1. Introduction

Semiconductor-based nanophotonics have developed rapidly thanks to the established wafer quality and advanced nanofabrication technologies [1]. In particular, silicon (Si) and gallium arsenide (GaAs)-based nanophotonic devices such as low-loss waveguides and ultrahigh quality (Q) factor cavities have been demonstrated at the optical communication wavelengths (1.55 μm) [2–4]. Even though these semiconductors are transparent in the telecommunication range, the phenomenon of multiple photon absorption (MPA) frequently occurs due to high photon densities within nanophotonic structures such as photonic crystal waveguides and nanocavities because they can strongly confine photons within a tiny space. In fact, photonic crystal nanocavities suffer from MPA (particularly, two-photon absorption (TPA)) even at low input powers of a few μW [5–7] because of ultrasmall modal volume of the order of a cubic wavelength. In addition to the direct optical absorption due to TPA, carriers generated by TPA contribute to free-carrier absorption and carrier plasma shift, causing additional optical instability to cavity-based devices [5,7]. Most strategies for reducing these adverse effects have focused on shortening the lifetime of the generated carriers by using reverse P-i-N diodes to rapidly extract the carriers [8,9]. However, this process is limited by the speed of the electronic response, causing extraction to last on the order of several hundreds of picoseconds. Even under ideal circumstances this approach does not eliminate the initial optical loss incurred by TPA, only the subsequent losses and nonlinearities due to the generated carriers. To fundamentally eliminate the optical losses and non-linear response at high photon densities, the TPA phenomenon itself must be directly addressed. Recently, there have been significant efforts [10,11] to minimize TPA and its adverse effects using larger electronic bandgap (E_g) materials. This is motivated by the fact that the TPA coefficient decreases as 1/E_g³ [12,13]. However, complete inhibition of TPA has yet to be demonstrated experimentally because the tested bandgaps e.g. Al_xGa_1-xAs (E_g = 1.6~1.8 eV) are smaller than the energy of a pair of photons (2ћω~1.6 eV). Thus, it is desirable to utilize a sufficiently wide bandgap material to completely inhibit TPA and its side effects [14]. Very recently, we have developed photonic crystals made of silicon carbide (SiC), a wide bandgap material having E_g of 3.0 eV, and demonstrated both broadband operation from infrared to visible wavelengths and superior thermal stability [15–17]. In this work, we investigate the robustness of SiC photonic crystal nanocavity performance at high input powers. We compare the response of SiC and Si nanocavities to high input powers and demonstrate that SiC nanocavities inhibit TPA completely and also suppress higher-order MPA.

2. Samples and measurement setup

In order to investigate the superiority of SiC-based photonic crystals for the suppression of MPA phenomena at infrared ranges, we compare experimentally the optical response of a SiC photonic crystal nanocavity and a conventional Si nanocavity. We prepared Si and SiC photonic crystal nanocavities (see inset of Fig. 1 .) having similar resonant wavelength and Q factors: To realize similar resonant wavelengths near 1.55 μm, the lattice constant of the SiC photonic crystal was made larger than that of the Si because of the lower refractive index of SiC (n_SiC = 2.5~2.7, n_Si = 3.48). Furthermore, air-hole shifted cavities and heterostructured cavities are adopted for the Si an SiC photonic crystals, respectively, to obtain similarly high Q factors (8,000 and 10,000, respectively) [1,15]. The calculated modal volumes of the Si and SiC cavities are 0.73 (λ/n)³ and 1.71 (λ/n)³, respectively. An input waveguide is introduced nearby in order to couple light evanescently into each cavity. Detailed fabrication procedures of Si and SiC photonic crystal structures are described in references 15 and 18. The fabricated cavities are measured by the setup shown in Fig. 1. At first, we measured the intrinsic or linear characteristics of the cavities using a wavelength-tunable, continuous wave (CW) light source (λ = 1.52~1.63 μm) where input power to the waveguides are set to be as low as a few nW. The spectra are obtained by scanning the wavelength while measuring the intensity of light emitted from each cavity using an ultrasensitive photoreceiver. Next, we investigated the nonlinear characteristics of the cavities by inputting higher-intensity light pulses (up to 64 pJ). For this purpose, we used a wavelength-tunable, pulsed light source (λ = 1.53~1.56 μm, pulse width = 4 ps, repetition rate = 50 MHz), where the center wavelengths were tuned to the resonant wavelength of the cavities, and the spectra of light emitted from the cavities were measured using an optical spectrum analyzer (OSA) with a resolution of 0.1 nm.

