Control and Manipulation of Microwave Polarization and Power of a Frequency-Agile 198 GHz Gyrotron for Magnetic Resonance

Dynamic nuclear polarization (DNP) is a rapidly developing signal enhancement method that can be used to overcome the inherent low sensitivity of solid-state nuclear magnetic resonance (NMR). NMR signal intensity is boosted with DNP by transferring the much larger polarization of electron spins to nuclear spins using microwave irradiation close to the electron paramagnetic resonance (EPR) frequency [1‐5]. The maximum theoretical enhancement factor (γ_e/γ_n) is 657 for protons [6], resulting in much shorter experimental times. Such improvements in NMR sensitivity enable a growing repertoire of experiments on systems otherwise inaccessible, such as intact human cells [7‐9] and the surface of functional materials [10‐12]. The sample of interest is typically doped with unpaired electron spins, in the form of polarizing agents which are typically stable organic radicals [13].

DNP experiments are most often performed in combination with magic angle spinning (MAS), a method that can greatly improve spectral resolution by averaging anisotropic interactions of the nuclear spin Hamiltonian. MAS instrumentation, i.e., the stator for spinning gas supply and the sample container/rotor, greatly complicates the integration of a resonant structure to improve the B_1e fields. Therefore a high power microwave source, such as a gyrotron oscillator, is often employed to generate high B_1e fields for DNP. The development of stable high power microwave sources (e.g., gyrotrons) [14] and strides in probe technology for low temperature MAS [15‐18] have promoted DNP application to higher magnetic fields, combining high-sensitivity and high-resolution in solid-state NMR [19‐22].

While high power microwave sources are readily applied in continuous wave DNP they become even more important in pulsed DNP applications, as higher B_1e fields are required to control electron spins during DNP matching conditions. Unlike several continuous wave DNP mechanisms, pulsed DNP performance does not decrease with increasing magnetic fields, and is efficient at high temperatures [2, 23]. Pulsed DNP methods at high magnetic fields constitute an important step forward for DNP.

Gyrotrons are high power sources generating coherent electromagnetic radiation in the millimeter- and submilli-meter-wavelength regions and are well-suited for continuous wave and pulsed DNP. Indeed gyrotrons can produce frequency-chirped microwaves and their power exceeds the power of other microwave sources (klystrons, traveling-wave tubes, solid-state microwave generators) [24‐26]. Inside the interaction cavity of gyrotrons high power microwaves are generated in rotating high-order modes and then transformed in the mode converter into a linearly polarized Gaussian-like beam which approximates well the HE₁₁ hybrid mode supported in a circumferentially corrugated circular waveguide [26‐29]. As the interaction with electron spins in DNP and EPR experiments is polarization sensitive, it is important to understand and characterize the microwave polarization generated by the gyrotron.

A combination of hardware capabilities, namely a powerful frequency-agile gyrotron developed in this research group [30], a DNP spectrometer and a quasi optical system including a Martin-Puplett interferometer can improve current solid-state NMR methods [31]. The Martin-Puplett interferometer (MPI) [32] allows adjustment of microwave polarization from linear to circular (and anything in between) by changing the path length in the interferometer. If circularly polarized radiation is used for DNP, B_1e field intensities are optimized while sample heating is minimized as electron spins only absorb circularly polarized irradiation in the direction of Larmor precession [33, 34]. The novelty of this study is the characterization of the output generated by the frequency-agile gyrotron and the unexpected finding that elliptically polarized microwaves are produced. Through the adjustment of the microwave properties (power, frequency and polarization) the beam can be tailored, for example, for DNP experiments or future induction-mode EPR detection [35].

In this manuscript, first a detailed description of the experimental setup designed for the generation of microwaves and their transmission to the sample is given. Also a procedure for the adjustment of microwave power and polarization is provided in Section 2. Then, the evaluation of the microwave polarization at the gyrotron output and the calibration of the quasi optical system is presented in Section 3. Finally, the results of this analysis and the demonstration of quasi optical system operation is presented in Section 4. Furthermore, Section 4 shows the DNP enhancement dependence on the microwave polarization.

Versatile instrumentation including a frequency-agile gyrotron as the microwave source for DNP, a quasi optical system with an MPI and a DNP NMR spectrometer is presented. A custom-built 198 GHz gyrotron, capable of generating frequency-chirped microwaves has already been implemented by this research group [30, 36]. Through microsecond-adjustment of the anode voltage, the microwave frequency can be swept over a bandwidth of 335 MHz. Such microwave chirps can be employed for electron decoupling, or time-domain DNP with MAS [37, 38].

