Topological radiation from vortex masers

Domain: physics
Published: 2025-11-28
Editorial outcome: minor_revision

Abstract
Vortex singularities in acoustic and electromagnetic fields are instrumental degrees of freedom in advanced wavefront-shaping schemes and robust high-throughput communications. Laser sources that emit coherent vortices in free space have been demonstrated at optical frequencies, however their microwave counterparts, vortex masers, have remained entirely unexplored, despite their promising application potential as low-noise quantum sources and sensors. Here, we demonstrate a room-temperature maser emitting pulses of electromagnetic radiation with polarization and phase vortices, based on the physics of 3D topological vectorial singularities. Nontrivial microwave photons with polarization winding are emitted from a maser made of a sub-wavelength dielectric cavity filled with an organic gain medium. By topping the cavity with a chiral metasurface, the circular polarizations decouple, allowing the masing of pulses with nonzero orbital angular momentum revealed through nontrivial wavefront winding. Our work paves the way for multi-dimensional vortex and singularity emission from volumetric coherent microwave sources, topological photonic radiation, and novel practical applications of masers.

Introduction
Vortices are topological singularities in complex fields that significantly expand the spatial degrees of freedom of waves, enabling transformative applications in high-capacity communications, super-resolution imaging, and particle trapping1–4. Vortex generation has been demonstrated across diverse planar architectures, including spatially distributed metasurfaces3,5–7, photonic crystals8–10, bound states in the continuum11–15, and ring resonators16–19, spanning from conventional acoustic setups to cutting-edge nano-optical and atomic platforms20.

Typically, these implementations feature large 2D planar surfaces that generate vortices in the normal direction based on the dispersion of collective modes or large-scale resonances. On the other hand, vortex emission from a subwavelength emitter presents greater challenges due to the small volumes involved, and the required extension of coherent vortex generation mechanisms beyond 2D8,21–23. Such dimensional extension of topological singularities and of their applications is in general nontrivial, and is at the heart of current research in topological physics24–26.

Regarding wave-emitting devices, vortex generation has been primarily focused on the optical regime through photoluminescence and lasing mechanisms. However, masers27–29, the microwave progenitor of optical lasers, despite their broad applications in fields such as deep-space communications30, astronomy31, and quantum sensing32,33, have so far been restricted to the emission of topologically trivial fields, and have not yet been empowered by more advanced functionalities such as vortex emission in one or several simultaneous directions.

Here, we demonstrate a pulsed multi-directional vortex maser based on a cubic subwavelength dielectric cavity filled with pentacene-doped p-terphenyl (pc:pt) crystal as the gain medium27,34,35, which exhibits emission of microwave photons with topological polarization vortices perpendicular to each of its faces. Direct observation of pulses with orbital angular momentum (OAM) is realized by coupling this cavity with a spin-selective metasurface. Additionally, we verified the simultaneous coexistence of masing signals in three orthogonal directions and the associated singularities induced by the vortices. This extends the principles of active topological photonics, previously confined to optical lasers, into the microwave regime, where coherent emission of this complexity has not been achieved. It provides critical insights into how such coherent states can enhance performance, reduce noise, and enable more precise control over electromagnetic fields.

We believe that such multi-directional vortex masers can provide new degrees of freedom in an next generation of volumetric coherent microwave sources36, by exploiting multidimensional topological vortices and singularity emission in quantum sensing or communication applications.

Results
Concept of topological multi-directional vortex maser
Figure 1a presents the topological multi-directional vortex maser, constructed around a symmetric, standalone cubic strontium titanate (STO, with relative permittivity ε r=318) cavity of deep-subwavelength size, within which cylindrical monocrystals of pentacene-doped p-terphenyl are inserted, serving as the gain medium necessary for masing at room temperature. Upon pumping with yellow light (592 nm), population inversion can be established and stimulated emission can occur29,34, leading to the radiation of microwave vortex photons from each surface of the cube in the normal direction. This is enabled by the special eigenmode of the symmetric cube, which we designed to support topological polarization singularities along these six directions (see Supplementary Fig. S1).

The cubic STO cavity supports a unique eigenmode in which the electric field intensity vanishes at the center (E x=0 and E y=0 forming nodal lines and crossing at the center point as vectorial zero), while the polarization angle ϕ p=arg E x+iE y undergoes a continuous 2π winding on planes parallel to the cube faces. The drilled voids concentrate magnetic fields, ensuring efficient coupling with the spin-polarized triplet transitions in the gain medium. This synergy between cavity symmetry, vectorial topology, and gain–cavity interaction constitutes the physical foundation of the maser’s multi-directional vortex emission. This provides a physical picture of the mechanism underlying the 3D topological singularities, underscoring the novelty of our work: the first realization of a coherent volumetric source where topological polarization singularities are intrinsically embedded in the eigenmode itself, rather than imposed externally.

The transitions leading to masing within the gain medium are known and well documented in other works27,37–39, however, for the reader’s convenience, we reproduce a simplified Jablonski diagram in Fig. 1b. The 592-nm optical pump initially excites pentacene molecules from the ground state S 0 to the excited state S 1 through internal conversion (IC). About 62.5% of these molecules cross to triplet state T 2 with spin polarization (known as intersystem crossing), then relax to sublevels X, Y, and Z within state T 1. This creates a population inversion with ratios of 0.76:0.16:0.08. When the gain medium is placed within a microwave cavity resonant at approximately 1.45 GHz, stimulated maser transitions occur between the X and Z sublevels, depleting the population inversion and generating coherent microwave emission.

