Photonic Band-Gap Resonators for High-Field/High-Frequency EPR of Microliter-Volume Liquid Aqueous Samples

Abstract

High-field EPR provides significant advantages for studying structure and dynamics of molecular systems possessing an unpaired electronic spin. However, routine use of high-field EPR in biophysical research, especially for aqueous biological samples, is still facing substantial technical difficulties stemming from high dielectric millimeter wave (mmW) losses associated with non-resonant absorption by water and other polar molecules. The strong absorbance of mmW’s by water also limits the penetration depth to just fractions of mm or even less, thus making fabrication of suitable sample containers rather challenging. Here we describe a radically new line of high Q-factor mmW resonators that are based on forming lattice defects in one-dimensional photonic band-gap (PBG) structures composed of low-loss ceramic discs of λ/4 in thickness and having alternating dielectric constants. A sample (either liquid or solid) is placed within the E=0 node of the standing mm wave confined within the defect. A resonator prototype has been built and tested at 94.3 GHz. The resonator performance is enhanced by employing ceramic nanoporous membranes as flat sample holders of controllable thickness and tunable effective dielectric constant. The experimental Q-factor of an empty resonator was ≈520. The Q-factor decreased slightly to ≈450 when loaded with a water-containing nanoporous disc of 50 μm in thickness. The resonator has been tested with a number of liquid biological samples and demonstrated about tenfold gain in concentration sensitivity vs. a high-Q cylindrical TE₀₁₂-type cavity. Detailed HFSS Ansys simulations have shown that the resonator structure could be further optimized by properly choosing the thickness of the aqueous sample and employing metallized surfaces. The PBG resonator design is readily scalable to higher mmW frequencies and is capable of accommodating significantly larger sample volumes than previously achieved with either Fabry-Perot or cylindrical resonators.

Graphical abstract

1. Introduction

High-field EPR is highly advantageous for the studies of structure and dynamics of molecular systems possessing unpaired electron spins [1]. The continuing growth of this field is supported by the expanding availability of state-of-the-art continuous wave (CW) and pulsed spectrometers operating at 94, 130, 263, and 275 GHz (see e.g., refs. [2–13]). These frequencies fall into the millimeter wave (mmW) or extremely high frequency (EHF) range as per the International Telecommunication Union designation for the band of radio frequencies in the electromagnetic spectrum from 30 to 300 GHz. Experimental capabilities for EPR at resonant frequencies of up to 1.5 THz have been also demonstrated (e.g., [14, 15]). Despite this growing availability, however, routine use of mmW EPR for aqueous samples above the freezing point is still encountering several technical challenges [16]. The latter primarily stem from an unfavorable combination of much smaller wavelengths of mmW field vs. λ=3 cm corresponding to the conventional X-band (9 GHz) and the unavoidable high dielectric losses in water over the entire mmW frequency range [17, 18]. Moreover, the strong absorbance of mm-waves by the water molecules (at 13-36 dB/mm [19]) limits the penetration depth to just fractions of mm or even less, thus making fabrication of suitable sample containers rather challenging (see e.g., ref. [20]). These are just some of the main technical reasons why the concentration sensitivity of HF EPR still lags behind the conventional X-band EPR [21] even though the Boltzmann magnetization increases with the field.

Currently, the majority of the probeheads for HF EPR could be classified into the following three types: (i) non-resonant sample holders (e.g., [12, 22]), (ii) fundamental mode (FM) n-moded volume cavities (typically, cylindrical TE_01n–type, n= 1,2) (e.g., [4, 23, 24]), and (iii) Fabry-Perot (FP) resonators (e.g., [25, 26, 20, 27, 16]). The non-resonant (NR) sample holders offer, perhaps, the easiest handling of EPR samples [28] at the expense of the effective Q-factor dropping to single digits. Nevertheless, even for NR EPR probehead structures the geometry and volume of containers for lossy liquid aqueous samples have to be carefully optimized in order to obtain the maximum EPR signal [22]. The increased sample volume of such probeheads partially compensates for the very low Q-factor and yields an acceptable signal-to-noise ratio (SNR) if sufficiently high B₁ fields can be generated. Flowever, the latter may require the use of expensive high power mmW sources such as, for example, the 1 kW W-band extended interaction klystron (EIK) tubes employed at Cornell [29] and in the HYPER spectrometer [12] with less than a handful of other installations worldwide. Nevertheless, the relative simplicity together with a possibility to achieve a high filling factor and a nearly absent ring-down makes non-resonant sample holders attractive for some of the pulsed and CW HF EPR applications.

Fundamental-mode (FM) n-moded volume resonators (typically n=1,2), such as cylindrical TE_01n-type cavities, offer high Q-factors (for instance, Q≈4,000 for an unloaded TE₀₁₂ resonator at W-band has been reported [30]). Flowever, they require ultra-small sample tubes for aqueous samples (i.d.=100-200 μm) and such miniature tubes are rather delicate to handle. FM resonators operating at higher resonant frequencies require smaller tubes even for non-lossy samples in order to maintain optimal geometry of the resonant mode. For example, a sample tube having i.d. of just 150 μm has been employed for placing non-lossy samples into a FM cylindrical 275 GHz resonator cavity having Q≈1,000 [8]. Since the dimensions of the FM EPR resonators scale down with the mmW length, the optimal volume of aqueous samples in cylindrical cavities reaches only several tens of nl at W-band [24] and reduces to 2-12 nl at 260 GHz [31, 32]. Although the high B₁ field conversion factors of such resonators are advantageous for pulsed EPR even at modest incident powers provided by solid state sources, CW EPR experiments suffer from saturation and rapid passage effects [6] as well as large microphonic noise induced by the magnetic field modulation. Finally but not lastly, as emphasized by Denysenkov and Prisner “… manufacturing such fundamental mode cavities with high quality factors becomes increasingly difficult at decreasing wavelengths” [32].

Fabry-Perot (FP) resonators adapted by EPR from optics [16] have two main advantages over SM cavities: (i) larger sample size/volume and (ii) compatibility with quasioptical components employed to minimize the transmission losses in a mmW bridge while enabling the induction-mode detection by an effective separation of the excitation and reflection mmW beams [33, 12]. The coupling of FP resonators is most efficiently achieved by a conductive mesh that acts as a partially reflective mirror [16]. For FP resonators the main figure of merit is finesse, $\mathcal{F}$, which expands the concept of Q-factor applicable to the FM resonators to multimode structures. Similar to the Q-factor, finesse $\mathcal{F}$ characterizes the resonator losses vs. the stored energy. However, to make this parameter independent of the resonator length, the losses are counted per roundtrip between the resonator mirrors; whereas the Q-factor accounts for losses per oscillation cycle [34]. Consequently, depending on the distance between the mirrors, the high Q-factor of a FP resonator does not necessarily translate into high B₁ fields generated at the sample which is placed within one of the E₁=0 nodes because the B₁ field is also stored at other multiple E₁ nodes along the quasioptical mmW path. Another major drawback of FP resonators for their use in EPR is stemming from the largely inevitable high resistive losses in the mesh that become especially problematic at mmWs because the resistivity of metals increases rapidly with frequency (e.g., [35]). Indeed, the reported finesse $\mathcal{F}$ values drop from 500 to 30 upon increasing the resonant frequency from 90 to 600 GHz [16] with $\mathcal{F}=500$ being the maximum achievable value for an empty resonator at W-band [28]. Unfortunately, the finesse of loaded FP resonators decreases even further because of additional mmW losses and/or unwanted mmW beam scattering by the sample itself. Because the FP resonators are based on optical principles, a high finesse is only achievable if the separation between the mirrors is several-fold greater than the wavelength, λ. For such a geometry even a small angle scattering caused by the sample would yield significant distortions of the planar wave front after being reflected multiple times, thereby degrading the finesse. This problem worsens for aqueous samples due to the very high loss tangent of water at mmW frequencies. For FP resonators loaded with aqueous samples, the values of $\mathcal{F}=60$ were reported at W-band [29] and $\mathcal{F}=50-100$ at 260 GHz [32, 36]. Finally, the filling factor, η, of FP resonators is usually low because the sample occupies only a tiny fraction of the large resonator volume as dictated by its quasioptical design [16].