The internal mode converter inside the gyrotron transforms the TE_5,2 mode generated in the interaction cavity into a Gaussian-like beam, which couples well to the HE_1,1 mode supported in an overmoded, corrugated waveguide [39, 40]. The corrugated waveguide combined with mitre bends and a waveguide taper efficiently transmit the microwaves to the sample inside the NMR magnet.

In this manuscript a quasi optical system [41, 42] is implemented at the output of the 198 GHz frequency-agile gyrotron. One of the major advantages of such systems is that they have a very low insertion loss and are broadband [43]. The quasi optical system (Thomas Keating Ltd., Fig. 1) consists of several refocusing (I-IV) and flat mirrors (a-b), two free-space attenuation stages (RWGP1/2), and an MPI, which allows the selection between horizontal/vertical linear, right-/left-handed circular or elliptical microwave polarization.

The microwave beam path through the quasi optical system is indicated by green arrows in Fig. 1. The two free-space rotating wire grid polarizer (RWGP1/2) function as attenuation stages, where the angle of the wires can be set to any angle 𝜃₁ or 𝜃₂ between 0^∘ and 360^∘. Here, 𝜃₁ or 𝜃₂ indicates the direction of the wires where 0^∘ corresponds to horizontal wires. When the polarization of the microwaves is parallel to the wires in the grid then the beam is reflected. If the wires are perpendicular to the beam polarization, then the beam is transmitted. A fixed wire grid polarizer (FWGP1) with vertical wires (𝜃₃ = 90^∘) ensures that horizontal linear polarization is used as an input for the MPI. The MPI (outlined in red in Fig. 1) consists of a fixed wire grid polarizer (FWGP2) with wires at an angle of 45^∘, two roof mirrors, and a micrometer translation stage for one of the roof mirrors. In the MPI the beam is equally split by FWGP2, resulting in two beams with ± 45^∘ polarization. As the polarization is neither parallel nor perpendicular to the axis of the roof mirrors the polarization is rotated by 90^∘. Adjustments of the roof mirror mounted on the translation stage cause a difference in the path length between the two beams resulting in a phase change which determines the polarization of the output beam. The two beams recombine at the FWGP2 after being redirected and having the polarization flipped by the roof mirrors. Depending on the path length difference, microwaves with either horizontal/vertical linear, circular, or elliptical polarization are generated, thereby moving on a great circle around the Poincaré sphere [44]. The path length difference corresponds to twice the position shift Δ performed by the micrometer. If the path length difference (2 ⋅ Δ) is equal to a quarter integer or three-quarter integer value of the wavelength, the output beam will be circularly polarized (left- and right-handed, respectively). Similarly, if 2Δ corresponds to a half-integer value of the wavelength, then the polarization will be vertical linear, and if 2Δ is equal to an integer value of the wavelength, then the output will be horizontal linear. Any other path length difference will result in elliptical polarization. With a few focusing and flat mirrors the recombined beam couples directly into the output waveguide. The microwaves then travel through the waveguide, several mitre bends, and a waveguide taper until reaching the sample in the 7 T NMR magnet.

For the DNP experiments a sample of ¹³C- and ¹⁵N-labelled urea (4 M) doped with the nitroxide biradical AMUPol (20 mM) in DNP juice (d8-glycerol:D₂O:H₂O (60:30:10)) was used and a custom-built cryogenic DNP apparatus including a 4-channel MAS NMR probe [45] with 3.2 mm zirconia rotors was employed.

As described in the previous section (Section 2), the microwaves pass through several components in the quasi optical system that are used to manipulate the transmitted power and the polarization. To determine the characteristics of the microwaves at the exit of the quasi optical system and verify the operation of the quasi optical system, the following procedure using the Malus’s law (Section 3.1) or the Jones matrix formalism (Section 3.2) was used to calculate the power and analyze the polarization. From this, the theoretically calculated power can be compared to the measured power, and the rotating wire grids RWGP1 and RWGP2 can be set in order to maximize the output power of the quasi optical system.

The global error function corresponding to the normalized sum of the individual errors 𝜖 (Eq. 4 in Section 3.1) of the different 𝜃₂ was computed and is displayed as a function of the defined parameters 𝜃_i (initial polarization) and R (power ratio) at the two different operating points of the gyrotron in Fig. 2a and b.

