Antenna Model for Wire Lasers

An antenna model is proposed for long ($L\gg \lambda$) lasers with subwavelength cross sections (wire lasers). It is shown that the far-field pattern of the wire lasers is determined by the ratio of the wavelength to the length. The radiation of the wire laser is predicted to be concentrated in a narrow beam $\Theta \simeq \sqrt{2\lambda /L}$ for laser modes where the longitudinal phase velocity is in synchronism with the velocity of light in air. Experimental results obtained using a terahertz quantum cascade wire laser are in agreement with the model.

Figure 1

The dependence of the normalized far-field intensity determined by the square of the longitudinal factor $|F_i^z{|}^2$ on the angle with respect to the axis of the wire laser (a) for different ratios of the longitudinal phase velocity of the laser mode $c_L$ to the velocity of light $c$. (b) for different ratios of the laser length $L$ to the wavelength $\lambda$ in the case of the phase synchronism. Note the two main lobes in the case of the phase synchronism ($c_L/c=1$) in the forward direction and backward direction along the laser axis with the width $\Theta \simeq \sqrt{2\lambda /L}$.

Figure 2

(a)–(b) Calculated angular dependence of the far-field intensity in the plane perpendicular to the longitudinal axis of the laser for $c/c_L=3.3$ and different ratios of the length $L$ and the wavelength $\lambda$ of the laser. An “equirectangular projection” has been used; scales are given in degrees. (c)–(d) experimental beam patterns from terahertz QCL’s with the same $L/\lambda$ ratios. Note the circular structure; the angular width of the circles decreases with the increase of $L/\lambda$.