Broadband wavelength conversion in a silicon vertical-dual-slot waveguide

: We propose a silicon waveguide structure employing silica-ﬁlled vertical-dual slots for broadband wavelength conversion, which can be fabricated using simple silicon-on-insulator technology. We demonstrate group-velocity dispersion tailoring by varying the width of the core, the slots and the side strips, and put forward a method to achieve spectrally-ﬂattened near-zero anomalous group-velocity dispersion at telecom wavelengths. A proposed structure provides a group-velocity dispersion parameter β 2 of − 60 ps 2 / km with an eﬀective mode area A eﬀ of 0 . 075 µ m 2 at 1550 nm. This structure is predicted to signiﬁcantly broaden the bandwidth of wavelength conversion via four-wave mixing, which is validated with experimentally measured 3 dB bandwidth of 76 nm. ©


Introduction
Four-wave mixing (FWM) in silicon waveguides makes possible a number of key features within classical optical communication systems, such as all-optical signal processing [1], and within quantum communication systems, such as photon-pair generation [2,3].The most studied technology is wavelength conversion [4][5][6] via degenerate FWM, which requires highly nonlinear silicon waveguides with engineered group-velocity dispersion (GVD).More specifically, efficient FWM takes place when phase matching is satisfied, which requires an anomalous GVD to cancel the Kerr-induced nonlinear phase shift [7].Such anomalous GVD is characterized by β 2 (ω p )<0, where β 2 is the second-order derivative of the propagation constant and ω p is the pump frequency.Moreover, in wavelength converters, special effort is made to ensure a broad bandwidth.Therefore, a near-zero GVD at the pump wavelength is desired (| β 2 (ω p )| ≈ 0) so that phase matching is satisfied at a large pump-signal detuning, where the region in between benefits from effective parametric gain.Additionally, spectrally-flattened GVD also attracts research interest in applications such as supercontinuum generation [8].
The key resource for GVD tailoring is to design the cross-sectional dimension of the waveguide.Previous research has mainly focused on the geometry of the silicon core [4], but this provides only few degrees of freedom, hence it remains a challenge to achieve spectrally-flattened nearzero anomalous GVD.Recently, sandwich structures [8][9][10][11][12][13][14][15][16][17][18] and slot structures [17][18][19][20][21][22][23][24][25][26][27][28] with flexible geometrical dimension have been developed.The basic concept of these structures is to introduce slots between silicon strips, and use other materials to fill the slots.Based on the mature standard silicon-on-insulator (SOI) technology, the vertical-slot structure is more feasible than the horizotal-sandwich structure because the silicon strips and the slots can be fabricated simultaneously [29,30].Meanwhile, the cladding and the slots can be designed to have the same material.Therefore, the fabrication procedure of GVD-engineered slot structure is more convenient than that of the sandwich structure, in which multilayers require extra accurate deposition steps.Note that partial filling of the slots may take place due to the nonuniform deposition, which however can be mitigated by using the suitable deposition procedures [31,32].
In this paper, we propose a new structure of silicon waveguides that employs silica-filled vertical-dual slots.In our structure, the field is mainly confined in the silicon core, rather than in the slot as the single-slot structures [19][20][21][22][23][24][25][26][27]33].Although an ultra-small effective mode area A eff can be achieved when the optical field is mainly confined in the single slot, such a small A eff does not always enable an ultra-high nonlinear coefficient γ, given by γ = ωn 2 /cA eff .Therefore, by using a slot material with smaller intensity-dependent nonlinear refractive index n 2 than silicon, such as silica, may result in a lower nonlinear coefficient.Moreover, the refractive index contrast along the horizontal direction between the center core and the equivalent cladding, silicon side strips included for the proposed structure, is smaller than that for the corresponding silica-cladded strip structure.The reduction in refractive index difference enables a larger degree of control over the anomalous waveguide dispersion, which can be tailored to carefully compensate the normal material dispersion of silicon.This stands in contrast to the case of the strip structure, in which the waveguide dispersion typically over-compensates the silicon dispersion.Here, we demonstrate GVD tailoring by varying the width of the core (W c ), the slots (S) and the side strips (W s ), and put forward a method to obtain spectrally-flattened near-zero anomalous GVD in the telecom wavelength range, including S-, C-and L-band (1460 nm-1625 nm), by shifting the zero-dispersion wavelengths.We take the silica filling ratio of the slots into account, and discuss its impact on GVD.Moreover, by using standard SOI technology, we fabricate a sample and demonstrate a wavelength conversion experiment, which to our best knowledge is the first explicit proof of the proposed structure.

