# Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications

^{*}

## Abstract

**:**

^{2}while realizing high Rabi frequencies of up to 10 MHz in an ensemble of NV centers.

## 1. Introduction

## 2. Microfabrication Methods

## 3. Numerical Simulation and Optimization

## 4. Experimental Setup and Methods

## 5. Antenna Performance

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Jaskula, J.C.; Bauch, E.; Arroyo-Camejo, S.; Lukin, M.D.; Hell, S.W.; Trifonov, A.S.; Walsworth, R.L. Superresolution optical magnetic imaging and spectroscopy using individual electronic spins in diamond. Opt. Express
**2017**, 25, 11048–11064. [Google Scholar] [CrossRef][Green Version] - Barson, M.S.; Peddibhotla, P.; Ovartchaiyapong, P.; Ganesan, K.; Taylor, R.L.; Gebert, M.; Mielens, Z.; Koslowski, B.; Simpson, D.A.; McGuinness, L.P.; et al. Nanomechanical sensing using spins in diamond. Nano Lett.
**2017**, 17, 1496–1503. [Google Scholar] [CrossRef][Green Version] - Pham, L.M.; DeVience, S.J.; Casola, F.; Lovchinsky, I.; Sushkov, A.O.; Bersin, E.; Lee, J.; Urbach, E.; Cappellaro, P.; Park, H.; et al. NMR technique for determining the depth of shallow nitrogen-vacancy centers in diamond. Phys. Rev. B
**2016**, 93, 045425. [Google Scholar] [CrossRef][Green Version] - Arai, K.; Belthangady, C.; Zhang, H.; Bar-Gill, N.; DeVience, S.; Cappellaro, P.; Yacoby, A.; Walsworth, R.L. Fourier magnetic imaging with nanoscale resolution and compressed sensing speed-up using electronic spins in diamond. Nat. Nanotechnol.
**2015**, 10, 859–864. [Google Scholar] [CrossRef] - Grinolds, M.; Warner, M.; De Greve, K.; Dovzhenko, Y.; Thiel, L.; Walsworth, R.L.; Hong, S.; Maletinsky, P.; Yacoby, A. Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins. Nat. Nanotechnol.
**2014**, 9, 279–284. [Google Scholar] [CrossRef][Green Version] - Doherty, M.W.; Struzhkin, V.V.; Simpson, D.A.; McGuinness, L.P.; Meng, Y.; Stacey, A.; Karle, T.J.; Hemley, R.J.; Manson, N.B.; Hollenberg, L.C.; et al. Electronic properties and metrology applications of the diamond NV- center under pressure. Phys. Rev. Lett.
**2014**, 112, 047601. [Google Scholar] [CrossRef] [PubMed][Green Version] - Plakhotnik, T.; Doherty, M.W.; Cole, J.H.; Chapman, R.; Manson, N.B. All-optical thermometry and thermal properties of the optically detected spin resonances of the NV–center in nanodiamond. Nano Lett.
**2014**, 14, 4989–4996. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kucsko, G.; Maurer, P.C.; Yao, N.Y.; Kubo, M.; Noh, H.J.; Lo, P.K.; Park, H.; Lukin, M.D. Nanometre-scale thermometry in a living cell. Nature
**2013**, 500, 54–58. [Google Scholar] [CrossRef] [PubMed] - Doherty, M.W.; Manson, N.B.; Delaney, P.; Jelezko, F.; Wrachtrup, J.; Hollenberg, L.C. The nitrogen-vacancy colour centre in diamond. Phys. Rep.
**2013**, 528, 1–45. [Google Scholar] [CrossRef][Green Version] - Goldman, M.L.; Doherty, M.; Sipahigil, A.; Yao, N.Y.; Bennett, S.; Manson, N.; Kubanek, A.; Lukin, M.D. State-selective intersystem crossing in nitrogen-vacancy centers. Phys. Rev. B
**2015**, 91, 165201. [Google Scholar] [CrossRef][Green Version] - Goldman, M.L.; Sipahigil, A.; Doherty, M.; Yao, N.Y.; Bennett, S.; Markham, M.; Twitchen, D.; Manson, N.; Kubanek, A.; Lukin, M.D. Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers. Phys. Rev. Lett.
