ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Ginzburg N. S., Peskov N. Y., Sergeev A. S., Zaslavskij V. J., Arzhannikov A. V., Sinitsky S. L. Two-dimensional distributed feedback as a method for generation of powerful coherent radiation from spatially-extended relativistic electron beams. Izvestiya VUZ. Applied Nonlinear Dynamics, 2020, vol. 28, iss. 6, pp. 575-632. DOI: 10.18500/0869-6632-2020-28-6-575-632

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 88)
Language: 
Russian
Article type: 
Article
UDC: 
621.385

Two-dimensional distributed feedback as a method for generation of powerful coherent radiation from spatially-extended relativistic electron beams

Autors: 
Ginzburg Naum Samuilovich, Institute of Applied Physics of the Russian Academy of Sciences
Peskov Nikolai Yu., Institute of Applied Physics of the Russian Academy of Sciences
Sergeev Aleksandr Sergeevich, Institute of Applied Physics of the Russian Academy of Sciences
Zaslavskij Vladislav Jurevich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

The purpose of the research presented in the review is to analyze a new feedback mechanism  – two-dimensional (2D) distributed feedback, and to study the possibility of using this mechanism for generation of powerful spatially-coherent radiation. Such 2D distributed feedback is implemented by applying 2D Bragg structures, which represent sections of planar or coaxial waveguides with the 2D-periodical corrugation and can be considered as an analog of the 2D photonic crystals. Methods. Theoretical analysis of 2D Bragg structures and powerful relativistic masers based on them was carried out in the framework of the coupled-waves method using geometrical and quasi-optical approximations. High selectivity of 2D Bragg structures was confirmed by the simulations and «cold» electrodynamic tests. Results. Simulations of the dynamics of oscillators with 2D distributed feedback shows that the transverse (relative to the electron beam propagation) wave-fluxes that occur in 2D Bragg structures lead to synchronization of the radiation of different parts of wide electron beams and establishment of a stable single-mode generation at the transverse sizes of the systems of up to ∼ 102 ...103 wavelengths. Operability of novel feedback mechanism has been demonstrated experimentally in planar and coaxial Free-Electron Masers realized in the 4-mm and 8-mm wavelength bands, where a stable narrow-band generation with a record output power of up to 100 MW level is achieved at the transverse sizes of the system of about 50 wavelengths. Conclusion. Theoretical and experimental studies have shown that the 2D distributed feedback is an effective method for obtaining coherent radiation of millimeter and submillimeter ranges with a power level of ∼ 108 ...1010 W from relativistic electron beams of sheet and tubular configurations formed by the high-current accelerators. From a practical point of view, it also attractive to use the 2D feedback mechanism for synchronization of a laser active media, in particular, semiconductor heterolasers.

Reference: 
  1. Bastrikov A.N., Bugaev S.P., Kiselev I.N., Koshelev V.I., Sukhushin K.N. Formation of hollow microsecond electron beams at MV voltages in a diode. Technical Physics. The Russian Journal of Applied Physics, 1988, vol. 58, no. 3, pp. 483–494 (in Russian).
  2. Arzhannikov A.V., Nikolaev V.S., Sinitsky S.L., Yushkov M.V. Generation and transport of 140 kJ ribbon electron beam. J. Appl. Phys, 1992, vol. 72, no. 4, p. 1657–1663.
  3. Arzhannikov A.V., Sinitsky S.L. Kiloampere electron beams for pumping oscillations in vacuum and plasma. Novosibirsk: Novosibirsk State University, 2016, 258 p. (in Russian).
  4. Arzhannikov A.V., Samtsov D.A., Sinitsky S.L., Stepanov V.D. Angular divergence of electrons in generating two ribbon beams in a single accelerating diode (simulation, experiment). Sibirsky Fizichesky Zhurnal, 2020, vol. 15, no. 1, pp. 24–42 (in Russian).
  5. Kovalev N.F., Petelin M.I. Mode selection in high-frequency relativistic electron generators with distributed interaction. In: Relativistic High-Frequency Electronics. Gorky: Institute of Applied Physics of Academy of Sciences of USSR, 1981, is. 2, pp. 62–101 (in Russian).
  6. Rabinovich M.I., Trubetskov D.I. Introduction to the Theory of Vibrations and Waves. Moscow, Nauka, 1984 (in Russian).
