By I.V. Minin, O.V. Minin
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Additional resources for Diffractional Optics of Millimetre Waves (Series on Optics and Optoelectronics)
We split the integration range into rings, each consisting of two parts, and transform the expression for ﬁeld to the form N ð F þ ð2n þ 1Þ=2 KA X Uð0; 0; FÞ ¼ ð1 þ F=SÞ expðikSÞ dS i n¼0 F þ 2n=2 ð F þ ð2n þ 2Þ=2 þ ð1 þ F=SÞ expðikSÞ dS : F þ ð2n þ 1Þ=2 The imaginary parts of the integrands in each of the terms have identical sign, and each term can reach large values. The division of the region used above corresponds to dividing the real circular aperture into annular zones (Fresnel zones) whose radii are given by the formula rn ¼ ðFn þ n2 2 =4Þ1=2 : Evidently the diﬀractive element described above focuses radiation like a lens.
Verniers were used to measure displacements of the receiver. 5 level of the modulation frequency. The shape of the signal was monitored on the oscilloscope. 12. Zone-plate-based diﬀractive object lenses for the 140 GHz frequency band: (a) of amplitude type, (b) of phase-inversion type. 13. Principal diagram of the experimental setup: 1, attenuator; 2, directional coupler; 3, wavemeter; 4, microwave receiver; 5, selective nanovoltmeter; 6, HF signal generator; 7, optical bench; 8, open end of waveguide; 9, protection shields; 10, MWDO element; 11, digital recording oscilloscope; 12, continuous recording plotter.
10. The functions A0 and A1 describe the distributions of ﬁeld amplitude and radiation intensity, respectively, and the functions È0 and È1 are the ﬁeld phases that determine the direction of propagation of the radiation. We consider only phase elements that do not change the amplitude of the incident radiation and therefore can assume A0 ðx; y; zÞ ¼ A1 ðx; y; zÞ in the area of the transforming elements. As an example, let us consider a reﬂecting optical element. 10). The direction of propagation of the incident radiation is given by the vector grad È0 ðx; y; zÞ, and the direction of propagation of the reﬂected radiation, by the vector grad È1 ðx; y; zÞ.