The slow light photonic crystal waveguide design described in the previ- ous section was fabricated on SOI wafer through e-beam lithography and
3.4 Demonstration of tunable delay
Figure 3.10: (a) Microscope image of the fabricated slow light photonic crystal waveguide. (b) Measured transmission (blue) and group index curve (black); the simulated group index curve (red), shifted in wavelength, is also reported for com- parison. (c) Experimental (black) and theoretical (red) estimate of propagation loss for this particular design.
RIE dry-etch, and membraned in a dilute HF solution, as detailed in sec- tion 2.3. The e-beam writing was performed using a writefield of 100 µm×
100 µm, and therefore waveguides of greater length are inevitably affected by stitching errors (Fig. 2.12), on the order of 30–50 nm. To minimise the optical effect of stitching errors, short waveguide sections with elongated pe- riod along the propagation direction are used at the writefield boundaries, as schematically shown in Fig. 3.9. Such regions operate in the fast-light regime, which is much less sensitive to the effects of stitching errors [76], and are the same as the fast-light interfaces used to efficiently couple light into slow modes (see section 2.2).
Figure 3.10a shows a microscope picture of the fabricated waveguide, of length 300µm (excluding the fast-light coupling and stitching sections). The first 80µm of the waveguide are used as the tuning section where adiabatic wavelength conversion takes place, whereas the remaining 220µm-long sec- tion acts as the dispersive medium. According to Eq. (3.1) and accounting for the highest calculated dispersion |β2,max| ∼ 87.4 ps2/mm, we estimate
the minimum pulse duration that can propagate through the 220 µm-long delay section to be 4.38 ps. The transmission and group index curve of the waveguide were characterised using the setup described in section 2.4, and are shown in Fig. 3.10b; the calculated curve from Fig. 3.8b is repeated here (shifted in wavelength) for comparison. Note that we are mostly interested in the shape of the group index curve, rather than its exact wavelength: the operating wavelength of the final fabricated device differs from the simulated
Figure 3.11: (a) Schematic of the setup used for the characterisation of the tunable delay line [172]. An input broadband probe pulse enters the device from left, and the resulting output is detected via interference with a reference pulse. The arrival of a pump laser pulse makes the optical properties of the device time dependent. The timing between the probe and the pump pulses is controlled via a mechanical stage. (b) Schematic of the delay line used to generate a train of two input probe pulses for demonstrating manipulation at the single bit level.
curve — and may vary for different waveguides on the same chip — due to many factors, including the real refractive index of silicon, and the actual slab thickness and hole radius. The propagation loss was also estimated, by comparing the transmission of the 300µm-long waveguide to that of wave- guides of shorter lengths (80, 150 and 220 µm) on the same chip, and is shown in Fig. 3.10c. The experimental curve follows a trend similar to the group index curve itself, which becomes more clear when comparing Fig. 3.10c to Fig. 3.10b: the loss increases steadily up to the local maximum of the group index ng ∼ 75 at 1565 nm; then, as the group index decreases,
the loss is also reduced, before increasing abruptly due to backscattering becoming the dominant loss mechanism (see also section 2.2). This trend explains the loop appearing in the loss curve when plotted as a function of the group index, as in Fig. 3.10c.
The tunable delay experiments were performed by our collaborators from the NanoOptics group of the FOM Institute AMOLF, Amsterdam, through use of a spectral interferometry setup, shown schematically in Fig. 3.11a. A Ti:sapphire laser of centre wavelength 810 nm, duration 100 fs FWHMI and repetition rate 80 MHz generates the pump pulses, which are focussed onto the sample surface using cylindrical lenses; a slit in the far-field ensures the homogeneous excitation of the tuning region and prevents the delay re- gion from being illuminated. The pump energy absorbed inside the silicon is estimated as ∼2.5% of the incident pump energy, and can be varied up to a maximum of∼50 pJ. The free-carrier lifetime was measured as 200 ps. Pulses from the Ti:sapphire laser are also passed in an optical parametric oscillator to generate synchronised broadband probe pulses of centre wave- length 1550 nm and duration 180 fs FWHMI. Part of the input probe pulse is coupled into the waveguide, whereas the remaining part travels through a reference path, and the two recombine and interfere at the output. The intensity spectra of the reference pulse, of the waveguide output pulse, and
3.4 Demonstration of tunable delay
Figure 3.12: Response of the tunable delay line to an input probe pulse of centre wavelength 1563 nm and duration 4.7 ps. (a) Intensity spectrum and (c) arrival time of the output signal for different pump-probe delays τ. The black dotted curves indicate the peak position of Gaussian fits to the data, for eachτ. (b) and (d) show wavelength spectra and arrival times along theτ-cuts indicated by white dashed lines in (a) and (c), respectively. Red curves (τ =−40 ps) correspond to the untuned probe pulse; blue curves (τ=−9.3 ps) correspond to the tuned probe pulse. The tuned pulse is blue-shifted by 2.9 nm and exits 11.2 ps earlier than its unpumped counterpart. Grey circles are Gaussian fits.
of their superimposition are measured with an OSA (resolution 0.1 nm) and are used to retrieve the complex-valued output electric field in the frequency domain [173]. The probe energy is maintained at low levels (∼10 pJ) to avoid nonlinear effects. The measurement is repeated varying the timing between the pump and the probe pulses, which is set by a mechanical stage.
