The Fundamental Physics of Directive Beaming at Microwave and Optical Frequencies in Terms of Leaky Waves Saman Kabiri, Master’s Student Dept. of Electrical and Computer Engineering Texas A&M University Course: Laser Spectroscopy Instructor: Dr. Hans Schuessler Monday, November 26 th, 2012

Outline - Introduction and Motivation - Definition of Antenna’s Parameters - Antennas Based on a PRS - Directive Beaming at Optical Frequencies 2

Outline - Introduction and Motivation - Definition of Antenna’s Parameters - Antennas Based on a PRS - Directive Beaming at Optical Frequencies 3

Introduction Directive beaming occurs in antenna design where a narrow beam is desirable by using fairly simple planar structure excited by a single source. This topic is fairly rich, and extending from the 1950s until the present time. Several applications: 1- Construction of novel highly directive antenna 2- Optical effect such as narrow beaming of light from a subwavelength aperture 3- Enhanced transmission of light from a subwavelength aperture The purpose of this talk is to give a common explanation of the directive-beaming phenomenon in terms of leaky wave. Leaky-wave theory is used to present simple design formulas. 4

Introduction Three main structures are used as highly directive antenna. 5 Three main structures Fabry-Perot cavity Metamaterial structures Directive beaming at optical frequencies

Introduction Three main structures are used as highly directive antenna. 6 Three main structures Fabry-Perot cavity Metamaterial structures Directive beaming at optical frequencies

Outline - Introduction and Motivation - Definition of Antenna’s Parameters - Antennas Based on a PRS - Directive Beaming at Optical Frequencies 7

Definition of Antenna’s Parameters 8 A radiation pattern is a graphical representation of the far-field properties of an antenna. Principle plane: –E-plane: Contains the electric vector –H-plane: Perpendicular to the E-plane containing the magnetic field Field components and the pattern measurement scheme for an ideal dipole E-plane radiation pattern H-plane radiation pattern

Definition of Antenna’s Parameters 9 Directivity is the ratio of the maximum power radiated from an antenna in one direction in respect to the power radiated from an isotropic antenna. Therefore, the directivity of an isotropic antenna is 1. The directivity of an actual antenna can vary from 1.76 dB for a short dipole, to as much as 50 dB for a large dish antenna. Directivity of an actual antenna comparing to an isotropic antenna

Outline - Introduction and Motivation - Definition of Antenna’s Parameters - Antennas Based on a PRS - Directive Beaming at Optical Frequencies 10

11 Antennas Based on a PRS A leaky-wave antenna made from a PRS over a grounded substrate layer

12 Antennas Based on a PRS A symmetric pencil beam at broadside

13 Antennas Based on a PRS Various types of PRS surfaces have been developed so far: A) Multiple dieletric-superstrate PRS B) Periodic metal patch PRS C) Periodic slot PRS D) Periodic wire or metal strip grating PRS Different PRS surfaces

14 Antennas Based on a PRS (1)

The PRS structure showing the leaky parallel-plate modes emanating from the dipole source. Antennas Based on a PRS The two modes have different wavenumbers: 15 From the figure and Snell’s law (1) Equation (1) is an approximate result for the optimum substrate thickness, which assumes an ideal parallel-plate waveguide. By considering the loading effect of the PRS on the waveguide cavity, equation (1) can be modified as where The transmission line model of the PRS

The far field from the TEN model is given by Antennas Based on a PRS 16 The normalized admittance is either the TM or the TE value, depending on whether the beam is being optimized in the E-plane or the H-plane. The admittances in these planes are different for conical beam, so that the beam cannot be optimized simultaneously in both planes. An analysis based on the transverse equivalent network (TEN) shows that the TM z and TE z leaky modes have nearly the same wavenumber, and furthermore, the phase and attenuations constants are nearly the same, so that

For an air substrate, the scan angle is limited to 60º. To allow for a single conical beam that can scan down to endfire, the substrate must have a refractive index sufficiently large, satisfying Antennas Based on a PRS 17 Design Restrictions

The pattern bandwidth is defined as Antennas Based on a PRS 18 Radiation Characterizations Directivity is approximately related to the E-plane and H-plane half-power beamwidth (angle in radians between the -3-dB points)

Antennas Based on a PRS 19 Table 1. Expression for Peak Field value

Antennas Based on a PRS 20 Table 2. Expression for Beamwidth

Antennas Based on a PRS 21 Table 3. Expression for Bandwidth The product of directivity and pattern bandwidth for a broadside can be calculated. The result for this figure of merit (FoM) is

Antennas Based on a PRS 22 Results Far field pattern radiation for the slot PRS structure (a) E-plane pattern for a broadside design, (b) H-plane pattern for a broadside design, (c) E-plane pattern for a 45º scan angle, and (d) H-plane pattern for a 45º scan angle

Antennas Based on a PRS 23 Normalized susceptance of the slot PRS

Antennas Based on a PRS 24 In this figure, patterns for a metal patch PRS structure for varying substrate thicknesses is shown using an air substrate at a frequency of 12 GHz. The substrate thickness is varied so that the beam scans from broadside to 45º. For a scan angle beyond 60º an undesirable secondary beam forms. This especially pronounced for the 75º scan, where a secondary beam (pointing at about 43º) is larger than the primary beam at 75º. Another secondary beam at about 12º is also observed in this case. Various substrate thicknesses are used to obtain different scan angles

Outline - Introduction and Motivation - Definition of Antenna’s Parameters - Antennas Based on a PRS - Directive Beaming at Optical Frequencies 25

Directive Beaming at Optical Frequencies 26

On the exit face, the aperture acts as a source which is fairly well approximated as a magnetic line source. The source radiates into space, producing a direct “space- wave” radiation. In addition, the source launches a plasmon surface wave that propagates away from the source in both directions. Directive Beaming at Optical Frequencies 27

Directive Beaming at Optical Frequencies 28

1.D. R. Jackson, P. Burghignoli, G. Lovat, F. Capolino, C. Ji, D. R. Wilton, and A. A. Oliner, “The Fundamental Phyiscs of Directive Beaming at Microwave and Optical Frequencies and the Role of Leaky Waves,” Proceeding of the IEEE, vol. 99, pp , T. Zhao, D. R. Jackson, and J. T. Williams, “General formulas for 2D leaky wave antennas,” IEEE Trans. Antenna Propag., vol. 53, no. 11, pp , Nov References 29

Thank You 30