As indicated by the red circles in the contour plots (Fig. 2a and b), minimum global errors of 0.028 and 0.017 were found for a gyrotron accelerating voltage of 8.25 kV and 9.5 kV, respectively. The parameters 𝜃_i and R of the minima for both gyrotron operating points coincide, indicating that the gyrotron is generating the same output with regard to polarization independent of the accelerating voltage, beam current, and emitter temperature. 𝜃_i was found to be equal to 60^∘ and R to 0.5. These results reveal that half of the initial power contribution is circularly polarized while the other half is linearly polarized with a polarization of 60^∘ with respect to the horizontal plane. The elliptically polarized microwaves generated by this 198 GHz gyrotron are in contrast to the expected purely linearly polarized output of gyrotrons. In general, internal mode converters of gyrotrons are usually designed to transform the high-order mode of the cavity into a linearly polarized beam [26‐29]. A possible explanation for this finding could be imperfections in the mode converter of the 198 GHz gyrotron. As demonstrated later in this section, the gyrotron output can nonetheless be converted to any desired polarization with the MPI.

As imperfections in the launcher might impair the Gaussicity of the microwave beam, a qualitative analysis of the beam profile was performed. As shown in Fig. S1 in the Supporting Information, the microwave beam profile at the entrance of the quasi optical system fits a Gaussian beam well for the two different operating parameters of the gyrotron used in this work. Furthermore, the beam profiles obtained at different polarizations, measured at the end of the quasi optical system, were similar in shape.

The theoretically calculated power, using a power ratio R of 0.5 and an initial polarization 𝜃_i of 60^∘, fits the recorded data points quite well, as is shown in Fig. 3. For the sake of clarity only one example (𝜃₂ = 70^∘) is displayed; the rest of the data plots can be found in Fig. S2 in the Supporting Information. The dotted line in Fig. 3 corresponds to the theoretically calculated power using completely linear polarized microwaves with a polarization of 60^∘ as input. Clearly, the deviation from the dotted line to the measured data is quite pronounced. This shows that this gyrotron does not produce completely linearly polarized microwaves, but elliptical polarization instead.

The theoretical power P (P_theo,j) as described in Section 3 was calculated using the optimal parameters R of 0.5 and 𝜃_i of 60^∘. P was not only compared to the measured data points (Fig. 3) but was also plotted in Fig. 4a as a function of the angles of the rotating grids 𝜃₁ and 𝜃₂ (RWGP1 and RWGP2). Theoretically the highest power is obtained by setting 𝜃₁ to 36^∘ and 𝜃₂ to 110^∘ and corresponds to 54% of the initial power. Thus a considerable amount of power is deposited into the loads (46% of the power). The loss in power results from the fact that the incoming microwave beam produced by the gyrotron is not linearly polarized. The FWGP1 has vertical, fixed wires which prevents to achieve maximum power, considering an initial power of half circular and half linear polarization (with 𝜃_i = 60^∘). Upon exchanging the FWGP1 grid (𝜃₃ = 90^∘) with a grid with horizontal wires (𝜃₃ = 0^∘) (Eq. 2 in Section 3.1), a theoretical maximum of 69% of the initial power is obtained at the end of the quasi optical system by adjusting the angle of RWGP1 and RWGP2 to 72^∘ (𝜃₁) and 170^∘ (𝜃₂) respectively (Fig. 4b). These settings (𝜃₁ = 72^∘, 𝜃₂ = 170^∘, 𝜃₃ = 0^∘) were used for the following DNP experiments.

The primary advantage of the MPI in the quasi optical system is the ability to modify incoming microwave polarization to any desired polarization — for example, circular or linear polarization. By changing the position of the adjustable roof mirror with the micrometer, the beam goes continuously through vertical linear, left-handed circular, horizontal linear, right-handed circular, vertical linear polarization, etc. In between the purely linear and circular polarization, elliptically polarized microwaves are produced.