One way to improve the resonator performance at mmW frequencies would be to overcome resistive losses in metallic parts that unavoidably increase with the frequency. For example, replacing flat metallic end walls of a FM cylindrical cavity resonator operating at 19 GHz by a Bragg reflector composed of low-loss dielectric materials was shown to dramatically increase the resonator Q-factor [37]. This effect is attributed to the very low losses of the specific dielectric materials vs. the high resistivity losses of metals employed to reflect mmW. For FP resonators, a similar approach can be undertaken as described by Krupka and coauthors for 39 GHz FP design [38], although without an application to EPR. Specifically, an addition of two single-crystal quartz layers to each of the metal mirrors of a near-hemispherical FP resonator operated in the TEM_0,0,25 mode yielded a 4.3-fold increase in Q-factor. Unfortunately, a technical implementation of this elegant idea for EPR would be rather challenging. Firstly, in order to replace the focusing mirror one would have to fabricate a Bragg reflector in the form of thin dielectric layers of near-hemispherical shapes from quartz with a micron precision. Secondly, the optimal mechanical positioning of an aqueous sample in such a resonator would be virtually impossible without significant perturbations of the TEM_00q mode.

To the best of the authors’ knowledge, there is only one literature report on constructing and using a FP resonator with Bragg reflectors for EPR experiments, specifically, using reflectors composed of Al₂O₃ and zirconium tin titanate [39]. A Teflon lens was glued to one of the Bragg reflectors to confine the beam between the mirrors. The resonator was directly attached to the fundamental mode rectangular waveguide for EPR detection in a transmission mode. The transmission at resonance was ca. −20 dB, thereby demonstrating a rather poor efficiency for potential EPR applications. It is likely that an inefficient coupling of the fundamental mode waveguide to an oversized photonic mirror and high scattering losses on the Teflon lens were the main causes for such a suboptimal resonator performance.

Here we report on a new resonator/probehead design for HF EPR that is based on forming lattice defects in one-dimensional (1D) photonic crystals. Defects in photonic crystals are known to behave as high Q-factor resonators in nanophotonics [40] but have not been used yet in EPR to the best of the authors’ knowledge. In order to demonstrate the applicability and utility of 1D photonic crystals as efficient resonators for mmW EPR, we have employed mmW field simulations, and then constructed and tested several periodic arrangements of planar layers having alternating dielectric permittivities. Each structure was designed to have a defect where an EPR sample was placed, thus creating a narrow frequency pass band outside which the mm-waves are effectively reflected. The defect also creates a resonant structure confining the mm-waves. In the past, defects in the photonic crystals have been shown to greatly enhance both the Kerr and Faraday effects in a thin ferromagnetic material layer [41]. Losses from the highly absorptive liquid aqueous samples are minimized by placing the sample effectively within the electric E=0 node. A similar result has been obtained theoretically by placing a ferromagnetic metal layer at the node of the electric field in a photonic crystal [42]. We note that 1D photonic crystals exhibit the largest E=0 nodes vs. 2D and 3D photonic structures, thus, allowing for larger sample dimensions. The latter is especially advantageous for EPR and, potentially, for Dynamic Nuclear Polarization (DNP) NMR. Finally, 1D photonic crystals are relatively easy to fabricate and use in practice as demonstrated here by a prototype probehead constructed and tested for 94 GHz (W-band) CW EPR using a series of liquid aqueous samples at room temperature.

In addition, we describe a general approach to aqueous sample holders for EPR that is based on nanoporous anodic aluminum oxide (AAO) membranes. Similarly to FP resonators, the ideal sample geometry for PBG resonators is also that of a flat thin film. Such a shape would match the field contours of the fundamental mode in the resonator, decrease the mmW scatter, and position the sample within the E=0 node. While such a shape requirement appears to be fully compatible with thin films, it represents a known problem for aqueous samples that have to be placed in containers having a thin flat geometry on a micron scale. One example of the latter was provided by Barnes and Freed who described a holder etched in quartz discs for 17 μm-thick water samples [20]. Instead of the quartz plates, here we have utilized AAO membranes, which were previously applied as a mechanical alignment media for lipid bilayers and membrane proteins in EPR and NMR studies [43–49]. A shallow dielectric layer of nanoporous anodic aluminum oxide (AAO) on top of a metallic aluminum substrate was also employed as a loaded surface waveguide to enable surface-enhanced Raman spectroscopy (SERS) of protein binding to lipid bilayers formed in AAO pores [50, 51]. A particular advantage of AAO nanopores is that this chemically inert ceramic material could be fabricated to a specific thickness with sub-μm accuracy and its porosity could be readily controlled to adjust its effective dielectric properties.

2. Experimental Section

a). 1D Photonic Band Gap Resonator for 94 GHz EPR.

Ceramic quarter-lambda wafers composed of Yttria-stabilized zirconia polycrystal (YTZP, thickness: 140±12.7 μm), alumina (AL, thickness: 252±12.7 μm), both from CoorsTek Golden Inc. (Golden, CO) and aluminum nitride (ALN, thickness: 0.0107±0004”, Valley Design Corp. Operations, Inc., Shirley, MA) were cut in-house into discs of 16 mm in diameter using an Epilog Zing Series (Epilog Laser Inc., Golden, CO) laser cutter/engraver. S1-UV Fused Silica discs (diameter: 16.000±0.127 mm, thickness: 0.400±0.127 mm) were purchased from Esco Optics Inc., (Oak Ridge, NJ). Air gaps of ~λ/4 thickness between the solid dielectric layers were formed by using thin Rexolite^® 1422 (a cross-linked polystyrene, McMaster-Carr Supply Company, Elmhurst, IL) rings with o.d.=16 mm, i.d.=15 mm, and thickness of 0.75 mm. Aluminum foil of 0.05 mm in thickness (McMaster-Carr) was employed to form a metallic mirror. The resonator body frame (cf. Fig. 3A) was fabricated from Ultem 1000 (standard unfilled polyetherimide, McMaster-Carr) and attached by brass screws to WR10 bulkhead adapter (SAGE Millimeter, Inc., Torrance, CA). The sample/resonator holding ring was machined from Rexolite^® while other miscellaneous parts for initial bench tests were machined from aluminum. The conical aperture of a standard 22 dB gain horn (Custom Microwave Inc., Longmont, CO) was reduced to i.d.=14 mm and the modified horn was used to feed mmW from a rectangular WR10 waveguide into the PBG resonator. Simulations of the electromagnetic field distribution were carried out using Ansys HFSS software package from Ansys, Inc. (Canonsburg, PA).

Figure 3.

(A) Simulations of mmW |B₁| field distribution at the resonant frequency of 92.9 GHz (W-band) for the “split defect” PBG resonator configuration shown in Fig. 2B. (B) Calculated reflection coefficient (S₁₁) for this PBG resonator yields Q~2,500 for the resonator loaded with a flat 40 μm – thick nanoporous holder containing an aqueous sample (not clearly visible at this scale). Incident microwave power of 4 W was assumed in the simulations. See the text for details on the resonator, sample geometry, and dielectric constants used in simulations.

b). W-band (94 GHz) EPR spectrometer.

W-band (94.3 GHz) EPR spectra were acquired using a continuous wave (CW) spectrometer constructed at NCSU [10]. The spectrometer employs a cryogen-free superconducting magnet (maximum field of 12.1 T) with an integrated 0.12 T superconducting sweep coil to provide accurate scans of the magnetic field in the vicinity of the target value (Cryogenic Ltd, London, UK). The homodyne microwave bridge is of a single-channel design similar to the one described earlier [6]. A varactor-controlled low-noise (phase noise ca. 75 dB/Hz at 100 kHz) Gunn oscillator (ZAX Millimeter Wave Corporation, Upland, CA) was frequency locked to the EPR resonator using an in-house-built AFC circuit operating at 70 kHz. The oscillator has an output power of 60 mW which yields about 30 mW at the resonator after ca. 3 dB combined losses from the narrow band circulator, isolator, and an oversized WR-28 section of the waveguide, which is employed to transmit the 94 GHz field along the magnet bore with minimal losses. All CW W-band EPR spectra were measured at room temperature using 100 kHz magnetic field modulation provided by the SRS830 lock-in amplifier (Stanford Research Systems Inc., Sunnyvale, CA).

c). Aqueous sample for cylindrical TE102-mode W-band cavity resonator.

