Hybrid magnonic systems are promising modular components for quantum transduction and sensing applications owing to their capability of connecting distinct quantum platforms [1].
Strong and coherent hybridization of magnons with phonons, microwave photons, and optical light have been demonstrated, with the observation of characteristic phenomena that bestow emerging quantum engineering functionalities [2][3][4][5][6].
Among the various systems, the photon-magnon hybridization [7,8] remains the primary testbed for exploring many coherent phenomena emerging from hybrid magnonics, such as coherent [9][10][11] and dissipative [12,13] couplings, nonreciprocal transmission [14,15], remote communication [16][17][18], magnetically-induced transparency [19][20][21], super-strong coupling [22], zero-reflection [23], and PT-symmetric singularities [24,25]. These numerous coupling manifestations have largely benefited from the capability of engineering the tailored modes, in which two most prominent engineering tasks are 'mode-profile manipulation' and 'mode amplification', and they apply to both the photon and magnon counterparts.
On the magnon side, the mode profiles can be tuned via excitation schemes [26], external magnetic field [20,27], and size and geometry of the magnet (including nanostructured samples) [28]. The amplification of magnons, however, has been recognized as a long-standing challenge [5], but recent progresses have indicated promising solutions via engineering the combined spatial and temporal magnon profiles [29,30]. On the photon side, new microwave resonator designs, especially in the planar geometry [7], have been studied for improved quality factors (Q-factors) and mode profiles dedicated to photon-magnon systems. For example, diabolo cavity [31], dark mode resonance [32], spiral resonator [33], and spoof surface plasmons [34] have been designed and implemented beyond conventional stripline [35] or lumped types [36]. For amplification of photon modes, additional semiconductor gain [37] or feedback loops [38,39] can be incorporated, as have been recently demonstrated to support novel gain-driven magnon polaritons [40,41] and long-distance photon-magnon coherence [42].
Due to the near-field nature of the photon-magnon coupling, the microwave surface plasmon mode [43] is one of the most intriguing candidates, which offers simultaneously a rich variety of mode profiles and superior Q-factors. One particularly interesting manifestation pertinent to photon-magnon systems is the spoof-localized surface plasmon (spoof-LSP) modes [44][45][46][47],
with appealing features such as highly concentrated EM fields near the surface, a weak coupling to radiative waves, deep sub-wavelength excitation, and superior sensitivity to the dielectric environment. These nice properties have made spoof-LSPs favorably adopted in GHz-THz photonics that embrace a wide range of applications [43][44][45][46][47][48][49][50]. Recently, spoof-LSPs have been implemented in photon-magnon coupled systems using a spiral resonator design [51]. The enhanced coupling strength and highly tunable mode profiles have rendered them highly promising contenders for engineering photon-magnon hybrids. However, the possibility of further boosting photon-magnon coupling using actively driven spoof-LSP modes has remained elusive.
In this work, we study a gain-assisted spoof-LSP mode by integrating the resonator with a low-noise amplifier circuit. Instead of using the spiral design, the spoof-LSP resonator is composed of a corrugated ring with a slit to easily incorporate the gain circuit elements. We demonstrate that the Q-factor of the passive resonator is very sensitive to the different magnetic loads placed atop, but can be significantly increased upon applying the gain, and, subsequently lead to an increased photon-magnon coupling strength with a Y 3 Fe 5 O 12 (YIG) sphere.
We integrate the corrugated ring resonator structure in line with a microwave stripline for transmission experiments, as illustrated in Fig. 1(a). To enhance the stripline-resonator capacitive coupling, we soldered two additional 15-pF capacitors on the respective ends of the resonator. To incorporate the amplifer chip, a slit has been cut in the corrugated ring, and the solder pads are also fabricated as necessary to support the biasing circuit.
The microwave laminate board is Rogers TMM10i with a metal layer thickness of 35 Ćm, a total thickness of 1.27 mm, and a relative dielectric constant of the substrate Ċ Ĩ of 9.8. The corrugated ring resonator parameters are listed as follows: the number of grooves Ċ = 21, inner radius Ĩ = 5.2 mm, and the central strip width ĝ Ĩ = 0.8 mm. The groove height is ℎ = 2.25 mm, the period is Ħ = 2ÿ(Ĩ + ĝ Ĩ + ℎ)/Ċ = 2.47 mm, and the groove width is ė = 0.988 mm. The gap between the micro-stripline and the grooved ring resonator is ĝ ģ = 0.5 mm.
The biasing circuit structure, depicted in Fig. 1(a), uses metallic pads to mount the lumped components, including capacitors, inductors, and resistors. The amplifier chip is the BGA low-noise amplifier (Infineon), with dimensions 2 mm × 2.1 mm × 0.9 mm. The lumped components in the biasing circuit were selected based on the specs of the amplifier chip. The gain of the amplifier chip is controlled by using an external dc voltage, tunable from 0 to 4.1 V.
The transmission characteristic of the structure was measured by using a vector-network analyzer (VNA, PicoVNA-106, Pico Technology Ltd).