  7. Trubetskov D.I., Khramov A.E. Lectures on Microwave Electronics for Physicists. Two Volumes. Moscow, Fizmatlit, 2003 (in Russian).
  8. Cherepenin V.A. Relativistic multiwave oscillators and their possible applications. PhysicsUspekhi, 2006, vol. 49, no. 10, pp. 1097–1102.
  9. Bugaev S.P., Kanavets V.I., Klimov A.I., Koshelev V.I., Cherepenin V.A. Relativistic multiwave Cerenkov generator. Tech. Phys. Lett., 1983, vol. 9, pp. 596.
  10. Bratman V.L., Gubanov V.P., Denisov G.G., Korovin S.D., Polevin S.D., Rostov V.V., Smorgonsky A.V. Experimental study of a sectioned microwave generator with a relativistic electron beam. Tech. Phys. Lett., 1988, vol. 14, no. 1, pp. 9–13 (in Russian).
  11. Gaponov A.V., Goldenberg A.L., Grigoryev D.P., Orlova I.M., Pankratova T.B., Petelin M.I. The induced synchrotron radiation of electrons in hollow cavities. JETP Letters, 1965, vol. 2, no. 9. pp. 430–435 (in Russian).
  12. Rusin F.S., Bogomolov G.D. Generation of electromagnetic oscillations in an open resonator. JETP Letters, 1966, vol. 4, no. 6, pp. 160–162.
  13. Glyavin M.Yu., Denisov G.G., Khazanov E.A. From millimeter to microns – IAP RAS powerful sources for various applications. Proc. of the 3rd Int. Conf. «Terahertz and Microwave Radiation: Generation, Detection and Applications» (TERA-2018), N.Novgorod, Oct. 22–25, 2018. EPJ Web of Conferences, 2018, vol. 195, p. 00001.
  14. Thumm M.K.A., Denisov G.G., Sakamoto K., Tran M.Q. High-power gyrotrons for electron cyclotron heating and current drive. Nuclear Fusion, 2019, vol. 59, no. 7, p. 073001.
  15. Kovalev N.F., Petelin M.I., Reznikov M.G. Resonator: USSR Patent No. 720592, 1980.
  16. Bratman V.L., Denisov G.G., Ginzburg N.S., Petelin M.I. FEL’s with Bragg reflection resonators: Cyclotron autoresonance masers versus ubitrons. IEEE J. Quant. Electr, 1983, vol. QE-19, no. 3, p. 282–296.
  17. Kogelnik H., Shank C.V. Coupled-wave theory of distributed feedback lasers. J. Appl. Phys, 1972, vol. 43, p. 2327–2335.
  18. Yariv A. Quantum Electronics. John Wiley and Sons Inc., N.Y., 1975.
  19. Bratman V.L., Denisov G.G., Ofitserov M.M. Masers at the cyclotron autoresonance of the millimeter wave range. In: Relativistic High-Frequency Electronics. Gorky: Institute of Applied Physics of Academy of Sciences of USSR, 1983, is. 3. pp. 127 (in Russian).
  20. Bekefi G., DiRienzo A., Leibovitch C., Danly B.G. A 35 GHz Cyclotron Autoresonance Maser Amplifier. Appl. Phys. Lett, 1989, vol. 54, p. 1302–1304.
  21. Alberti S., Danly B.G., Gulotta G., Giguet E., Kimura T., Menninger W.L., Rullier J.L., Temkin R.J. Experimental study of a 28 GHz high-power long-pulse Cyclotron Autoresonance Maser oscillator. Phys. Rev. Lett, 1993, vol. 71, no. 13, p. 2018–2021.
  22. Bratman V.L., Denisov G.G., Kol’chugin B.D., Samsonov S.V., Volkov A.B. Experimental demonstration of high-efficiency Cyclotron-Autoresonance-Maser operation. Phys. Rev. Lett, 1995, vol. 75, no. 17, p. 3102–3105.
  23. Cooke S.J., Cross A.W., He W., Phelps A.D.R. Experimental operation of a cyclotron autoresonance maser oscillator at the second harmonic. Phys. Rev. Lett., 1996. vol. 77, p. 4836–4839.