Aqueous samples were drawn by capillary action into clear fused quartz capillaries (i.d.=0.20 mm, o.d.=0.33 mm, VitroCom, Mountain Lake, NJ), with the ends sealed with Critoseal^® (Leica Microsystems GmbH, Wetzlar, Germany). The sample was centered in the resonator using a nylon holder so that the sealed ends remained outside the cavity. For such a resonator the active length of the aqueous sample is about 2 mm [23] and, therefore, the active sample volume is ≈63 nl.

d). AAO sample holders.

Two types of nanoporous AAO membranes of different porosity and pore morphology were employed as sample holders for liquid model biological samples. Initial experiments with liquid aqueous solutions were carried out using Whatman Anodise membranes (GE Healthcare, Pittsburgh, PA) having ca. 60 μm in thickness. Examination of these substrates with SEM (Fig. 1A) revealed a disordered pore morphology with pore diameter d=245±−38 nm and porosity of 48%. Experiments with lipid bilayers and membrane peptides were carried out with AAO exhibiting a highly homogeneous pore morphology and fabricated in-house as described earlier [43]. The latter substrates were ca. 50 μm thick, had average pore diameter of d=54.2±2.4 nm and porosity of 25% (Fig. 1B).

Figure 1.

Representative SEM images of Whatman Anodise (A) and in-house fabricated AAO (B). From the analysis of larger scale images the average pore diameters and porosity are d=245±38 nm and 48% for (A) and d=54.2±2.4 nm and 25% for (B), respectively.

Larger pieces of the AAO substrates were annealed to ca. 700 °C to decrease background EPR signals down to the noise level and then laser-cut into o.d.=12 mm disks forming nanoporous containers for aqueous samples. Liquid samples were deposited into AAO nanochannels by capillary action since the alumina surface is hydrophilic [52] while the macroscopically aligned lipid nanotubular bilayers were formed by self-assembly as described elsewhere [43]. The AAO disc was placed on top of the mirror, excess of liquid was removed by a cotton swab, and then a pre-cut o.d.=13.5 mm disc of fluorinated ethylene propylene (FEP) tape with a silicone adhesive (2 mil thickness, CS Hyde Company, Lake Villa, IL) was placed on top of the disc to seal the sample. Any remaining excess of liquid was squeezed out and the edges of the disc were additionally sealed with a thin layer of silicone grease (Dow Corning^® high vacuum grease, Dow Corning Corp., Midland, MI). No sample drying was apparent for at least 4-6 hrs.

The total sample volume was estimated by the difference in the AAO disc weight before and after the sample deposition.

e). Chemicals and solvents.

Nitroxide spin probes Tempol (4-hydroxy-2,2,6,6-tetramethyl-piperidine 1-oxyl) and 5DSA (5-doxyl-stearic acid, 2-(3-carboxypropyl)-4,4-dimethyl-2-tridecyl-3-oxazolidinyloxy) and Gd³⁺-DOTA complex (diethylenetriamine-pentaacetic acid gadolinium(III) dihydrogen salt hydrate) were purchased from MilliporeSigma (Burlington, MA). Perdeuterated Tempone (or PDT, perdeuterated 4-oxo-2,2,6,6-tetramethyl-1-piperidi-nyloxy) was purchased from Cambridge Isotope Laboratories, Inc. (Tewksbury, MA). 3-Carboxy-Proxyl (1-Oxyl-2,2,5,5-tetramethyl-2,5-dihydro-1H-pyrrole-3-carboxylic acid) was generously donated by Dr. Maxim A. Voinov (North Carolina State University). Gramicidin from Bacillus brevis was purchased from Fischer Scientific Co. LLC (Pittsburgh, PA), as a mixture of gramicidin A, B, and C. Synthetic phospholipids were purchased from Avanti Polar Lipids (Alabaster, AL) as chloroform solutions (>99% pure) and used without further purification. All other chemicals and solvents were purchased from VWR International (Radnor, PA) or MilliporeSigma, unless otherwise indicated, and used without additional purification.

f). Preparation of spin-labeled gramicidin A and lipid bilayers.

A mixture of gramicidin A, B, and C containing ~ 85% of gramicidin A [53] was covalently modified at the C-terminus with 3-carboxy-proxyl using a modified literature procedure [54]. After completing the reaction the mixture was diluted with water, the precipitate formed was collected on a filter, washed with 5 ml of water, dried on air, re-dissolved in a mixture CHCl₃:CH₃OH (95:5 v/v), and the crude product was separated on a preparative SiliaPlate Extra Hard Layer TLC plate (Silica gel 60 Å F254; SiliCycle Inc., Quebec City, Quebec, Canada) using CHCl₃:CH₃OH (95:5 v/v) mixture as an eluent. The band corresponding to spin-labeled gramicidin A was verified by mass spectrometry. The peptide was then re-purified on a preparative TLC plate (Silica gel 60 Å F254; Merck KGaA, Darmstadt, Germany) with the same CHCl₃:CH₃OH eluent. Spin-labeled gramicidin A was reconstituted into multilamellar DMPC (1,2-dimyristoyl-sn-glycero-3-phosphorylcholine) lipid bilayers using a literature procedure [54].

Multilamellar lipid bilayers (10% to 25% lipids by weight) were prepared from DMPC and DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) using the methods described earlier [55]. DOPC bilayers were doped with 1 mol% of 5DSA similar to ref. [56].

3. Results and Discussion

3.1. Electromagnetic field simulations.

For electromagnetic field simulations we have considered two possible configurations of a 1D PBG EPR resonator (Fig.2). Both configurations are based on forming 1D photonic crystals from a stack of dielectric discs having alternating dielectric constants, ε₁ ≠ ε₂. The discs have the same diameters d >> » and their thicknesses are equal to λ/4 where λ is the wavelength in the corresponding dielectric material. In general, the thickness of the dielectric layers could be (2n + 1)λ/4, where n = 0, 1, 2 …. The stack was arranged so that the disc with the larger ε₂ was always facing the incoming mmW front such as, for example, the TE₁₁ mode provided by an oversized circular waveguide.

Figure 2.

A schematic representation of two possible configurations for 1D PBG EPR resonators. 1D photonic crystal is formed by a stack of discs of alternating dielectric constants ε₁ < ε₂ (light and dark brown, respectively) with ε₁ layer being adjacent to the sample. All discs have the same diameters d >> λ and their thicknesses are (2n + 1)λ/4, where n = 0, 1, 2…, and λ in the mmW length in the corresponding dielectric media. One side of the stack is open for mmW excitation (red) using either TE₁₁ or HE₁₁ mode, while the opposite side is terminated with a reflective (metallic) mirror (dark gray) to achieve a reflection mode operation. A flat EPR sample such as, for example, a lossy aqueous solution (blue), forms a defect in the 1D photonic crystal. When the defect is placed in the middle of the crystal a “full defect” configuration is achieved (A). Alternatively, the sample can be placed directly on the reflective mirror (“split defect” configuration (B)). See text for details.

