1. Introduction

Slow light on an optical chip [1,2] offers the potential for chip-scale nonlinear optical devices with ultralow power consumption based on the enhanced interaction between matter and the slowly propagating light within. A decade ago, we showed that a line defect in a photonic crystal (PhC) slab exhibits a small group velocity v_g near the photonic band edge [3]. It has also been shown that shifted lattices in the vicinity of a line defect of a PhC modulate the waveguide dispersion and this results in a small v_g with reduced group-velocity dispersion (GVD) [4,5]. On-chip slow light enhanced optical nonlinearity has recently been intensively studied by using such line-defect-based slow light PhC waveguides; optical pulse propagation with self-phase modulation (SPM) and nonlinear absorption are being investigated in silicon- [4,5] and AlGaAs-based [6] PhC waveguides. Strong free carrier absorption in silicon achieved optical signal regeneration [7]. Third-harmonic generation realized on-chip green light emission [8]. SPM and strong anomalous waveguide dispersion achieved soliton pulse compression [9], and four-wave mixing (FWM) is being investigated for all-optical wavelength conversion and switching [10–15].

In addition to a small v_g, the strong spatial confinement of light is important for nonlinearity enhancement. It has recently been shown [14,15] that the effective mode area A_eff of line-defect PhC waveguides increases as a function of the group index n_g, thus reducing the effective nonlinearity. However, even with such an enlarged spatial field, slow-light PhC waveguides still exhibit strong optical nonlinearity [2,4,5,7,8,10,11,14,15]. Therefore, if the waveguide can support both a small v_g and a strong spatial confinement of light, further nonlinearity enhancement can be expected.

A coupled-resonator optical waveguide (CROW), which consists of a one-dimensional periodic array of optical cavities coupled weakly to one another, is a promising candidate for a slow-light waveguide [16]. The waveguiding mode in the CROW underlies the extended mode formed by the nearest-neighbor coupling of the periodically arranged cavities. This is analogous to a situation where the atoms in a crystal lattice are coupled with each other and form a continuous electron band. The group velocity v_g in the CROW can be characterized as v_g = L_cc/τ_h, where L_cc is the cavity pitch and τ_h is the characteristic hopping time of light propagating between neighboring cavities [1]. Here τ_h is determined by the inter-cavity coupling, which is a variable parameter obtained by setting L_cc and the inter-cavity barrier structure, however, its upper limit is approximately determined by the photon lifetime (~inverse of the cavity Q) for each cavity. If τ_h is much longer than the individual cavity lifetime, light cannot propagate through the CROW. Therefore, small and high-Q cavities are necessary if we are to achieve a small v_g in the CROW.

We have already fabricated a CROW based on width-modulated cavities in a silicon PhC line defect and demonstrated slow-light transmission with a v_g as small as c/170, where c is the speed of light in a vacuum [17]. The v_g value is the smallest of any CROW yet demonstrated including arrayed point defect silicon photonic crystals [18], polymer microspheres on a silicon V groove [19], and a chain of silicon micro-ring resonators [20–22]. This small v_g originates from both a tiny (almost wavelength-sized) mode volume and a high Q of as large as one million in our width-modulated cavities [23,24], each of which contributes to the small L_cc and τ_h, respectively [17].

Owing to a small v_g, our CROW is expected to exhibit the slow light enhancement of optical nonlinearity as in other types of slow light waveguides based on PhC line defects. In this work, first, we reveal that the A_eff of our CROW is very small according to the result of a 3-D FDTD calculation of the resonant field. Next, we perform an FWM experiment to show the high optical nonlinearity of our CROW. FWM has been demonstrated in various slow-light waveguides as described above, thus we can directly compare our and other results. In addition, FWM is important not only in classical applications, but also in quantum information science such as quantum-correlated photon pair generation [25]. Hence, it is worth performing an FWM experiment to explore the future prospects for our CROW. Finally, we compare our experimental results with those for other nonlinear waveguides in terms of the smallness of v_g and the spatial confinement of light.

