Choe, M.S.

Choi, E.M.

Litvak, A.G.

Sawant, A.

Thumm, M.

Choe, M. S.

Choi, E. M.

Litvak, A. G.

KITopen

  The gyrotron – a natural source  of high-power orbital angular momentum millimeter-wave beams M. Thumm1, A. Sawant2, M.S. Choe3, E.M. Choi2,3 1Karlsruhe Institute of Technology (KIT), IHM and IHE, Karlsruhe, Germany, manfred.thumm@kit.edu 2Department of Electrical Eng., Ulsan National Inst. of Science and Technology (UNIST), Ulsan, South Korea 3Department of Phys-ics, Ulsan National Institute of Science and Technology (UNIST), Ulsan, South Korea  Abstract Orbital angular momentum (OAM) of electromagnet-ic-wave beams provides further diversity to multiplexing in wireless communication. The present report shows that higher-order mode gyrotrons are natural sources of high-power OAM millimeter (mm) wave beams. The well-defined OAM of their rotating cavity modes operating at near cutoff frequency has been derived by photonic and electromagnetic wave approaches. Introduction Orbital Angular Momentum (OAM) [1] carried by light beams (vortex beams) was discovered earlier and has been widely employed in many applications such as optical tweezers, optical drives of micro-machines, atom trapping, and optical communication. OAM provides an additional dimension (diversity) to multiplexing tech-niques which can be employed in addition to convention-al multiplexing methods to achieve higher data rates. OAM beams have been thoroughly studied and used in the optical regime [2] but in the mm-wave region, they are still under investigation. In this frequency band, there are difficulties associated with beam-splitting and beam-combining processes as well as with the use of spiral phase plates for generation of OAM, since the wavelength is much larger compared to those at optical frequencies.  Here we introduce the natural generation of high-power OAM modes excited by gyrotrons with axial out-put of the rotating higher-order transverse electric mode TEm,p where m and p are the azimuthal and   radial mode index, respectively. Such output radiation could be used for long-range wireless communication. To achieve high frequency stability and a narrow line width, a phase lock-ing system can be utilized to control the electron beam energy. The long-term stability can be guaranteed by a reference clock. A line width as narrow as 1 Hz has been obtained [3]. OAM of Rotating Gyrotron Modes Helically propagating rotating TEm,p modes in a cir-cular waveguide can be decomposed into a series of cy-lindrical plane waves, each propagating at the Brillouin angle B relative to the waveguide axis. The angular mo-mentum possessed by such a ray (which is tangential to the caustic of the mode) can be expressed as ˆˆˆ ˆc cL Lz r p R r p R p z          here Rc = (m/Xm,p)R0 is the caustic radius of the operating mode, where Xm,p  is the pth root of the derivative of the Bessel function Jm, R0 is the waveguide radius and where Φ sinsin B Bp p θ k θ  , sin Bθkk and ,0m pχkR . Therefore, ,Φ 0, 0ˆ ˆm pcm pχmL R p z R m zkχ kR      The ratio between the total angular momentum LN  and total energy WN of N photons is given by  NNNm mW NLω ω   where  is the angular frequency of the operating cavity mode which is close to the cutoff frequency  cut = cXm,p/R0 in the cylindrical cavity section. Here c is the velocity of light in vacuum. Therefore follows m/ = Rc/c, which means that the OAM is proportional to the absolute caustic radius. This is the result of the photonic approach to derive the OAM. The same value follows from the electromag-netic wave approach for the total OAM of a gyrotron cav-ity mode within a given waveguide volume per total energy of the electromagnetic wave in the same volume [4]. At a given frequency the OAM increases with in-creasing azimuthal mode number m, whereas for fixed m it decreases with increasing frequency. Modes that have a linear polarization may possess a so-called Spin Angular Momentum (SAM) if their right-hand and left-hand rotation components are different. Table 1 summarizes the SAM and OAM features of dif-ferent types of TE modes.   Table 1. Intensity on axis I0, possible spin angular momentum (SAM) and orbital angular momentum (OAM) of gyrotron  TE modes in circular waveguides  Mode Family I0 SAM (Polarization) OAM TE0,p no no no TE1,p yes yes no TEm,p   (m >1) no no yes Gyrotrons with OAM mm-Wave Output Beams UNIST has been operating a 65 kW W-band  gyro-tron with diode-type magnetron injection gun (MIG), TE6,2  cavity mode and quasi-optical output in the linearly polarized fundamental Gaussian TEM0,0 mode [5]. In case that the quasi-optical output mode converter would be removed and exchanged with a mode-conserving non-linear diameter up-taper, one would have the essential feature of a OAM gyrotron with axial mm-wave output configuration where the cavity mode is directly emitted      DOI: 10.1051/, 04014 (2017) 714901EPJ Web of Conferences epjconf/2014910th International  Workshop  2017  "Strong  Microwaves  and  Terahertz  Waves:  Sources  and  Applications"4014© The Authors,  published  by EDP Sciences.  