Figure 1c displays a photograph of the fabricated multi-directional vortex maser, featuring a STO cubic cavity with three identical cylindrical holes drilled perpendicular to each pair of opposing faces. Cylindrical pieces of the gain medium are loaded into these holes, forming a compact integrated device with dimensions of ~0.07 wavelengths. Through an intuitive and accessible design, this symmetrically configured system achieves enhanced volume-level light-matter interaction for topological wave emitting, as we show below.

Eigenmode with topological singularities
Figure 2 characterizes the cubic cavity eigenmode that exhibits multiple topological polarization singularities arising from the localized resonance (see also Supplementary Fig. S1 for additional details). It’s noteworthy that the functionality of the air holes is twofold: they create a special resonance that hosts polarization singularities along all three orthogonal directions (normal to the cube faces), while simultaneously providing a void space with concentrated magnetic field, maximizing the interactions with the magnetic dipoles in the gain medium. The topological singularities in our system are intrinsic to the eigenmode itself, providing enhanced flexibility and stability compared to systems where the topology is externally imposed.

When viewed at any cut plane parallel to the cube’s surface, the simulated electric field profile consistently exhibits a ring-shaped distribution with a zero singularity at the center and high amplitude in the surrounding region (Fig. 2a). The resultant polarization angle map reveals a 2π winding around each singularity (corresponding to a topological charge of ±1), confirming the vortex nature of the electric eigenmode in multiple directions (Fig. 2b). These zero-intensity singularities are real-space topological defects of the electric vector field immersed in 3D space: the total instantaneous polarization vorticity over any surface enclosing the resonator is 2, consistent with the Poincaré-Hopf theorem. Additionally, the corresponding magnetic field is strongly enhanced and confined within the air holes (Fig. 2c; see Supplementary Fig. S4 for cut plane view of field localization), facilitating the interaction between cavity resonance and gain medium for masing action throughout the device volume.

To validate these results, we experimentally measured the reflection spectrum using two orthogonal electric probes (Fig. 2d). The probe orientation is shown in Supplementary Fig. S2a. Due to the strong spatial polarization anisotropy of the eigenmode, the tangential and radial probes will exhibit markedly different resonant spectra. The Fano-like shape observed in the reflection spectrum results from interference between the localized high-Q eigenmode and a weakly radiative background channel, a common feature in open resonator systems. For the radial probe aligned with the polarization state, a clear resonance occurs at 1.4494 GHz with a high-quality factor (Q factor) of 5130, which falls within the gain linewidth of the pentacene molecule (see Supplementary Fig. S3). We then experimentally mapped the electric field intensity and polarization angle by positioning the two orthogonal probes at various points, using polar coordinates on a plane parallel to the cube’s surface. The resulting maps in Fig. 2e, f confirm experimentally the vortex-like intensity profile and polarization angle winding of the radiated electric field, in excellent agreement with simulation predictions.

Topological multi-directional vortex masing
To achieve masing action from the cubic cavity, we optically pumped the gain medium using a multimode fiber, which delivers high-power pulses from a laser source to efficiently excite the gain medium within the cube (see “Methods” and Supplementary Fig. S5 for the detailed optical pumping setup). Figure 3a presents the experimentally measured masing spectrum in the frequency domain, demonstrating successful generation of microwave photons at 1.4493 GHz, characterized by a narrow linewidth of 0.165 MHz. The small frequency difference between the reflection and maser spectra arises from the shift in cavity resonance caused by the insertion of the pentacene:p-terphenyl crystals and fine-tuning with metallic mirrors for optimal overlap with the gain medium linewidth (see Supplementary Fig. S2). This narrow linewidth is attributed to the high-Q resonance of the cubic cavity. The masing threshold was determined by varying the pump laser energy and measuring the corresponding output power of masing signals. As shown in Fig. 3b, a pronounced threshold behavior is observed, with an abrupt increase in masing output after the low masing threshold of 4.5 mJ. On the other hand, the time-domain measurement of the pulses is shown in Fig. 3c. The intensity of the masing signal displays a pulsed envelope that rises and decays within approximately 40 µs. Once the masing signal becomes prominent—typically within a 10–30 µs time window—the associated polarization angle reaches a relatively stable state, as evidenced by the flat plateau highlighted in the shaded region of Fig. 3d, which also implies the presence of stable spatial vortex structures thanks to the coherence of the emission. Under repeated excitation with successive laser pulses, the short-time Fourier transform shown in Fig. 3e captures multiple masing events as hot spots, confirming the stability and robustness of vortex masing under long-term operation, both in the time and frequency domains.

To verify the topological multi-directional vortex masing, Fig. 3f experimentally demonstrates the spatial distribution of the microwave emission in three directions perpendicular to the surfaces of the cubic cavity. This is achieved by mapping the emitted electric field intensity and polarization angle across three distinct cube faces: Face 1 (top), Face 2 (front), and Face 3 (left). The presence of consistent ring-shaped intensity profiles and accompanied polarization winding patterns on all three surfaces confirm the successful realization of coherent multi-directional vortex masing.

