We consider a microring cavity resonator schematically shown in Fig. 1(a). The cavity is based on an InGaAsP gain material system that can be applied to the C-band of the optical communication.43 Note that the microring cavity can support whispering gallery mode (WGM) that carries significant OAM. However, due to the mirror symmetry of the cavity, counterclockwise and clockwise eigen-WGMs circulating inside the cavity coexist in pairs, enabling their carried OAMs to cancel each other.27 To achieve the OAM of an individual WGM, it is essential to employ an efficient selection mechanism of either counterclockwise or clockwise modes. Conventional bulk optics showed that the unidirectional ring laser was achieved by placing a nonreciprocal isolator in the light path.44 The isolator can break the reciprocity between counterpropagating lights, which attains the unidirectional energy flow. Nevertheless, this technique is not applicable at the micro and nanoscale since it is a formidable challenge to realize the microscale isolators.26

The recent development of PT symmetry has provided another promising approach for obtaining the unidirectional power circulation by modulating gain and loss to form an exceptional point (EP) at which multiple eigenstates coalesce into one.45,46 Therefore, herein we employ the EP to achieve the OAM laser emission. The microring resonator is made by depositing 50 nm thick GST225 and 600 nm thick InGaAsP dual-layers onto an InP substrate. The refractive index of InGaAsP and InP are 3.42 and 3.17, respectively.26 The grating with a complex refractive index is designed with alternate bilayer Cr/Ge and single-layer Ge patches placed above GST225 along the azimuthal direction (\(\theta\)) periodically, corresponding to modulations of gain/loss (\({n}^{{\prime }{\prime }}\)) and the real part index (\({n}^{{\prime }}\)) in the cavity, respectively:

$$n=\left\{ {\begin{array}{*{20}{c}} {{n_0}+in^{\prime\prime}} \\ {{n_0}+n^{\prime}} \end{array}} \right.\begin{array}{*{20}{c}} {{\text{2}}\pi b/m<\theta <2\pi \left( {b+1/4} \right)/m} \\ {{\text{ 2}}\pi (b+3/8)/m<\theta <2\pi \left( {b+5/8} \right)/m} \end{array}$$

1

where \({n}_{0}\) is the unperturbed part of the refractive index (effective index of GST225/InGaAsP stacked layers), \(m\) the azimuthal number of the targeted WGM, \(b\) integer number from {0, \(m-\) 1}. Assuming a slight change of index variation and insignificant scattering loss in the PT microring resonator, we express the coupled mode equations for the desired WGM order by,26

$$\left( {\begin{array}{*{20}{c}} {\frac{{dA}}{{Rd\theta }}} \\ {\frac{{dB}}{{Rd\theta }}} \end{array}} \right)=\left( {\begin{array}{*{20}{c}} {i{k_0}}&{i(n^{\prime}+n^{\prime\prime})\kappa } \\ {i(n^{\prime} - n^{\prime\prime})\kappa }&{i{k_0}} \end{array}} \right)\left( {\begin{array}{*{20}{c}} A \\ B \end{array}} \right)$$

2

where \(A={A}_{0}{e}^{ikR\theta }\) and \(B={B}_{0}{e}^{ikR\theta }\) represent the clockwise and counter-clockwise propagating harmonic waves, \(R\) the microring resonator radius, \({k}_{0}\) the wavenumber of the modes in the unmodulated ring resonator, and \(\kappa\) the coupling between the clockwise and counterclockwise modes. By solving the coupled mode equations originating from the modulations of the complex index and gain/loss presented in Eq. 1, we derive the WGM complex wavenumber,

$$k={k_0} \pm \kappa \sqrt {{{n^{\prime}}^2} - {{n^{\prime\prime}}^2}}$$

3

the coupling between the two modes disappears at\({n}^{{\prime }}={n}^{{\prime }{\prime }}\). As a result, the EP occurs: two counter-propagating WGMs coalesce and accidentally degenerate. A unidirectional laser robustly emits, explained by semiconductor rate equations in the supplementary information. As a result, the counterclockwise WGM unidirectionally circulates in the cavity carrying large OAM through the azimuthally continuous phase evolution.28 The OAM relating to the unidirectional power oscillation is extracted upward into free space by implanting grating along the microring perimeter. It was shown that a WGM only emitted into a free-space beam by satisfying the angular phase-matching condition,26

