We describe nonlinear properties of a GaInP photonic crystal Fabry-Perot resonator containing integrated reflectors. The device exhibits an extremely large static nonlinearity due to a thermal effect. Dynamical measurements were used to discriminate between the thermal and Kerr contributions to the nonlinearity. The high frequency nonlinear response is strictly due to the Kerr effect and the efficiency is similar to that obtained in self-phase modulation and four wave mixing experiments. The waveguide dispersion and the wavelength dependent integrated reflectors yield a series of transmission peaks with varying widths which determine the maximum speed at which the device can operate. Switching and wavelength conversion experiments with 92ps and 30ps wide pulses were demonstrated using pulse energies of a few pJ. The switching process is Kerr dominated with the fundamental response being essentially instantaneous so that the obtainable switching speed is strictly determined by the resonator structure.
© 2012 Optical Society of America
Nonlinear photonic crystal (PhC) resonators are key components for future all-optical high speed low energy consuming switching and signal processing functionalities. Different configurations of passive [1–4] and active (usually employing embedded quantum dots)  structures have been reported in recent years. Most PhC resonators are nano scale devices and exhibit ultra-high Q values . This entails operation in a regime where quantum optics processes dominate while from a practical point of view, it poses many fabrication challenges. One such nano cavity  demonstrated a record low, sub femto Joule switching energy based on carrier effects but being a single mode cavity, it enables only switching and not wavelength conversion. A different type of a highly nonlinear PhC cavity which is based on a macro-size Fabry-Perot (FP) resonator was introduced in . A π/3 phase shift was obtained in that device under static conditions with a pump power of only 2mW. That resonator comprised a 1.3mm long simple W1 GaInP PhC waveguide whose cleaved end facets served as the end reflectors. The large static nonlinearity was attributed to a hybrid Kerr and thermal process and the device also exhibited high speed operation.
This paper reports on a FP resonator based on a low loss PhC GaInP waveguide which incorporates integrated reflectors (implemented by adding a few holes to the defect line) [8, 9] and is terminated by mode converters . The size, periodicity and location of the holes determine the complex, wavelength dependent, transfer function of the reflector and hence of the resonator. While the reflector type and the mode converters are well known, the combination makes for a compact useful device having superb dynamical properties and offering many potential applications. Dynamical characterizations in the small-signal regime reveal an extremely large response at frequencies below 500kHz consistent with a significant thermal contribution to the nonlinearity. At high frequencies, the response is strictly due to the Kerr effect and is limited by the resonator life time. The combination of the wavelength dependence of the group index and of the Bragg-like reflector results in a series of transmission resonances with varying spectral widths. This offers many degrees of freedom in terms of speed and energy when choosing the pump and probe wavelengths in all-optical switching and wavelength conversion experiments. The dependence on the resonance width of small-signal modulation responses in a wavelength conversion configuration and of switching efficiencies was quantified and the results prove that the nonlinearity is strictly due to the instantaneous Kerr effect so that the bandwidth is determined by the resonator structure. Large signal wavelength conversion and switching using 92ps and 30ps wide pulses were also demonstrated with switching energies of a few pJ. These are the first demonstration of all-optical switching in a semiconductor PhC device based exclusively on the instantaneous Kerr effect.
2. PhC Fabry-Perot resonator design and simulation results
The integrated resonator is shown schematically in Fig. 1. It consists of a low loss W1 waveguide whose ends are terminated by mode converters which enhance the input and output coupling and prevent reflections from the facets . The resonator is created by placing identical reflectors, composed of a few holes within the defect line [8, 9]. Figure 1 shows an exemplary cavity geometry formed by three holes reflectors. The positions of the two holes at the mirror termination (shaded holes in Fig. 1) are shifted by a small amount relative to the well-ordered PhC in order to decrease the radiation losses .