2. Samples and FDTD simulation

Figure 1(a) is a schematic of our CROW. The CROW is based on width-modulated line-defect cavities in a two-dimensional silicon photonic crystal with a triangular lattice of air holes fabricated by electron-beam lithography and dry etching [23,24]. The lattice constant a of our silicon PhC chip is 420 nm, the hole radius is 0.25a and the thickness of the PhC slab is 0.5a. Local width modulation of a 0.98$\sqrt{3}$a wide line defect achieves high-Q and wavelength-sized cavity. The displacements of the red and green holes toward the outside are 8 and 4 nm, respectively. The shifted holes create optical nanocavities with a mode volume of 1.7(λ/n)³, where λ is the wavelength of light and n is the refractive index of silicon [24]. Here we chose L_cc as 5a, which yields n_g ~40 as shown later, so that CROW nonlinearity can be compared with that of the slow-light-engineered PhC line defect waveguides exhibiting a comparable n_g [5,11]. Here n_g increases monotonically with increase of L_cc, as the intercavity hopping time decreases by increased neighboring decoupling. The relationship between L_cc and n_g including the loss is discussed in [17] in detail. The cavity number N_cav is 200, thus the total CROW length becomes 420 μm. To couple the light into the CROW, line-defect PhC waveguides are introduced at both ends of the CROW as indicated by purple holes. The width of the access line defect is 1.05$\sqrt{3}$a, yielding n_g of approximately 5. The length of each element is shown in Fig. 1(a). In addition, the PhC waveguides are connected to silicon-wire waveguides (SWWs) (600 nm wide and 200 nm high). As a reference waveguide, we prepared another PhC waveguide whose CROW section we replaced with a W1.05 silicon PhC waveguide as shown in Fig. 1(b). As shown in Fig. 1, light is guided from left to right by lensed fibers for the coupling. For the following discussion, we label the optical powers at several important positions as shown in Fig. 1. Please note that P_i and P_o indicate the powers in the lensed fibers.

 

Fig. 1 (a) Schematic of a CROW comprised of width-modulated line-defect ultrahigh-Q nanocavities. W1.05 PhC line-defect waveguides and silicon access waveguides are introduced at each end of the CROW. We also indicate the optical powers at several important positions to clarify later discussions. (b) The reference waveguide was implemented without a CROW.

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First, we estimate the A_eff of our CROW using a 3-D FDTD calculation. Figure 2(a) shows examples of simulated resonant electromagnetic fields (lower half) of the CROW for various N_cav values, shown with the corresponding structures used in each calculation (upper half). Assuming the spatial mode has a uniform waveguiding structure along the propagation axis, we calculate A_eff as

 

Fig. 2 (a) Top views of extended modes in a CROW for various N_cav by 3-D FDTD simulation (lower half) with corresponding PhC structures (upper half). Note that the color plot is in a logarithmic scale. The regions indicated by the dashed squares are the integration ranges used for supermode-volume calculation. (b) Effective supermode volume (left axis) and area (right axis) calculated from the electric field distribution under Eq. (2) and Eq. (1), respectively, as a function of cavity number.

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We then derived A_eff in this way for various N_cav. The results are plotted in Fig. 2(b) with the corresponding V_eff. We performed the calculation in the N_cav < 10 range due to the long calculation time required for a large-scale CROW. We see that V_eff is proportional to N_cav – 1 since for a single cavity whose z_Ncav = z₁ (i.e. no integral region in our definition). We also obtained an almost constant A_eff against the variation of N_cav, with an average A_eff value of 0.04 μm². To compare our result with conventional line-defect waveguides, we evaluated A_eff of a PhC W1 waveguide in our definition. In this case, we calculated V_eff by the integration of propagating field based on Eq. (1) using a finite period of the waveguide along z axis as the integral range, and then divided the V_eff by the length of the period. The obtained A_eff was 0.04 μm² at n_g = 5 and 0.08 μm² at n_g = 25. Hence, our CROW exhibited A_eff value comparable to a line-defect waveguide in the fast light region and smaller to that of the slow light region. Such a small A_eff of our CROW can be regarded as the result of the strong (wavelength-sized) confinement of light achieved by individual cavities. The fluctuation of A_eff in Fig. 2(b) is because the fraction of the optical field outside the integration range varies depending on the shape of the resonant field determined by N_cav. Thus, the fluctuation is expected to become small for a larger N_cav with the fraction outside the range. We note that our definition of V_eff in Eq. (2) is different from the definition