One can envision two possible one-dimensional PBG resonator configurations that differ by the location of the defect where the sample is placed. In the first configuration a defect is formed by breaking the periodicity of the alternating dielectric layers in the middle of the dielectric stack by replacing a dielectric layer with a sample. We will refer to such a configuration as “full defect” PBG resonator (Fig. 2A). A sample (either liquid or solid) in a form of a flat disc is placed in the middle of the defect, exactly at the location of the E = 0 node of the standing wave confined in the crystal defect. In the second “split defect” configuration a reflective mirror is placed in the middle of the defect (Fig. 2B), thus, replacing the second half of the dielectric stack with its reflected image. Thus, the “split defect” structure is essentially equivalent to the “full defect” resonator but operating in the reflection mode. While the “full defect” configuration is advantageous because it does not suffer from the absorptive mmW losses occurring in the reflective mirror, the “split defect” configuration is simpler to realize in practice because it could be fabricated from a lesser number of moving parts. Even more important for practical applications is the ability to frequency-tune the split defect PBG resonator by adjusting the position of the reflective mirror relative to the dielectric stack with the sample being attached directly to the mirror.

For the initial simulations we have considered a “split defect” PBG resonator formed by a 1D photonic crystal composed of five (5) λ/4 quartz (ε = 4) discs separated by air gaps which are also λ/4 –thick. The diameter of the quartz discs was chosen to be D = 14 mm or ≈ 17 λ and the discs were assumed to be enclosed by a cylinder with conductive walls (designated in Figs. 2 and 3A by light gray color). As a reasonable approximation, resistivity losses at the cylinder walls were neglected because the electric field in this region of the resonator is small due to its highly oversized diameter (i.e., D >> »). The resistive losses in the conductive mirror were expected to be minor vs. those incurring in the metallic coupling meshes of FP resonators and were neglected as well. The sample holder was modeled as a flat disc (diameter: 14 mm, height: 40 μm) composed of nanoporous anodic aluminum oxide (AAO) with pores filled with water. The bulk dielectric properties of such a composite sample are expected to be in-between those of pure water and γ-Al₂O₃ that the pores are mainly composed of. The dielectric properties of pure water at mmW frequencies have been studied extensively [18] and an extrapolation of the available data for 25 °C [57] yields ϵ′ = 7.8 and tan(δ) = 1.87 at 93 GHz. Fewer data are available on ceramic Al₂O₃ but Song et al. reported ϵ′ = 9.21 at 13.38 GHz with negligible losses tan(δ) = 0.000084 [58]. We note that the volume of AAO pores can be readily varied by adjusting the anodization and pore enlargement procedures from ca. 10% to 80% [59]. Such fabrication flexibility would presumably allow for varying the effective bulk dielectric properties of AAO sample holder filled with an aqueous sample. Thus, for the initial proof-of-principle calculations we have chosen an intermediate value of ϵ′ = 9.0 and tan(δ) = 0.7. Incident microwave power of 4 W was assumed in the simulations.

Figure 3A shows FIFSS (Ansys, Canonsburg, PA) simulations of the mmW |B₁| field distribution at the resonant frequency of 92.9 GHz (W-band). The simulations show that the |B₁| field is primarily concentrated at the sample and then decays in the dielectric discs away from the mirror. The calculated reflection coefficient (Fig. 3B) yields high Q-factor (Q~2,500) even when the resonator is loaded with a lossy aqueous sample.

3.2. Relationship between finesse and Q-factor for a 1-D photonic crystal resonator composed of N λ/4 dielectric layers.

As briefly discussed in the Introduction section, optical multimode resonators are better characterized by finesse $\mathcal{F}$ rather than the quality factor Q. The latter parameter has been initially developed for LC circuits and FM microwave cavities, in which the sample can be readily placed in the only available electric-field E₁ = 0 node of the standing wave. In resonators built on optical principles, such as FP structures, the separation between the mirrors is significantly greater than λ, thus, resulting in significantly more energy stored along the quasioptical path vs. smaller FM cavities. Since the losses in optical FP resonators occur primarily at the mirrors, the high total energy stored in FP structures would result in very high effective Q-factors even though the magnetic energy stored within the individual E₁ = 0 nodes and the corresponding magnitude of the magnetic field component |B₁| could be rather small. For such multi-mode structures a better value of merit for the resonator performance is finesse, $\mathcal{F}$.

Several definitions of $\mathcal{F}$ for ideal FP resonators, i.e., when the absorption processes between the mirrors are negligible, can be found in the literature [60]. Typically, one defines the finesse $\mathcal{F}$ as a ratio of the linewidth of the transmission or reflection signal (the full width at half maximum, FWFIM) and the free spectral range, FSR [61]:

$$\mathcal{F}=\frac{\mathit{FSR}}{\mathit{FWHM}}=\frac{\pi }{2\arcsin \left(\frac{1-r_1{r}_2}{2\sqrt{r_1{r}_2}}\right)},$$ (1)

where r₁ and r₂ are the amplitude reflectivities of the mirrors. When the finesse is high, i.e. r₁ and r₂ are close to 1, the Taylor series approximation yields:

$$\mathcal{F}\approx \frac{\pi }{1-r_1{r}_2}=2\pi \frac{U}{\delta U_{\mathit{diss}}}=\frac{Q}{n},$$ (2)

where U is the total energy stored in the resonator, $\delta U_{\mathit{diss}}=U(1-r_1^2{r}_2^2)\approx 2U(1-r_1{r}_2)$ is the energy dissipated per roundtrip, Q is the resonator Q-factor, and n is the number of half-wavelengths between the mirrors. This simple relationship between finesse $\mathcal{F}$ and Q-factor is typically employed in the EPR literature when describing the performance of FP resonators (e.g., [62, 29, 32, 36]).

Note that eq. (2) is valid only for a uniform non-lossy dielectric medium confined between the mirrors. For a PBG resonator the energy stored is non-uniform along the resonator length and this should be taken into account. Here we derive an analogous equation for the finesse of 1D PBG resonator composed of N pairs of dielectric plates with alternating ε₁ and ε₂ dielectric constants having λ/4 thickness.

Let us start with an empty FP resonator in which the total electromagnetic energy stored can be written as:

$$U={\int }_0^{V_{\mathit{Res}}}\frac{1}{2}({\epsilon }_0{E}^2+{\mu }_0{H}^2)dV,$$ (3)

where ε_o and μ₀ are the permittivity and permeability of the free space, (vacuum or air) respectively, and the integral is taken over the resonator volume. If one neglects the beam variation along the resonator length, L, (i.e., in the direction of the beam propagation), this equation can be approximated as:

$$U={\int }_0^{V_{\mathit{Res}}}\frac{1}{2}({\epsilon }_0{E}^2+{\mu }_0{H}^2)dV\approx sL{E}_0^2\approx \mathit{ns}\frac{\lambda }{2}{E}_0^2,$$ (4)

since it can be easily shown that the magnetic and electric energies stored from 0 to λ/4 along the standing wave path in a uniform medium are identical. In eq.(4) n is the number of half-wavelengths between the mirrors, E₀ is the amplitude of the electric field in the B₁=0 node, and s is the proportionality coefficient determined by the mmW front surface area.

As already noted above, for a 1D standing wave in a medium composed of alternating dielectric layers of λ/4 in thickness, the electric energy is equal to the magnetic energy, leading to the following relation between the maxima for the electric and magnetic components of the EM field:

$$\epsilon E_0^2=\mu H_0^2,$$ (5)

For the split-defect PBG structure shown in Fig. 2, the total electromagnetic energy stored in the resonator is a sum of the energies stored in the sample and in each of the dielectric layers that can be readily calculated from the continuity conditions for the electric and magnetic fields at the respective dielectric boundaries.