We conducted additional experiments to probe the masing signals at different distances and their associated topological polarization singularities. The results are in Supplementary Fig. S10. The observed coexistence of these features confirms our multi-directional vortex maser as a volumetric masing source carrying multidimensional topological singularities. Notably, this topological multi-directional vortex maser represents a significant advancement in higher-dimensional light sources36, distinguished by its nontrivial spatial structure extending beyond a planar plane to 3D distributions, pulsed operation, and multi-directional emission. To advance the functionality and reconfigurability of the cubic multi-directional vortex maser, we demonstrate a system comprising two stacked-and-twisted cubic cavities capable of manipulating the masing vortex state on the higher-order Poincaré sphere (see Supplementary Fig. S11), where each point on the sphere represents a distinct topological vortex distribution rather than a single polarization state. Experimentally, we achieved controlled vortex twisting up to 120°, establishing the capability to program multidimensional vortex emissions with tailored topological characteristics. This method provides enhanced control over the spatial features and structured fields in coherent microwave radiation.

Maser pulses with orbital angular momentum
Having demonstrated maser pulses with polarization vortices, we now construct masing pulses with orbital angular momentum, which necessitates breaking the locally planar phase fronts of the emission. If we picture the linear polarization emitted from our maser as a superposition of right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) light, we know, due to spin-orbit locking40,41, that each of these circular components taken separately exhibits an inherently nontrivial OAM with opposite topological charges. When observing the phase under one of the two circular eigenstates, the topological 2π phase manifests itself as an OAM phase vortex (see “Methods” for a theoretical proof). A polarization-selective metasurface can therefore be used to force the maser to emit only one circular polarization, which results in OAM masing. Therefore, we built a chiral metasurface and placed it near our masing cavity to turn the system into a coherent OAM microwave source.

The simulated phase fronts emitting from the cubic cavity exhibit spiral distributions under the two circularly polarized states, as shown in Fig. 4a and d for RCP and LCP, respectively (see also Supplementary Fig. S6 for the topological OAM phase distribution at different positions away from the maser cube). The chiral metasurfaces required to force the maser to emit selected circular polarization states are illustrated in Fig. 4b and e (see “Methods” for details on the design and fabrication of the chiral metasurfaces). Under the same pumping conditions, the phase profile was experimentally reconstructed by performing cross-correlation analysis between time-domain signals from two probes—one scanned across the metasurface while the other remaining fixed as the reference. The experimentally measured phase of the transmitted component exhibits opposite nontrivial topological charges ±1 for RCP and LCP states (Fig. 4c and f), providing direct evidence of the realized topological OAM masing. Note that despite the visual resemblance with previous figures, these panels represent the winding of the phase front, very different from the polarization windings previously reported in absence of metasurface. To access higher-order OAM states, additional engineering strategies are required, such as mode hybridization, where multiple cavity modes with distinct polarization singularities are coupled to form composite eigenstates with larger winding numbers.

Methods
Polarization and phase vortex
Polarization vortices correspond to spatial singularities in the polarization vector field, where the local polarization angle is defined as ϕ p(r)=arg(E x+iE y), and exhibits a 2πm winding around a singularity, with m the polarization topological charge and r the spatial coordinate. In contrast, phase vortices are associated with the azimuthal phase winding of the scalar field amplitude, ϕ(r)=mθ, where θ is the azimuthal coordinate and m denotes the OAM charge. While polarization vortices are vectorial in nature and stem intrinsically from the cavity eigenmode, phase vortices emerge when spin degeneracy is lifted by the chiral metasurface, which enforces emission in a single circular polarization channel and thereby converts vectorial singularities into OAM states.

According to the Poincaré–Hopf theorem, the sum of topological charges of all vector field singularities on a closed surface must equal the Euler characteristic of the surface. For a topologically equivalent sphere enclosing the cavity, the Euler characteristic is 2. Thus, the total polarization vorticity over any closed surface surrounding the resonator is constrained to be 2, consistent with Fig. 2b.

Design and fabrication of the STO cube
The cubic cavity was designed using eigenmode solvers in COMSOL Multiphysics for obtaining the optimal magnetic Purcell factor, and vortex electric field. A vortex pattern is confirmed with a continuous transformation of polarization angle from −π to π, corresponding to a topological charge of 1. The evaluation of emissions from the 3D topological eigenmode is simulated through dipole excitation within the cavity. The optimized cavity has a length of 14.1 mm and a hole radius of 2.5 mm, which was then fabricated in bulk SrTiO 3 with all surfaces polished by Hefei Kejing Materials Technology Co., Ltd.

Pentacene:p-terphenyl crystal growth
The pentacene-doped p-terphenyl crystals (0.1% mol/mol) are grown using the vertical Bridgman method. Initially, commercially purchased p-terphenyl (A14833, Alfa Aesar) is purified by sublimation under high-vacuum (≤10−6 mbar) sublimation purification and then mixed with as-received pentacene powder (P2524, TCI Europe NV). The mixture is loaded into a double-layered ampoule (5 mm inner diameter), and a 1 mm diameter Pyrex rod is inserted to create a central hole through the crystal. The ampoule is then sealed under high vacuum and subjected to a controlled growth process in a Bridgman furnace: 12 h of melting at 240 °C for homogenization, followed by a 14-day descent at 0.53 mm/h towards the 80 °C zone. After growth, the furnace is gradually cooled down to room temperature. Finally, the crystal is cut using a diamond saw and separated from the ampoule and rod (see Supplementary Fig. S2).

