Fig. 1a depicts a schematic diagram of the experimental system which consists of three elliptical waveguides with the center one being lossy. Similar non-Hermitian architectures have been studied before, based on microwave platforms¹⁶ and integrated photonic platforms^29,30 with the adoption of classical light. In this work, femtosecond laser direct writing techniques^34-36 were employed to fabricate the device in boroaluminosilicate glasses, and the measurement results showed both classical light and single photons. The technique in this work allows the fabrication of three-dimensional waveguide arrays and the proposed idea may inspire the design of three-dimensional on-chip non-Hermitian devices. In the system, the straight waveguide S exhibits a loss of ∼40 dB/cm, which is achieved by re-exposing the waveguide at equally-spaced points (see Methods). This technique can create an array of scatterers that induces significant scattering/transmission losses for photons propagating in waveguide S. The loss of a single scatterer is highly tunable since it strongly depends on the exposure time and laser power (Fig. 1c). In the defined “EP encircling region” (with length L = 14 mm), the two gap distances g₁ and g₂ are designed to be varying (also see Fig. 1b for top view) so that an EP is dynamically encircled. The two end facets of waveguide 1 are referred to as port 1 and 1′ and so forth for waveguide 2.

Electromagnetic waves propagating in the paraxial waveguides system is governed by a Schrodinger-like equation $H\left(z\right)=\left(\begin{array}{ccc}0& {\kappa }_1\left(z\right)& 0\\ {\kappa }_1\left(z\right)& i\gamma & {\kappa }_2\left(z\right)\\ 0& {\kappa }_2\left(z\right)& \delta \end{array}\right),$, and the 3 × 3 non-Hermitian Hamiltonian is expressed as follows:

Where, κ₁ and κ₂ are coupling coefficients that can be determined from g₁ and g₂ (inset of Fig. 2a), γ = 6 × 10⁻⁵k₀ denotes the loss of waveguide S with k₀ being the vacuum wave number, and δ is a detuning parameter (see Supplementary materials, Sec. I for details on fitting the Hamiltonian). The eigenvalues of the Hamiltonian are the change of the waveguide propagation constant introduced to that of an individual lossless waveguide. We labeled eigenmodes polarized along the y-axis as vertical-polarized modes (V-modes) and studied their EPs at wavelength of 810 nm in a g ‒ α ‒ δ 3D parameter space, where we have introduced g = (g₁ + g₂)/2 and α = (g₁ ‒ g₂)/(g₁ + g₂). Fig. 2a plots the positions of all the EPs (of second-order) which form two types of exceptional lines (ELs). The dashed EL is located on the δ = 0 plane and satisfies ${\kappa }_1^2+{\kappa }_2^2={\gamma }^2/4$. The solid ELs located at ${\kappa }_1={\kappa }_2=\sqrt{\left|\delta \right|\gamma /2}$ appear in the region δ ≠ 0 and their existence is a consequence of the passive anti-PT symmetry of the system. Detailed derivations and discussions were left on the origin of the ELs as well as the effective Hamiltonian of the system which is passive anti-PT-symmetric (i.e., anti-PT-symmetric but the diagonal term is shifted by a constant) to Supplementary materials, Sec. II, and here we only focus on the EP (see the yellow star) in a g‒α 2D parameter space with a fixed value δ = 9 × 10⁻⁶k₀ (see the grey surface).

Fig. 2b and c plot the real part and imaginary part of the eigenvalues E_H of the Hamiltonian in the g‒α parameter space, respectively. An EP (marked by the star) can be found as the coalescence of the red sheet and the blue sheet. This EP links the symmetric phase and broken phase (marked by white dashed lines), which can be defined by the symmetry of the eigenfunctions. The inset of Fig. 2c shows the eigenfunctions at g = 10 µm and α = 0 (calculated using COMSOL³⁷, also see Fig. S1). The broken eigenmode symmetry confirms that this point is in the broken phase. Considering that the real/imaginary parts of the eigenvalues bifurcate/coalesce there, it can be safely stated that our system is passive anti-PT-symmetric.

A loop is created to encircle the EP, with the above point in the broken phase as the starting/end point (see the loop in Fig. 2a). The loop formula is given in Methods section. Following which the sample in Fig. 1a was fabricated. A wave incident through port 1 or 2 and exit through port 1′ or 2′ follows a counter-clockwise loop, while the wave excited through port 1′ or 2′ leads to a clockwise-loop process. The Hamiltonian equation (see Fig. S2 for details) was solved with these four ports being excited respectively, and the state evolution trajectories were summarized on the energy sheets in Fig. 2d-g. It should be emphasized that the process in Fig. 2f is more complicated than that of the other three, since the initial state will encounter a nearly degenerate region (which is marked by the yellow dashed line in Fig. 2b) which is resulted from the exceptional line on the δ = 0 plane in Fig. 2a. When crossing this region, the power is almost equally redistributed into two eigenstates, so that the evolution trajectory was plotted on both the red and grey sheets there (also see Fig. S2 for a more detailed explanation). Fortunately, these complicated evolution details will not affect the mode conversion results, since it was found that the output state for counter-clockwise loops is always the mode localized in waveguide 2 (Fig. 2d and e), whereas clockwise loops result in a final state in waveguide 1 (Fig. 2f and g). This is the phenomenon of chiral mode switching, which has been realized in passive PT-symmetric systems for symmetric/antisymmetric modes, i.e., coupled modes localized in two waveguides^21,24. In contrast, our system enables the chiral transmission of on-chip fundamental modes that are bounded in only one waveguide owing to the topological structure of passive anti-PT-symmetric energy surfaces. The mechanism underlying the chiral phenomenon is that the eigenstates tend to stay on the lowest-loss energy sheet (i.e., the blue sheet), otherwise non-adiabatic transitions^19-21 (NATs) from higher-loss sheet to lower-loss sheet would occur (see the NAT in Fig. 2e and f).