This  is  an  open  access  article  distributed  under  the  terms  of  the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). through the dielectric tube window into free space. Of course, propagation of higher-order OAM beams generat-ed by gyrotrons in free space results in a large diffraction angle, which however, can be compensated by the wave-guide diameter taper section that is added after the gyro-tron cavity to reduce the Brillouin angle B of the output wave and by employing focusing lenses to reduce the diffraction. Provided that the gyrotron would also be equipped with a triode-type MIG, the tube could be elec-tronically switch between co- and counter-rotating cavity modes (right- and left hand OAM) and between two cavi-ty modes with different magnitude of OAM (see table 2).  Table 2. Possible operating cavity modes with different OAM of the 65 kW UNIST W-band gyrotronCavityModeXm,n Frequency(GHz)Relative CausticRadius m/Xm,nTE6,2 11.734936 94.8 0.51TE10,1 11.770877 95.1 0.85Fig. 1. Spin angular momentum (SAM) (left), where the electric field is twisting, and orbital angular momentum (OAM) (right), where the phase does the twisting [4] Fig. 2. Theoretical amplitude (a) and phase (b) of the time-averaged total electric field of the co-rotating 95 GHz modes TE6,2 (left) and TE10,1 (right) (in 10 mm distance from a 20 mm diameter aperture) Figure 2 shows the analytically calculated amplitude and phase of the time-averaged total electric field of the co-rotating 95 GHz TE6,2 and TE10,1 mode, respectively. The phase patterns show m-1 spirals. Several Ku/Ka-band 10-to-30-kW-class gyrotrons for technological applications operate in a low-order OAM cavity mode (e.g. TE2,1, TE2,2, TE3,2, or TE2,3) which also serves as axial output mode [6].   In the early 1990-ties the Research Center Karlsruhe (FZK, now KIT) performed very successful experiments with an axial output 140 GHz, 0.5 MW TE10,4-mode gyro-tron [7] having an electronic efficiency of approximately 33%. The tube was equipped with a non-linear up-taper from the 16.22 mm diameter cavity to the 70 mm diame-ter output waveguide with a frequency tunable double-disk, FC75 face cooled sapphire window. The high-power measurement of the output mode content using a 70 mm diameter wavenumber spectrometer [8] resulted in a puri-ty of the co-rotating TE10,4 output mode better than 98%.  At those times, such 0.5–1.0 MW-class short-pulse gyrotrons employing asymmetric cavity modes with non-linear up-tapers and axial output through the collector also were built by several industrial manufacturers [6], e.g.:  8 GHz, TE5,1 and 110 GHz, TE6,4 (THOMSON), 84 GHz, 110 GHz and 140 GHz, TE15,2 (VARIAN), 110 GHz, TE12,2 and TE22,2 (VARIAN), 120 GHz, TE12,2 and TE22,12(JAERI, TOSHIBA). References 1. Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes// Phys. Rev. A 1992. V. 435, P. 8185-8189.2. Wang, J., Yang, J.-Y., Fazal, I.M., Ahmed, N., Yan, Y., Huang, H., Ren, Y., Yue, Y., Dolinar, S., Tur, M., Willner, A.E.Terabit free-space data transmission employing orbital angular momentum multiplexing // Nat. Photon. 2012. V. 6, P. 488.3. Fokin, A.P., Denisov, G.G., Glyavin, M.Yu., Golubiat-nikov, G.Yu., Lubyako, L.V., Morozkin, M.V., Movschevich, B. Z.,Tsvetkov, A.I. High precision frequency stabilization of a 100 W/263 GHz continuous wave gyrotron // Proc. 18th IEEE Int. Vacuum Electronics Conference (IVEC 2017), London, UK, 2017, GII-4.4. Sawant, A., Choe, M.S., Thumm, M., Choi, E.M. Orbital angular momentum (OAM) of rotating modes driven by elec-trons in electron cyclotron masers // Accepted for publication in Scientific Reports – Nature, 20175. Kim, S.G., Sawant, A., Lee, I., Kim, D., Choe, M., Won, J.-H., Kim, J., So, J., Jang, W., Choi, E.M. System devel-opment and performance testing of a W-band gyrotron // J. Infrared Milli Terahz Waves 2016. V. 37, No. 3. P. 209-229.6. Thumm, M. State-of-the-art of high power gyro-devices and free electron masers // KIT Scientific Reports 2016, V. 7717, KIT Scientific Publishing, Karlsruhe,    Germany 7. Piosczyk, B., Kuntze, M., Borie, E., Dammertz, G., Dum-brajs, O., Gantenbein, G., Möbius, A., Nickel, H.-U., Thumm, M. Development of high-power 140 GHz gyrotrons at KfK for applications in fusion // Fusion Technology 1992, eds. C. Ferro, M. Gasparotto, H. Knoepfel, Elsevier Science Publishers B.V. 1993 P. 618-622.8. Kasparek, W., Müller, G. The wavenumber spectrum- eter – an alternative to the directional coupler for multimode analysis in oversized waveguides // Int. J. Electronics 1988 V.64  P.5-20.     DOI: 10.1051/, 04014 (2017) 714901EPJ Web of Conferences epjconf/2014910th International  Workshop  2017  "Strong  Microwaves  and  Terahertz  Waves:  Sources  and  Applications"40142

The gyrotron – a natural source of high-power orbital angular momentum millimeter-wave beams

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The gyrotron – a natural source of high-power orbital angular momentum millimeter-wave beams

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