3. Linear transmission property

Figure 3(a) shows the linear transmission spectrum of the CROW and the reference line-defect waveguide, measured with a wavelength-tunable cw laser emitting TE polarized light at around 1.55 μm. First, for the reference waveguide, the average transmission loss is approximately 18 dB, which consists of in- and out-coupling losses η_Ref ( = P_iR/P_i and P_o/P_oR in Fig. 1) of 8 dB per facet and a linear propagation loss α_Ref in a W1.05 PhC waveguide of 2 dB/mm measured by the cut-back method in a similar sample. The fringe in the spectrum of the reference waveguide originates from the Fabry-Perot interference caused by reflections at both facets [26]. Meanwhile, the CROW exhibited a clear transmission band of 4 to 5 nm, which is much wider than that of a single nanocavity (~1 pm) [23,24]. Such a wide transmission band can be obtained with the coupled-cavity structure [16,17]. Spectral peaks, whose number corresponds in principle to the number of cavities, are the fingerprint of the extended mode [17]. Comparing the average transmittances of the reference waveguide and that of the CROW at around the band center (as indicated by the dashed lines in Fig. 3(a)), the CROW’s average additional loss is estimated to be approximately 7 dB. The excess loss is presumably due to additional coupling losses η_C at both ends of the CROW (corresponding to P_iR/P_iC and P_oC/P_oR in Fig. 1) and the propagation loss in the CROW α_CROW that arises from scattering and intrinsic decays at each cavity.

 

Fig. 3 (a) Transmission spectra and (b) time-of-flight measurement of group-delay spectra for the CROW (left) and the reference PhC line-defect waveguide (right). (c) Group-index spectrum of the CROW extracted from the difference between the traveling-times of the CROW and the reference waveguide (using data of (b)), with the fitted polynomial function of λ (solid curve).

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We measured the dispersion property of the CROW using the time-of-flight (TOF) method with optical pulses. Figure 3(b) is a density plot of the output-waveform spectra of optical pulses with a duration of 100 ps. The optical pulses were obtained with a wavelength-tunable cw laser followed by an electro-absorption (EA) modulator. Output optical pulses from the samples were measured directly with a high-speed optical sampling oscilloscope (bandwidth: 80 GHz) synchronized with a gate signal applied to the EA modulator. The horizontal axis in Fig. 3(b) shows the center frequency of each optical pulse, while the vertical axis is the time relative to the gate signal’s arrival. The intensities in each figure are normalized independently. Compared with the reference waveguide, an obvious propagation delay of greater than 50 ps can be obtained for the entire CROW band. It is also observed that the group velocity becomes slower as the wavelength approaches to the band edges of the CROW, as expected from the tight-binding approximation [17]. Although we could evaluate the dispersion property of the CROW also using spectral peak positions as shown in [17], the method is not effective when N_cav is as large as our present device whose several spectral peaks united so are indistinguishable. This time we solved this problem by adopting TOF method. The phase-shift method is widely used in usual dispersion measurements [27], however, the use of this approach resulted in a noisy group delay spectrum in the presence of strong reflection at the facets in our CROW.

Next, we evaluate the n_g value of our CROW from the difference between the traveling times of two samples. Here, the CROW length of 420 μm is taken into account. An extracted group-index spectrum obtained using the data in Fig. 3(b) is shown in Fig. 3(c). A group index n_g of more than 30 was obtained across the CROW band. In accordance with the tight-binding model [16], in principle, the group velocity is at its largest at the band center and decreases toward zero around the band edge. However, an asymmetric group-index spectrum was obtained in our CROW. This is presumably due to the original anomalous dispersion in the W1 waveguide [3] that is as wide as the width-modulated section in our CROW. Note that not only resonators, but also periodic dielectric components yield the tight-binding mode. Hence, our CROW could be understood also as a periodic structure of W1 line-defect waveguides. We infer our asymmetric n_g spectrum is a result of the symmetric spectrum in the tight binding structure incorporated with a strong anomalous dispersion with a considerable variation of n_g up to 100 [3] in the W1 waveguide. On the other hand, the finite v_g around the band edges is due the finite length of the CROW and localization of light along the propagation axis as reported in [28]. We fitted our result with a polynomial function of wavelength λ (up to the third order) shown as a solid curve. The fitted function is set at n_g(λ) for the FWM phase matching calculation as shown in Sec. 4.1.