Design and fabrication of metasurfaces
The polarization singularities introduce vectorial vortices that possess inherent spin-orbit locking, which can be decomposed by two circular states as |E (ϕ) 〉=eiϕ|R〉+e−iϕ|L〉, where |R〉, |L〉 are the RCP and LCP states and ϕ is the polarization angle. A nontrivial winding of ϕ results in opposite topological charges in phase components of RCP and LCP40,41. This lays the foundation for showing OAM pulses from the vortex maser. Simulation integrating STO cube and metasurface for blocking RCP or LCP component is conducted and verified in COMSOL Multiphysics (see Supplementary Fig. S7). Efficient OAM phase is detected after vector vortex passes through the metasurface. The metasurfaces are fabricated on a low-loss dielectric substrate (Taizhou Wangling, F4BTMS1000) with permittivity of 10.2 and tangential loss of 0.002. Copper gratings are deposited on double sides of each substrate. The fabricated metasurfaces have a thickness of 6.35 mm and side length of 108 mm (see Supplementary Figs. S8 and S9).

Optical setups
A schematic optical path is illustrated in Supplementary Fig. S5. The output beam from an optical parametric oscillator is divided using a beamsplitter (15%: 85%): the transmitted beam is shrunk using a telescope and measured by a power meter (Gentec-EO, Pyroelectric detector); the reflected beam is coupled into a multi-mode optical fiber (core diameter of 1 mm) using a plano-convex lens. To filter the spatial profile of the focused beam and protect the optical fiber, a precise pinhole is placed in front of the optical fiber. The other end of the optical fiber enters the pentacene:p-terphenyl (pc:pt) crystal for efficient optical pumping.

Maser characterization
Passive and active characterization of the maser platform are conducted using a vector network analyzer (Rohde & Schwarz ZNA67) with a magnetic probe for resonant frequency tuning and an oscilloscope (Tektronix) with electric probes for measurement of time-domain masing pulses, respectively.

