Ultralow-energy electro-absorption modulator consisting of InGaAsP-embedded photonic-crystal waveguide

Demand has been growing for electrical-to-optical (E-O) converters with ultralow energy consumption towards on-chip photonic systems such as a high-throughput communication link and a large-scale switch system.^1,2 Especially, the construction of such photonic systems over a CMOS layer is a promising way to realize a functional photonic network-on-chip (PhNoC) architecture.^1,3 To compete with future electrical interconnect technologies, the energy consumption for photonic on-chip-com applications has to be less than 10 fJ/bit according to an analysis presented in Ref. 4. This poses the significant design challenge of realizing extremely small optical modulators with an ultra-small device capacitance C that are driven with a low driving voltage V_pp. These two requirements are generally in a trade-off relationship with each other because a long modulator leads to a large C but has a strong light-matter interaction, and consequently V_pp required for sufficient modulation becomes low. V_pp as low as 0.5 V, which is compatible with CMOS drive levels, can reduce the number of or even eliminate the need for driver amplifiers, which consume a huge amount of external energy. Furthermore, low C and low V_pp can reduce the dissipation energy needed for charging/discharging the device capacitance during modulation (CV_pp²). Recent advances on silicon-photonics technology show the substantial energy reduction of optical modulators.^5–8 A high-Q micro-ring resonator approach for small C and V_pp has been actively studied, one of which has reported the record-low dissipation energy of 1 fJ/bit.⁵ However, since there are a variety of transmitter/switch applications which demand the highly flexible wavelength management, broadband modulators are needed. Hence, it has been regarded that it is essentially important to reduce the energy consumption of broadband modulators. In this study, we aim for achieving a waveguide-type modulator that operates in ultralow energies even close to the resonator type.

An electro-absorption modulator (EAM) has generally a shorter length and/or low V_pp than an electro-optic modulator (EOM) such as a Mach-Zehnder-interferometer (MZI) type because the strong electro-absorption change near the band-edge wavelength can be utilized for intensity modulation. Various forms of the EAM with a III–V waveguide and a group-IV waveguide have been reported, some of which have a fast modulation bit rate exceeding 40 Gbit/s.^9–15 InP-based-waveguide EAMs that include multi-quantum wells (MQWs) can have a modulator length as short as 100 μm and V_pp as low as 1 V thanks to the strong EA modulation by the quantum-confined Stark effect (QCSE),^12–15 although some have exhibited C exceeding a hundred fF, resulting in a large charging energy. Recently, compact and low-C EAMs have also been exploited during the development of high-index-contrast waveguide structures. Some of these EAMs are based on a SiGe- and Ge-based waveguide^2,7,8 fabricated on a silicon-on-insulator platform and had a device length of less than 100 μm, resulting in C < 10 fF while maintaining V_pp of a few V. However, it has been concerned that any EAM consumes the additional energy due to the photocurrent flow under the external bias voltage,^16,17 besides the capacitance charging energy. For the SiGe-based EAM mentioned above, the reverse bias voltage required for modulation was generally high, for example, 4 V, which should cause much larger energy consumption than the charging energy, as discussed in Section V. To suppress this energy with the reduction of the reverse voltage, the strong light confinement accompanied with a strong absorption change should be desired.

Photonic crystal (PhC) waveguides are promising for compact modulators because of their strong light confinement and consequent strong light-matter interaction. A Si PhC waveguide incorporating a high group index has been employed for configuring a MZI-based EOM.¹⁸ On the other hand, an EAM based on a PhC waveguide has never been realized. We have developed a fabrication technique of functional PhC nanodevices by embedding an ultra-small InGaAsP region in an InP-PhC platform using a buried heterostructure (BH) formation, and we have already demonstrated ultra-small nanolasers,¹⁹ photodetectors,²⁰ and all-optical memories.²¹ All of these devices have an ultra-small BH region with a length of a few μm, and therefore it is possible to integrate them with a short p-i-n junction which leads to a small device capacitance. An EAM can be constructed in a similar way, for which the composition of embedded InGaAsP is properly adjusted to obtain strong optical nonlinearity at the operation wavelength. The BH formation brings a good overlap between the PhC waveguide, the nonlinear region, and the narrow depletion region, which should lead to the low-voltage operation that cannot be expected with a non-BH device. This results in both low V_pp and low C in a modulation that is applicable to off-chip/on-chip communication.