4. Four-wave mixing experiments

4.1 Wavelength dependence of FWM

We used two independent wavelength-tunable cw lasers as a pump (p) and a signal (s) source in the FWM experiment. Although the transmission band of the CROW is high, here we chose the cw experiment rather than the pulsed experiment. Using cw lasers we can reduce errors in the nonlinearity estimation, which requires an extra estimation of the peak intensity in the pulsed case. The pump laser was amplified by an erbium-doped fiber amplifier, and subsequently filtered by a tunable band-pass filter consisting of a fiber circulator and a fiber-Bragg grating with a full-width at half maximum (FWHM) of 0.5 nm to suppress background noise. The pump and the signal beams were combined by a 50/50 directional coupler, and then TE polarized by a half and a quarter waveplate before being coupled to the PhC waveguides with a lensed fiber. They were then collected from the waveguide output by another lensed fiber, and the overall output spectrum was measured directly with an optical spectrum analyzer (OSA) with a spectral resolution of 0.05 nm.

The observed FWM spectrum is shown as a density plot in Fig. 4(a) (left, CROW; right, reference waveguide). Here the signal wavelength λ_s (vertical axis) was scanned across the CROW transmission band, while the pump wavelength λ_p was fixed at 1545.45 nm, which was around the band center of the CROW. Here, the pump and signal powers coupled to the W1.05 PhC waveguide P_iR(p) and P_iR(s) were 1.6 and 0.47 mW, respectively. These values were obtained from the coupling efficiency to the reference waveguide η_R and the power before the PhC chip P_i. In addition, we assumed these values as also the coupled powers to the first W1.05 line-defect section of the waveguide containing the CROW as shown in Fig. 1(a). For both samples, we see almost straight lines consisting of created idler peaks (as indicated), which appear almost symmetric with the signal line with respect to the pump wavelength. This idler frequency can be explained by the energy conservation of the FWM;

 

Fig. 4 (a) Density plots of the FWM spectrum for various signal wavelengths, exhibiting output idlers following FWM energy conservation (Eq. (4)). The resolution of the OSA was 0.05 nm. (b) Signal-wavelength-dependence of the idler power extracted from (a). Background noise of the incident pump and signal lasers is subtracted.

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Next, in Fig. 4(b) we show measured idler intensities (background subtracted) as a function of λ_s obtained from the result in Fig. 4(a). Here the vertical axis corresponds to P_o (the power coupled to the output lensed fiber) in Fig. 1. It is noteworthy that the idler peaks of the CROW were more than one order of magnitude larger than that of the reference waveguide. The only difference between these two measurements is the presence of the CROW section in the sample as shown in Fig. 1. In addition, the CROW has a larger coupling loss than the reference waveguide because of the extra connection loss of η_C ( = P_iR/P_iC and P_oC/P_oR in Fig. 1). Therefore, the pump and signal intensities coupled to the CROW (P_iC(p) and P_iC(s)) should be smaller than those coupled to the reference waveguide (P_iR(p) and P_iR(s)). Taking these factors into account, we can conclude that the CROW exhibited higher nonlinearity than the reference waveguide.

To evaluate the nonlinearity quantitatively, first, we estimate the FWM conversion efficiency η_FWM from the result. η_FWM is usually defined as the ratio of the output idler power to the input signal power inside the waveguide. Therefore, for the η_FWM of the CROW, we should use the powers in the CROW P_oC(i) and P_iC(s). However, instead we use the estimated powers in the W1.05 reference waveguide for the CROW’s nonlinearity as

If we used the powers coupled to the CROW section, η_FWM = P_oC(i)/P_iC(s) = P_o(i)/P_i(s)/(η_R²η_C²), which cause an overestimation by the uncertain η_C in the present experiment. The η_FWM of Eq. (5) gives us the conversion efficiency that is always lower than the actual value, thus it never gives us overestimated nonlinearity.

The conversion efficiency η_FWM obtained from the experiment is plotted in Fig. 5 , as a function of λ_s for various λ_p values in the CROW band. Here the data at λ_p = 1545.45 nm correspond to the result in Fig. 4. We see that there is an FWM gain band for all λ_p values. We also see that the top of the η_FWM band increases with increases in λ_p. This corresponds to the measured dispersion property in Fig. 3(c), in which v_g becomes smaller as λ_p becomes longer. This indicates slow light enhanced nonlinearity. Meanwhile, the FWM gain band becomes narrow with λ_p around the band edges because the dispersion slope becomes steep near the band edges. The spectral fluctuation in the measured conversion efficiency is due to the fringe of the transmission spectrum in Fig. 3(a).

 

Fig. 5 FWM conversion efficiency dependence on signal wavelength measured for various pump wavelengths set in the CROW transmission band. The solid curve is the simulation underlying the model of uniform waveguide structure along the propagation axis of CROW.