where \(m\) is the azimuthal order of the targeted WGM and \(w\) is the number of sidewall equidistant scatters around the microring resonator. The negative integer \(m\) corresponds to the opposite propagating direction of the WGM. The \({\eta }_{rad}\) phase shift per unit azimuthal angle, or azimuthal propagation constant of the emitted light, provides the azimuthal component of the wave vector carrying OAM. The propagation constant of the radiation mode along the z-direction is given by

$${k}_{rad, z}=\sqrt{{(2\pi /\lambda )}^{2}-{\left({\eta }_{rad}R\right)}^{2}}$$

5

where \(\lambda\) is the free-space wavelength. The radiated light is a vortex beam with a topological charge \(p=m-w\). The topological charge in scalar vortex is associated with the OAM of vector vortex. The amount of OAM carried by the emitted light is \(p\text{\hslash }\), where \(\text{\hslash }=h/2\pi\) and \(h\) is Plank’s constant. The protrudent grating can only couple the WGM into free-space vortex beam mode with a certain OAM index \(p\), since the extra vortex beam without satisfying Eq. 1 cannot couple into free space. Thus, we have an extremely simple yet efficient single-mode OAM emitter strategy, where \(p\) takes an integer number determined by the variation between integers \(m\) and \(w\). Eq. 1 shows that the angular grating diffracts the light confined in an \(mth\)order WGM (carrying an OAM of \(m\text{\hslash }\) per photon16) into a free-space light, varying the OAM by an amount of \(w\text{\hslash }\) per photon in the process. Once the microring cavity is fabricated, the \(w\) is fixed, however, the \(m\) can be varied by exciting the selected WGM. Thus, the OAM can be changed by tuning the cavity resonance by changing the refractive index of the cavity, offering a tunable vortex lasing. Inspired by this concept, we propose a tunable OAM emission from a PT symmetry microring cavity, where the frequency of OAM (cavity resonant frequency) is modulated by switching the GST225 state between amorphous and crystalline.

The real, \({n}_{G}\) (solid lines) and imaginary, \({k}_{G}\) (dashed lines) parts of the complex refractive index, \({N}_{G}={n}_{G}+i\times {k}_{G}\) of a 50 nm thick planar GST225 layer for the amorphous (red lines) and crystalline (blue lines) phases are presented in Fig. 1(b). The \({N}_{G}\) was measured by variable angle spectroscopic ellipsometry (VASE). The measured data were fitted by a Tauc-Lorentz model. The sharp change in \({N}_{G}\) produces the tunable microring cavity resonances. The refractive index changes of GST225 originate from a bonding change from predominantly covalent in the amorphous phase to resonant bonds in the face-centered cubic crystalline phase.41 This unique optical property is realistic, known and mainly applied to data storage devices. Noteworthy, the reversible phase change in GST225 is exceedingly repeatable and a billion cycles were experimentally illustrated in data storage devices.47,48 The GST225 alloys have thus recently been applied to the field of tunable nanophotonics.35–38

The cavity is normally illuminated by using a plane-wave source. The OAM microlaser unidirectional power stream forced at the modulation of EP offers stable and efficient single-mode lasing with good sideband suppression. The peak resonance corresponds to an OAM lasing mode, it can be calculated using the following equation,

$${\lambda _{\text{m}}}=\frac{{2\pi {n_e}R}}{m}$$

6

where \(m\) is the azimuthal order of the targeted WGM, \(R\) is the radius of the microring cavity, \({n}_{e}\) is the equivalent refractive index of the microcavity. Here, the \({n}_{e}\) changes with the phase change of GST225 from 2.25 to 2.28. Based on Eq. 6, the resonant peak shifts to the longer wavelength (from 1544.5 nm to 1565.9 nm) owing to the phase change of GST225 between amorphous and crystalline. The quality (\(Q\)) factor of the microring cavity maintains a large value of ~ 37500. This enables the cavity to be a promising candidate for a tunable single mode OAM laser operation.