In order to test the MPI the power at the end of the quasi optical system was measured as a function of the micrometer position by having a wire grid polarizer with a fixed angle of 180^∘ (horizontal wires) in front of the calibrated calorimeter. As shown in Fig. 5, a sinusoidal behavior is observed where the peaks with maximum power correspond to the generation of vertical linear polarization (transmission through the 180^∘ grid) while the minima represent horizontal linear polarization. At the point of inflection circularly polarized microwaves are obtained. The period δ of the fitted sine function in Fig. 5 amounts to 0.756 mm, corresponding to the change in position Δ of the roof mirror. The path length difference between the two beams caused by adjusting the micrometer by Δ amounts to 2 ⋅Δ = 1.512 mm and should correspond to the wavelength of the microwaves. Indeed a frequency of 197.952 GHz was determined with a frequency measurement system from Bridge 12 Technologies, Inc. which corresponds to a wavelength λ_mw of 1.515 mm. It is worth mentioning that the frequency sweeps generated by the frequency-agile gyrotron (e.g., with a bandwidth of 300 MHz) would only result in a negligible change in polarization as the frequency-swept microwaves pass through the MPI.

Next, the dependence of the DNP enhancement on the different microwave polarizations was investigated. Although similar experiments have been reported previously [53, 54], here DNP enhancement improvements were demonstrated using an elliptically polarized gyrotron output. ¹H NMR spectra with and without microwaves were collected for the model compound ¹³C- and ¹⁵N-labelled urea (4 M) doped with the nitroxide biradical AMUPol (20 mM) in DNP juice (d8_glycerol:D₂O:H₂O (60:30:10)). In order to record spectra with different microwave polarizations, the position of the adjustable roof mirror in the MPI was varied in increments of 50 μ m. The parameters of the frequency-agile gyrotron and the MPI were adjusted in order to produce microwaves with a frequency of 197.735 GHz and a power of 2.5 W incident on the sample. The power is estimated based on a power measurement performed outside the bore of the magnet and a measured power loss over the last section of the waveguide. This power level ensures that the DNP experiments are performed in the linear enhancement versus microwave power regime of AMUPol [55]. A maximum DNP enhancement (𝜖 = I_MWon/I_MWoff) of 127 was achieved with the correct handed circularly polarized microwaves as shown in Fig. 6a. We attribute the relatively low maximum enhancement to lower microwave power and slightly higher temperature, as compared to previous studies [56].

Figure 6b displays the effect of the microwave polarization on the DNP enhanced signal intensity. As expected, the data shows a periodic behavior with a period of the fit function (shown in blue in Fig. 6b) equal to 0.767 mm, in good agreement with half of the wavelength of the 197.735 GHz microwaves. Only the component of the microwave radiation rotating in the same direction as the electron spin precession is absorbed and leads to spin transitions [33, 34]. As known from the position of the micrometer (Fig. 5) the maxima of the curve in Fig. 6b correspond to the correct handedness of circular polarization and minima to the opposite handedness of circular polarization. At the inflection points vertical and horizontal linear polarized microwaves were produced by the MPI. While circularly polarized microwaves lead to maximum and minimum DNP enhancements in Fig. 6b, circular polarization in Fig. 5 corresponds to the inflection points. Therefore a shift in the sinusoidal behavior is observed when comparing Fig. 5 and Fig. 6b. An increase in signal intensity of 34% for circular polarization versus linear was observed, i.e., the enhancement with circularly polarized microwaves was 1.3 times higher than with linear polarization. This is in line with previously reported experimental values [53, 54]. The enhancement dependence on the power is not straight-forward as it is specific to the DNP mechanism. Furthermore changes in polarization might occur when the microwaves enter the stator and pass through the NMR coil or reflect from the rotor surface. In addition, the microwaves propagate to the sample at the complementary angle of the magic angle of about 54.7^∘. As the DNP enhancement depends on the microwave polarization perpendicular to the magnetic field B₀, the effective power experienced by the sample is reduced. This effect is supposed to be small according to Thurber and Tycko [53].

An interesting observation is that even with the wrong handedness of circular polarization, significant enhancement was still observed. This was noticed in other studies [53, 54] as well and may be attributed to partly incorrectly polarized microwaves generated by scattering at the NMR coil and sample holder.

A quasi optical system including an MPI was implemented to control the microwave power and polarization emitted from a frequency-agile 198 GHz gyrotron. The analysis of the microwave polarization revealed that the gyrotron output is elliptically polarized, which is in contrast to the expected linear polarization. Here we utilize an MPI to effectively convert elliptical polarization input to achieve similar DNP gains as previous studies. While DNP enhancements are optimized at the correct handed circularly polarized microwave irradiation, linear polarization will allow for future induction-mode EPR detection. With the control over the microwave beam properties presented here, the basic framework for dual DNP-EPR operation at 7 T was established. Combining improvements with sensitivity from DNP and EPR detection will provide a platform for novel experiments that will push the frontiers of both EPR and DNP.