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Next, we try to fit the experimental data in Fig. 5 to estimate waveguide nonlinearity. For the calculation, we assume that our CROW has a uniform waveguide structure along the propagation axis to evaluate the “effective” waveguide nonlinearity as we did with the A_eff calculation. In this case, η_FWM is governed by [10–13]

It is known that γ_eff is proportional to n_g² [1,2]. This is due to the slow light effect and can be explained as a prolonged interaction length by n_g combined with the enhanced peak intensity of the shrunken optical pulses also by n_g. Therefore, γ_eff(λ) = κ₀ n_g(λ)² where κ₀ can be a constant in the small detuning of our experiment. We chose the κ₀ value so that η_FWM in Eq. (6) well describes the experimental results. The calculated η_FWM is represented by the solid curves in Fig. 5 for κ₀ = 5. Although the model of the introduced waveguide structure is simple, the calculation captures the experimental results well, especially the dependence of the peak gain values on λ_p. As a result, we obtained γ_eff = 7,200 /W/m at λ_p = 1545.2 nm (n_g = 36) and 13,000 /W/m at λ_p = 1547.2 nm (n_g = 49). These values are compared with those of other nonlinear waveguides in Sec. 5. To the best of our knowledge, this is the first experimental report of a γ_eff value exceeding 10,000 /W/m in silicon-based nonlinear waveguides (note that γ_eff = 13,439 at n_g = 66 is estimated by using a theoretical simulation of a silicon slow-light waveguide [7]). On the other hand, the calculated and experimental gain bandwidths are different especially at λ_p = 1545.15 nm. The possible reason for this is a discrepancy between the measured n_g data and the fitted function (in Fig. 3(c)) used for the η_FWM calculation. The difference becomes large at λ < 1544 nm, which corresponds to the region where the data and the η_FWM simulation diverge. Therefore, an imperfect fitted function may have caused the discrepancy. Another possible reason for the discrepancy is that Eq. (6) is insufficiently accurate to describe our device. Although we assumed that the CROW has a uniform waveguiding field along the propagation axis, the extended modes are not exactly uniform as seen in Fig. 2(a). Further study will require a comparison of these results with detailed theory such as that provided in [29–31].

4.2 Pump power dependence of the FWM

The measured pump-power dependence of the conversion efficiency η_FWM in our CROW is shown in Fig. 6 . Here λ_p = 1545.08 nm (n_g = 36) and λ_s = 1544.75 nm for the blue symbols and λ_p = 1547.13 nm (n_g = 49) and λ_s = 1546.75 nm for the red symbols. We chose the conditions so that the pump, signal and idler wavelengths would exhibit high transmittance simultaneously. Again, we used a pump power P_iR(p) (>P_iC(p)) to avoid possible overestimation of nonlinearity. The experimental results show clear P² dependence, corresponding to the two-photon excitation process of the FWM. The solid curves are calculated values based on Eq. (6) with γ_eff as a free fitting parameter. From the fitting, we have obtained significantly high nonlinearities of γ_eff = 18,600 /W/m at λ_p = 1545.08 nm and γ_eff = 25,000 /W/m at λ_p = 1547.13 nm. We confirmed that the reason for the depletion at high excitation for λ_p = 1547.13 nm was the depletion of the output pump power caused by the red shift of the high transmission peak resulting from the thermo-optic effect, as reported for other silicon nonlinear devices in the cw regime [32–34].

 

Fig. 6 Pump-power dependence of idler conversion efficiency. The solid curve is a fitting by Eq. (6) with γ_eff as a free parameter.

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5. Discussions and conclusion

We observed the highly enhanced optical nonlinearity of our CROW. The parameters we obtained are summarized in Table 1 along with those of other nonlinear waveguides whose cores are crystalline silicon. By using silicon as the core material, we can directly compare structural nonlinearities.