Let us consider an empty split-defect PBG resonator. Then for an air gap (ε₀ = 1) between the metallic mirror and the nearest dielectric layer (ε₁ having ~ λ/4 thickness and an effective surface area s the energy stored is:

$$U_0\approx s\frac{\lambda }{4}{E}_0^2$$ (6)

At the boundary between the air gap and the first dielectric layer, the electric field is continuous (i.e., the tangential components are equal, E₀ = E₁) while the magnetic field has a node. Because in a dielectric medium with permittivity ε₁ the wavelength ${\lambda }_1=\lambda ∕\sqrt{{\epsilon }_1}$, the energy stored in the first dielectric layer can be estimated as:

$$U_1\approx s\frac{\lambda }{4\sqrt{{\epsilon }_1}}{\epsilon }_1{E}_0^2=\sqrt{{\epsilon }_1}s\frac{\lambda }{4}{E}_0^2$$ (7)

In eq. (7), both the increased electric field amplitude and decreased thickness of the dielectric layer have been taken into account. At the next boundary between the first dielectric layer (ε₁ and the second dielectric layer (ε₂) the magnetic field is continuous, while the electric field has a node. Assuming that μ₁ = μ₂, ${\epsilon }_2{E}_2^2={\epsilon }_1{E}_1^2={\epsilon }_1{E}_0^2$ and the energy stored in this layer is, therefore:

$$U_2\approx \frac{{\epsilon }_1}{\sqrt{{\epsilon }_2}}s\frac{\lambda }{4}{E}_0^2$$ (8)

Similarly, at the next dielectric boundary $E_3=\sqrt{{\epsilon }_1∕{\epsilon }_2}{E}_0$ and the total electromagnetic energy stored in the third layer is:

$$U_3\approx s\frac{\lambda }{4\sqrt{{\epsilon }_1}}{\epsilon }_1{E}_3^2=\frac{{\epsilon }_1^{\frac{3}{2}}}{{\epsilon }_2}s\frac{\lambda }{4}{E}_0^2={\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{1}{2}}{U}_2$$ (9)

Similarly:

$$U_4\approx \frac{{\epsilon }_1^2}{{\epsilon }_2^{\frac{3}{2}}}s\frac{\lambda }{4}{E}_0^2={\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{1}{2}}{U}_3$$ (10)

and so forth. The eqs. (6–10) clearly show that if ε₁ < ε₂ then each consecutive dielectric layer stores less mmW energy than the preceding one (i.e., U_n < U_n−1) with the highest energy U₀ being at the sample position. This is in a contrast to Fabri-Perot resonators in which the energy is distributed equally between the nodes. Clearly, in order for 1D PBG resonator to enhance B₁ at the defect layer where sample is positioned, the layer with the lower ε₁ must be adjacent to the defect to satisfy the ε₁ < ε₂ condition.

By summing these equations for a PBG resonator consisting of a λ/4 air gap and N pairs of λ/4 dielectric plates with alternating ε₁ and ε₂ dielectric constants, one obtains the following expression for the total energy U stored:

$$U\approx \left\{1+\sqrt{{\epsilon }_1}\left(1+{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{1}{2}}+\cdots +{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{2N-1}{2}}\right)\right\}s\frac{\lambda }{4}{E}_0^2$$ (11)

By comparing eqs. (11) and (4) one can deduce an effective n_eff for the split-defect PBG resonator:

$$n_{\mathit{eff}}\approx \frac{1}{2}\left\{1+\sqrt{{\epsilon }_1}\left(1+{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{1}{2}}+\cdots +{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{2N-1}{2}}\right)\right\}$$ (12)

so that finesse $\mathcal{F}$ the 1D PBG split defect resonator could be related to the Q-factor in a form analogous to eq.(2) for the Fabry-Perot structure, namely:

$$\mathcal{F}=\frac{Q}{n_{\mathit{eff}}}=2Q{\left\{1+\sqrt{{\epsilon }_1}\left(1+{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{1}{2}}+\cdots +{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{2N-1}{2}}\right)\right\}}^{-1}$$ (13)

In passing, we note that for the full defect structure, the total energy would simply be double that for the split-defect structure, and the expression for the finesse becomes the same as eq. (13) except for an additional factor of 2, viz.:

$$\mathcal{F}=\frac{Q}{2n_{\mathit{eff}}}=Q{\left\{1+\sqrt{{\epsilon }_1}\left(1+{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{1}{2}}+\cdots +{\left(\frac{{\epsilon }_1}{{\epsilon }_2}\right)}^{\frac{2N-1}{2}}\right)\right\}}^{-1}$$ (14)

Finally we note that while finesse of a FP resonator characterizes the stored energy per number of half-wavelengths between the mirrors (cf. eq. (2)), the parameter $\mathcal{F}$ for PBG resonator introduced in eqs. (13) and (14) characterizes the stored energy at the defect site where an EPR sample is located. Thus, ideally, one should keep n_eff as low as possible by, for example, choosing materials with ε₁ = 1 and ε₂ >> 1 (n_eff → 1 at ε₂ → +∞).

The simulations of the split-defect PBG resonator shown in Fig. 3 yield Q ≈ 2,500. According to eq. (13) this value translates into an effective finesse of $\mathcal{F}\approx 1,700$. Contrary to the FP resonator with equally distributed magnetic field energy between the E₁ nodes, this demonstrates that for the split defect PBG resonator a large portion of all mmW energy is localized at the defect site. Based on these encouraging results a prototype of a “split defect” resonator for W-band EPR has been designed and tested.

Design of a “split defect” PBG resonator for W-band EPR.

A schematic cross-section of the “split effect” photonic band-gap resonator is shown in Fig. 4. A standard gain horn (Custom Microwave Inc., Longmont, CO) provided for a conversion from the fundamental TE₁₀ mode of the rectangular WR10 waveguide to an approximately oversized circular TE₁₁ mode. A WR10 bulkhead adapter was attached to the horn and also to the cylindrical outer frame made of Ultem^™1000 by using standard brass screws. A 1D photonic crystal was formed from a stack of λ/4 dielectric discs that were placed inside a Rexolite holder (an aluminum holder was also used for bench tests) and pressed against the horn with a silicone O-ring to mechanically stabilize and align the structure held by four (4) tightening screws. A reflective mirror was attached to a threaded Ultem plunger and a sample was positioned directly on the mirror, thus forming a “spit defect” PBG structure. The mirror was cut from a 50 μm thick adhesive aluminum foil and glued to the tuning plunger. The frequency of the PGB resonator was tuned by rotating the plunger, which resulted in a parallel displacement of the mirror with respect to the dielectric stack. A coil for 100 kHz magnetic field modulation was wound inside a grove in the Ultem body (Fig. 4) to enable phase sensitive detection of continuous wave (CW) EPR signal.

Figure 4.

A schematic cross-section of the constructed “split effect” photonic band-gap (PBG) resonator for W-band EPR. 1D PBG resonance structure is formed by discs with alternating dielectric constants ε₁ and ε₂ that are pressed against the standard gain conical horn. The “split effect” PBG structure is formed by an aluminum mirror attached to the flat end of a threaded plunger with the sample mounted directly on the mirror. The frequency tuning is achieved by turning the plunger by a knob causing the mirror to move with respect to the PBG dielectric stack. In some tests the dielectric discs forming the PBG resonator were confined within a solid aluminum frame.

The resonator assembly shown in Fig. 4 readily allowed for testing various 1D photonic crystal arrangements. The following four arrangements provided the best results but different EPR background signals and Q-factors as discussed in the next section: 1) A total of eight alternating λ/4 discs composed of yttria stabilized zirconia (YTZP) and alumina, 2) a total of eight alternating λ/4 discs composed of YTZP and aluminum nitride (ALN), 3) three quartz λ/4 discs with three 0.75 mm air gaps in between (the gaps were formed by inserting thin Rexolite rings as described in the Experimental Section) 4) a total of ten alternating λ/4 YTZP and quartz discs. As previously noted, for all the photonic crystal periodic arrangements the layer closest to the sample and the reflective mirror was always the one with the smaller dielectric constant.

Reflection tests of a “split defect” PBG resonator for W-band EPR.

The PBG resonator was tested using a varactor-controlled GUNN oscillator (VCO) operating at 94–95 GHz and a homodyne test bridge. The reflected mmW power was measured by an unbiased W-band detector based on a Shottky diode and connected to a Tektronix DPO 7000 series oscilloscope. As expected, the resonance mode (cf. Fig. 5A) is observed when the distance between the mirror and the multilayered dielectric structure was ≈ λ/4 (i.e., half of the thickness of the ≈ λ/2 defect). Other higher-order minima also appear separated by ca. λ/2 distance intervals (not shown). Figure 5A shows two experimental curves for the reflected power vs. frequency for an empty resonator when tuned to ca. 94.31 GHz (black line) and then detuned by placing the mirror against the first dielectric plate (red line). Subtraction of the two curves yields the reflection vs. frequency curve corrected for the bridge reflection (blue line).