Numerical GVD tailoring
In our proposed structure, the slots and the side strips are located symmetrically on both sides of the center core, as shown in Fig. 1.We initially assume that the slots are fully filled, and therefore all regions except the center core and the side strips, are assumed to have the refractive index of silica.The height of the center core and the side strips is 250 nm, determined by the silicon layer thickness of the SOI wafer.We focus on the fundamental transverse electric (TE 01 ) mode, and use a finite difference mode solver [34] to simulate the mode profile.As the proposed structure is symmetric, we use the labels W c -S-W s (width of core-slot-side strip, in units of nanometers) to represent the different dimensions.Figure 2 shows the GVD parameter β 2 as a function of wavelength for different waveguide design.In Fig. 2(a), we consider how GVD depends on W c , in the configuration W c -150-150.Increasing the value of W c results in a red shift of the zero-dispersion wavelengths.This tendency stops at W c =650 nm, where β 2 >0 for all considered wavelengths.Figure 2(b) shows the configuration 550-S-150, for which the GVD is normal when S=50 nm and S=100 nm, but exhibits an increasingly large wavelength region of anomalous GVD as S increases from 150 nm to 250 nm. Figure 2(c) shows the configuration 550-150-W s , which results in anomalous GVD at telecom wavelengths for S ≤ 200 nm.Noteworthy, the impact on GVD induced by varying W s is much smaller than that induced by varying S.
As shown in Fig. 2, some waveguide dimensions result in two zero-dispersion wavelengths around 1550 nm.Such behavior is interesting from the perspective of achieving a spectrallyflattened near-zero GVD.In the following, we denote these two wavelengths as ZDW S (short wavelength) and ZDW L (long wavelength), respectively, and consider the case that the region in between is anomalous.We vary the three geometric parameters to make ZDW S = 1460 nm and ZDW L = 1625 nm, giving rise to anomalous GVD in a spectral region that covers S-, C-and L-band.More specifically, for a given W c , we can find the suitable sets of S and W s to make ZDW S at 1460 nm and ZDW L at 1625 nm, respectively.As shown in Fig. 3, the blue solid curve represents the S-W s corresponding to ZDW S = 1460 nm, while the red dashed curve represents the S-W s corresponding to ZDW L = 1625 nm.Using the crossover point of the two curves, we get proposed dimensions of 520-86-54, 540-112-76, 550-129-98, and 570-167-234.Note that small W s helps to avoid the independent beam guidance of side-strip modes, while large S increases the silica filling ratio of the slots [31,32], which further mitigates the uncertainty of the actual GVD induced by partial filling.Therefore, there is a trade-off between W s and S, and we choose a suitable dimension of 550-129-98.We use the weighted average refractive index n s , which has been widely used in photonic crystal fibers [35], to evaluate the filling ratio.Although such a simple calculation does not quantify the material distribution of the slots in detail, it remains valid to characterize the impact of partial filling of the slots.Figure 4(a) shows β 2 versus wavelength for the chosen dimension of 550-129-98, with n s varying from 1 (filling ratio of 0%), 1.11 (filling ratio of 25%), 1.22 (filling ratio of 50%), 1.34 (filling ratio of 75%) to 1.45 (filling ratio of 100%).At all wavelengths | β 2 | becomes larger with decreasing n s .At 1550 nm, β 2 is −900 ps 2 /km, −700 ps 2 /km, −500 ps 2 /km, −300 ps 2 /km, when the filling ratio is 0%, 25%, 50%, 75%, respectively.Hence, the higher the filling ratio is, the smaller | β 2 | one gets.It is worth noting when the slots are 100% filled by silica, β 2 at all wavelengths is anomalous with a maximal value of | β 2 | = 60 ps 2 /km, which is one-tenth signal were combined, and the power was monitored by a powermeter (PM).Two polarization controllers (PCs) were used to optimize the polarization, so that a minimal alignment loss through the TE-polarized PCGCs was obtained.The propagation loss was measured to 3 dB/cm through a cut-back method, while the minimal insertion loss reached 15 dB.The transmittance of the PCGCs was symmetric at 1550 nm with a 3 dB bandwidth of 30 nm [36].The output power of the signal and idler was measured through an optical spectrum analyzer (OSA).Measurement Simulation, 100% filled Simulation, 0% filled Fitted, 55% filled Simulation, no slots Fig. 6.Simulations and measurement of η in a wavelength range of 1490 − 1610 nm.Green diamond: measurement, blue solid: simulations when the filling ratio is 100%, blue dashed: simulations when the filling ratio is 0%, black solid: fitted simulations when the filling ratio is 55%, red solid: simulations of the corresponding strip structure.