Masing field mapping
Two orthogonal electric field probes, mounted on a motorized rotary arm with an adjustable radius, were utilized to map the vortex-masing field distribution in polar coordinates. The amplitude and polarization of the electric field at each position were determined by analyzing the ratio of masing amplitudes and phase difference between the two probes. To retrieve the masing phase vortex, one probe is fixed, and the other is sweeping across a surface above the metasurface. The relative phase between two probed fields can be extracted from the cross-correlation operation between time-domain pulsed signals and finding the maximum lags.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents a study on topological radiation from vortex masers, demonstrating a room-temperature pulsed maser with polarization vortices based on a subwavelength cubic strontium titanate (STO) cavity. Specifically, a chiral metasurface is used to decouple circular polarizations, thereby realizing the masing of phase vortices. I think the topic is interesting and the paper is well-written. Both theoretical and experimental results are well presented. I have some minor questions/comments that need to be clarified:\n1. The authors mentioned in the ABSTRACT that the room-temperature maser emitting pulses of electromagnetic radiation with polarization and phase vortices. It is recommended that the authors supplement detailed elaboration on the polarization vortices and phase vortices, as well as their differences.\n2.In the manuscript, the eigenmode of cubic STO cavity exhibit a zero-intensity singularity at the center and a 2π polarization angle winding. Could the authors elaborate on two points: First, why the 2π polarization angle winding corresponds to a topological charge of ±1; Second, why the total instantaneous polarization vorticity over any surface enclosing the resonator is 2?\n3. The cubic STO cavity generates vortices on all faces, relying on its high structural symmetry. Can a dodecahedral STO cavity achieve vortex masing with more emission directions?\n4.The decoupling effect of the chiral metasurface is key to generating OAM. However, the current version of the manuscript only mentions the metasurface’s material and its functional role, without providing any simulation results related to the metasurface itself.\n5. Is there a way to generate OAM without metasurface? When a metasurface is adopted, the STO cavity lacks advantages —this is because the metasurface itself is capable of generating OAM directly .\n6, How to tune the emission frequencies of the maser?\n7, Can the maser generate OAM with arbitrary topological charges?", "reviewer_2": "In this manuscript, the authors have carefully studied the vortex maser emission from a cubic SrTiO3 cavity with pentacene crystals. Under an optical excitation at 592 nm, vortex laser emission has been acheived in all three dimensions. The entire cavity is much smaller than the wavelength. I have the following comments for the authors.\n1. The fundamental physics of this research is the 3D topological vectorial singularities. This point has been shown with numerical simulation in both main text and Fig. S1. But the corresponding mechanism has not been discussed yet. A physical picture is sugguested to highlight the novelty of this research.\n2. The size information os the cavity is missing. It should be added to either the figure caption or in the main text. Scale bar should also be added to all the images.\n3. The resonant position in reflection spectrum and maser spectrum is slightly different (~0.1 MHz, close to the laser linewidth). What is the reason? Meanwhile, the reflection spectrum shows a fano shape. This has not been discussed yet.\n4. In page 5, the authors stated \"they create a special resonance with multiple topological polarization singularities in all normal directions\". This sentence is quite confusing. I think the authors try to discuss the singularity in all three directions. The corresponding topological charge should be added to avoid confusion.\n5. For the case of transition from vortex laser to vortex maser, the absence of vortex maser cannot show the novelty and importance of this research. Maser operates at a much longer wavelength than laser. It is well known that almost all the techniques in lasers can be applied to maser too. Some techniques taht are missing in laser can also be realzied in maser, e.g., three dimensional control in this research. The authors should provide a more convincing reason for this research."}, "author_response": "Reply to Reviewer #1\nComment: This manuscript presents a study on topological radiation from vortex masers,\ndemonstrating a room-temperature pulsed maser with polarization vortices based on a\nsubwavelength cubic strontium titanate (STO) cavity. Specifically, a chiral metasurface is\nused to decouple circular polarizations, thereby realizing the masing of phase vortices. I\nthink the topic is interesting and the paper is well-written. Both theoretical and\nexperimental results are well presented. I have some minor questions/comments that need\nto be clarified:\nResponse: We sincerely thank you for the positive assessment of our work and for\nhighlighting the interest and clarity of our manuscript. Below, we provide detailed\nclarifications in response to your minor comments.\nComment 1: The authors mentioned in the ABSTRACT that the room-temperature maser\nemitting pulses of electromagnetic radiation with polarization and phase vortices. It is\nrecommended that the authors supplement detailed elaboration on the polarization vortices\nand phase vortices, as well as their differences.\nResponse: We thank you for this valuable suggestion.\nIn the revised manuscript, we have clarified the distinction between polarization vortices\nand phase vortices with explicit mathematical descriptions. Polarization vortices\ncorrespond to spatial singularities in the polarization vector field, where the local\npolarization angle is defined as\n𝜙 (𝒓) = arg)𝐸 +𝑖𝐸 -,\n! \" #\nand exhibits a 2πm winding around a singularity, with m the polarization topological charge.\nIn contrast, phase vortices are associated with the azimuthal phase winding of the scalar\nfield amplitude,\n𝜙(𝒓) = 𝑚𝜃,\nwhere θ is the azimuthal coordinate and m denotes the orbital angular momentum (OAM)\ncharge. While polarization vortices are vectorial in nature and stem intrinsically from the\ncavity eigenmode, phase vortices emerge when spin degeneracy is lifted by the chiral\nmetasurface, which enforces emission in a single circular polarization channel and thereby\nconverts vectorial singularities into OAM states.\nThese distinctions have been explicitly added to the revised manuscript as a new section in\nMethods: Polarization and phase vortex.\nComment 2: In the manuscript, the eigenmode of cubic STO cavity exhibit a zero-intensity\nsingularity at the center and a 2π polarization angle winding. Could the authors elaborate\non two points: First, why the 2π polarization angle winding corresponds to a topological\ncharge of ±1; Second, why the total instantaneous polarization vorticity over any surface\nenclosing the resonator is 2?\nResponse: We thank the reviewer for raising these important points.\nWe thank you for raising this important question, which allows us to clarify the topological\ninterpretation of our results.