) and 2(i)]. Therefore, using the newly defined parameter space, we demonstrated all features of free-space EP devices while enabling single coupled resonators system EP on an integrated platform.

Monitoring small eigenvalue splitting requires accurate simultaneous amplitude and phase measurements. To achieve the integrated monitoring of these quantities, we combine our single particle integrated EP system and the junction-waveguides with a four-port integrated MZI [see Fig. 3(a)]. The photonic integrated circuit (PIC) components include edge couplers to couple broadband beams (1000–1400 nm) in and out of the circuit, Y-splitters and combiners to separate the beam into the reference and sensing arms and recombine them for interference measurements, and junction-waveguides to efficiently couple the guided mode to the coupled nanobars system [see Figs. 3(a) and 3(b)]. Note that all the components have been inversely designed to achieve optimized performance.

To accurately extract the complex eigenvalues of the coupled gold nanobars system, we need to measure a spectrum in a band of about 400 nm. Therefore, even the best grating couplers with an ultra-broadband working spectrum (e.g., >70nm [52]) cannot be used in our circuit, leading us to use edge couplers instead, due to their higher efficiency in broadband light coupling [53]. The waveguide material is designed to be silicon nitride, Si3N4 (refractive index ∼2.0 [54]), to provide better coupling to the surrounding water (refractive index ∼1.33 [49]) than silicon, Si (refractive index ∼3.6 [55]).

The designed four-port integrated MZI outputs three intensities: the reference, the signal, and the phase, allowing for simultaneous amplitude and phase measurements of the material in the sensing arm junction [see Figs. 3(a) and 3(c), 3(d)]. By measuring the output intensities for PICs with and without the coupled nanobars [see Figs. 3(c) and 3(d)], we can precisely extract the transmittance and phase of the plasmonic system [see Figs. 3(e) and 3(f)]. Utilizing complex S-matrix fitting [50,51], the transmittance and phase values can be translated into the system eigenvalues. It should be noted that while transmittance measurements alone can provide sufficient data to extract eigenvalues, the highly sensitive phase measurements, due to their inherent background noise stability, enable the detection of very small deviations from the designed point.

The designed integrated EP biosensor is combined with a microchannel, covering the detection zone [see Figs. 1(c) and 1(d)], to sense biomarkers through specific attachment to the functionalized gold nanobars. Attracted particles locally vary the refractive index of the medium surrounding the nanobars, leading to complex eigenvalue splitting. To assess the sensing performance of the integrated EP, we studied the system response under different perturbation scenarios. First, the refractive index of the medium around the nanobars was varied uniformly to analyze the complex eigenvalue splitting under bulk and local refractive index changes (see Fig. 4). We compared both DP (where only resonant frequencies are crossing) and EP to show the superior performance of the latter.

Under bulk and local perturbations, we observed the expected square root behavior in both resonant frequency and loss rate splitting. However, the bulk perturbation, which includes a much larger perturbed volume, only enhanced the observed splitting by less than 20% compared to the local perturbation covering 10 nm around each nanobar. This is due to the strong localized surface plasmons around the corners of the nanobars. Moreover, the loss rate splitting shows a stronger response compared to resonant frequency splitting, highlighting the importance of phase sensing for more sensitively induced scattering measurements. In contrast to EP’s square root behavior, DP shows a linear response with smaller splitting even at high perturbation values, especially under local perturbation, revealing that the turnover point has been significantly shifted compared to the free-space EP metasurface [26]. Additionally, the loss rate splitting shows negative splitting with about five times less splitting compared to the EP design, emphasizing the superior performance of the integrated EP sensor. Note, in practice, the local refractive index perturbation may be accompanied by variations in the buffer solution refractive index value (bulk refractive index); however the observed combined effect on the sensitivity of the sensor is minimal under practical buffer solution content variations (see Fig. 6). The presented EP sensor with best refractive index sensitivity of about 536 nm/RIU outperforms state-of-the-art photonics sensors, VINPix and Slotted-VINPix, with sensitivities around 356 and 437 nm/RIU, respectively [24]. It should be noted that the integrated EP performance will depend on the quality of the fabrication as described in Appendix B.

The second and more realistic sensing scenario we investigated is based on randomly attached nanoparticles with an average diameter of 10 nm and 100 nm, representing proteins and exosomes, respectively. We analyzed the system’s response under 10 random distributions of particle attachments with a defined number of particles among both nanobars, and recorded the corresponding complex splitting, assuming uniform functionalization of the gold nanobars (see Fig. 5).

The induced complex splitting for both types of particles exhibits non-linear and fluctuating behavior, complicating the sensing process, as demonstrated by the comparison of resonant frequency and loss rate splitting [see Figs. 5(a)–5(d)]. However, our statistical analysis revealed that the standard deviations of the complex splitting can be used to cluster the number of attached particles [see Figs. 5(e) and 5(f)]. Specifically, for 10 nm particles, we can determine if more than seven particles are attached, as the standard deviation values show a noticeable increase. For 100 nm particles, this method is sensitive enough to detect a single attached particle, given the significant distinctions in the loss rate splitting standard deviation (at single attached particle level). Note that the standard deviation values for 100 nm attached particles are an order of magnitude greater than those for 10 nm particles, enabling precise single molecule detection [see Figs. 5(e) and 5(f)]. Therefore, we have developed a single molecule sensitive biosensor capable of not only detecting individual particles but also clustering the number of particles through statistical analysis of the measured splitting. Note, the single molecule sensing technique relies on the statistics of the complex splitting rather than the actual values; however, for a larger concentration of particles, the sensing strategy is similar to the explained method for the local refractive index variation analysis. A larger number of particles around gold nanobars can be estimated as a uniform medium with an effective refractive index corresponding to the concentration of particles [56]. Regarding the sensitivity to quantum noise, we note that we proposed a classical sensor, and the latter has been shown to be limited by manufacturing disorder [26]. Quantum noise analysis of EP sensors has been discussed in recent papers [57–60].

In this article, we presented a novel approach to achieve integrated EP for a general plasmonic system, requiring at least two distinct resonators, demonstrating a single particle EP for the first time. The designed EP system was inserted into the modified four-port integrated MZI by inventing a new type of slot-waveguide, called the junction-waveguide, to enhance the coupled nanobars’ interaction with the guided mode. We demonstrated on-chip amplitude and phase measurements of the EP system using the designed PIC, showing a systematic approach to monitor complex eigenvalue splitting under different types of perturbations. Through perturbation analysis, we demonstrated the superior performance of the integrated EP, showing a square root response compared to the linear behavior of the DP system. Our analysis revealed that the designed sensor has single molecule sensitivity for nanoparticles with an average size of 100 nm (e.g., exosomes) and is capable of distinguishing as few as eight nanoparticles with an average size of 10 nm (e.g., proteins) using sensing statistics analysis. The novel introduced integrated EP biosensor has great potential in revolutionizing point-of-care technologies by providing a compact single molecule sensitivity platform for early disease diagnosis.