Figure 5.

(A) Experimental mmW reflection vs. frequency curve for an empty 1D PBG resonator tuned to ca. 94.31 GHz (black line) and detuned by placing the mirror against the first dielectric plate (red line). Subtraction of the two curves yields the reflection vs. frequency curve corrected for the bridge reflection (blue line). (B) Corrected reflection curves for empty 1D PBG resonators confined by an aluminum (solid blue line) and Ultem (solid red line) frames and the aluminum frame resonator loaded with a nanoporous Whatman AAO disc (height h= 60 μm, diameter d=12 mm) soaked in water (solid green line). The total volume of water inside nanopores is ≈5 μl. Best fits to eq.(15) with an additional linear correction term are shown as dashed lines which are essentially indistinguishable from the experiment. The corresponding Q-factors of the coupled resonators were Q_L = 423 (aluminum frame, empty), Q_L = 368 (Ultem frame, empty) and Q_L = 366 (aluminum frame, loaded with wet AAO). In all experiments the 1D PBG structure was formed by 8 alternating λ/4 discs of YTZP and alumina.

Figure 5B shows background-corrected reflection curves for empty and loaded 1D PBG resonators formed by 8 alternating λ/4 discs of YTZP and alumina when housed inside an aluminum and Ultem holders and also for the aluminum holder resonator when loaded with a Whatman^™ AAO disc containing approximately 5 μl of water at room temperature. The reflection curves were simulated using the following equation [63]:

$$\text{Reflected}\text{Power}(\mathit{dB})=10\cdot {\mathit{log}}_{10}{\mid \Gamma \mid }^2$$ (15)

where

$${\mid \Gamma \mid }^2=\frac{{(1-{\beta }^2+{\zeta }^2)}^2+4{\zeta }^2{\beta }^2}{{[{(1+{\beta }^2)}^2+{\zeta }^2]}^2}$$ (16)

and $\beta =\frac{\text{Unloaded}Q-\text{factor}}{\text{Radiation}Q-\text{factor}}=\frac{Q_U}{Q_R}$ is the coupling parameter (β=1 for a critically coupled resonator), $\zeta =2Q_U\frac{{\nu }_0-\nu }{{\nu }_0}$ is the normalized frequency offset, and ν₀ is the resonant frequency. The fitting of the experimental curves of Fig. 5B was further improved by adding a small linear background correction (a_o + a₁ν) to the eq. (15). Parameters ν₀, Q_U, Q_R, a₀ and a₁ were varied to obtain the best fits which were essentially indistinguishable from the experimental curves of Fig. 5B. Finally, the loaded Q-factor, Q_L, (i.e., Q-factor of the coupled resonator) was obtained as:

$$\frac{1}{Q_L}=\frac{1}{Q_U}+\frac{1}{Q_R}$$ (17)

These simulations yielded Q_L = 423 and 368 for empty 1D PBG resonators confined by an aluminum or Ultem frame, respectively. The Q-factor for the aluminum frame resonator has decreased slightly from 423 to 362 when a water-containing AAO disc was loaded into the resonator. It should be noted that these experimental Q-factors are, however, much lower than Q ≈ 2,500 obtained from the simulations assuming a pure TE₁₁ input mode (cf. Fig 3). One likely reason for the observed drop in the experimental Q-factors is a suboptimal performance of the standard gain conical gain horn as the resonator excitation source. Indeed, the mmW front is expected to be highly curved at the horn output, thus likely causing unwanted interferences and reflections inside the PBG resonator. This hypothesis remains to be verified since at the moment of writing this report a suitable transition to produce a pure TE₁₁ mode output was not available to the authors. Another possible reason for the significantly lower Q-factor of the experimental resonator may be misalignments and geometric imperfections of the resonator components. Such misalignments may cause unwanted scattering of the mmW field inside the resonator and also excite some spurious modes.

The most encouraging observation, however, was a moderately small decrease in the experimental Q-factor when the resonator was loaded with a highly lossy aqueous sample of several microliters volume (cf. Fig. 5B). The nanoporous ceramic AAO nanopores employed here for liquid aqueous samples provided for the disc flatness at the micron scale and such flat shape was proven to be essential for the resonator performance. Indeed, when the AAO disc was replaced by a tiny semispherical water droplet, the resonance “dip” in the reflected signal vanished immediately, thus, indicating a dramatic loss in the Q-factor and coupling. The observed Q-factor loss has also confirmed that the resonant mmW field was indeed excited at the defect site of the photonic crystal. At the same time the observation of only moderate decrease in Q for the flat aqueous samples is consistent with the sample location in the vicinity of the resonant mmW E₁=0 node and demonstrated the overall tolerance of the resonator structure to small sample holder imperfections.

It is worthwhile to note here that, despite some imperfections in the PBG resonator prototype design (probably mainly due to the imperfect TE₁₁ excitation mode), by using eq.(13) to convert the experimental Q-factor of the resonator loaded with a liquid aqueous sample we obtain for the equivalent resonator finesse $\mathcal{F}\approx 120$. This value of $\mathcal{F}$ is higher than the finesse reported to date for FP EPR resonators loaded with lossy biological samples [31] [32] [36]. We attribute this gain in finesse observed for the PBG resonator to (i) an efficient confinement of the mmW energy within the photonic structure defect, (ii) an effective separation of the E₁ and B₁ fields, and (iii) a rapid decay of the mmW field within the dielectric structure away from the defect (cf. Fig 3A and the corresponding discussion).

CW EPR of liquid biological samples at room temperature using W-band PBG resonator.

Various tests of a “split defect” PBG resonator for a series of liquid aqueous solutions and hydrated lipid bilayers have been performed. We start with a comparison of the PBG resonator performance vs. that of a high-Q cylindrical TE₀₁₂-mode cavity tuned to ca. 94.3 GHz. The first test was carried out using the homodyne W-band bridge and superconducting magnet system described above with a sample of 100 μM aqueous solution of nitroxide Tempol. For the PBG resonator the total volume of the Tempol solution occupying AAO nanopores was ≈5 μl although the active volume is expected to be about half of that. By contrast, the active volume of the aqueous sample inside the high-Q resonator capillary was estimated to be only 63 nl. Figure 6 shows room temperature W-band CW EPR spectra of the same Tempol solution recorded using 0.3 s time constant and 100 kHz magnetic field modulation of slightly different amplitudes: 0.8 G for the PBG tests and 0.6 G for the TE₀₁₂-type resonator. While the experimental spectrum obtained with PBG resonator was essentially noise-free, a baseline slant was particularly notable in the high field region of the spectrum (Fig. 6A). Such a baseline is attributed to paramagnetic defects in the dielectric materials (mainly in alumina discs) that were reduced in the subsequent tests (vide infra). We also note that AAO sample holders may also exhibit EPR signals depending on the anodization process [64, 65]; however, the intensity of such signals could be greatly reduced by annealing above 700 °C [64]. All the AAO sample holders employed in this study were annealed to effectively remove the background signals as verified by EPR (not shown).

Figure 6.

Comparison of room temperature single-scan (time constant 0.3 s) experimental EPR spectra of 100 μM aqueous solution of nitroxide Tempol obtained using a “split defect” PBG resonator (A) and a high- Q (≈ 3,500) cylindrical TE₀₁₂-type resonator cavity (B) and the same NCSU-built homodyne mmW bridge. These CW EPR spectra were measured using 100 kHz magnetic field modulation with amplitude 0.8 G (A) and 0.6 G (B). The PBG resonator was assembled from 8 alternating YTZP and alumina discs. The baseline arising from EPR signals from the dielectric stack was corrected (B, solid line) and the spectra were least-squares filled to a fast motion model (B, dashed line). (C) Residual of the fit, i.e., the difference between the baseline-corrected and the simulated spectra. A small portion of the fit residual is also shown using × 100-fold amplification (D). The signal-to-noise ratio (SNR), defined as the ratio of the maximum peak-to-peak signal amplitude to twice the standard deviation of the flat portion of the residual is >1,100. The spectrum using TE₀₁₂-type resonator required no baseline correction (E) and the fit residual (E) revealed no differences between the experiment and the fit. A portion of a residual using ten-fold amplification is also shown (SNR≈96).