\na) Topological charge of ±1.\nThe polarization angle is defined as\n𝜙 (𝒓) = arg)𝐸 +𝑖𝐸 -,\n! \" #\nAround a singularity where the field amplitude vanishes, the phase of the polarization\nvector winds continuously as one traverses a closed contour. The topological charge q is\ngiven by the winding number:\n1\n𝑞 = 5𝑑𝜙 ,\n2𝜋 !\n%\nwhere Γ is a closed loop around the singularity. A single 2π winding corresponds to 𝑞 =\n±1, with the sign determined by the direction (clockwise or counterclockwise) of the\nwinding. This definition is standard for polarization singularities and matches our\nsimulation and experimental observations.\nb) Total polarization vorticity of 2.\nThe cubic eigenmode hosts multiple polarization singularities embedded in three-\ndimensional space. According to the Poincaré–Hopf theorem, the sum of topological\ncharges of all vector field singularities on a closed surface must equal the Euler\ncharacteristic of the surface. For a topologically equivalent sphere enclosing the cavity, the\nEuler characteristic is 2. Thus, the total polarization vorticity over any closed surface\nsurrounding the resonator is constrained to be\n8𝑞 = 2,\n&\n&\nconsistent with our calculated eigenmode, which exhibits two unit-charge singularities\nwhen summing over each cut-plane, 1+1+(-1) = 1 for Fig. 2b and the other three surfaces\nto 1, finally leading to an overall charge of 2. This conservation ensures that the observed\nsingularities are robust and topologically protected.\nWe have added these explanations to the revised manuscript as a new section in Methods:\nPolarization and phase vortex.\nComment 3: The cubic STO cavity generates vortices on all faces, relying on its high\nstructural symmetry. Can a dodecahedral STO cavity achieve vortex masing with more\nemission directions?\nResponse: We really appreciate your forward-looking question. In principle, yes—other\nhigh-symmetry dielectric resonators (including Platonic solids such as a dodecahedron)\ncan be engineered to support eigenmodes whose polarization field exhibits singularities\naligned with multiple face normals, enabling multi-directional vortex emission. The key\nrequirement is not the cube per se but the existence of a 3D eigenmode with (i) ring-like\nintensity and a central zero on planes parallel to the emitting faces, and (ii) a nontrivial\nwinding of the local polarization angle around those zeros. One concern may be that the\ndodecahedral boundary will reduce the Q factor if surface curvature or machining\ntolerances increase radiation or ohmic loss.\nIn short, a dodecahedral STO cavity is a promising extension and could yield a richer set\nof emission directions if one designs an eigenmode whose polarization singularities are\noriented along the desired face normal. We have added a brief discussion of this potential\nin the outlook (Page 12) of the revised manuscript:\n“Other high-symmetry dielectric resonators, including Platonic solids such as the\ndodecahedron, can be engineered to support eigenmodes in which the polarization field\nexhibits singularities aligned with multiple face normals, thereby enabling multi-\ndirectional vortex emission.”\nComment 4: The decoupling effect of the chiral metasurface is key to generating OAM.\nHowever, the current version of the manuscript only mentions the metasurface’s material\nand its functional role, without providing any simulation results related to the metasurface\nitself.\nResponse: We thank you for pointing out this important aspect. In the revised manuscript,\nwe now provide additional simulation results and explanations regarding the metasurface’s\ndecoupling function. Specifically, the metasurface enforces spin-selective transmission by\nblocking either the RCP or LCP component of the incident field. This functionality was\nvalidated using full-wave simulations.\nThe simulated spiral phase fronts are shown in Supplementary Fig. S7, where the\nmetasurface selectively converts vectorial polarization vortices into scalar OAM vortices\nwith opposite topological charges for RCP and LCP channels.\nThese additional results and explanations have been incorporated into the Methods:\nDesign and fabrication of metasurfaces and Supplementary Information (Figs. S6-S9).\nComment 5: Is there a way to generate OAM without metasurface? When a metasurface\nis adopted, the STO cavity lacks advantages—this is because the metasurface itself can\ngenerate OAM directly.\nResponse: We appreciate your very thoughtful question.\na) Regarding OAM without a metasurface.\nIn principle, one may achieve intrinsic spin selection in the resonator by (i) introducing\nweak geometric chirality (boundary/perturbations), (ii) adding gyrotropy (e.g., magneto-\noptic materials), or (iii) engineering non-Hermitian coupling to favor a single circular\neigenchannel. We emphasize, however, that such approaches typically increase system\ncomplexity, reduce the quality factor, raise the masing threshold, and may challenge or\nhinder uniform optical pumping as well as Purcell optimization.\nb) The concern that “the metasurface itself can generate OAM directly”.\nMetasurfaces designed as helical phase plates or PB holograms can indeed create OAM\nfrom a trivial input, but that is not the component we use here. Our device uses a compact\nspin-selective grating whose role is analyzable selection (RCP/LCP) rather than spatially\nvarying phase imprinting. The central focus of this work is the realization of a nontrivial,\nmultidimensional coherent microwave source.\nWe have added this point in Page 10\n“A polarization-selective metasurface can therefore be used to force the maser to emit only\none circular polarization, which results in OAM masing. Therefore, we built a chiral\nmetasurface and placed it near our masing cavity to turn the system into a coherent OAM\nmicrowave source.”\nComment 6: How to tune the emission frequencies of the maser?\nResponse: We thank you for this pertinent question. In our system, the maser emission\nfrequency is primarily determined by the cavity resonance of the subwavelength STO cube,\nwhich must overlap with the masing transition between the spin sublevels of the pentacene:\np-terphenyl (pc:pt) gain medium. Tuning the emission frequency requires reconfiguring the\ncavity, providing one remains within the gain bandwidth. Larger reconfigurability requires\ntuning the cavity frequency and modifying the sublevels, which can be achieved by\nimparting a small magnetic field to the gain medium.\nWe can explicit several strategies to fine-tune the resonance frequency:\nGeometric tuning. Varying the cube dimension or hole radius shifts the eigenmode\nfrequency, offering fine geometric control during fabrication.\nDielectric tuning. Since the cavity resonance scales with the permittivity, temperature\ncontrol of the high-index STO host material provides an efficient tuning mechanism. Small\ntemperature variations induce measurable frequency shifts due to the strong dielectric\ndispersion of STO in the microwave regime.\nMagnetic or strain perturbations. Weak symmetry-breaking perturbations—such as\ninserting dielectric rods, applying strain, or local loading with magneto-optic materials—\ncan lift mode degeneracies and shift resonance frequencies, while still preserving the\ntopological vortex characteristics.