 

Fig. 1 Schematic picture of the optical setup used to measure the characteristics of nanocavities at high input energies. Insert images of nanocavities used in experiment.

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3. Measured results

The intrinsic resonant spectra of the cavities measured using low power CW light are shown as dashed lines in Fig. 2 . From the spectra, we see that the cavities have similar resonant wavelengths (λ_Si = 1.539 μm and λ_SiC = 1.559 μm) and Q factors (Q_Si = 8,000 and Q_SiC = 10,000). The solid lines in Fig. 2 show the spectra of the Si and SiC nanocavities measured for various input energies of pulsed light. Here, the input energy is defined as the energy of the light pulse actually coupled into the waveguides, and was estimated from the transmission intensity of the waveguides as schematically shown in Fig. 1. In the case of the Si nanocavity, as the input energy is increased, the peak wavelengths of the spectra shift toward shorter wavelengths even at input energies as low as 0.6 pJ. This phenomenon is due to the decrease of refractive index caused by the plasma effect of the MPA-generated carriers. Furthermore, the peak intensities in the Si cavity do not increase with input energy. This can be attributed to the MPA itself and the free carrier absorption by the MPA generated carriers. By contrast, the waveforms in the SiC cavity spectra do not change: no shift of the resonant wavelength was observed even at input energies of 64 pJ, which are 100 times higher than the maximum energy that can be applied to the Si nanocavity without causing deformation of the waveform. Furthermore, the peak intensities for the SiC cavity simply increased linearly with input energy, indicating that nonlinear absorption doesn’t occur. Note that the input energy of 64 pJ is the maximum performance of our measurement system and not a limit imposed by MPA in the SiC nanocavity. It is clear that the SiC-based photonic crystal can sufficiently suppress MPA for this wavelength (~1.56 μm) at least up to input pulse energies of 64 pJ.

 

Fig. 2 Spectra of the vertical emission from the nanocavities for various input energies. (a) In Si higher energies lead to spectral blue shift due to TPA without significant increase in overall emission. (b) In SiC peak emission increases linearly with input energy and shows complete inhibition of TPA.

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4. Analysis and discussion

In order to analyze the experimental results shown in Fig. 2 theoretically, we built on the model described in [7] and developed a nonlinear response model including MPA and its side effects in a photonic crystal structure. The photonic crystal structure consists of a waveguide and a cavity to form a two-port system shown schematically in Fig. 3 . Here, a is defined as the amplitude whose magnitude squared corresponds to the energy within the cavity (U = |a|²). S₁ is the amplitude whose magnitude squared corresponds to the light power introduced into the waveguide. S₂ is the amplitude whose magnitude squared corresponds to the light power emitted from the cavity to free space.

 

Fig. 3 The model of two-port system consisting of a waveguide and a cavity.

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The equation for the evolution of the cavity mode in time can be expressed using coupled-mode theory (CMT) [19]

The resonant angular frequency ω'₀ is assumed to be determined by the original resonant frequency of the cavity ω₀ and the frequency shift caused by the refractive index decrease due to plasma effect of the MPA-generated free-carriers as show by Eq. (6).

To perform the nonlinear CMT simulation, we solve Eqs. (1)-(7) simultaneously, using the physical parameters of Si and SiC [7,21,22], where the input light is set to be a Gaussian pulse: S₁ = Aexp(-t²/Δt²)exp(jω₀t) with Δt = 4 ps.