  24. Wang M., Wang Z., Chen J., Lu Z., Zhang L. Experiments of a raman free electron laser with distributed feedback cavity. Nucl. Instr. and Meth. in Phys. Research A, 1991, vol. A304. p. 116–120.
  25. Mima K., Imasaki K., Kuruma S., Akiba T., Ohigashi N., Tsunawaki Y., Tanaka K., Yamanaka C., Nakai S. Theory and experiments for the induction linac FEL. Nucl. Instr. and Meth. in Phys. Research A, 1991, vol. A285. p. 47–52.
  26. Ciocci F., Bartolini R., Doria A., Gallerano G.P., Giovenale E., Kimmitt M.F., Messina G., Renieri A. Operation of a compact free-electron laser in the millimeter-wave region with a bunched electron beam. Phys. Rev. Lett, 1993, vol. 70, p. 929–931.
  27. Chu T.S., Hartemann F., Danly B.G., Temkin R.J. Single-mode operation of a Bragg Free-electron maser oscillator. Phys. Rev. Lett, 1994, vol. 72, p. 2391–2395.
  28. Ginzburg N.S., Kaminsky A.A., Kaminsky A.K., Peskov N.Yu., Sedykh S.N., Sergeev A.P., Sergeev A.S. High-efficiency single-mode Free-Electron Maser oscillator based on a Bragg resonator with step of phase of corrugation. Phys. Rev. Lett, 2000, vol. 84, p. 3574–3577.
  29. Ginzburg N.S., Peskov N.Yu., Sergeev A.S. Use of two-dimensional distributed feedback in free electron lasers. Tech. Phys. Lett., 1992, vol. 18, no. 9, pp. 23–28 (in Russian). 
  30. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Arzhannikov A.V., Sinitsky S.L. Super-power freeelectron lasers with two-dimension distributed feedback. Nuclear Instr. and Meth. in Phys. Research A, 1995, vol. A358. p. 189–192.
  31. Kovalev N.F., Orlova I.M., Petelin M.I. Transformation of waves in a multimode waveguide with corrugated walls. Radiophys. Quantum Electron., 1968, vol. 11, no. 5, pp. 783–786 (in Russian).
  32. Denisov G.G., Reznikov M.G. Corrugated cylindrical resonators for short-wave relativistic microwave generators. Radiophys. Quantum Electron., 1982, vol. 25, no. 5, pp. 562–569 (in Russian).
  33. Ginzburg N.S., Peskov N.Yu., Sergeev A.S. Two-dimension double-periodic Bragg resonators for free-electron lasers. Optics commun, 1993, vol. 96, no. 4–6. p. 254-258.
  34. Ginzburg N.S., Peskov N.Yu., Sergeev A.S. Electrodynamic properties of two-dimensional Bragg resonators. J. Comm. Technology Electron., 1995, vol. 40, no. 5, pp. 8–21.
  35. Ginzburg N.S., Malkin A.M., Peskov N.Yu., Sergeev A.S. Mechanism of free electron maser self-excitation using coupled propagating and trapped modes. Tech. Phys. Lett., 2006, vol. 32, no. 10, pp. 896–900.
  36. Peskov N.Yu., Ginzburg N.S., Golubev I.I., Golubykh S.M., Kaminsky A.K., Kozlov A.P., Malkin A.M., Sedykh S.N., Sergeev A.S., Sidorov A.I., Zaslavsky V.Yu. Powerful oversized W-band free-electron maser with advanced Bragg resonator based on coupling of propagating and cut-off waves. Appl. Phys. Lett, 2020, vol. 116, p. 0006047.
  37. Peskov N.Yu., Ginzburg N.S., Denisov G.G., Sergeev A.S., Arzhannikov A.V., Sinitsky S.L., Kalinin P.V., Stepanov V.D. Electrodynamic properties of two-dimensional Bragg resonators of planar geometry. Optics Commun, 2001, vol. 187, no. ER4-6. p. 311-316.
  38. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Denisov G.G., Kuzikov S.V., Zaslavsky V.Yu., Arzhannikov A.V., Kalinin P.V., Sinitsky S.L., Thumm M. Observation of the high-Q modes inside resonance zone of 2D Bragg structures. Appl. Phys. Lett, 2008, vol. 92, p. 103512.