**2015**, 114, 145502. [Google Scholar] [CrossRef][Green Version] - Barry, J.F.; Schloss, J.M.; Bauch, E.; Turner, M.J.; Hart, C.A.; Pham, L.M.; Walsworth, R.L. Sensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys.
**2020**, 92, 015004. [Google Scholar] [CrossRef] - Bernardi, E.; Nelz, R.; Sonusen, S.; Neu, E. Nanoscale sensing using point defects in single-crystal diamond: Recent progress on nitrogen vacancy center-based sensors. Crystals
**2017**, 7, 124. [Google Scholar] [CrossRef][Green Version] - Hahn, E.L. Spin echoes. Phys. Rev.
**1950**, 80, 580. [Google Scholar] [CrossRef] - Carr, H.Y.; Purcell, E.M. Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments. Phys. Rev.
**1954**, 94, 630–638. [Google Scholar] [CrossRef] - Gullion, T.; Baker, D.B.; Conradi, M.S. New, compensated carr-purcell sequences. J. Magn. Reson. (1969)
**1990**, 89, 479–484. [Google Scholar] [CrossRef] - Viola, L.; Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A
**1998**, 58, 2733. [Google Scholar] [CrossRef][Green Version] - Cywiński, Ł.; Lutchyn, R.M.; Nave, C.P.; Sarma, S.D. How to enhance dephasing time in superconducting qubits. Phys. Rev. B
**2008**, 77, 174509. [Google Scholar] [CrossRef][Green Version] - Slichter, C.P. Principles of Magnetic Resonance; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013; Volume 1. [Google Scholar]
- Degen, C.L.; Reinhard, F.; Cappellaro, P. Quantum sensing. Rev. Mod. Phys.
**2017**, 89, 035002. [Google Scholar] [CrossRef][Green Version] - Turner, M.J.; Langellier, N.; Bainbridge, R.; Walters, D.; Meesala, S.; Babinec, T.M.; Kehayias, P.; Yacoby, A.; Hu, E.; Lončar, M.; et al. Magnetic field fingerprinting of integrated-circuit activity with a quantum diamond microscope. Phys. Rev. Appl.
**2020**, 14, 014097. [Google Scholar] [CrossRef] - Mizuno, K.; Ishiwata, H.; Masuyama, Y.; Iwasaki, T.; Hatano, M. Simultaneous wide-field imaging of phase and magnitude of AC magnetic signal using diamond quantum magnetometry. Sci. Rep.
**2020**, 10, 1–10. [Google Scholar] [CrossRef] [PubMed] - Horsley, A.; Appel, P.; Wolters, J.; Achard, J.; Tallaire, A.; Maletinsky, P.; Treutlein, P. Microwave device characterization using a widefield diamond microscope. Phys. Rev. Appl.
**2018**, 10, 044039. [Google Scholar] [CrossRef][Green Version] - Glenn, D.R.; Fu, R.R.; Kehayias, P.; Le Sage, D.; Lima, E.A.; Weiss, B.P.; Walsworth, R.L. Micrometer-scale magnetic imaging of geological samples using a quantum diamond microscope. Geochem. Geophys. Geosyst.
**2017**, 18, 3254–3267. [Google Scholar] [CrossRef] - Simpson, D.A.; Tetienne, J.P.; McCoey, J.M.; Ganesan, K.; Hall, L.T.; Petrou, S.; Scholten, R.E.; Hollenberg, L.C. Magneto-optical imaging of thin magnetic films using spins in diamond. Sci. Rep.
**2016**, 6, 1–8. [Google Scholar] [CrossRef] [PubMed] - Clevenson, H.; Trusheim, M.E.; Teale, C.; Schröder, T.; Braje, D.; Englund, D. Broadband magnetometry and temperature sensing with a light-trapping diamond waveguide. Nat. Phys.
**2015**, 11, 393–397. [Google Scholar] [CrossRef][Green Version] - Nowodzinski, A.; Chipaux, M.; Toraille, L.; Jacques, V.; Roch, J.F.; Debuisschert, T. Nitrogen-vacancy centers in diamond for current imaging at the redistributive layer level of integrated circuits. Microelectron. Reliab.