Generally, it is difficult to determine accurate MPA coefficients because they are strongly dependent on material bandgaps and qualities (e.g. free carrier density, defects and crystallographic orientation) [21,23]. In particular, β_SiC⁽⁴⁾ is unknown in the telecommunication range. Therefore, we determined values of β_Si⁽²⁾ and β_SiC⁽⁴⁾ by fitting the above CMT simulations to the experimental results shown in Fig. 2. The calculated results of nonlinear optical response of the Si nanocavity for various β_Si⁽²⁾ are plotted in Fig. 4 . For the purposes of comparison, we show the spectra for β_Si⁽²⁾ set to 2.0 cm/GW and 0.5 cm/GW in Figs. 4(a) and 4(b), respectively. The waveforms and peak wavelengths for the former are inconsistent with the experimental results shown in Fig. 2(a) while the latter matches experiment quite closely. In order to determine the value of β_Si⁽²⁾ more clearly from experiment, we plot the calculated the normalized peak intensity and the shift of the peak wavelengths for various input energies as a function of β_Si⁽²⁾, as shown in Figs. 4(c) and 4(d), respectively. The experimental results for each input energy, plotted as solid circles, consistently indicate β_Si⁽²⁾ of ~0.5 cm/GW (shaded region in the figures). The value of the β_Si⁽²⁾ is in good agreement with the value reported in [21].

 

Fig. 4 Calculated results of optical responses of a Si cavity for various β_Si⁽²⁾. (a), (b) The spectra of β_Si⁽²⁾ = 2.0 cm/GW and 0.5 cm/GW in the Si cavity. (c), (d) The normalized peak intensity and peak wavelength shift for various β_Si in the Si cavity, respectively (here, experimental results are also plotted as the solid circles).

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Similarly, we investigated the optical responses of the SiC nanocavity for various β_SiC⁽⁴⁾ as shown in Fig. 5 . Even when β_SiC⁽⁴⁾ is set to be as small as 2.0 × 10⁻⁴ cm⁵/GW³ the peak resonant wavelengths are visibly shifted toward shorter wavelengths as seen in the spectra of Fig. 5(a). Figures 5(b), 5(c) and 5(d) show that peak intensity and peak wavelength of the SiC cavity are maintained, even at the extremely high energies seen in experiment (Fig. 2(b)), when β_SiC⁽⁴⁾ is less than 2.0 × 10⁻⁵ cm⁵/GW³. This implies that no nonlinear effects occur. Through additional calculations we checked that the significant suppression of multiple photon absorption in the SiC cavity is due not to the modal volume of the cavity but to the wide electronic bandgap of the material. An amplified higher-power laser source and higher input coupling efficiency [5] in the experimental setup provides higher input energy, it would cause four photon absorption in the SiC cavity and allow the value of β_SiC⁽⁴⁾ to be identified definitely. The small β_SiC⁽⁴⁾ means that even when a strong light intensity of 1 GW/cm² is inputted in SiC photonic crystal nanocavity, the optical absorption loss is as small as 2.0 × 10⁻⁵ /cm. This is an experimental verification of the very small multiple photon absorption of SiC material at the telecommunication range. It implies that SiC-based photonic crystals not only completely inhibit the undesirable nonlinear phenomena of two and three photon absorption, but also sufficiently suppress four photon absorption to be unobservable up to an input energy of 64 pJ at telecommunication wavelength range.

 

Fig. 5 Calculated results of optical responses of a SiC cavity for various β_SiC⁽⁴⁾. (a), (b) The spectra of β_SiC⁽⁴⁾ = 2.0 × 10⁻⁴ cm⁵/GW³ and 2.0 × 10⁻⁵ cm⁵/GW³ in the SiC cavity. (c), (d) The normalized peak intensity and peak wavelength shift for various β_Si in SiC cavity, respectively (here, experimental results are also plotted as the solid circles in shaded region).

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5. Conclusion

In summary, we experimentally demonstrated that photonic crystals made of SiC can completely inhibit two-photon and three-photon absorption at telecommunication wavelengths of 1.55 μm. We compared SiC-based and Si-based nanocavities with high Q factors of ~10,000, and found that the SiC-based nanocavity suppresses nonlinear absorption and to below detectable levels and exhibits no change of resonant spectrum shift even at input energies 100 times higher than that is maximally allowed for equivalent Si-based nanocavities to maintain optically stable operation. We believe these results will open a route for the realization of nanophotonics devices that are very optically stable without multiple photon absorption even at high input energies, and will lead to applications such as harmonic generation [24], parametric down conversion, and Raman amplification with very high efficiency and low loss.