The reflectivity of a single reflector was simulated using a commercial software package (Lumerical) . The parameters used in the two-dimensional finite-difference-time-domain (2D-FDTD) calculations are: period a = 493nm, hole radius r = 0.22a, shift of the holes at the mirror terminations s = 0.2a. To account for the vertical confinement the effective refractive index of neff = 2.17 is used here. The calculated power reflectivity spectrum dependence on the number of holes forming the mirror is shown in Fig. 2. For a given wavelength the reflectivity increases up to five holes and then saturates at a level of about 90%. The reflectivity spectra show a periodic modulation which is superimposed on a general increase of about 10% for the one and two holes mirrors. For a larger number of holes, the spectra exhibit only the periodic modulation. The functional form of the reflectivity spectra is consistent with measurements described in section 3.1. The calculated reflectivity values are smaller than the actual ones due to errors introduced by the approximate two dimensional model.
3. Experimental results
The PhC FP resonators were fabricated using standard processes . The PhC array has a period of a = 488nm, a hole radius r = 0.22a and the GaInP slab is 180nm thick. The W1 waveguide is terminated by mode converters which enhance the input and output coupling and prevent reflections from the facets . Two sets of resonators were fabricated; one with two holes and the other with three holes forming the reflectors. These holes have the same radius (0.22a) as the rest of the array and the holes at each mirror termination are shifted by s = 0.2a. The length of both resonators was 250μm. The bandgap of GaInP is 1.9eV which prevents losses due to free carriers, induced by two photon absorption in the 1550nm wavelength range. Any fast nonlinearity exhibited by the resonator we describe is exclusively due to the Kerr effect. Thermally induced nonlinearities are also present but these are very slow.
For linear transmission measurements, the resonators were fed by the broad band amplified spontaneous emission (ASE) of an Erbium doped fiber amplifier (EDFA) and the output was measured by an optical spectrum analyzer (OSA). Pump-probe configurations were used to characterize static and dynamic nonlinearities. In the static case, the pump was an amplified tunable CW signal, the probe a weak broad band ASE and the response was measured with the OSA. For dynamic nonlinear measurements, the pump was modulated and the probe was a CW tunable laser with sufficiently low power to avoid any nonlinear shift in the resonator response. The probe was filtered at the output prior to detection by a cascade of two tunable band pass filters, ensuring that the pump and probe waves were properly separated and could be observed one at a time. Small-signal response measurements were performed using a scalar network analyzer configuration comprising a scanning microwave synthesizer and a spectrum analyzer with a 40GHz optical receiver connected to its input port. For large-signal wavelength conversion and switching measurements, the pump was modulated by 92ps or 30ps wide pulses. The filtered probe output was detected by a fast DC coupled detector and measured using a sampling oscilloscope.
3.1. Linear characteristics
The first result we present compares, in Fig. 3, linear transmission spectra of resonators having two and three holes reflectors, measured over a span of about 2nm. The resonator in the two holes case (shown in black) has an estimated finesse and Q value (measured at 1554nm) of 13.7 and 28,000, respectively. These values increase by a factor of about three for the three holes case (shown in red). Pump-probe characterizations of the three holes resonators were somewhat unstable due to their narrow spectral transmission width and therefore, detailed characterization used resonators with two holes reflectors.
Linear transmission spectroscopy of the PhC resonator was obtained by using the ASE probe with the pump turned off. Figure 4(a) shows the normalized measured transmitted spectrum with clear FP modes spanning the entire 40nm wavelength range. The spectral dependence of the group index, ng, was extracted from the mode spacing and is plotted in Fig. 4(b) together with a quadratic fit (shown in a solid line). ng increases with wavelength in accordance with the classical dispersive band diagram of W1 type PhC waveguides. The finesse spectrum was extracted from the transmission function and is presented in Fig. 4(c). The finesse increases with wavelength and is changing periodically, which is qualitatively consistent with the calculated reflectivity shown in Fig. 2. One more significant property of the transfer function (Fig. 4(a)) is the wavelength dependent resonance width which is plotted in Fig. 4(d). Similar to the finesse spectrum, the resonance width shows a periodic modulation which is superimposed on a general decrease for long wavelengths.
