Manipulating frequency-dependent diffraction, the linewidth, center frequency and coupling efficiency using periodic corrugations

Abstract

In this paper, we demonstrate an approach to couple freely propagating THz pulses onto a metal wire waveguide utilizing grating as various shaped grooves; rectangular, triangular and circular grooves fabricated directly into the metal. Using broadband THz pulses incident on the wire, we use metal segments containing number of uniformly, symmetric spaced grooves around subwavelength aperture to launch surface propagating multi-cycle pulses along the wire. THz radiation detected at the end of the waveguide with grooves showed overall improved signal amplitude and increased bandwidth as compared to that for the non-machined waveguide. We observe a one-to-one correspondence between the groove number and the number of oscillations in the THz wave form radiated from the end of the waveguide. We further demonstrate that this coupled radiation is radially polarized. Although the alteration of cross-sectional parameters of the grooves, the shape of the individual grooves, in a controlled manner should allow for arbitrarily shaped THz pulses to be launched on the waveguide, all of which compared to rectangular grooves’ output signal and the efficient shaped groove has been chosen.

Appendix

Upon solving the boundary conditions that Ez and Hϕ are continuous at the surface of the conductor which is consistent for r = a, the following equations are obtained for which γ_c, γ and h can be determined.

$$\mu \frac{\gamma }{{k^{2} }}\frac{{H_{0}^{{\left( 1 \right)}} \left( {\gamma \alpha } \right)}}{{H_{1}^{{\left( 1 \right)}} \left( {\gamma \alpha } \right)}} = \mu _{c} \frac{{\gamma _{c} }}{{k_{c}^{2} }}\frac{{Z_{0} \left( {\gamma _{c} \alpha } \right)}}{{Z_{1} \left( {\gamma _{c} \alpha } \right)}}$$

(9)

$$\gamma^{2} - \gamma_{c}^{2} = k^{2} - k_{c}^{2} = k^{2} \left( {1 + j\frac{{\sigma \mu_{c} }}{\omega \varepsilon \mu }} \right) \cong \frac{{\sigma \mu_{c} }}{\omega \varepsilon \mu }$$

(10)

To deduce γ _c , γ and h from the above equations, Goubau used different approximations, one of which is to consider that the radius of the conductor is large compared to the skin depth of the metal (γca ≫ 1). For example at 1 THz, copper wire of radius 600 μm, the skin depth of the metal is 0.07 μm. Z0 and Z1 in Eq. (0.8) can be replaced by,

$$\begin{aligned} & Z_{0} \left( x \right) \cong \left( {\frac{\pi }{2}} \right)^{{\frac{ - 1}{2}}} \cos \left( {x - \frac{\pi }{4}} \right) \\ & x \to \infty \\ \end{aligned}$$

(11)

$$\begin{aligned} & Z_{1} \left( x \right) \cong \left( {\frac{\pi }{2}} \right)^{{\frac{ - 1}{2}}} \cos \left( {x - \frac{3\pi }{4}} \right) \\ & x \to \infty \\ \end{aligned}$$

(12)

Upon approximating that the conductor radius is not too large, i.e. (γca ≪ 1) than we can replace H0 and H1 as,

$$\begin{aligned} & H_{0} \left( x \right) \cong \frac{2j}{\pi }\ln \left( { - j0.89x} \right) \\ & x \to 0 \\ \end{aligned}$$

(13)

$$\begin{aligned} & H_{1} \left( x \right) \cong \frac{2j}{\pi } \\ & x \to 0 \\ \end{aligned}$$

(14)

Thus Eq. (9) is simplified to,

$$- \mu \frac{{\gamma^{2} a}}{{k^{2} }}\ln \left( { - j0.89\gamma a} \right) = \mu \frac{{\gamma_{c} }}{{k_{c}^{2} }}\cot \left( {\gamma_{c} a - \frac{\pi }{4}} \right)$$

(15)

where $\cot \left( {\gamma_{c} a - \frac{\pi }{4}} \right)$ approaches +j since γc becomes complex. Now, Eq. (15) can be written as:

$$\xi \ln \xi = \eta$$

(16)

$$\xi = \left( { - j0.89\gamma \alpha } \right)^{2}$$

(17)

$$\eta = 2\left( {0.89} \right)^{2} \frac{{k^{2} a\mu_{c} }}{{\left| {k_{c} } \right|\mu }}e^{{\frac{i3\pi }{4}}} = \left| \eta \right|e^{{\frac{i3\pi }{4}}}$$

(18)