Experimental results were shown with the adoption of classical laser light at 810 nm (MDL-III, CNI). Fig. 3a-d show the output images (measured by XG500, XWJG) of the V-modes with excitations at different ports. When port 1 or port 2 is excited corresponding to a counter-clockwise loop to encircle the EP, the output power in waveguide 2 is always significantly larger than that in waveguide 1 (Fig. 3a and b). If only taking waveguide 2 into consideration, the output power in Fig. 3a (∼2.78 mW) is much higher than that in Fig. 3b (∼0.39 mW). This is ascribed to the fact that the process that is adiabatic (i.e., port 1 in, port 2′ out, also see Fig. 2d) would exhibit a lower loss than that with a NAT (i.e., port 2 in, port 2′ out, also see Fig. 2e). In order to further demonstrate this point, the top-view light diffraction patterns in the device for the above two cases were depicted in Fig. 3e and f (photographed by Zyla 5.5 s CMOS, Andor). Since light in waveguide S can be strongly diffracted by the array of scatterers and then captured by our camera, these “noises” were lowered when plotting Fig. 3e and f in order to make the patterns in waveguide 1 and 2 more clear. Fig. 3e shows an adiabatic transfer of light from waveguide 1 to waveguide 2, whereas Fig. 3f depicts a process with a NAT and light also exits the device via port 2′ but with a much lower intensity. The clockwise route can be investigated in the same way, as shown in Fig. 3c and d, where the output mode is mainly localized in waveguide 1. These measurements clearly demonstrate the chiral mode switching dynamics, and the NAT indicated by the power difference is another evidence of such dynamics.

Investigations on the bandwidth of the chiral phenomenon was performed with the adoption of a tunable laser (ranging from 730 to 860 nm, Tsunami, Spectra-Physics). The S parameters S_m,n of the system was measured, which is defined as the transmission from port n to port m, where, m, n = 1, 2, 1′, or 2′. Fig. 3g and h plot the ratio of S parameters (see the inset for definitions) for counter-clockwise loops and clockwise loops, respectively. It is found that, in the grey region (∼790 to 820 nm), S_2′,1 and S_2′,2 are the predominant S parameters for counter-clockwise loops, while S_1,1′ and S_1,2′ dominate the output for clockwise loops. These results indicate the EP-encirclement induced chiral mode switching. All the above measurements were performed for the V-modes, and the S parameters were also measured for horizontal-polarized modes (H-modes that are polarized along the x-axis). The corresponding results are given in Fig. 3i and j, in which the chiral mode switching behavior can also be found but in a different wavelength range (∼740 to 780 nm). Such difference should be attributed to dispersion of the eigenmodes as well as the birefringence of the fabricated waveguides. Full results of the S parameters are given in Figs. S4 and S5.

Experiments in the single-photon regime were conducted to show that the above chiral transmission phenomenon also applies to single photons. In the quantum regime, the eigenstates supported in the system are richer than those in the classical system. More specifically, at the starting/end point of the encircling loop, the waveguides system supports classical-like states including $|1_1{0}_{\mathrm{S}}{0}_2〉$ and $|0_1{1}_{\mathrm{S}}{0}_2〉$, where the subscript and the number indicate the waveguide and the photon number within, respectively. Moreover, the quantum system also supports superposition states that have no classical counterparts such as $\left(|1_1{0}_{\mathrm{S}}{0}_2〉+e^{i\phi }|0_1{0}_{\mathrm{S}}{1}_2〉\right)/\sqrt{2}$, where, φ depicts a phase. These quantum states are often used on photonic chips for various applications. Therefore, it is necessary to verify whether these single-photon states can be employed for the chiral transmission by dynamically encircling the EP.

The experimental setup is depicted in Fig. 4a, where pairs of indistinguishable photons at 810 nm were generated by a BBO crystal. One photon was launched into one port of the fabricated sample and the other photon propagated in an optical fibre. Two avalanche photodetectors at the output side of the system were employed to measure their photon coincidences (see Methods), which can demonstrate the evolution dynamics of single photons in the device.