3.2. Nonlinear static response
Static pump-probe measurements observed over a probe wavelenght span of 2nm centered at 1551.5nm are presented in Fig. 5(a). The black line describes the ASE probe transmission with the pump off. The red line shows the clearly red-shifted transmission obtained with a 2.9mW pump aligned with a fringe at 1540.5nm whose width is 12.6GHz. The quoted power level accounts for the coupling loss and corresponds to the power coupled into the input waveguide (see Fig. 1). Hereafter, all stated powers are those coupled into the input PhC waveguide. The transmission resonances shown were not normalized and their difference in amplitude represent variations in the reflector transfer function as well as some frequency dependent losses in the waveguide (possibly due to disorder). The CW pump induces in this probe wavelength range a phase shift δφ of π/3 radians, similarly to the previously reported FP resonator . The induced fringe shift was examined across the entire transmission spectrum of the resonator while the pump wavelength and power were kept constant as in Fig. 5(a). The static nonlinear γ value was extracted for each fringe shift according to the formulation γ = δφ/4PL with P and L being the circulating pump power and the resonator length, respectively . The γ dependence on probe wavelength is shown in Fig. 5(b) with the inset showing the linear γ dependence on group index at the probe wavelength, consistent with theoretical predictions . The γ values in Fig. 5(b) are about two orders of magnitude larger than the corresponding values obtained from self-phase modulation (SPM)  and four wave mixing (FWM)  experiments in similar waveguides. This large nonlinearity is attributed to a thermal effect as has been previously reported in  and in .
3.3. Nonlinear dynamic response
The dynamic response of the resonator depends on two factors, the fundamental response of the enhanced nonlinearity and the structural limitations imposed by the natural life time of the cavity. The experiments described below represent all-optical switching schemes with the control (pump) and data (probe) optical signals aligned to two distinct FP resonances.
3.3.1. Small-signal regime
For nonlinear small-signal characterization we employed a wavelength conversion scheme where the modulated pump was aligned with a fringe having a large spectral width of 35GHz while the probe was tuned to the fringe peaks of various spectral widths. Figure 6(a) shows normalized wavelength converted frequency responses for five exemplary cases where the probes were aligned with resonances having spectral widths ranging from 19GHz to 5.5GHz. The modulation bandwidths correspond to the resonance spectral widths. For an instantaneous nonlinear response such as the Kerr effect, the modulation bandwidth is determined by the fringe widths of both the pump and the probe, actually their product. Such dependence is shown in Fig. 6(b); the dependence is linear proving that the wavelength conversion is induced by an instantaneous process and is structurally limited. Since large signal experiments (described in section 3.3.2) prove that the fast pump causes an index increase, we conclude that the observed fast nonlinearity is due to the Kerr effect.
The lowest frequency in the measurements described in Fig. 6(a) was 50MHz. A separate set of wavelength conversion measurements was performed at very low frequencies, 50KHz to 500KHz. The response at these low frequencies was more than two orders of magnitude larger than that in the low frequency range of Fig. 6(a) but dropped off fast beyond 500KHz. The large nonlinear response at low frequencies indicates that a thermal effect has indeed a major contribution to the very large static response shown in Fig. 5 as well as in  and .
3.3.2. Large-signal regime
The large-signal nonlinear response was examined in the time domain using a pulsed pump. In the first experiment, 92ps wide pump pulses with a peak power of 200mW were aligned with a fringe whose width was 7GHz. Figure 7(a) compares the input (solid line) and output (dotted line) pulses, with their amplitudes normalized and the probe turned off. The output pulse is slightly distorted since the fringe spectral width is smaller than the bandwidth of the 92ps wide pulse. Figure 7(b) and (c) show normalized converted probe waveforms for a probe tuned to a fringe with a spectral width of 20GHz (shown in blue),13GHz (shown in green) and 5.5GHz (shown in red). The probe powers in the three cases were 0.7mW, 0.7mW, and 1.1mW, respectively. All converted pulses in Fig. 7(b) and 7(c) are somewhat distorted. The pump and converted pulses were in phase (as in Fig. 7(b)) when the probe was tuned to a valley on the long wavelength side of the fringe. The wavelength detuning from the resonance peak for the 20GHz, 13GHz and 5.5GHz wide fringes were 223pm, 116pm and 46pm, respectively. Tuning the probe to a fringe peak yields converted pulses which are out of phase with the pump. This is shown in Fig. 7(c). The results shown in Fig. 7(b) and 7(c) prove that the nonlinearity induces a red shift to the fringes, consistent with a Kerr nonlinearity. The converted probe aligned with the narrower fringe exhibits a larger contrast. The induced refractive index change and hence the red-shift in spectral position of the fringes are determined by the pump pulse. Since the converted pulse is obtained from the shifting fringe crossing the CW probe, a narrower fringe causes a larger change in probe transmission which yields a pulse with a larger contrast. The responses in both Fig. 7(b) and Fig. 7(c) show some ringing at late times. These are a natural response of narrow fringes to short pulses .
