3. Evaluaci´ on de modelos de clasificaci´ on
3.3. Comparaci´on de clasificadores
Second-harmonic generation (SHG) is the simplest second-order nonlinear interaction, and thus the most convenient way to perform a nonlinear characterisation. As previ- ously reviewed in Chapter 3, SHG involves the upconversion of an input FF wave at
ωFF to its SH frequency at ωSH = 2ωFF. By tuning the frequency of the FF wave,
the phase-mismatch between the FF and the SH waves is varied. This results in the generation of a SHG tuning curve (see Fig. 3.8), which shows the quality of the de- vice (see section 3.5). The normalised conversion efficiency can be obtained from the peak of the curve, the effective interaction length can be deduced from the bandwidth at full-width-half-maximum (FWHM), the dispersion of the waveguide is given by the phase-matching wavelength, whilst the uniformity of the device is reflected in the shape of the curve.
Figure 4.16 shows a schematic illustration of the experimental setup used in this nonlinear characterisation via SHG. The source for generating the tunable FF wave for our SHG experiment was an all-fibre amplified tunable diode laser. A CW tunable diode laser ”HP 8168C” operating at a constant power of 1.5 mW was externally modulated by an electro-optics modulator (EOM), and then amplified by an erbium-doped fibre amplifier (EDFA). The source produced a train of 200 ns pulses with a repetition rate of 100 kHz, and an average (peak) power of∼68 mW (∼2 W). The source was tunable from 1528 to 1565 nm in steps of 0.02 nm. This tunability is within the C-band, the region of interest of this research work. Since the pulses are extremely long, i.e. much longer than the waveguide, we can consider them as CW during the experiment, enabling the use of analysis presented in Chapter 3.
Next, the FF pulse train was out-coupled into free-space using a microscope objec- tive, and the appropriate input polarisation was selected by a polarising beam-splitter (PBS). A fibre polarisation controller (FPC) was necessary prior to the out-coupling to maximise the appropriate polarisation component. Afterward, the FF pulse train
HP 8186C Tunable laser diode
PBS
10X
QPM waveguide
EDFA
FPC
EOM
FPC
Pa!ern
Generator
Oscilloscope
ωFF ωFF ωFF ωSH ωSH Si PIN detector InGaAs detector Dichroic mirror photodiode 200ns rep. rate = 100kHz Computer10X
Figure 4.16: Schematic illustration of the experimental setup for the nonlinear character- isation via SHG.
was injected into the waveguide using a 10× microscope objective. The FF and the SH waves at the waveguide output were collected by another 10×microscope objective, before being separated by a dichroic mirror and measured by InGaAs and Si PIN de- tectors, respectively. The tunable source and the detectors were computer controlled to perform the wavelength scan and the data acquisition.
It is well-known that LiNbO3 is sensitive to photorefractive effects at room temper-
ature, where charge migration (by photovoltaic effect) followed by electro-optic effect induce refractive index changes.35 Photorefractive effects shift the phase-matching wave-
length, degrade the conversion efficiency by altering the phase-matching condition, and cause instabilities due to variation of effective index value. The effects can be severe at visible wavelengths and are enhanced in waveguide devices due to the high optical intensity. Photorefractive effects can be significantly reduced by heating the devices. In our experiment, the sample was heated by placing it in a copper block connected to a thin resistor operated at a constant electrical current. According to our measurements, the time required for the temperature to shift by 0.50C was much longer than the time
required to complete the wavelength scan. Hence, we may consider the temperature
was constant in each characterisation.
From all of the QPM structures and waveguides in our device, we are interested in the ones that had a QPM period of Λ = 15µm and a waveguide nominal width of w = 6µm. We found that such devices supported single propagating mode and had a phase-matching wavelength in the region of interest. There were three such waveguides on the sample, but one was accidentally damaged and thus could not be used. Second-harmonic generation tuning curves for the remaining two, measured at a temperature of∼940C, are shown in Fig. 4.17. The phase-matching wavelength of both PPLN waveguides, as observed from Fig. 3.2, was 1537.7 nm. Note that these tuning curves should be identical. The bandwidth [Eq. (3.20)] of Figs. 4.17(a) and 4.17(b) were 0.56 and 0.75 nm, respectively. The theoretical bandwidth of a 2.6 cm long bulk PPLN, as calculated using the Sellmeier equation,36 was ∆λ = 0.42 nm, from which
we can deduce the effective interaction lengths for Figs. 4.17(a) and 4.17(b) to be 1.9 and 1.5 cm, respectively. The discrepancy between calculated and measured bandwidths implies that the whole length of the device is not efficiently used in the interaction due to the nonuniformities in the device, which can be further verified from the distorted shape of the SHG tuning curves. Although the latter device whose SHG tuning curve is depicted in Fig. 4.17(a) had a shorter effective interaction length than the one depicted in Fig. 4.17(b), the fact that Fig. 4.17(b) is more distorted than Fig. 4.17(a) makes us to prefer working with the latter.
In addition, we can infer from this characterisation, that the device had a higher dispersion than bulk PPLN, because of the waveguide dispersion. For bulk PPLN, the theoretical gratings period for phase-matching the same wavelength at the same condition (1537.7 nm at ∼940C) is 18.4µm, which is longer than the gratings period used in the experiment. This fact implies that the wave vector mismatch ∆β=β2−2β1
of our device is greater than the bulk PPLN, and thus a larger reciprocal lattice vector
K, or equivalently, a shorter QPM period, is needed.