A simple polynomial correction allowed for removing most of the baseline from the experimental spectrum of Fig. 6A (solid line). This baseline-corrected spectrum (Fig. 6B, solid line) was least-squares fitted to a fast motion nitroxide model using the software described earlier [66, 55, 67]. The fit residual, i.e. the difference between the baseline-corrected experimental spectrum and the simulation, reveals only negligible deviations between the fit and the model (Fig. 6C). By taking an approximately flat portion of the residual (such as one shown in Fig. 6C in × 100-fold amplification) we have estimated the noise standard deviation a and calculated the signal-to-noise ratio as a ratio of the maximum peak-to-peak signal amplitude and 2σ (SNR>1,100, a similar approach to determining SNR has been described earlier [68]).

The TE₀₁₂-type resonator has unloaded Q≈3,500 and yields the maximum EPR signals for aqueous samples when loaded into 0.2 mm i.d. quartz capillaries. Because such a resonator is constructed from thin gold foil it has no detectable background [10, 24] and least-squares fitting does not require extensive baseline correction (Fig. 6D and E). Following the same procedure, SNR was estimated at SNR≈96. Based on these estimates the prototype “split defect” PBG resonator based on YTZP and alumina provided at least ten-fold gain in concentration sensitivity for an aqueous solution of nitroxide radicals albeit at the cost of a background EPR signal from the alumina discs.

Recently, labeling of biological macromolecules with Gd³⁺-chelates has been gaining interest as an alternative to nitroxides for distance measurements at W-band and higher frequencies [69–74]. The primary reasons for such developments are: (i) chemical stability of Gd³⁺-based molecular tags in intracellular environment [72] that results in a rapid reduction of common nitroxides to EPR-silent hydroxylamines and oxidation to oxoammoniums, (e.g., [75]) and (ii) significant narrowing of Gd³⁺ EPR line with an increase in magnetic field/frequency (e.g., [76, 77]). Such line narrowing facilitates measurements of Gd³⁺ to Gd³⁺ distances up to 3.4 nm as was demonstrated recently by CW EPR at 240 GHz and 30 K [74]. Clearly, EPR distance measurements based on evaluation of Gd³⁺ linewidth broadening would benefit from moving from cryogenic (30 K as in ref. [74]) to higher temperatures and from having a better signal-to-noise ratio.

Motivated by these recent studies, we have performed proof-of-principle measurements of an aqueous solution of typical Gd³⁺ complex Gd-DOTA using “split-defect” PBG resonator and compared that with cylindrical TE₀₁₂-type resonator cavity – all at room temperature (Fig. 7). Concentration of Gd-DOTA was 150 μM, which is by a factor of four lower than the Gd³⁺ concentration employed in ref. [74] (note that ref. [74] specifies 300 μM as a concentration of Gd³⁺ dimers). In order to decrease the resonator background EPR signal, the photonic crystal was formed by a total of 10 alternating YTZP and quartz plates. Room temperature single-scan EPR spectrum obtained from 150 μM aqueous solution of Gd-DOTA did not require a baseline correction and demonstrated an excellent SNR≈140 (Fig. 7A and B). In comparison, single-scan W-band spectrum from the same of Gd-DOTA solution but measured using TE₀₁₂ resonator revealed a noticeable noise and SNR of only ≈20 (Fig. 7C and D). We note that the experimental spectrum of Fig. 7A was recorded at modulation amplitude of just 0.8 G that is significantly smaller than 3.5 or 7.0 G that could be applied for this signal with ≈14.5 G peak-to-peak linewidth.

Figure 7.

Comparison of room temperature single scan experimental W-band EPR spectra of 150 μM aqueous solution of Gd³⁺-DOTA obtained using a “split defect” PBG resonator (A) and a high- Q (Q ≈ 3,500) cylindrical TE₀₁₂-type resonator cavity (C). Experimental parameters were the same as in Fig.4 except that the PBG resonator was formed from 10 alternating YTZP and quartz discs and modulation amplitudes were 0.8 G (A) and 1.0 G (C). Least-squares fits are superimposed with the spectra and the corresponding fit residuals are shown at the bottom as (B) and (D) including a ten-fold amplified portion (B). The signal-to-noise ratios for (A) are (C) are ≈140 and ≈20, respectively.

We note that at the same incident microwave power the detector voltage corresponding to the EPR signal is proportional to the product (Q ∙ η), where η is the resonator filling factor [16] [78]. Thus, we compared the detector voltage corresponding to the EPR signal at the same incident mmW for the two loaded resonators and found that (Q ∙ η) of the PBG structure is at least fourfold higher when compared to the TE₀₁₂ cavity. This is likely due to an increase in the filling factor η in the former case that overweighs a decrease in the Q-factor. The even more favorable signal-to-noise ratio observed for the PBG resonator is related to the resilience of the mostly dielectric PBG structure to “microphonic” noise which is typically observed for the fundamental mode (FM) n-moded volume resonators because of their metallic structures and very high Q-factors (≈2,000-3,000 even for the loaded resonators). The high–Q cavities would also effectively convert phase noise of the mmW sources into amplitude noise, thus decreasing the benefits of operating at higher mmW power level and imposing strict requirement on mmW oscillators [6]. For example, for these reasons the signal-to-noise ratio of EPR spectra detected with our TE₀₁₂-type cylindrical resonator do not improve upon increasing the incident mmW power above ca. 0.3 mW. Flowever, no microphonic noise and/or the noise from the mmW oscillator were observed with the PBG resonator even at the maximum 20-22 mW power. It is also likely that the prototype of the PBG resonator we tested has a lower B₁ conversion factor (i.e., lower B₁ at the same incident power) than the TE₀₁₂ cavity simply because the former exhibited a lower Q-factor while allowing for a much higher sample volume.

As already noted before, the PBG resonators built using YTZP-Alumina dielectric layers demonstrated the highest Q-factors among the other structures we have tried so far (Q_L = 423, Fig. 5B). However, such resonators exhibit strong background EPR signals over a broad range of the magnetic fields even at room temperature. These signals arise primarily from alumina wafers as was confirmed by acquiring W-band spectra from an empty PBG resonator and also alumina powder using background-free cylindrical TE₀₁₂ resonator (not shown). The background signals were found to be much smaller in the YTZP-ALN arrangement and nearly absent for YTZP-quartz photonic crystals. Based on a comparison of experimental W-band EPR spectra we estimate that the product (Q ∙ η) is a factor ≈1.6 smaller for YTZP-ALN structure and a factor of ≈2.8 smaller for YTZP-quartz vs. the best YTZP-Alumina combination.

An additional sensitivity test of the W-band split-defect PBG resonator for aqueous samples is shown in Figure 8. The sample was made from just 1 μM aqueous solution of perdeuterated nitroxide Tempone in water soaked into and sealed inside a Whatman AAO sample holder. In order to suppress background EPR signals from the ceramics, the photonic crystal was formed by alternating 4 YTZP and 4 ALN discs. While the background is still detectable (cf. Fig. 8A), it is significantly smaller than the one observed for YTZP/alumina resonator (Fig. 6A). Note that the concentration of nitroxide in Fig. 6A is 100-fold greater than in Fig. 8A. This demonstrates the proportional >100-fold decrease in the resonator background signals that has been achieved with the YTZP/ALN structure. It is worthwhile to note here that the nitroxide EPR signal obtained using this YTZP/ALN structure is only a factor ≈1.5 smaller than the one measured with the 8-disc YTZP/alumina photonic crystal.

Figure 8.

