Therefore, for the fundamental beam exiting the sample through the nanowire layer, the SH signal should have a large component due to the nanowires. By translating the sample relative to the fundamental beam we probe regions with and without the nanowires, without changing the angle of incidence on the sample.
In the experiment, the setup from Fig. 2.4(a) is slightly modified. A Ti:Sapphire laser is used to generate pulses at 850 nm with a duration of ∼2 ps full width at half maximum at a repetition rate of 80 MHz. The fun- damental is focused to a spot of ∼ 30 µm by a lens with a focal length of 100 mm. Since the nanowire layer acts as a highly scattering medium for radi- ation at 425 nm [36], a lens with a high NA of 0.5 and a focal length of 8 mm is used to collect the SH signal in transmission. The collimated second harmonic is focused onto a Peltier cooled CCD. A combination of the Newport band- pass filter FSR-BG39, with a transmission region of≈ 350–600 nm, and the Thorlabs shortpass filter FES0550, with a cut-on wavelength of about 550 nm, is inserted before the CCD to filter out the fundamental beam, and ensure the detection of the second harmonic signal only.
The dashed and solid bars in Figure 2.8 correspond to the SH signal origi- nating from the region without and with nanowires, respectively. The average second harmonic signal generated in the region without nanowires (horizontal dashed line) is ≈ 17 times larger than the average second harmonic signal generated in the region with nanowires (horizontal solid line). Apparently, nanowires on the sample do not lead to enhanced second harmonic genera- tion in the forward direction. We speculate that the main contribution of the nanowires is to scatter the second harmonic generated in bulk GaP to angles inside the high refractive index substrate. This scattered second harmonic signal is not collected by our setup. Unfortunately, the current experimental data do not distinguish between scattered light and light generated by the nanowires, preventing a more detailed quantitative analysis.
2.5
Conclusion
The coherence length for second harmonic generation in bulk GaP at a wave- length of 1535 nm is more than two times larger then the wire length of short GaP nanowires with a length of ≈ 1.3 µm. As a result, the contribution to the SH signal originating from the substrate is likely to be larger than the contribution originating from the nanowire layer.
In order to separate and identify the second harmonic due to the nanowires, we tried to eliminate the substrate contribution to the SH signal by exploring
2. Second harmonic generation in gallium phosphide nanowires
the symmetry of the nonlinear tensorχ(2), and by an experiment at a second harmonic wavelength of 425 nm at which GaP is highly absorbing. Stacking faults in the nanowires lead to a locally different crystal structure (wurtzite) compared to bulk GaP (zincblende). With currently available samples, we were unable to define an appropriate experimental geometry to exploit this symmetry and generate signal from nanowires only. For second harmonic generation at an absorbing wavelength, the obtained experimental data can be explained by SH generated in the substrate and scattered by the nanowires. Replacing the GaP substrate with another substrate that has a very low, if not zero, second-order nonlinear susceptibility, while maintaining the original orientation of the nanowires, is probably the best way to study the second harmonic generation in ensembles of aligned nanowires [42].
Chapter 3
Second harmonic generation in
freestanding AlGaAs photonic
crystal slabs
3.1
Introduction
Ever since the introduction as materials that can inhibit spontaneous emis- sion [5] or localize light [6], photonic crystals have been recognized as struc- tures that are able to tailor the propagation of light [9, 10]. These photonic crystals consist of a dielectric material arranged on a periodic lattice with a lattice constant comparable to the wavelength of light. Nowadays, photonic crystals find application in high Q, small mode volume cavities, in slow-light waveguides and numerous other applications that make use of the intriguing linear optical properties of photonic crystals. The nonlinear optics of photonic crystals, in particular second harmonic generation (SHG) is less intensively re- searched. Nevertheless, photonic crystals are interesting for nonlinear optics since they may combine high field intensities with optical properties that can be tuned by structure design.
In order to achieve highly efficient second harmonic generation in a small volume, a material with a large effective nonlinear susceptibilityχ(2)ef f must be used and the phase-matching condition must be met [29]. The phase-matching condition ensures that all waves generated inside the material interfere con- structively. In most materials this condition is not fulfilled due to the material dispersion, but phase matching can be achieved using birefringent materials. The main obstacle in using III-V materials such as GaAs and GaP, that re- spectively have a more than 70 and 30 times larger χ(2)ef f than that of a BBO crystal [31, 32], is the fact that GaAs and GaP are not birefringent and phase-
3. Second harmonic generation in freestanding AlGaAs photonic crystal slabs
matching is not easily satisfied. Phase matching can be satisfied in a device with periodically alternating layers of low and high index of refraction or by periodically poling the orientation of the χ(2) material. An existing phase mismatch can be compensated by adding or subtracting a suitable reciprocal lattice vector G resulting in what is called quasi-phase-matching [33, 43–45]. Second harmonic generation can be further enhanced significantly by a strong spatial confinement of both the fundamental and the SH optical fields [46], that enhances the field intensities. Two-dimensional (2D) photonic crystal slabs, i.e., slabs of dielectric GaAs material perforated with a lattice of holes, are interesting in this respect.
Cowan et al. [47] show theoretically how to exploit the leaky modes of a freestanding 2D photonic crystal slab to achieve both quasi-phase-matching and strong spatial confinement. The authors predict an enhancement of SH signal in reflection of more than 6 orders of magnitude.
Mondia et al. [48] investigate experimentally SHG in reflection from a 2D square lattice of holes in GaAs supported on an Al2O3 cladding layer. The authors use very short (150 fs) pulses and vary the angle of incidence and the frequency of the fundamental beam. This enables them to make both the fundamental and the SH wave resonant with the leaky modes of the structure. In this quasi-phase-matched configuration they achieve a SH enhancement of more than 1200 times compared to the noise level in the experiment. Torres et al. [49] present a theoretical and experimental study of SHG in reflection from a 1D GaN photonic crystal. They report a SH enhancement of more than 5000 times, compared to an unpatterned GaN slab, when the quasi-phase-matching condition is satisfied.
We study in this chapter the influence of leaky modes at both the funda- mental and SH frequency on SHG in reflection from afreestanding2D photonic crystal slab, i.e., a slab that is surrounded by air on both sides. In principle, this would lead to a stronger confinement of the field and may therefore lead to more efficient SHG compared to earlier experiments. The photonic crystal consists of a regular 2D square array of holes drilled in ∼150 nm thick slab of Al0.35Ga0.65As material. Compared to earlier experiments in literature we use a narrow linewidth pulsed laser at 1.535µm and tune the angle to probe the resonant coupling of both the fundamental and SH wave to the modes of the structure and how this affects the SH signal. We measure a SH en- hancement of more than 4500 × compared to the signal from the photonic crystal away from resonance, and a SH enhancement of 35000 × relative to the second harmonic signal from the unpatterned Al0.35Ga0.65As region on the wafer. These enhancements are significantly larger compared to enhancements