Using the dependence of converted pulse contrast on the probe fringe resonance width (as in Fig. 7(b)), it is possible to extract the nonlinear γ coefficient which is relevant at high frequencies. For a given contrast we deduce the spectral distance required to change the transmission by the same amount in the static transmission of the same fringe. This spectral distance defines the induced nonlinear phase δφ and hence allows calculating the nonlinear coefficient γ. The γ values so obtained are shown in Fig. 7(d) for the three probe wavelengths; the dependence on wavelength is similar to that of the static γ shown in Fig. 5(b). However, these γ values, ≈ 1000W−1m−1, are similar to those obtained in SPM and FWM experiments in similar waveguides over the same wavelength range. We conclude therefore that the nonlinear responses are induced by the Kerr nonlinearity with no contribution from the low frequency thermal effect and all the high frequency limitations are structural in nature.
The required energy for switching or wavelength conversion was evaluated for 92ps wide pump pulses which were aligned with a fringe of 35GHz width while the converted probe, with a power of 1.2mW, was aligned on a fringe having a width of 5.5GHz. The converted switching contrast obtained for various coupled pump pulse energies are shown in Fig. 8 and the inset shows some measured pulse shapes. For contrasts of 30% to 50%, the required switching energies are in the range of 5pJ to 12pJ, respectively. These switching energies are about one order of magnitude larger than the desirable levels according to  and therefore the resonators need further optimization. For example, the most efficient cavities  have a small volume but these are single mode cavities and can not be used for wavelength conversion or other processing applications where the control signal and the data to be manipulated all-optically are detuned in wavelength. In comparison to nonlinear waveguides used for switching which are not based on PhC, the present devices are quite efficient. For example, predicted powers for switching an interferometer based on second harmonic generation  calls for powers of hundred of Watts compared to the sub 1W level used here. Also, operation of a switchable all-optical delay line  and switching of microring resonators  (both based on GaAs-AlGaAS waveguides) requires intensities in the 1 − 10GW/cm2 which is more than an order of magnitude larger than the switching intensity in the present devices. Finally, it is important to note that high speed operation of the present resonator is based exclusively on the Kerr effect and has no carrier plasma related contribution and therefore, its inherent speed is always determined by the structure and is not limited by the material response.
The large-signal response was also tested with 30ps pump pulses tuned to the peak of a 35GHz wide fringe. Normalized pump pulse transmission is shown in Fig. 9(a). The input pulse is shown in solid line and the output pulse in dotted line. The transmitted pulse reveals no distortion as expected in this wide bandwidth fringe. Switching experiments were performed with a 1.2mW CW probe tuned to the peak of a narrow, 5.5GHz wide, fringe. The converted probe outputs for different pump energies are shown in Fig. 9(b). The traces are very similar to the 92ps pulses in shape but are undergoing more distortion due to the wider spectral content of the input pulses. The switching energies are similar; a converted contrast in the range of contrast of 20% − 60% requires pump pulse energy of 5 − 20pJ.
To conclude, we have described nonlinear static and dynamic characteristic of a GaInP PhC FP resonator which contains integrated reflectors and end facet mode converters. The waveguide dispersion and the frequency dependent transfer function of the integrated reflectors yield a series of transmission peaks with varying resonance width. Under static and low frequency (below 500kHz) conditions, the nonlinearity is extremely large due to a thermal effect. At high frequencies, the response is lower by two orders of magnitude as the nonlinearity is induced by the Kerr effect. Structural parameters determine the speed at which the device can be used in wavelength conversion or switching experiments. This was demonstrated in small-signal modulation as well as pulsed switching with 92ps and 30ps wide pulses. The results constitute the first clear demonstration of Kerr effect for optical switching in a semiconductor PhC device. Resonators designed with low Q values have the potential for ultrafast all-optical switching within a photonic chip.
This research was supported by the project GOSPEL within the seventh framework of the European Commission.
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