  39. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Zaslavsky V.Yu., Arzhannikov A.V., Kalinin P.V., Sinitsky S.L., Thumm M. High-selective two-dimensional Bragg resonators of planar geometry: theoretical, computational and experimental study. J. of Appl. Phys, 2012, vol. 112, p. 114504.
  40. Yablonovitch E. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett, 1987, vol. 58, p. 2059–2062.
  41. https://en.wikipedia.org/wiki/Photonic_crystal#References
  42. Ginzburg N.S., Peskov N.Yu., Sergeev A.S. Dynamics of free-electron lasers with two-dimension distributed feedback. Optics commun, 1994, vol. 112, p. 151–156.
  43. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Phelps A.D.R., Konoplev I.V., Robb G.R.M., Cross A.W., Arzhannikov A.V., Sinitsky S.L. Theory and design of a free-electron maser with twodimensional feedback driven by a sheet electron beam. Phys. Rev. E, 1999, vol. 60, no. 1, p. 935–945.
  44. Ginzburg N.S., Peskov N.Yu. Nonlinear theory of a free electron laser with a helical wiggler and an axial guide magnetic field. Phys. Rev. ST - Accel. and Beams, 2013, vol. 16, p. 090701. 4
  45. Ginzburg N.S., Malkin A.M., Peskov N.Yu., Sergeev A.S., Zaslavsky V.Yu., Zotova I.V. Powerful terahertz free electron lasers with hybrid Bragg reflectors. Phys. Rev. ST - Accel. and Beams, 2011, vol. 14, p. 042001.
  46. Arzhannikov A.V., Ginzburg N.S., Zaslavskii V.Yu., Kalinin P.V., Peskov N.Yu., Sergeev A.S., Sinitsky S.L. Bragg Deflectors of Wave Fluxes for High-Power Relativistic Masers. Technical Physics. The Russian Journal of Applied Physics, 2019, vol. 64, no. 5, pp. 711–719.
  47. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Arzhannikov A.V., Sinitsky S.L. Planar free-electron lasers with combined 1D/2D Bragg mirror resonators: A theoretical study. Tech. Phys. Lett., 2000, vol. 26, no. 8, pp. 701–704.
  48. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Phelps A.D.R., Robb G.R.M. Mode competition and control in free electron devices with one and two dimensional Bragg resonators. IEEE Trans. on Plasma Science, 1996, vol. 24, no. 3, p. 770–781.
  49. Arzhannikov A.V., Ginzburg N.S., Zaslavsky V.Yu., Ivanenko V.G., Ivanov I.A., Kalinin P.V., Kuznetsov A.S., Kuznetsov S.A., Peskov N.Yu., Sergeev A.S., Sinitsky S.L., Stepanov V.D. Generation of spatially coherent radiation in free-electron masers with two-dimensional distributed feedback. JETP Letters, 2008, vol. 87, no. 11, pp. 618–622.
  50. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Arzhannikov A.V., Sinitsky S.L. A two-dimensional distributed feedback used for synchronization of a multibeam planar free-electron maser system. Tech. Phys. Lett., 2001, vol. 27, no. 3, pp. 240–244.
  51. Ginzburg N.S., Zaslavsky V.Yu., Peskov N.Yu., Sergeev A.S., Arzhannikov A.V., Kalinin P.V., Kuznetsov S.A., Sinitsky S.L., Stepanov V.D. Theory of a planar free-electron maser with transverse electromagnetic flux circulation in a 2D Bragg mirror. Technical Physics. The Russian Journal of Applied Physics, 2006, vol. 51, no. 12, pp. 1618–1623.
  52. Arzhannikov A.V., Ginzburg N.S., Zaslavsky V.Yu., Kalinin P.V., Peskov N.Yu., Sergeev A.S., Sinitsky S.L., Stepanov V.D., Thumm M. Generation of powerful narrow-band 75-GHz radiation in a free-electron maser with two-dimensional distributed feedback. Tech. Phys. Lett., 2013, vol. 39, no. 9, pp. 801–804.