Figure 1(b) shows the measured ď 21 spectra with varying dc voltage applied to the amplifer in the presence of a YIG sphere (whose photon-magnon coupling properties will be discussed later).
We observed selective amplification in the transmission spectra close to the eigen-frequencies of the spoof-LSP resonator, i.e. a band localized around 2.2 GHz and 2.6 GHz, as well as a sharp resonance near 4.2 GHz (inset of Fig. 1(b)). The mode near 2.6 GHz corresponds to a dipolar mode and the one near 4.2 GHz is a quadrupole mode (details to be discussed later). No significant amplification effect was found for other frequencies in the measured range.
We then focus on the sharp resonance at ∼4.2 GHz corresponding to the quadrupole mode. One notable feature of spoof-LSPs in contrast to common waveguide modes is their high sensitivity to local dielectric environments, which can be readily modified by adding the magnetic load atop the resonator surface. To examine this effect, we tested four Y 3 Fe 5 O 12 (YIG) samples with various geometries and dimensions. The magnetic loads were all placed at the bottom of the resonator ring, an optimal location that we identified for photon-magnon coupling via a preliminary position test. This coupling sensitivity to sample location has also been demonstrated in previous reports for similar localized resonator modes [33, 51, 52]. This observation can be explained by considering the spatial profile of the LSP mode, which is typically highly surface localized, but decays rapidly along the surface normal [51].
To further examine the spoof-LSP mode profiles, we performed spatial mapping experiments on the out-of-plane electric field (ā İ ) and magnetic field (þ İ ) components using tip and loop probes, respectively. The probes are custom-made from a coaxial cable assembly with an unterminated end. The diameter of the loop probe is estimated to be ∼ 0.8 mm. The probe scans across the resonator plane using a set of precise piezoelectric stages, with a raised height of ∼ 1 mm from the surface. The mapping experiments were performed without any YIG sample nor applied magnetic field. For the ā İ maps, the 2.625-GHz mode exhibits a twofold symmetry and is a fundamental dipole LSP mode, while the 4.195-GHz mode manifest a fourfold symmetry and corresponds to a quadrupole LSP mode. The field amplitude of both modes are significantly bolstered by the gain. As an example, an intermediate transition state at 3.765 GHz was also shown, whose field amplitude, however, remains nearly the same with respect to the additional gain.
Similarly, for the þ İ maps, the 2.625-GHz mode exhibits a twofold winding-spiral geometry and is consistent with a fundamental dipole LSP mode. The 4.195-GHz mode manifests a fourfold symmetry and corresponds to a quadrupole LSP mode. In particular, a field hotspot is identified at the bottom of the corrugated ring. Likewise, the field amplitude of both modes are significantly bolstered by the gain. The same intermediate transition state at 3.765 GHz was also shown, indicating a weak susceptibility to the external gain, as in the ā İ case.
In addition to the experimental measurement results presented in Section II and III, we here provide full wave simulation of the spoof-LSP structure and compare the simulated port responses and field distributions with the measured data, shedding further light on the resonant modes of the spoof-LSP. As shown in Figure 4 (a), a 3D model of the spoof-LSP structure is constructed in Ansys HFSS, including the spoof-LSP resonator, feed lines, amplifier bias layout and all passive circuit elements. The amplifier as an active circuit is not included here. Considering that the resonant behavior of the spoof-LSP is dominated by the passive resonator, and that the active amplifier only adds loading effects, we expect to see similar resonant behaviors as the measured results. To gain more insight on the field distributions of the resonant modes, the vertical E and H fields (namely ā İ and Ą İ ) above the spoof-LSP are sampled at a distance of 1mm from the resonator (similar to the measurement probe setup). Figure 4 (c) and (d) shows the ā İ and Ą İ fields at 2.2 GHz, which clearly display a field distribution of a dipole resonator when ignoring the field disruption caused by the amplifier layout circuits. Figure 4 (e) and (f) shows the ā İ and Ą İ fields at 4.39 GHz, and a clear quadrupole resonator response with four-fold symmetry can be identified. The resonance near 3.51 GHz is an anti-resonance due to the combined effect of the dipole and quadrupole resonances, as discussed later in this section. Note that there is slight field disruption near the amplifier region due to layout of the biasing circuits. However, in general, the simulated field distributions at both frequencies (2.2 GHz and 4.39 GHz) agree closely with the measured data at 2.625 GHz and 4.195 GHz in Figure 3. The specific locations of the peaks and nulls in the field distribution could vary due to the loading effects of the amplifier in measurement, but as expected, the resonant behaviors are dominated by the passive spoof-LSP structure.