**2015**, 55, 1549–1553. [Google Scholar] [CrossRef][Green Version] - Chipaux, M.; Tallaire, A.; Achard, J.; Pezzagna, S.; Meijer, J.; Jacques, V.; Roch, J.F.; Debuisschert, T. Magnetic imaging with an ensemble of nitrogen-vacancy centers in diamond. Eur. Phys. J. D
**2015**, 69, 1–10. [Google Scholar] [CrossRef][Green Version] - Le Sage, D.; Arai, K.; Glenn, D.R.; DeVience, S.J.; Pham, L.M.; Rahn-Lee, L.; Lukin, M.D.; Yacoby, A.; Komeili, A.; Walsworth, R.L. Optical magnetic imaging of living cells. Nature
**2013**, 496, 486–489. [Google Scholar] [CrossRef][Green Version] - Steinert, S.; Ziem, F.; Hall, L.; Zappe, A.; Schweikert, M.; Götz, N.; Aird, A.; Balasubramanian, G.; Hollenberg, L.; Wrachtrup, J. Magnetic spin imaging under ambient conditions with sub-cellular resolution. Nat. Commun.
**2013**, 4, 1–6. [Google Scholar] [CrossRef][Green Version] - Pham, L.M.; Le Sage, D.; Stanwix, P.L.; Yeung, T.K.; Glenn, D.; Trifonov, A.; Cappellaro, P.; Hemmer, P.R.; Lukin, M.D.; Park, H.; et al. Magnetic field imaging with nitrogen-vacancy ensembles. New J. Phys.
**2011**, 13, 045021. [Google Scholar] [CrossRef] - Steinert, S.; Dolde, F.; Neumann, P.; Aird, A.; Naydenov, B.; Balasubramanian, G.; Jelezko, F.; Wrachtrup, J. High sensitivity magnetic imaging using an array of spins in diamond. Rev. Sci. Instrum.
**2010**, 81, 043705. [Google Scholar] [CrossRef][Green Version] - Maertz, B.; Wijnheijmer, A.; Fuchs, G.; Nowakowski, M.; Awschalom, D. Vector magnetic field microscopy using nitrogen vacancy centers in diamond. Appl. Phys. Lett.
**2010**, 96, 092504. [Google Scholar] [CrossRef][Green Version] - Ariyaratne, A.; Bluvstein, D.; Myers, B.A.; Jayich, A.C.B. Nanoscale electrical conductivity imaging using a nitrogen-vacancy center in diamond. Nat. Commun.
**2018**, 9, 1–7. [Google Scholar] [CrossRef][Green Version] - Thiel, L.; Rohner, D.; Ganzhorn, M.; Appel, P.; Neu, E.; Müller, B.; Kleiner, R.; Koelle, D.; Maletinsky, P. Quantitative nanoscale vortex imaging using a cryogenic quantum magnetometer. Nat. Nanotechnol.
**2016**, 11, 677–681. [Google Scholar] [CrossRef][Green Version] - Pelliccione, M.; Jenkins, A.; Ovartchaiyapong, P.; Reetz, C.; Emmanouilidou, E.; Ni, N.; Jayich, A.C.B. Scanned probe imaging of nanoscale magnetism at cryogenic temperatures with a single-spin quantum sensor. Nat. Nanotechnol.
**2016**, 11, 700–705. [Google Scholar] [CrossRef] - Appel, P.; Ganzhorn, M.; Neu, E.; Maletinsky, P. Nanoscale microwave imaging with a single electron spin in diamond. New J. Phys.
**2015**, 17, 112001. [Google Scholar] [CrossRef] - Tetienne, J.P.; Hingant, T.; Kim, J.V.; Diez, L.H.; Adam, J.P.; Garcia, K.; Roch, J.F.; Rohart, S.; Thiaville, A.; Ravelosona, D.; et al. Nanoscale imaging and control of domain-wall hopping with a nitrogen-vacancy center microscope. Science
**2014**, 344, 1366–1369. [Google Scholar] [CrossRef] - Grinolds, M.S.; Hong, S.; Maletinsky, P.; Luan, L.; Lukin, M.D.; Walsworth, R.L.; Yacoby, A. Nanoscale magnetic imaging of a single electron spin under ambient conditions. Nat. Phys.
**2013**, 9, 215–219. [Google Scholar] [CrossRef][Green Version] - Maletinsky, P.; Hong, S.; Grinolds, M.S.; Hausmann, B.; Lukin, M.D.; Walsworth, R.L.; Loncar, M.; Yacoby, A. A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres. Nat. Nanotechnol.