  53. Arzhannikov A.V., Thumm M.K.A., Burdakov A.V., Burmasov V.S., Ginzburg N.S., Ivanov I.A., Kalinin P.V., Kasatov A.A., Kurkuchekov V.V., Kuznetsov S.A., Makarov M.A., Mekler K.I., Peskov N.Yu., Polosatkin S.V., Popov S.S., Postupaev V.V., Rovenskikh A.F., Sergeev A.S., Sinitsky S.L., Sklyarov V.F., Stepanov V.D., Vyacheslavov L.N., Zaslavsky V.Yu. Two ways for high-power generation of subterahertz radiation by usage of strong relativistic electron beams. IEEE Trans. on Terahertz Science and Technology, 2015, vol. 5, no. 3, p. 478–485.
  54. Arzhannikov A.V., Ginzburg N.S., Kalinin P.V., Kuznetsov S.A., Malkin A.M., Peskov N.Yu., Sergeev A.S., Sinitsky S.L., Stepanov V.D., Thumm M., Zaslavsky V.Yu. Using two-dimensional distributed feedback for synchronization of radiation from two parallel sheet electron beams in free-electron maser. Phys. Rev. Lett, 2016, vol. 117, no. 11, p. 114801.
  55. Arzhannikov A.V., Ginzburg N.S., Denisov G.G., Kalinin P.V., Peskov N.Yu., Sergeev A.S., Sinitsky S.L. A traveling-wave ring resonator with Bragg deflectors in a two-stage terahertz free-electron laser. Tech. Phys. Lett., 2014, vol. 40, no. 9, pp. 730–734.
  56. Arzhannikov A.V., Ginzburg N.S., Zaslavsky V.Yu., Kalinin P.V., Peskov N.Yu., Sandalov E.S., Sergeev A.S., Sinitsky S.L., Stepanov V.D. Planar THz FELs Based on Intense Parallel Sheet Electron Beams and Intracavity Wave Scattering. Bulletin of the Russian Academy of Sciences: Physics, 2019, vol. 83, no. 2, pp. 140–145.
  57. Flyagin V.A., Khizhnyak V.I., Manuilov V. N., Moiseev M.A., Pavelyev A.B., Zapevalov V.E., Zavolsky N.A. Investigations of advanced coaxial gyrotrons at IAP RAS. Int. J. of Infrared and Millimeter Waves, 2003, vol. 24, no. 1, p. 2–17.
  58. Piosczyk B., Dammertz, G., Dumbrajs O., Drumm O., Illy S., Jin J., Thumm M. A 2-MW, 170-GHz coaxial cavity gyrotron. IEEE Trans. on Plasma Sci, 2004, vol. 32, no. 2, p. 413–417.
  59. Kovalev N.F. On the two-dimensional Bragg resonator. Radiophys. Quantum Electron., 2003, vol. 46, no. 4, pp. 267–280. 
  60. Vainstein L.A. Electromagnetic waves. M: Sovetskoye Radio, 1957, 440 p. (in Russian).
  61. Ginzburg N.S., Peskov N.Yu., Sergeev A.S. Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators. Technical Physics. The Russian Journal of Applied Physics, 2003, vol. 48, no .12. pp. 1554–1564.
  62. Ginzburg N.S., Konoplev I.V., Sergeev A.S. Use of two-dimensional distributed feedback for synchronization of radiation in FELs with tubular REBs of large diameter. Technical Physics. The Russian Journal of Applied Physics, 1996, vol. 66, no. 5, pp. 108–117 (in Russian).
  63. Bratman V.L., Moiseev M.A., Petelin M.I. On the theory of gyrotrons with a non-fixed structure of a high-frequency field. Radiophys. Quantum Electron., 1973, vol. 16, no. 4, pp. 622–634 (in Russian).
  64. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Zaslavsky V.Yu., Konoplev I.V., Fisher L., Ronald K., Phelps A.D.R., Cross A.W., Thumm M. Mechanism of azimuthal mode selection in twodimensional coaxial Bragg resonators. J. of Appl. Phys, 2009, vol. 105, no. 12, p. 124519.
  65. Ginzburg N.S., Zaslavsky V.Yu., Peskov N.Yu., Sergeev A.S. Nonlinear theory of coaxial freeelectron masers with 2D distributed feedback (quasi-optical approximation). Technical Physics. The Russian Journal of Applied Physics, 2010, vol. 55, no. 3, pp. 326–336.