\nIn the Supplementary Fig. S2, we also show the capability of frequency tuning via\nmoveable metallic plates around the cubic cavity, acting as a perturbation:\n“Configuration of the vortex maser experiment setup with two-sidewall metal holder and\ntwo movable plates for fine-tuning resonance of cubic cavity, enabling masing vortices in\nthree dimensions and related measurement.”\nComment 7: Can the maser generate OAM with arbitrary topological charges?\nResponse: We thank you for this insightful question. In the current design, the maser\ngenerates OAM states with topological charge of ±1, which directly arises from the spin–\norbit–locked decomposition of the cavity’s vector vortex eigenmode into its RCP and LCP\ncomponents.\nTo access higher-order OAM states, additional engineering is required. Possible strategies\ninclude mode hybridization, in which multiple cavity modes with distinct polarization\nsingularities are coupled to form composite eigenstates with larger winding numbers, and\nthe use of stacked or twisted cubes. As demonstrated in Supplementary Fig. S11, two\nstacked and rotated STO cubes enable controlled twisting of the vortex emission on the\nhigher-order Poincaré sphere, a concept that may be further extended to synthesize higher-\norder OAM distributions.\nWe have clarified in the revised manuscript that while the present device demonstrates\ncoherent OAM masing with charge 1, there is no fundamental restriction of the underlying\nconcept with respect to extensions toward arbitrary higher-order charges through cavity\nengineering.\nWe added this point in Page 1.\n“To access higher-order OAM states, additional engineering strategies are required, such\nas mode hybridization, where multiple cavity modes with distinct polarization singularities\nare coupled to form composite eigenstates with larger winding numbers.”\nReply to Reviewer #2\nComment: In this manuscript, the authors have carefully studied the vortex maser emission\nfrom a cubic SrTiO3 cavity with pentacene crystals. Under an optical excitation at 592 nm,\nvortex laser emission has been acheived in all three dimensions. The entire cavity is much\nsmaller than the wavelength. I have the following comments for the authors.\nResponse: We sincerely thank you for the constructive suggestions and comments. We\nhave provided point-by-point responses below and carefully revised the manuscript to\ninclude the requested clarifications and additional details where appropriate.\nComment 1: The fundamental physics of this research is the 3D topological vectorial\nsingularities. This point has been shown with numerical simulation in both main text and\nFig. S1. But the corresponding mechanism has not been discussed yet. A physical picture\nis suggested to highlight the novelty of this research.\nResponse: We thank you for this insightful comment. In the revised manuscript, we have\nadded a clear physical picture to highlight the mechanism and novelty of the 3D topological\nvectorial singularities. The cubic STO cavity supports a unique eigenmode in which the\nelectric field intensity vanishes at the center (𝐸 = 0 and 𝐸 = 0 forming nodal lines and\n\" #\ncrossing at the center point as vectorial zero), while the polarization angle 𝜙 (𝒓) = arg)𝐸\n! \"\n+𝑖𝐸 - undergoes a continuous 2π winding on planes parallel to the cube faces. This\n#\nconfiguration gives rise to polarization vortices with unit topological charge in multiple\ndirections. Importantly, the distribution of these singularities is not accidental—it is\nmandated by the Poincaré–Hopf theorem, which enforces that the total polarization index\nover a closed surface enclosing the resonator must equal 2. This ensures that the observed\nvortices are robust, symmetry-protected, and cannot be removed by small perturbations.\nPhysically, this eigenmode can be understood as a topologically twisted vectorial resonance:\na dipolar-like mode reshaped by cubic symmetry into a three-dimensional configuration\nwhere polarization singularities are simultaneously radiated toward all six faces. The\ndrilled voids concentrate magnetic fields, ensuring efficient coupling with the spin-\npolarized triplet transitions in the pentacene:p-terphenyl gain medium. This synergy\nbetween cavity symmetry, vectorial topology, and gain–cavity interaction constitutes the\nphysical foundation of the maser’s multidirectional vortex emission.\nWe believe that this physical interpretation not only clarifies the origin of the 3D vectorial\nsingularities but also underscores the novelty of our work: the first realization of a coherent\nvolumetric source where topological polarization singularities are intrinsically embedded\nin the eigenmode itself, rather than imposed externally. This discussion has been\nincorporated into the revised manuscript in Page 5,\n“The cubic STO cavity supports a unique eigenmode in which the electric field intensity\nvanishes at the center (𝐸 = 0 and 𝐸 = 0 forming nodal lines and crossing at the center\n\" #\npoint as vectorial zero), while the polarization angle 𝜙 (𝒓) = arg)𝐸 +𝑖𝐸 - undergoes a\n! \" #\ncontinuous 2π winding on planes parallel to the cube faces. The drilled voids concentrate\nmagnetic fields, ensuring efficient coupling with the spin-polarized triplet transitions in the\ngain medium. This synergy between cavity symmetry, vectorial topology, and gain–cavity\ninteraction constitutes the physical foundation of the maser’s multidirectional vortex\nemission. This provides a physical picture of the mechanism underlying the 3D topological\nsingularities, underscoring the novelty of our work: the first realization of a coherent\nvolumetric source where topological polarization singularities are intrinsically embedded\nin the eigenmode itself, rather than imposed externally.”\nComment 2: The size information on the cavity is missing. It should be added to either the\nfigure caption or in the main text. Scale bar should also be added to all the images.\nResponse: We thank you for pointing this out. We have included the precise size\ninformation of the cubic STO cavity in both the Methods section and the relevant figure\ncaption in Fig. 2.\n“The cavity has a side length of 14.1 mm and a hole radius of 2.5 mm.”\nIn addition, scale bars have now been added to all optical and simulated field distribution\nimages to provide clear dimensional reference.\nWe believe these additions improve the clarity and completeness of the manuscript.\nComment 3: The resonant position in reflection spectrum and maser spectrum is slightly\ndifferent (~0.1 MHz, close to the laser linewidth). What is the reason? Meanwhile, the\nreflection spectrum shows a fano shape. This has not been discussed yet.\nResponse: We thank you for these questions. The small frequency difference between the\nreflection resonance and the maser emission arises from the measurement conditions. The\nreflection spectrum was taken with the hollow cubic cavity prior to inserting the gain\nmedium. Once the pentacene:p-terphenyl crystals are inserted, their dielectric index\nslightly shifts the cavity resonance, accounting for the ~0.1 MHz difference. In addition,\nduring active operation we employed metallic mirrors to fine-tune the resonance frequency,\nensuring optimal overlap with the gain medium linewidth. These combined effects explain\nthe observed shift.