(A) Experimental room temperature single-scan W-band (94.26 GHz) EPR spectrum of 1 μM aqueous solution of perdeuterated nitroxide Tempone obtained using a “split defect” PBG resonator formed by total of 8 alternating YTZP and ALN discs. The spectrum was recorded with 100 kHz modulation with 0.8 G in amplitude, time constant of 1 s, and 21 mW of incident power. The broad background was filtered out and the resulting spectrum (B) was least-squares fitted to a fast motion model. The fit residual (C) shows no significant deviations between the experiment and the fit after background filtering/subtraction. A portion of the fit residual (C) is shown by ten-fold amplification. Signal-to-noise ratio is SNR≈103.

As can be seen from Fig. 8, fast motion EPR signal from nitroxide in liquid water is readily detectable using just a single scan at concentrations as low as 1 μM with an excellent signal-to-noise ratio (SNR≈103). While the broad EPR signal originating from YTZP/ALN discs is still detectable, it is readily filtered out from the sharper nitroxide lines using the methods described earlier [79]. The resulting spectrum (Fig. 8B) has been least-squares fitted to a fast motion model with the fit residual (Fig. 8C) demonstrating the appropriateness of both background correction and the EPR spectra fitting procedure.

While other nanoporous and mesoporous materials could be possibly employed as the sample holders for liquid samples in PBG EPR resonators, nanoporous AAO membranes hold an advantage of also serving as an alignment media for lipid bilayers and membrane proteins (e.g., [43–49]). In order to provide the first proof-of-concept of employing PBG resonator EPR technology and AAO samples holders to study macroscopically aligned lipid bilayers and membrane proteins at biologically relevant temperatures and hydration levels, we have deposited DOPC lipid bilayers doped with 1 mol% of EPR membrane probe 5-Doxyl stearic acid radical (5DSA) into an in-house fabricated AAO disc. The nanopores were filled with excess of water and sealed as described in the Experimental section. A room-temperature single scan W-band EPR spectrum of the sample (Fig. 9A) obtained with the 6-disc YTZP/ALN resonator was essentially noise-free. The spectrum is consistent with the orientation of 5DSA molecules so that the nitroxide magnetic z-axis is perpendicular to the external magnetic field and undergoing a rotational motion about z-axis resulting in a partial averaging of g_x and g_z spectral features (approximate positions of the principal axis g-matrix components are indicated in Fig. 9A). Such an orientation and rotational dynamics of 5DSA is indeed expected upon partitioning in the lipid nanotubular bilayers confined by AAO nanochannels with the pore axes directed along the external magnetic field B₀ and the bilayer director being perpendicular to B₀.

Figure 9.

Experimental single-scan W-band EPR spectra of fully hydrated spin-labeled samples macroscopically aligned by nanochannels of in-house fabricated AAO holder. (A) EPR spectrum of nanotubular DOPC bilayers doped at 1 mol% 5DSA and aligned by AAO nanopores at 19 °C. Approximate positions of the principal axis g-matrix components are indicated by arrows. (B) EPR spectra of spin-labeled dimeric gramicidin A channel formed in nanotubular DMPC at 25 °C. AAO nanopores were filled with either water (thin line) or 2.4 M aqueous KCL solution (thick line) resulting in approximately double occupancy of K⁺ in the dimeric gA channel. All spectra were measured with an 8 disc YTZP/ALN resonator using 1 s time constant and 0.8 G modulation amplitude. See text for details.

Another example of the general utility of our PBG resonator is provided by W-band EPR spectra of spin-labeled gramicidin A (sl-gA) channel formed in DMPC lipid bilayers. gA is a 15-residue polypeptide which dimerizes in the bilayer to form a membrane-spanning pore of 4.5-Å in diameter pore accommodating ions and a single file of water molecules. The dimer is formed, however, only in lipid bilayers, such as the DMPC bilayers, which provide proper hydrophobic match for the right-handed β-helix [80, 81]. Previous X-band (9 GHz) EPR studies of gA with free hydroxyl at the C-terminus labeled with a nitroxide revealed not only anisotropic rotational dynamics of the nitroxide molecular tag but also sensitivity of the EPR spectra to the so-called diffusion-tilt angle, i.e., the angle between the main rotation diffusion axis of the molecule and the magnetic z-axis of the nitroxide [54]. The latter data were obtained for planar DMPC lipid bilayers that were macroscopically aligned by isopotential spin-dry ultracentrifugation (ISDU). Figure 9B shows W-band EPR spectra of gA labeled as at the same position and incorporated into the same DMPC bilayers as reported by Dzikovski et al. [54]. The macroscopic alignment of lipid bilayers in AAO nanochannels provides for the perpendicular orientation of the director vector of the lipid bilayers with respect to B₀. The spectra measured at 25 °C (i.e., above the main phase transition of DMPC bilayers that remains largely unaffected by the nanopore confinement [82, 83]) revealed a high degree of macroscopic alignment for the nitroxide probe with the g_z spectral features suppressed in comparison with the g_x and g_y components (Fig. 9B). Similar relative changes in the component intensities were observed with X-band EPR [54] as measured at the perpendicular orientation of the bilayer aligned by glass plates.

Excellent signal-to-noise ratio and a negligible contribution from the resonator background allowed for observing changes in W-band EPR spectra of sl-gA when the gA/DMPC–loaded AAO disc was exposed to 2.4 M KCI (cf. thin- and thick-line EPR spectra in Fig. 9B). Such an exposure is expected to generate approximately double occupancy of K⁺ in the dimeric gA channel, or one ion per monomer, and a conformational change involving at least the channel opening as was indicated by earlier ¹⁷O solid state NMR studies [48]. If this is indeed the case, such a change would affect the nitroxide diffusion-tilt angle which would be reflected in high-resolution W-band EPR spectra of sl-gA as was observed in our experiment (Fig. 9B).

4. Conclusions

The design and experimental tests of the first successful prototype for the radically new line of EPR resonators based on 1D photonic band-gap (PBG) structures have been reported. Such resonators are particularly promising for mmW frequencies where the repertoire of EPR probeheads remains rather limited, particularly for lossy liquid biological aqueous samples above the freezing temperatures. We believe that such photonic band-gap resonators will be useful for a wide variety of applications including: (i) CW and pulsed high field / high frequency (HF) EPR of aqueous biological samples having a few μl in volume using low-power cost-efficient mmW sources without the need for expensive tube-based devices like ElKs, and TWTs capable of generating up to ca. 1 kW power; (ii) Improving concentration sensitivity of HF EPR by at least tenfold even for liquid aqueous samples; and (iii) Studies of soluble and membrane proteins labeled with nitroxides and Gd³⁺ chelates that are currently hampered by low sensitivity of the existing high field EPR probeheads.

We have also described a novel type of aqueous sample holders for high-field EPR that are based on nanoporous anodic aluminum oxide (AAO) membranes. A particular advantage of AAO nanopores is that this chemically inert ceramic material could be fabricated to a specific thickness with sub-μm accuracy and its porosity could be readily controlled to adjust its effective dielectric properties. Furthermore, AAO nanopores serve as a versatile mechanical alignment media for lipid bilayers and membrane proteins, thus, providing an additional gain in resolution.

Compared to the single-mode EPR cavities, 1D photonic band-gap resonators accommodate a much larger sample volume by increasing the resonator diameter while overall flatness of the sample is required for its performance. Potentially, the PBG structure could incorporate multiple defects allowing for multiple sample layers, thereby increasing the sample volume even further. The use of novel materials with very high dielectric constants and low losses [84] would make the size of the resonator comparable to the dimensions of the aqueous sample layer and eliminate the background signal from the resonator.

In addition, the PBG resonator design could be employed for the development of integrated probeheads for simultaneous excitation and detection of both the electronic and nuclear spins. This includes combined radiofrequency/mmW probeheads for ENDOR, liquid-state DNP, and DNP-enhanced studies of membrane proteins by solid-state NMR and EPR at essentially the same experimental settings.

Highlights.

• High-Q resonator for millimeter wave EPR has been designed, modelled, and tested

• The resonator is based on forming a detect in 1D photonic band gap structure

• Nanoporous ceramics is used for flat aqueous sample holders with tunable properties

• The resonator provides a tenfold gain in concentration sensitivity vs. cylindrical cavities