From these measurements we can characterise the time-dependent linear transfer function of the waveguide over the 60–70 nm bandwidth of the probe, which in turn allows us to determine the linear response of the system to any input probe pulse whose bandwidth is contained within the measured spectrum. A detailed description of this measurement technique is reported in Ref. [172]. The information on the delay of the waveguide output pulse with respect to the reference pulse is contained in their phase difference, which can be extracted in a similar way to what described in section 2.4 for the case of group index measurement.
The response of our tunable delay line to an input probe pulse of du- ration 4.7 ps FWHMI and centre wavelength 1563 nm, with an absorbed
Figure 3.13: Continuous tunability of the delay. (a-c) Wavelength spectra and (d-f) arrival times of 4.7 ps-long probe pulses for absorbed pump energies 0 (un- pumped), 17, 33 and 47 pJ. The input centre wavelength varies from 1562 nm (a,d), to 1563 nm (b,e) and 1564 nm (c,f). Frequency shifts and delay values are summarised in Fig. 3.14.
pump energy of∼47 pJ, is shown in Fig. 3.12. Figure 3.12a shows the out- put wavelength spectra for different pump-probe delaysτ. For τ <−20 ps the signal pulse travels through the tuning region before the arrival of the pump, and exits the waveguide untuned, as also indicated by the red spec- trum of Fig. 3.12b. The∼0.2 nm blue-shift of the central wavelength results from spectral filtering due to higher propagation loss at longer, slower wave- lengths. The transmission through the waveguide at this wavelength (Fig. 3.10b) was measured as -3 dB, due to the ∼100 dB/cm propagation loss in the slow light regime (Fig. 3.10c). For τ >0 ps the probe arrives after the pump and is rejected, as the free carriers are still present inside the tuning region. Atτ =−9.3 ps the probe and pump pulses have maximum overlap in the tuning region, and the probe is adiabatically blue-shifted by 2.9 nm to a new centre wavelength of 1559.9 nm (Fig. 3.12b, blue line). The transmis- sion of the converted pulse was -6.5 dB; accounting for−1.5 dB due to the
∼50 dB/cm linear loss in the fast light regime, we estimated the efficiency of the adiabatic conversion to be around -5 dB.
Figure 3.12c shows the probe pulse arrival time for different pump-probe delays τ, and demonstrates the operating principle of the tunable delay line. The untuned pulse (red curve of Fig. 3.12d) propagates through the waveguide with a group indexng,in = 39 and exits with a delay of 32.3 ps
with respect to the reference pulse. The blue-shifted pulse (blue curve of Fig. 3.12d), however, travels faster, at a group indexng,out= 17, and exits 11.2 ps
3.4 Demonstration of tunable delay
earlier than the unconverted pulse. Therefore, the observed wavelength conversion translates in the time domain into a∼2.4 pulse-widths change of delay.
The wavelength conversion process does not alter the spectral content of the signal, save for the frequency conversion: the widths of the red and blue pulses in Fig. 3.12b are the same in the wavelength domain. In the time domain, however, the higher group velocity dispersion at the original wavelength (Fig. 3.8b) causes the slow red pulse to be wider than the tuned pulse. Such broadening could be addressed by adding suitably engineered waveguide sections to operate dispersion compensation.
Note that our approach based on tuning of the signal rather than of the waveguide helps to balance the losses of tuned and untuned pulses. The converted pulse is subject to free-carrier absorption in the tuning section, but travels in a low-loss fast mode through the delay section. On the other hand, the unconverted pulse propagates in the lossier slow light regime, but does not suffer from conversion losses.
Finally, a fraction of the pumped pulse remains unconverted or partially converted, as can be seen from the residual peak around 1562 nm in the blue curve of Fig. 3.12b. This is light that was not contained in the tuning region during the entire pumping time: for example, the head and tail of the signal which, respectively, exit and enter the tuning region while the conversion is taking place, and therefore do not experience the full variation of refractive index in time. The interference between the converted and the partially converted light in the frequency domain translates into the presence of modulation fringes in the blue pulse of Fig. 3.12d in the time domain. Full conversion could be achieved by increasing the length of the tuning region or by compressing the input signal pulse by making it slower, but the present configuration is a good compromise between the amount of converted light with energy requirements, loss and dispersion.
The delays in our structure can be tuned continuously by adjusting the pump power, as demonstrated in Fig. 3.13. Figures 3.13a-c show the spectral response of the delay line to input probe pulses of duration 4.7 ps FWHMI and centre wavelengths 1562, 1563 and 1564 nm, for different absorbed pump energies. The corresponding outputs in the time domain are shown in Figs. 3.13d-f. The measured frequency shifts and tunable delays as a function of absorbed pump energies are summarised in Fig. 3.14. As can be seen from Fig. 3.14a, the frequency shift depends linearly on the absorbed pump energy and is independent of the input signal wavelength, as expected: the refractive index change causing the frequency shift is proportional to the density of generated free carriers, which in turn is proportional to the pump energy [144]. By fitting the data of Fig. 3.14a we obtain a frequency shift of ∼7.7 GHz/pJ. The amount of tunable delay for varying pump energy, instead, depends on the group index dispersion, and is therefore different for different input wavelengths (Fig. 3.14b). The highest tunable delay is
Figure 3.14: (a) Measured frequency shifts and (b) tunable delays as a function of absorbed pump energy for input probe wavelengths 1562, 1563 and 1564 nm. Circles correspond to the peak position of the pulses in Fig. 3.13. Lines are linear fits to the data. The frequency shift is directly proportional to the absorbed pump energy.
achieved here for input wavelength 1564 nm (ng,in∼75) and absorbed pump
energy 47 pJ, and is equal to 22.2 ps, or 4.7 pulse-widths.