**2012**, 7, 320–324. [Google Scholar] [CrossRef] - Rondin, L.; Tetienne, J.P.; Spinicelli, P.; Dal Savio, C.; Karrai, K.; Dantelle, G.; Thiaville, A.; Rohart, S.; Roch, J.F.; Jacques, V. Nanoscale magnetic field mapping with a single spin scanning probe magnetometer. Appl. Phys. Lett.
**2012**, 100, 153118. [Google Scholar] [CrossRef][Green Version] - Yang, L.-L.; Liu, Q.-Q.; Pan, X.-Y.; Chen, D.-M. Design and application of a near field microwave antenna for the spin control of nitrogen-vacancy centers. Chin. Phys. Lett.
**2010**, 27, 038401. [Google Scholar] - Rudnicki, D.; Mrózek, M.; Młynarczyk, J.; Gawlik, W. Microwave spectroscopy for diagnostics of nitrogen vacancy defects in diamond samples. Photonics Lett. Pol.
**2013**, 5, 143–145. [Google Scholar] [CrossRef][Green Version] - Mrózek, M.; Mlynarczyk, J.; Rudnicki, D.S.; Gawlik, W. Circularly polarized microwaves for magnetic resonance study in the GHz range: Application to nitrogen-vacancy in diamonds. Appl. Phys. Lett.
**2015**, 107, 013505. [Google Scholar] [CrossRef][Green Version] - Sasaki, K.; Monnai, Y.; Saijo, S.; Fujita, R.; Watanabe, H.; Ishi-Hayase, J.; Itoh, K.M.; Abe, E. Broadband, large-area microwave antenna for optically detected magnetic resonance of nitrogen-vacancy centers in diamond. Rev. Sci. Instrum.
**2016**, 87, 053904. [Google Scholar] [CrossRef] - Qin, L.; Fu, Y.; Zhang, S.; Zhao, J.; Gao, J.; Yuan, H.; Ma, Z.; Shi, Y.; Liu, J. Near-field microwave radiation function on spin assembly of nitrogen vacancy centers in diamond with copper wire and ring microstrip antennas. Jpn. J. Appl. Phys.
**2018**, 57, 072201. [Google Scholar] [CrossRef] - Chen, Y.; Guo, H.; Li, W.; Wu, D.; Zhu, Q.; Zhao, B.; Wang, L.; Zhang, Y.; Zhao, R.; Liu, W.; et al. Large-area, tridimensional uniform microwave antenna for quantum sensing based on nitrogen-vacancy centers in diamond. Appl. Phys. Express
**2018**, 11, 123001. [Google Scholar] [CrossRef] - Dong, M.; Hu, Z.; Liu, Y.; Yang, B.; Wang, Y.; Du, G. A fiber based diamond RF B-field sensor and characterization of a small helical antenna. Appl. Phys. Lett.
**2018**, 113, 131105. [Google Scholar] [CrossRef][Green Version] - Soshenko, V.; Rubinas, O.; Vorobyov, V.; Bolshedvorskii, S.; Kapitanova, P.; Sorokin, V.; Akimov, A. Microwave Antenna for Exciting Optically Detected Magnetic Resonance in Diamond NV Centers. Bull. Lebedev Phys. Inst.
**2018**, 45, 237–240. [Google Scholar] [CrossRef] - Alegre, T.P.M.; Santori, C.; Medeiros-Ribeiro, G.; Beausoleil, R.G. Polarization-selective excitation of nitrogen vacancy centers in diamond. Phys. Rev. B
**2007**, 76, 165205. [Google Scholar] [CrossRef][Green Version] - Bayat, K.; Choy, J.; Farrokh Baroughi, M.; Meesala, S.; Loncar, M. Efficient, uniform, and large area microwave magnetic coupling to NV centers in diamond using double split-ring resonators. Nano Lett.
**2014**, 14, 1208–1213. [Google Scholar] [CrossRef] - Herrmann, J.; Appleton, M.A.; Sasaki, K.; Monnai, Y.; Teraji, T.; Itoh, K.M.; Abe, E. Polarization-and frequency-tunable microwave circuit for selective excitation of nitrogen-vacancy spins in diamond. Appl. Phys. Lett.
**2016**, 109, 183111. [Google Scholar] [CrossRef] - Zhang, N.; Zhang, C.; Xu, L.; Ding, M.; Quan, W.; Tang, Z.; Yuan, H. Microwave magnetic field coupling with nitrogen-vacancy center ensembles in diamond with high homogeneity. Appl. Magn. Reson.
