4.6 Second-Harmonic Generation
107
0
1
2
3
4
5
10
14
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fundamental
Second harmonic
Fig. 4.17 Second-harmonic generation with imperfect phase matching, according to Armstrong et
al.
whether the second generation can take place inside the zero-index metamaterial
under consideration. For this purpose, the ZIM has been evaluated in the time domain
using COMSOL Multiphysics. The ZIM slab used was ten periods long and five
periods wide. A 1 W pulse of delay t 0 = 120 fs and width = 50 fs was allowed
to pass through the ZIM completely. The minimum spot size of the beam was
w0 =
Lλ 1
2πn 0
(4.99)
where L = 10a is the length of the ZIM, λ 1 = 1.55 µm is the fundamental wavelength, and n 0 = 1 is the refractive index of air. The nonlinear susceptibility of silicon
has been taken to be 15 pm/V. The Fourier transform of the field obtained at the output probe results in the following spectrum. In Fig. 4.17, the prominent fundamental
peak is observed at f 1 = 192.5 THz (≡λ 1 = 1550 nm), and a tiny second-harmonic
peak is present at 394.4 THz (≈2 f 1 ). The tiny extra peak near zero is of the difference
frequency and is irrelevant. This analysis shows the potential of the considered zeroindex metamaterial for the second-harmonic generation. Now the next step should
be the calculation of the individual fields and to determine the conversion efficiency.
107
0
1
2
3
4
5
10
14
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fundamental
Second harmonic
Fig. 4.17 Second-harmonic generation with imperfect phase matching, according to Armstrong et
al.
whether the second generation can take place inside the zero-index metamaterial
under consideration. For this purpose, the ZIM has been evaluated in the time domain
using COMSOL Multiphysics. The ZIM slab used was ten periods long and five
periods wide. A 1 W pulse of delay t 0 = 120 fs and width = 50 fs was allowed
to pass through the ZIM completely. The minimum spot size of the beam was
w0 =
Lλ 1
2πn 0
(4.99)
where L = 10a is the length of the ZIM, λ 1 = 1.55 µm is the fundamental wavelength, and n 0 = 1 is the refractive index of air. The nonlinear susceptibility of silicon
has been taken to be 15 pm/V. The Fourier transform of the field obtained at the output probe results in the following spectrum. In Fig. 4.17, the prominent fundamental
peak is observed at f 1 = 192.5 THz (≡λ 1 = 1550 nm), and a tiny second-harmonic
peak is present at 394.4 THz (≈2 f 1 ). The tiny extra peak near zero is of the difference
frequency and is irrelevant. This analysis shows the potential of the considered zeroindex metamaterial for the second-harmonic generation. Now the next step should
be the calculation of the individual fields and to determine the conversion efficiency.