The dynamics of the states $|1_1{0}_{\mathrm{S}}{0}_2〉$ and $|0_1{0}_{\mathrm{S}}{1}_2〉$ were firstly tested, and single photons could enter and exit the sample via port 1, 2, 1′, or 2′. The measured photon coincidences at different output ports as a function of the input port are summarized in Fig. 4b and c for the V-modes. Fig. 4b shows that, for counter-clockwise loops, the photon coincidence measured at port 2′ is considerably larger than that at port 1′, no matter via which port the single photon was launched. The situation is just opposite for clockwise loops in Fig. 4c, where port 1 always shows the largest photon coincidence. In addition, for either counter-clockwise loops or clockwise loops, the photon coincidence of the adiabatic case (i.e., input from port 1 or port 2′) is also higher than that of the case with NATs (i.e., input from port 2 or port 1′).

Subsequently, the superposition states were tested by adding a 1:1 directional coupler (with port A and B) before the sample chip, and superposition states $\left(|1_1{0}_{\mathrm{S}}{0}_2〉+e^{i\phi }|0_1{0}_{\mathrm{S}}{1}_2〉\right)/\sqrt{2}$ can be generated at the input side of the sample. Here, φ denotes a phase difference which is equal to π/2 by choosing a proper length of the directional coupler in the experiment, but its value does not affect the measurement results since the device exhibits a chiral transmission feature. The measured photon coincidences are given in Fig. 4d and e for counter-clockwise loops and clockwise loops, respectively, where the chiral phenomenon is also observed. Therefore, by the dynamical encirclement of a second-order EP in the proposed passive anti-PT-symmetric system, the on-chip chiral transport of single photons has been realized, as single photons will most probably exit the device via waveguide 2 for left-to-right transmissions while via waveguide 1 for right-to-left transmissions. This chiral strategy would be useful for on-chip quantum applications that involve the path-encoding or polarization-encoding of single photons^38,39. For comparison, test on the dynamics of the H-modes was also conducted and the corresponding results were shown in Fig. 4f-i, where the chiral dynamics does not occur at 810 nm.

The waveguides were fabricated inside boroaluminosilicate glasses (Corning EAGLE 2000, n = 1.504) and the refractive index contrast between the waveguide and the background is ∼0.0025. To fabricate the sample, we focused a Ti:sapphire laser (Light Conversion Carbide 5W, repetition rate of 1 MHz, pulse energy of 200 nJ and pulse duration of 290 fs) 170 µm below the glass surface with the adoption of a ×40 microscope (NA = 0.75). An Aerotech system was employed to control the motion of the glass in order to write the waveguides. The waveguide exhibits a size of ∼6.85 µm × 5.23 µm under a writing speed of 40 mm/s. The transmission loss in waveguides 1 and 2 is ∼0.3 dB/cm, which is significantly lower than that in waveguide S.

The loss in waveguide S was introduced with the adoption of a re-exposure technique. To be specific, a normal waveguide S was firstly fabricatedand then equally-spaced points in waveguide S were re-exposed to introduce scatterers. The exposure time is 10 ms with the laser power of 140 mW and the distance between adjacent points is ∼10 µm. Under these conditions, the scattering loss induced by each scatterer was measured to be ∼0.04 dB, which is corresponding to a transmission loss in waveguide S of 40 dB/cm.

As depicted in Fig. 4a, a continuous-wave pump laser at 405 nm was used as the source. A half wave plate (HWP) and a polarization beam splitter (PBS) were employed to manipulate the polarization and intensity of the beam. After going through a Beta Barium Borate (BBO) crystal, indistinguishable pairs of photons at 810 nm were generated. Subsequently, an HWP and a quarter wave plate (QWP) were employed to control the polarization of each single photon. One single photon was injected into a single-mode fiber (SMF) and finally collected by an avalanche photodetector (APD). The other single photon was injected into the sample (the input port can be port 1, port 2, port 1′, or port 2′) and another APD was used at the corresponding output port to collect the single photon. Finally, coincidence measurement was performed based on the data collected by the two APDs. In the measurement of Fig. 4d, e, h, i, a directional coupled (DC) was added before the device in order to generate the superposition states. The DC with a splitting ratio of 1 : 1 consists of double waveguides on a chip, while the device in the current work was fabricated on another chip. The two chips were aligned but there still exist coupling losses. As a result, the measured photon coincidences in Fig. 4d, e, h, i are much lower than those in Fig. 4b, c, f, g.

The loop in the g-α parameter space takes the form: $g_1\left(z\right)=\cos \left(2\pi z/L+\pi /4\right)\sqrt{32{\cos }^2\left(2\pi z/L\right)+25{\sin }^2\left(2\pi z/L\right)}+6$ and $g_2\left(z\right)=\sin \left(2\pi z/L+\pi /4\right)\sqrt{32{\cos }^2\left(2\pi z/L\right)+25{\sin }^2\left(2\pi z/L\right)}+6$, where, the unit is µm. Then by defining g = (g₁+g₂)/2 and α = (g₁‒g₂)/(g₁+g₂), the system in the g-α parameter space can be studied.