**2016**, 47, 589–599. [Google Scholar] [CrossRef] - Yang, X.; Zhang, N.; Yuan, H.; Bian, G.; Fan, P.; Li, M. Microstrip-line resonator with broadband, circularly polarized, uniform microwave field for nitrogen vacancy center ensembles in diamond. AIP Adv.
**2019**, 9, 075213. [Google Scholar] [CrossRef][Green Version] - Mariani, G.; Nomoto, S.; Kashiwaya, S.; Nomura, S. System for the remote control and imaging of MW fields for spin manipulation in NV centers in diamond. Sci. Rep.
**2020**, 10, 1–10. [Google Scholar] [CrossRef] - Yaroshenko, V.; Soshenko, V.; Vorobyov, V.; Bolshedvorskii, S.; Nenasheva, E.; Kotel’nikov, I.; Akimov, A.; Kapitanova, P. Circularly polarized microwave antenna for nitrogen vacancy centers in diamond. Rev. Sci. Instrum.
**2020**, 91, 035003. [Google Scholar] [CrossRef] - Horowitz, V.R.; Alemán, B.J.; Christle, D.J.; Cleland, A.N.; Awschalom, D.D. Electron spin resonance of nitrogen-vacancy centers in optically trapped nanodiamonds. Proc. Natl. Acad. Sci. USA
**2012**, 109, 13493–13497. [Google Scholar] [CrossRef][Green Version] - Weiland, T. A discretization model for the solution of Maxwell’s equations for six-component fields. Arch. Elektron. Uebertrag.
**1977**, 31, 116–120. [Google Scholar] - Jelezko, F.; Gaebel, T.; Popa, I.; Gruber, A.; Wrachtrup, J. Observation of Coherent Oscillations in a Single Electron Spin. Phys. Rev. Lett.
**2004**, 92, 076401. [Google Scholar] [CrossRef] - Gruber, A.; Dräbenstedt, A.; Tietz, C.; Fleury, L.; Wrachtrup, J.; Borczyskowski, C.V. Scanning Confocal Optical Microscopy and Magnetic Resonance on Single Defect Centers. Science
**1997**, 276, 2012–2014. [Google Scholar] [CrossRef][Green Version] - MacQuarrie, E.R.; Gosavi, T.A.; Bhave, S.A.; Fuchs, G.D. Continuous dynamical decoupling of a single diamond nitrogen-vacancy center spin with a mechanical resonator. Phys. Rev. B
**2015**, 92, 224419. [Google Scholar] [CrossRef][Green Version] - Mizuno, K.; Nakajima, M.; Ishiwata, H.; Hatano, M.; Iwasaki, T. Electron spin contrast of high-density and perfectly aligned nitrogen-vacancy centers synthesized by chemical vapor deposition. Appl. Phys. Express
**2021**, 14, 032001. [Google Scholar] [CrossRef] - Osterkamp, C.; Mangold, M.; Lang, J.; Balasubramanian, P.; Teraji, T.; Naydenov, B.; Jelezko, F. Engineering preferentially-aligned nitrogen-vacancy centre ensembles in CVD grown diamond. Sci. Rep.
**2019**, 9, 1–7. [Google Scholar] [CrossRef] [PubMed] - Dréau, A.; Lesik, M.; Rondin, L.; Spinicelli, P.; Arcizet, O.; Roch, J.F.; Jacques, V. Avoiding power broadening in optically detected magnetic resonance of single NV defects for enhanced dc magnetic field sensitivity. Phys. Rev. B
**2011**, 84, 195204. [Google Scholar] [CrossRef][Green Version] - Rembold, P.; Oshnik, N.; Müller, M.M.; Montangero, S.; Calarco, T.; Neu, E. Introduction to quantum optimal control for quantum sensing with nitrogen-vacancy centers in diamond. AVS Quantum Sci.
**2020**, 2, 024701. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) A schematic representation of the $\mathsf{\Omega}$-shaped antenna and its implementation in a confocal microscope utilizing a piezo scanner (coaxial connector design by avitek, coaxial cable design by Steven Minichiello and objective design by thorfynn; source: https://grabcad.com accessed on 7 June 2021). (