  66. Ginzburg N.S., Zavolsky N.A., Nusinovich G.S., Sergeev A.S. Nonstationary theory of electron generators with diffraction extraction of radiation. Radiophys. Quantum Electron., 1986, vol. 29, no. 1, pp. 106–114 (in Russian).
  67. Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Phelps A.D.R., Cross A.W. The use of a hybrid resonator consisting of 1-D and 2-D Bragg reflectors for generation of spatially-coherent radiation in a coaxial free-electron laser. Physics of Plasmas, 2002, vol. 9, no. 6, p. 2798–2802.
  68. Ginzburg N.S., Zaslavsky V.Yu., Malkin A.M., Peskov N.Yu., Sergeev A.S. Frequency stabilization in free-electron masers with 2D and 1D distributed feedback. Technical Physics. The Russian Journal of Applied Physics, 2009, vol. 54, no. 9, pp. 1384–1388.
  69. Cross A.W., Ginzburg N.S., He W., Konoplev I.V., Peskov N.Yu., Phelps A.D.R., Ronald K., Sergeev A.S., Whyte C.G. Experimental studies of two-dimensional coaxial Bragg structures for a high-power Free-Electron Maser. Appl. Phys. Lett, 2002, vol. 80, no. 9, p. 1517–1519.
  70. Konoplev I.V., Cross A.W., Phelps A.D.R., He W., Ronald K., Whyte C.G., Robertson C.W., Ginzburg N.S., Peskov N.Yu., Sergeev A.S., Zaslavsky V.Yu., Thumm M. Co-axial Free-Electron Maser based on two-dimensional distributed feedback. Phys. Rev. E, 2007, vol. 76, p. 056406.
  71. Arzhannikov A.V., Cross A.W., Ginzburg N.S., He W., Kalinin P.V., Konoplev I.V., Kuznetsov S.A., Peskov N.Yu., Phelps A.D.R., Robertson C.W., Ronald K., Sergeev A.S., Sinitsky S.L., Stepanov V.D., Thumm M., Whyte C.G., Zaslavsky V.Yu. Production of powerful spatially coherent radiation in planar and coaxial FEM exploiting two-dimensional distributed feedback. IEEE Trans. on Plasma Sci, 2009, vol. 37, no. 9, p. 1792–1800.
  72. Ginzburg N.S., Zaslavsky V.Yu., Malkin A.M., Peskov N.Yu., Sergeev A.S. Cherenkov masers with two-dimensional distributed feedback. Tech. Phys. Lett., 2010, vol. 36, no. 1, pp. 83–87.
  73. Ginzburg N.S., Malkin A.M., Sergeev A.S., Zaslavsky V.Yu. Powerful surface-wave oscillators with two-dimensional periodic structures. Appl. Phys. Lett, 2012, vol. 100, no. 14, p. 143510.
  74. Ginzburg N.S., Ilyakov E.V., Kulagin I.S., Peskov N.Yu., Rozental R.M., Sergeev A.S., Zaslavsky V.Yu., Zheleznov I.V. Synchronization of radiation in an oversized coaxial Ka-band backward wave oscillator using two-dimensional Bragg structure. Phys. Rev. ST - Accel. and Beams, 2015, vol. 18, no. 12, p. 120701.
  75. Ginzburg N.S., Ilyakov E.V., Kulagin I.S., Malkin A.M., Peskov N.Yu., Sergeev A.S., Zaslavsky V.Yu. Theoretical and experimental studies of relativistic oversized Ka-band surface-wave oscilltor based on 2D periodical corrugated structure. Phys. Rev. Accel. and Beams, 2018, vol. 21, no. 8, p. 080701.
  76. Ginzburg N.S., Baryshev V.R., Sergeev A.S., Malkin A.M. Dynamics of semiconductor lasers with two-dimensional distributed feedback. Phys. Rev. A, 2015, vol. 91, no. 5, p. 053806.
  77. Ginzburg N.S., Peskov N.Yu., Zaslavsky V.Yu., Kocharovskaya E.R., Malkin A.M., Sergeev A.S., Baryshev V.R., Proyavin M.D., Sobolev D.I. 2D bragg resonators based on planar dielectric waveguides (from Theory to Model-Based Testing). Semiconductors, 2019, vol. 53, no. 10, pp. 1282–1286.
Received: 
29.07.2020
Accepted: 
13.10.2020
Published: 
30.11.2020