We introduce millimeter-wave silicon photonic crystal cavities as a versatile platform for the perturbative sensing of nanoscale materials. This dielectric-based platform is compatible with strong magnetic fields, opening avenues for studying quantum materials in extreme environments where superconducting cavities cannot operate. To establish the platform's performance, we cryogenically characterize a silicon photonic crystal cavity at 4.3 K, achieving a total quality factor exceeding $10^5$ for a 96 GHz mode. As a proof-of-concept for its sensing capabilities, we position a hexagonal boron nitride-multilayer graphene (hBN-MLG) heterostructure at an electric-field antinode of the cavity and measure the perturbative response at room temperature. The heterostructure induces a significant change in the cavity's resonance, from which we extract a total sample conductivity of approximately $5.1\times10^6$~S/m. These results establish silicon photonic crystal cavities as a promising platform for sensitive, on-chip spectroscopy of nanoscale materials at millimeter-wave frequencies.
The millimeter-wave (mm-wave) regime bridges the microwave and optical frequencies, providing unique opportunities for both fundamental science and emerging technologies [1][2][3][4][5][6][7][8][9][10][11][12]. This frequency range enables resonant access to elementary excitations and collective modes in quantum materials, rotational modes of small polar molecules, and the structural vibrations of large biomolecules [13][14][15][16][17][18]. Ultrafast terahertz (THz) time-domain spectroscopy is an indispensable tool in this landscape, yet its free-space architecture and optical gating can be challenging to implement in cryogenic or highfield environments. Moreover, typical detection mechanisms in time-domain THz spectroscopy, such as photoconductive antennas or electro-optic sampling, often suffer from limited sensitivity when probing very low-energy excitations or subtle electronic states [19,20].
Meanwhile, advances in mm-wave and THz integrated photonics have opened new avenues for miniaturizing future telecommunication and sensing systems [21][22][23]. The small wavelength of light at these frequencies and the excellent properties of silicon at mm-wave and THz wavelengths enable low-cost manufacturing approaches based on silicon micromachining.
In this Letter, we present a silicon mm-wave device for the perturbative sensing of material properties at ∼100 GHz. Although high-Q silicon photonic crystal cavities have been used for biosensing at frequencies ranging from mm-wave to optical [24][25][26][27][28], their application to nanoscale materials has not yet been explored. As an initial demonstration, we measured the perturbative effects ). The cavity linewidth can also change due to the introduction of the sample κi → κ ′ i (blue shading to red shading). (c) Rendering of a millimeter-wave photonic crystal cavity. To maximize the cavity’s perturbative response, the sample is introduced at an electric field antinode of the photonic crystal cavity fundamental mode. The solid arrow indicates half of the device’s length, 18.74 mm.
of thin multilayer graphene flakes (MLG) on the modes of a silicon photonic crystal cavity. Importantly, we measured the cryogenic performance of this cavity architecture for the first time, observing quality factors exceeding 10 5 in the W-band (75-110 GHz) [25,26,[29][30][31][32]. Unlike traditional free-space, time-domain approaches that mea-sure averaged material responses, perturbative sensing with a silicon photonic crystal cavity enables frequencydomain detection with inherent sub-wavelength field confinement. As depicted in Fig. 1, in perturbation-based sensing, changes to the cavity resonance frequency, ∆ω = ω ′ c -ω c , and internal linewidth, ∆κ i = κ ′ i -κ i , directly encode the complex permittivity, ε = ε ′ -jε ′′ . Consequently, a high quality factor, Q, is critical to detect small changes in ε.
Our millimeter-wave silicon photonic crystal cavity adapts optical frequency photonic crystal cavity design principles to achieve photonic confinement [33]. The design process, summarized in Fig. 2, involves first engineering a photonic bandgap through periodic index modulation, then introducing an optimized defect for mode confinement, and finally implementing linear tapers to interface with WR10 rectangular waveguides (see Section SI and Fig. S1a).
The periodic mirror cells create a photonic bandgap by coupling forward-and backward-propagating transverseelectric (TE) modes. Using finite-element simulations (COMSOL), we engineer a bandgap centered at 97.29 GHz with a 22.86 GHz span (23.5% fractional bandwidth), as shown in Fig. 2a,b. A resonant cavity is formed by introducing a defect cell, with a smooth cubic interpolation between the mirror and defect geometries [33]. A genetic algorithm was used to maximize the radiation-limited quality factor of the fundamental defect mode. The fundamental mode is defined as the mode with the fewest longitudinal variations in the electric field confined by the cavity. In this quasi-1D cavity, the resonance frequency decreases as the longitudinal mode number increases, due to the corresponding increase in the effective refractive index. Full-device, frequency-domain simulations predict a fundamental mode at 90.958 GHz with a total linewidth of ≈ 450 kHz, dominated by external coupling to the WR10 rectangular waveguides (see Fig. 2d). The complete design parameters as a function of unit cell index are shown in Fig. 2c.
We fabricated the photonic crystal cavities from intrinsic silicon (ρ Si ≥ 20 kΩ-cm) using the device geometry determined by the optimization procedure described above. The main features were defined by photolithography, and the silicon was etched using a reactive-ion etch (see Section SIV and the attached device DXF).
As a proof-of-concept, we integrated a two-dimensional quantum material heterostructure directly onto the silicon photonic crystal cavity (Fig. 3d,e). We utilized a dry-transfer technique in which hex
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