**b**) A schematic representation of the geometry of the $\mathsf{\Omega}$-shaped antenna design (note that the scale bar is approximate and the sketch does not give the exact geometry of the simulated antenna but illustrates the design in general). Microwave (MW) modes enter and leave the calculation domain via the waveguide ports indicated in red. Inset: Simulated MW radiation pattern. Here, strong directivity towards the sample is visible.

**Figure 2.**Process flow for Omega antennas. The color key: grey—glass substrate; blue—chromium; yellow—gold; green—adhesion promoter; red—photoresist; black—photomask; violet—UV-illumination.

**Figure 3.**(

**a**) Achievable MW amplitude for different inner radius values ${r}_{w}$. Points from different simulation runs. (

**b**) Calculation of the frequency-dependent ${S}_{11}$ parameter (back reflection coefficient) with a ground plane for the 50 $\mathsf{\mu}$m thick diamond (solid black) and the 300 $\mathsf{\mu}$m thick diamond (solid red) and without the ground plane (dashed lines). (

**c**) MW amplitude and Rabi frequency dependence on the distance to the antenna top surface. Rabi frequencies ${\mathsf{\Omega}}_{\mathrm{R}}$ were determined for a resonantly driven transition of the subset of nitrogen vacancy (NV) centers aligned in $\langle 111\rangle $ crystallographic direction. Input MW power equals 1 W.