Signal Wavelength [nm]
We measured the conversion efficiency, η, versus signal wavelength (see Fig. 6 green diamond).We also simulated η versus signal wavelength based on the model in [37].The in-waveguide power levels of the pump and the signal were set to 15 dBm and 0 dBm, respectively, in agreement with our experiments.The length of the waveguide was 1 cm, the linear loss was 3 dB/cm, the free carrier lifetime τ was 10 ns, other parameters were from [37].Two extreme cases were considered during the simulation: the blue solid in Fig. 6 represents the case where the silica filling ratio was 100% resulting in a 3 dB bandwidth of 116 nm; the blue dashed in Fig. 6 represents the case where the silica filling ratio was 0% with a 3 dB bandwidth of 48 nm.This strongly highlights the importance of achieving a high filling ratio.As expected, however, the measurements resulted in a 3 dB bandwidth of 76 nm, which is in between the two extremes.Therefore, to estimate the filling ratio of our waveguide sample, we used it as a fitting parameter.The best fit (black solid) corresponds to a filling ratio of 55%.As a comparison, we also simulated η for the corresponding strip structure (red solid).The maximal η was 1 dB higher than the measurement, but the 3 dB bandwidth of 52 nm was smaller.Thus, even though the proposed structure has the same fabrication procedure as the strip structure, we achieved broadening of the 3 dB bandwidth by a factor of 1.5 using the vertical-dual-slot waveguide.
The experimental measurement proves that the proposed structure enables GVD tailoring, which is the first explicit proof of such a concept to our best knowledge.However, the proposed structure comes across a problem of fully filling the slots, which can, in future work, be addressed and solved by using other cladding deposition approaches, for example, atomic layer deposition, or employing angled sidewalls of both the center core and the side strips [31].Moreover, other cladding materials can be considered to avoid the partial filling in the slots such as alumina and titania produced through the atomic layer deposition [38].Additionally, such a structure can be also applied to other on-chip platforms.

Conclusion
We have proposed a silicon waveguide structure that employs vertical-dual slots.Such a structure benefits from simple fabrication and flexibly tailorable group-velocity dispersion.We have accurately simulated the zero-dispersion wavelengths for the proposed structure, and obtained a spectrally-flattened near-zero anomalous group-velocity dispersion covering the whole telecom wavelength range.We have also fabricated the proposed waveguide sample, and demonstrated the wavelength conversion experiment achieving a measured 3 dB bandwidth of 76 nm, which is dramatically broadened compared to the corresponding strip waveguide, even with partial filling in the slots.Since the fabrication procedure of our proposed waveguide is the same as the standard strip waveguides, it has a potential to suffice various on-chip functionality using four-wave mixing.

Fig. 1 .
Fig. 1.The vertical-dual-slot structure.H: the height, W c : the width of the center core, S: the width of the slots, W s : the width of the side strips.