Note that the index modulation achieved by the paired bilayer Cr/Ge and single-layer Ge gratings engineers the cavity to EP; moreover, the protrudent scatters cannot change the EP due to its fixed number \(w=\)17. Therefore, we can vary the operating frequency by changing the GST225 state while maintaining the ring cavity at EP. Figure 2(a−c) present the simulations of the vortex laser radiation at the resonant wavelength of \(\lambda =\)1544.5 nm for the amorphous phase. The refractive index modulation leads to the EP, at which two counter-propagating WGMs coalesce to a counterclockwise WGM (\(m=\)16) circulating inside the cavity (Fig. 2(a)). Note that, the center of the WGM mass moves outwards due to the finite curve of the microring (centrifugal force), and the WGM is sensitive to the modulations introduced along the microring boundary. Thus, we place the scatters along the outer edge of the ring in order to efficiently extract the OAM lasing. The scatters protrude from the outer perimeter by \(\varDelta R=\)60 nm, and the scatter angular width is \({{\delta }}_{\theta }=\)0.03 in radian. They equidistantly locate around the outer edge of the cavity. The WGM (\(m=\)16) can couple with a vertically radiating vortex beam with specific OAM (\(p=\)1) by the scatters, and the OAM lasing mode radiates vortex beam into free space (Fig. 2(b)). The phase of electric (*E*-) field varies by 2\(\pi\) on one complete circle around the vortex center. The phase is interrupted at the center of the radiation path, showing a topological phase singularity point at the light axis (Fig. 2(c)). The wavelength of OAM laser radiation can be tuned by switching the state of GST225 between amorphous and crystalline. It is because the GST225 phase transition can change the refractive index of the ring cavity that in turn varies the cavity resonance. In Fig. 2(d-f), we investigate the vortex laser emission from the ring cavity at \(\lambda =\)1565.9 nm for the crystalline phase. As is seen, the field maps of the system are similar to the ones at \(\lambda =\)1544.5 nm (Fig. 2(a-c)), which implies that the unidirectional WGM with \(m=\)16 and OAM with \(p=\)1 can be excited to create a vortex beam. The homogeneous field intensity (\({\left|H\right|}^{2}\)) distributions of WGMs with \(m=\)16 for the amorphous (Fig. 2(a)) and crystalline (Fig. 2(d)) demonstrate the ideal mode properties. It indicates that the EP does not change with the GST225 phase.

The transversal distributions of the radial component \({H}_{r}\) (Fig. 2(b,e)) and the corresponding phase distributions arg(\({H}_{r}\)) (Fig. 2(c,f)) further show that the vortex beams scattered by the outer grating elements have the OAM orders of \(p=\)1 for both the amorphous and crystalline, accordingly. Therefore, the OAM laser emission with broadly tunable spectra (from 1544.5 to 1565.9 nm) can be attained by switching the phase of GST225 between amorphous and crystalline.

Moreover, GST225 can be crystallized partially by creating intermediate phases, possessing regimes of both amorphous and crystalline states.49 Such a unique characteristic is promising for a continuously tunable photonic device. The change of complex refractive index (or the crystallization level) is verified using the infrared reflectance measurement of the switching regime. In Eq. 7, we present the complex refractive index of partially crystallized GST225 using the Lorentz-Lorenz model,50 which can be broadly tuned by applying the gate voltage, \({V}_{g}\):

$$\frac{\epsilon \left(\omega \right)-1}{\epsilon \left(\omega \right)+2}=q\times \frac{{\epsilon }^{CT}\left(\omega \right)-1}{{\epsilon }^{CT}\left(\omega \right)+2}+(1-q)\times \frac{{\epsilon }^{AM}\left(\omega \right)-1}{{\epsilon }^{AM}\left(\omega \right)+2}$$

7

where \({\epsilon }^{AM}\left(\omega \right)\) and \({\epsilon }^{CT}\left(\omega \right)\) are the complex refractive index of GST225 for both amorphous and crystalline phases, respectively, and\(j\) is the crystallization ratio. To illustrate an actively tunable PT symmetry vortex lasing, a few more calculations are carried out to continuously engineer the ring cavity resonance, which in turn tunes the OAM mode, by partially crystallizing the GST225 layer.

The propagating WGM is lossy owing to the absorption and radiation. However, it can be compensated by the gain material (InGaAsP) under uniform pumping, and the lasing OAM mode emits vortex waves into air space. Figure 3(a) presents the 3D full wave (COMSOL) modeling of the gain effect in the vortex beam laser device at EP (\({n}^{{\prime }}={n}^{{\prime }{\prime }}=\) 0.01) at the crystallization ratio of \(j=\) 0, 0.2, 0.4, 0.6, 0.8 and 1, respectively. The gain improvement of the microcavity is achieved by uniformly pumping the InGaAsP ring. In the model, this feature is mimicked by enlarging the imaginary part of the background refractive index \({n}_{b}\). For the various \(j\), the quality (\(Q\)) factor is about 365 for the non-gain cavity (\({n}_{b}=\) 0). As increasing the gain coefficiency, the \(Q\) factor enhances by orders of magnitude, showing that the gain compensates for the loss.