Table 1. Nonlinear Constants of Silicon-Core Nonlinear Waveguides (evaluated at the telecom wavelength)

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It is clear from the γ_eff value that our CROW exhibited the highest nonlinearity. In addition, this is the first report of γ_eff exceeding 10,000 /W/m in a silicon waveguide. This significant nonlinearity enhancement is achieved in our waveguide where the slow-light mode co-exists with a small mode area, thanks to the strong light confinement achieved by wavelength-sized cavities. To estimate the degree of enhancement, we compare our γ_eff with that of a PhC line-defect slow-light waveguide based on a lattice shift. In Sec. 2, we roughly estimated that A_eff of our CROW is almost half of that of the W1 waveguide operating at slow light regime. Here we assume that the line-defect dispersion engineered slow light waveguide [11] exhibits similar A_eff to the W1 waveguide in large n_g regime. Taking account of n_g²/A_eff dependence of γ_eff as described above, γ_eff = 2,930 /W/m at n_g = 30 in [11] can be extrapolated as γ_eff ~8,400 /W/m at n_g = 36 with and γ_eff ~16,000 /W/m at n_g = 49. These estimated values show a good agreement with our experimental resultse. However, we infer that our CROW’s nonlinearity is potentially higher than these values, since we neglected the CROW’s additional losses of η_C and α_CROW yielding the total loss of 7 dB. In this work, we treated the CROW as a uniform waveguide along the propagation axis and characterized nonlinearity by n_g and A_eff for simplicity. However, the local field enhancement of the individual cavity must be treated based on more accurate characterization [29–31]. We believe that cavity enhancement effect become significant in our CROW with larger cavity pitch, which results in a significant discretization (separation) of the spatial supermode along the propagation axis significant. Hence, evaluation of optical nonlinearity in such CROW would be of interest.

Although the CROW’s nonlinearity was significantly high, the FWM gain bandwidth was lower than that of conventional nonlinear waveguides as seen in Table 1. This is because the dispersion was stronger than that of the other waveguides. However, this problem could be overcome. In Section 2 we mentioned that the asymmetric n_g spectrum in our CROW is because of the additional dispersion imposed by the original W1 line defect constructing the CROW. Conversely, the dispersion property can be controlled by modifying the structure of our CROW. This dispersion-engineered CROW will be the subject of further study. Even without a flattened dispersion, the CROW can still be used for such applications as chip-scale nonlinear pulse compression, where a strong dispersion property is key as well as high nonlinearity [9].

In silicon, high nonlinearity is accompanied by strong free-carrier effects. To avoid these effects we used cw lasers for an accurate evaluation of waveguide nonlinearity. Since free carriers are excited by two pump photons at the telecom wavelength, the FWM efficiency will be degraded during high excitation by the free-carrier absorption effect. However, our CROW structure is not restricted by its material. Chalcogenide glasses [35,36] and compound semiconductors with wide bandgaps [6,9,12] are used for PhCs with nonlinear functions without any free-carrier effects, and these are applicable to our CROW structure. Of course, efficient free-carrier effects in silicon without substituting the material have been attracting a lot of attention for a variety of applications including optical regeneration, pulse compression and variable delay [7,37,38].

On the application of CROWs to such all-optical signal processing, the oscillating spectrum is a considerable issue. In principle, if the number of cavities is infinite and the propagation loss is negligible, the CROW exhibits flat transmission property. In practice, a finite number of cavities, a propagation loss due to realistic structure, non-uniformity (disorder) of fabricated cavities and a finite coupling strength to the access waveguides cause the oscillating spectrum. Nevertheless, some factors could be improved. We have demonstrated that flatter transmission spectrum can be obtained by the “apodization” of the cavity pitch at the end of the CROW to increase the CROW-waveguide coupling strength [17]. Although our present CROW was not apodized since L_cc of 5a is in a minimum design of the pitch, a slower CROW with larger L_cc can be apodized. In addition, we have realized the largest N_cav (up to 400) in realized CROWs, thanks to the individual cavity’s high Q of 10⁶ [39]. Large N_cav also improves the flatness. Thus, along with these techniques incorporated with the improvement of the fabrication technology, the spectral response of very large scale CROW could be improved to some extent.

In summary, we have demonstrated significantly high waveguide nonlinearity in a CROW consisting of width-modulated nanocavities in a line defect of a silicon PhC slab. A FWM experiment revealed inherent strong nonlinearity with an effective nonlinear constant γ_eff exceeding 10,000 /W/m. This value is the highest yet reported for silicon-core nonlinear waveguides with an integrated structure. The remarkably high nonlinearity was obtained because the slow-light mode of the CROW exhibited the small effective modal area due to the wavelength-sized confinement of individual cavities. This CROW has the potential to provide a new stage for integrated waveguide photonics because of its noteworthy nonlinearity with a view to realizing on-chip devices with an ultralow power consumption.