To better explain the gain-driven resonator mechanism, we further investigated the intrinsic resonance response of the spoof-LSP structure and then combined it with the amplifier circuit and conducted some behavioral level simulation in Keysight ADS. showing resonances near 2 and 4 GHz, and anti-resonances near 1, 3 and 5 GHz. Such a response can be well represented using the equivalent circuit shown in Figure 5 (c) [53], where multiple series resonance circuits (Ė Ĥ ) are connected in parallel. Specifically, the lowest order mode Ė 0 is inductive and non-resonant. The 1st resonant mode Ė 1 represents the dipole mode near 2 GHz, and the 2nd resonant mode is the quadrupole mode near 4 GHz. Higher order modes can be included if responses at such frequencies are needed. For the gain-driven setup, the LSP structure is connected to the input and output of an amplifier, as shown in Figure 5 (c), forming a positive feedback loop, which is expected to enhance the resonance response. For simple demonstration, a behavioral amplifier is used in ADS for the simulation, with a gain of 13.6 dB, an input resistance of 130 Ohm and an output resistance of 95 ohm, estimated based on the data sheet of our adopted amplifier. Figure 5 (d) compares the LSP's input resonance response (ď 11 of the gain-driven LSP loop) with (blue line) and without (red line) the amplifier. We clearly see boosted oscillation near resonance frequencies due to inclusion of the amplifier. However, the actual resonance response will depend on the gain, input and output impedances (real and imaginary) of the physical amplifier, which are typically frequency dependent. Therefore, the simulation result in Figure 5 (d) only serves to demonstrate the general principle of the gain-driven LSP resonance.
Next, we study the photon-magnon coupling behaviors of the gain-assisted spoof-LSP mode.
Due to the LSP mode's sensitivity to additional magnetic load, we tested both the YIG sphere (representing minimal magnetic load) and the YIG disc (maximal magnetic load) to investigate the photon-magnon coupling effect. Although the ď 21 measurement can directly manifest the coupling between the stripline and the resonator, the resonator's coupling to YIG can only be reflected by scanning the magnetic fields and measuring the Ĝ -Ą contour plot. For this purpose, the YIG samples are placed at the bottom of the resonator ring as indicated in Fig. 6 Figure 6 shows the photon-magnon coupling spectra of the YIG sphere (a-d) and disc (e-h) samples near their respective Kittel modes at selective dc-voltage (gain) settings, 1, 2.3, 3.1, and 4.1 V. The photon-magnon contour plots are constructed from dČ/d Ĝ scans after subtracting the initial ď 21 background at zero magnetic field. [33,51] For the YIG sphere, at 1 V or below, the photon mode is still weak, rendering the coupling with the YIG magnon mode nearly negligible; as the gain increases, such as at 2.3 V, an anticrossing gap starts to emerge, indicating the establishment of the photon-magnon hybridization. Due to the slight asymmetry in the development of the photon mode profile versus the gain, see Fig. 1(b), the upper hybridized branch is more prominent than the low hybridized branch.
As the gain further increases, for example at 3.1 V, see Fig. 6(c), the photon mode becomes increasingly sharper and the lower branch starts to develop. Above 3.5 V, the coupling strength ĝ ceased to increase further, due to the full establishment of the photon mode profile, see Fig. 7 for a summary of the coupling strength ĝ. However, Further increasing the gain leads to a continuous enhancement of the coupling cooperativity even at the similar size of the anticrossing gap, because the cooperativity, ÿ = ĝ 2 /Ą Ħ Ą ģ , in which Ą Ħ and Ą ģ are the dissipation rates of the photon and magnon counterparts, respectively [54,55]. The evolution of the cooperativity against the dc voltage was summarized in Fig. 7(b). At 4.1 V (highest voltage used in the present work), the lower branch becomes strong enough and exhibits further hybridization with additional, higher-order spin-wave modes of the YIG sphere. However at the same time, the photon mode dissipation also slightly increased (leading to a corresponding reduction of the cooperativity), possibly due to the convoluted nonlinear couplings between the photon mode and multiple magnon resonances. In Fig. 7, we plot the coupling strength and cooperativity, respectively, for the YIG sphere and disc samples, using the pristine linewidths of the YIG magnon and LSP photon modes. Both the coupling and the cooperativity are found larger for the disc sample than with the sphere, primarily due to the larger magnetic volume of the disc matching the spatial mode profile of the spoof-LSP.
Finally, given the fixed spoof-LSP mode profile (e.g. shown in Fig. 3), the in-plane anisotropy of YIG thin films reduces the overall coupling efficiency to the photon mode. Such a coupling would be dependent on the anisotropy strengths, film thicknesses, and the gap distance between the YIG film and the resonator board surface, which would merit a separate study beyond the current parameter space.
To conclude, we designed and fabricated an actively controlled ring resonator accommodating a spoof-LSP mode, and demonstrated gain-assisted photon-magnon coupling with the YIG magnon mode under several different sample geometries. The achieved coupling amplification is largely benefited from the high Q-factors due to the additional gain provided by a semiconductor amplifier, that increases the Q-factor from a nearly null state (passive resonance) to more than 1000 for the quadrupole LSP mode. Our demonstration suggests an additional control knob for manipulating hybrid magnonics, using unconventional surface-plasmon modes leveraging an active amplification effect.