Thus, the OAM mode turns into a lasing mode and radiates vortex beam. Note that, the OAM mode is lasing at the different \({n}_{b}\) for the different \(j\). We then calculated the resonant frequency of the microring cavity at the different \(j\) by using Eq. 6. In Fig. 3(b), it is obvious that changing \(j\) allows direct control over the resonant frequency of the micro-ring laser. Herein, the \({n}_{e}\) is 2.249, 2.258, 2.265, 2.272, 2.276, and 2.280 at \(j=\) 0, 0.2, 0.4, 0.6, 0.8, and 1. As was shown in Fig. 3a, the peak \(Q\) factor of the cavity is maintained at around 37500 during the crystallizing process. In **Figure** S1 of the supplementary information, we show \({\left|H\right|}^{2}\), \({H}_{r}\), and arg(\({H}_{r}\)) of the micro-ring laser at the different crystallization ratios, \(j=\) 0, 0.2, 0.4, 0.6, 0.8 and 1, corresponding to the WGM order of \(p=\)1.

Such an OAM lasing is reconfigurable by reversibly switching the GST225 state between amorphous and crystalline. The GST225 dielectric possesses crystallization and melting temperatures of \({T}_{C}=\) 490 K and \({T}_{M}=\) 873 K, respectively. The amorphous GST225 can be crystallized by heating it beyond the \({T}_{C}\) whereas below the \({T}_{M}\).36 The crystalline GST225 is re-amorphized by rapidly increasing the temperature above the \({T}_{M}\). The reversible phase transition of GST225 can engineer the WGM order back and forth, offering the reconfigurable OAM lasing. Figure 4 illustrates an electric-thermal transfer model to investigate the temporal variation in the GST225 temperature within the micro-ring cavity. In Table S1 of the supplementary information, we show the thermoelectric characteristics of the materials employed in the simulation. Figure 4(a) shows that the temperature in the as-deposited amorphous (AD-AM) GST225 increases above \({T}_{C}\) by applying \({V}_{g}=\) 12 V for 25 ns. To crystallize the GST225 completely, a following annealing process is carried out to provide the required thermal energy to maintain the temperature above \({T}_{C}\) however below \({T}_{M}\) for ∼35 ns.51 The crystallization ratio (\(j\)) of the GST225 can be varied via time controlled electrical heating, that in turn, gradually changes the refractive index of GST255 to make the ring cavity resonant wavelength (OAM lasing mode) continuously sweep across the spectra from 1544.5 to 1565.9 nm (Fig. 3(b)). The temperature of crystalline GST225 layer drops down to the room temperature by disconnecting the \({V}_{g}\) because the heat scatters into the surrounding air.

To reversibly shift the operating wavelength from 1565.9 to 1544.5 nm, a backward re-amorphization (from crystalline to amorphous) is required, in which crystal lattice is molten and later quenched to 293 K to forbid the recrystallization of the atomic structure.52 A \({V}_{g}=\) 25 V with a biasing time of 10 ns is used to re-amorphise the GST225. The \({V}_{g}=\) 25 V offers a sufficient thermal energy to fast boost the temperature beyond the \({T}_{M}\) that melts the GST225. By shutting down \({V}_{g}\), the follow-up quick cooling quenches the melt in the amorphous phase. The forward wavelength tuning from 1544.5 to 1565.9 nm is again attained by adjusting \({V}_{g}\) back to 12 V. The 3D temperature distributions of the structure at 80 ns (crystallizing point) and 135 ns (melting point) are shown in Fig. 4(b,c), respectively. Figure 4(b) shows that the whole AD-AM GST225 dielectric layer can exceed the \({T}_{C}\) after 25ns under the \({V}_{g}=\) 12 V, whereas the peak temperature can be increased beyond \({T}_{M}\) after 10 ns under the \({V}_{g}=\) 25 V. Video 1 records the whole process of reversibly tuning the emission spectra of the micro-ring laser. Our proposed ring laser possesses exceptional performance for dynamically reconfigurable functions.