**Figure 4.**Field simulation results for a 50 $\mathsf{\mu}$m thick electronic grade diamond (

**a**–

**c**) and for a 300 $\mathsf{\mu}$m thick IIa diamond (

**d**–

**f**). All field data were taken 10 nm below the diamond sample’s top surface and correspond to a MW input power of 1 W. (

**a**,

**b**,

**d**,

**e**) Field distribution of the MW in x and y directions. (

**c**,

**f**) 2D maps of theoretically expected Rabi frequencies ${\mathsf{\Omega}}_{\mathrm{R}}$ for a resonantly driven transition of the subset of nitrogen vacancy (NV) centers aligned in $\langle 111\rangle $ crystallographic direction. The dashed circle marks the circumference of the aperture. Insets: detailed views of the aperture areas.

**Figure 5.**Comparison between sputtered and evaporated layers. The evaporated antennas show better performance in terms of radiated MW amplitude, as shown by the increased optically detected magnetic resonance (ODMR) contrast C ((

**a**), 8% vs. 22%), and Rabi frequency ${\mathsf{\Omega}}_{\mathrm{R}}$ ((

**b**), 800 kHz vs. 2.2 MHz, ${t}_{\pi}$ = $\pi $-pulse duration). Note that the ODMR resonance of the evaporated antenna is strongly power broadened ($\Delta \nu $ = FWHM). Points indicate the experimentally obtained data and solid curve denotes fits used to obtain the mentioned parameters.

**Figure 6.**(

**a**) Continuous ODMR measurements of an NV ensemble with an externally applied magnetic field. For the outermost resonance pair, a splitting of 181 MHz ± 1 MHz with high contrast (4.67% ± 0.06% at −15 dBm source MW power) was obtained. For the corresponding subset of NV centers, we determined a projection of the magnetic field on the NV axis of 6.45 mT ± 0.05 mT. (

**b**,

**c**) Characterization of the homogeneity of the radiated MW field amplitude perpendicular and parallel to the gap. While the amplitude parallel to the gap slightly depended on the distance to the gap, as expected, the amplitude perpendicular to the gap remained unaffected, showing that the full area of the aperture is reliably usable for spin manipulation protocols. (

**d**) Pulsed ODMR of one of the resonances showing the hyperfine transitions due to ${}^{14}\mathrm{N}$ nuclear spin coupling. The black points indicate the experimentally obtained data, solid black lines indicate the error bars and the solid red lines indicate either fits or simulated data.

**Figure 7.**(

**a**) Typical Rabi oscillation measurements, which are primarily used to obtain relevant pulse parameter to be used in multi-pulse sensing schemes. The measurement performed at ${\mathsf{\Omega}}_{\mathrm{R}}\approx $ 6.5 MHz. (

**b**) Spin-echo and Carr Purcell Meiboom Gill (CPMG)-n measurements with the NV ensemble performed with the pulse parameters obtained from (

**a**). The plots have been fit and scaled along the y-axis for comparison. The points show the experimentally obtained data, solid curves denote the fit and the dashed lines indicate the fit envelopes. The spin-echo measurements reveal ${T}_{2}\approx $ 167 $\mathsf{\mu}$s. Applying CPMG-8 pulse sequences leads to almost a fourfold improvement in the decoherence time of the spin state. From the fit, the calculated enhanced decoherence times for the CPMG-2/4/8 protocols were ≈245 $\mathsf{\mu}$s/≈425 $\mathsf{\mu}$s/≈638 $\mathsf{\mu}$s, respectively.

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**MDPI and ACS Style**

Opaluch, O.R.; Oshnik, N.; Nelz, R.; Neu, E.
Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications. *Nanomaterials* **2021**, *11*, 2108.
https://doi.org/10.3390/nano11082108

**AMA Style**

Opaluch OR, Oshnik N, Nelz R, Neu E.
Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications. *Nanomaterials*. 2021; 11(8):2108.
https://doi.org/10.3390/nano11082108

**Chicago/Turabian Style**

Opaluch, Oliver Roman, Nimba Oshnik, Richard Nelz, and Elke Neu.
2021. "Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications" *Nanomaterials* 11, no. 8: 2108.
https://doi.org/10.3390/nano11082108