\nRegarding the Fano-like line shape observed in the reflection spectrum, the resonance\ncouples simultaneously to a localized high-Q eigenmode and a weakly radiative\nbackground channel, producing the characteristic asymmetric Fano profile. This\ninterference effect is expected in open resonator systems.\nWe have clarified these two points in the revised manuscript:\nIn Page 8, “The small frequency difference between the reflection and maser spectra arises\nfrom the shift in cavity resonance caused by the insertion of the pentacene:p-terphenyl\ncrystals and fine-tuning with metallic mirrors for optimal overlap with the gain medium\nlinewidth (see Fig. S2).”\nIn Page 7, “The Fano-like shape observed in the reflection spectrum results from\ninterference between the localized high-Q eigenmode and a weakly radiative background\nchannel, a common feature in open resonator systems.”\nComment 4: In page 5, the authors stated \"they create a special resonance with multiple\ntopological polarization singularities in all normal directions\". This sentence is quite\nconfusing. I think the authors try to discuss the singularity in all three directions. The\ncorresponding topological charge should be added to avoid confusion.\nResponse: We thank you for pointing out this ambiguity. In the revised manuscript, we\nhave clarified the description of the eigenmode singularities. Specifically, the drilled voids\nin the cubic cavity create a resonance that hosts polarization singularities along all three\northogonal directions (normal to the cube faces). On each cut-plane, the polarization angle\n𝜙 (𝒓) = arg)𝐸 +𝑖𝐸 - exhibits a continuous 2π winding around the zero-intensity center,\n! \" #\ncorresponding to a topological charge of 1. These singularities are replicated on the three\nmutually orthogonal planes, ensuring multi-directional vortex emission.\nWe have revised the sentence in page 5, paragraph 2 to explicitly include the topological\ncharge and to state that the singularities occur along the three orthogonal directions, thereby\neliminating the confusion:\nIn Page 6, “It’s noteworthy that the functionality of the air holes is twofold: they create a\nspecial resonance that hosts polarization singularities along all three orthogonal directions\n(normal to the cube faces), while simultaneously providing a void space with concentrated\nmagnetic field, maximizing the interactions with the magnetic dipoles in the gain medium.\nWhen viewed at any cut plane parallel to the cube’s surface, the simulated electric field\nprofile consistently exhibits a ring-shaped distribution with a zero singularity at the center\nand high amplitude in the surrounding region (Fig. 2a). The resultant polarization angle\nmap reveals a 2π winding around each singularity (corresponding to a topological charge\nof ±1), confirming the vortex nature of the electric eigenmode in multiple directions (Fig.\n2b).”\nComment 5: For the case of transition from vortex laser to vortex maser, the absence of\nvortex maser cannot show the novelty and importance of this research. Maser operates at a\nmuch longer wavelength than laser. It is well known that almost all the techniques that are\nmissing in laser can also be realized in maser, e.g., three dimensional control in this\nresearch. The authors should provide a more convincing reason for this research.\nResponse: We thank you for raising this important point regarding the motivation and\nsignificance of our work.\nThe realization of a 3D vortex maser is a significant advancement because it extends the\nprinciples of active topological photonics—previously limited to optical lasers—into the\nmicrowave regime, where coherent emission has not been achieved at this level of\ncomplexity. Unlike lasers, which typically operate with vortex emission confined to 2D\ngeometries (e.g., planar metasurfaces), microwaves operate at much longer wavelengths,\nmaking it more challenging to achieve subwavelength cavities capable of supporting\ncomplex, multidimensional topological structures.\nOur work demonstrates the first room-temperature maser that produces 3D polarization\nvortices within a subwavelength cubic STO cavity, achieving multidirectional vortex\nemission that is also not possible in conventional laser systems.\nThe coherent emission of these vortex states in the microwave range is crucial because,\nunlike optical light, microwaves at room temperature can interact with materials and\nstructures in ways that allow for highly sensitive measurements, microwave quantum\ndevices, and advanced communication systems. The ability to generate coherent,\ntopologically structured microwave radiation opens up new avenues for quantum\ncomputing, microwave imaging, and signal processing where such coherent states are\nessential for enhancing performance, reducing noise, and enabling more precise control\nover electromagnetic fields.\nThe topological singularities in our system are intrinsic to the eigenmode itself, providing\nenhanced flexibility and stability compared to systems where the topology is externally\nimposed. This marks a key advancement in maser technology, enabling the generation of\ncomplex microwave light fields that are critical for applications requiring fine control over\nlight-matter interactions in the microwave regime.\nBy demonstrating 3D vortex emission in a compact, room-temperature maser, we not only\nextend topological wave engineering to the microwave domain but also create a new\nplatform for future nanophotonic, quantum, and communication devices.\nWe have expanded the introduction and conclusion of the revised manuscript to emphasize\nthese aspects and to make the novelty and importance of this research clearer.\nIn Page 4, “This extends the principles of active topological photonics, previously confined\nto optical lasers, into the microwave regime, where coherent emission of this complexity\nhas not been achieved. It provides critical insights into how such coherent states can\nenhance performance, reduce noise, and enable more precise control over electromagnetic\nfields.”\nIn Page 6, “The topological singularities in our system are intrinsic to the eigenmode itself,\nproviding enhanced flexibility and stability compared to systems where the topology is\nexternally imposed.”\nIn Page 12, “This concept also offers insights into optical and quantum regimes, where\nadvanced two-photon polymerization lithography can construct 3D cubes and meta-cubes\nassembled with quantum dots, perovskites, and quantum wells for topological light\nemission, thereby opening new avenues in structured light generation.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all my comments and revised the manuscript accordingly, I am happy to recommend it for publication in Nature Communications.", "reviewer_2": "I have carefully read the response letter and revised manuscript. The authors have clearly answered my questions. Even though I am not satisfied with the reply about laser and maser comment, I think the scientific finding in this research can be considered for publication now."}, "author_response": "Our reply: We thank the reviewer for their positive evaluation and recommendation for\npublication.\nOur reply: We appreciate the reviewer’s careful reading of our revision and constructive\nfeedback. We are grateful that the reviewer recognizes the significance of our findings and\nsupports publication."}]

Decision letter