In this work, we fabricated InGaAsP-embedded PhC waveguide EAMs and demonstrated their high-efficiency and high-speed modulation involving the Franz-Keldysh effect (FKE). We achieved a high modulation efficiency of 2.8–7.7 dB/V even for a short device length of 35–105 μm and fast modulation dynamics up to a bit rate of 56 Gbit/s. Low V_pp of less than 1 V and small C of the fF level of our PhC-EAMs resulted in a charging energy of only 1.6 fJ/bit. Another important feature was modulation with a very low reverse voltage range of less than 0.5 V. This results in the additional energy due to the photocurrent flow to be 0.2 fJ/bit (the minimum receivable optical energy of 0.5 fJ/bit was assumed for the 40-Gbit/s optical signal). As a result, the total energy consumption can be expected to remain at less than 2 fJ/bit. As far as we know, this energy is lower than that of any previous waveguide EAMs. Such an ultralow-energy consumption, as well as high speed broadband operation, and small footprint should be the most important part towards CMOS-integrated electro-optic processors on a chip.

Our PhC waveguide combined with a BH and lateral p-i-n junction can be of ultra-small size thanks to the strong photon and carrier confinement. Figures 1(a) and 1(b) show a schematic and scanning electron microscopy (SEM) image, respectively, which show an InP-PhC waveguide, a lateral p-i-n junction, and a BH in which to embed the InGaAsP. The operating principle for optical modulation is the FKE, which originates from the shrinkage of a semiconductor bandgap when an electric field is applied across the depletion region of a p-i-n junction.²² This results in the absorption increase in the wavelength range below the bandgap and also changes the refractive index through the Kramers-Kronig relation. These nonlinearities, which are related to the change in the electronic band structure, should be much stronger than the carrier-plasma absorption/dispersion effects that are generally utilized in a Si-based modulator. Therefore, we can expect our PhC waveguide with embedded InGaAsP material to perform better as a modulator in terms of device length and driving voltage.

Figures 2(a) and 2(b) show the waveguide band structure and corresponding group index n_g, respectively, which were simulated by the finite-element method (FEM). The 3-D supercell of an InP-PhC waveguide embedding InGaAsP with the photoluminescence peak of 1.45 μm was modeled. The refractive indices n of InP and InGaAsP were 3.17 and 3.44, respectively. The lattice constant a and the air-hole diameter 2r were 420 and 200 nm, respectively (2r/a = 0.476). The InP slab and the InGaAsP absorber were 250 and 150 nm thick, respectively, and InGaAsP was 400 nm wide. The waveguide width was set to 0.95W₀, where W₀ is the basic line defect width defined as the removal of one row of air holes (W1 waveguide). These parameters were used in the experiment described in Secs. III–V. The fundamental propagation mode (even mode) has large n_g near the cutoff wavelength called the slow-light effect, as seen in a conventional Si PhC waveguide.²³ On the other hand, the optical confinement factor (Γ) in the embedded InGaAsP region is given by $∫InGaAsPε|E|2d𝐫/∫Allε|E|2d𝐫$ and is plotted in Fig. 2(c). This indicates that the propagation mode profile is concentrated in the waveguide core region at a/λ = 0.28 and is evanescently extended towards the PhC region at a/λ = 0.27. The former and latter frequencies show group indices n_g of 5 and 30, respectively, and Γ values of 0.6 and 0.3, respectively. When the slow-down factor (n_g/n) is considered, the extinction ratio in the absorption modulation is given by exp(Δα(V)n_gΓL_EAM/n), where Δα(V) is a voltage-dependent material absorption change, and L_EAM is the EAM length. Therefore, the product n_gΓ is estimated and is 3 and 9 at small and large n_g frequencies, respectively. Since the previous conventional InGaAsP-based EAMs with InP cladding involving FKE or QCSE^13,15 generally have an n_gΓ value of around 1 or less, our present PhC-based structure has the potential to achieve a short EAM.

Due to the small physical dimensions of the p-i-n junction, the device capacitance should also be smaller than that of the previous devices. To see this effect, we simulated the capacitance using the parallel-plate model and 3-D FEM, as shown in Fig. 3(a). When the parallel-plate model was adopted, the device capacitance is given by C = ε₀ε_InGaAsPS/d, where ε₀ is the permittivity of vacuum, ε_InGaAsP = 12.4 is the relative permittivity of InGaAsP, S = L_EAM × 0.25 μm is the cross section of the doped region, d = 0.5 μm is the roughly estimated gap between the p and n regions, and L_EAM is the length of the EAM. The parallel-plate capacitance is plotted by the blue line in Fig. 3(a). However, the parallel plate model is not accurate especially when calculating a small junction because the fringe capacitance contribution by the p/n-doped region becomes dominant, and hence it is important to include the effects of the fringing fields as shown in Fig. 3(b). The fringe contribution is accurately included with the 3-D FEM model that had a doped region besides a BH region with a width of 5 μm, a thickness of 0.25 μm, and a length of L_EAM. The total capacitance obtained by the 3-D FEM (plotted in red) indicates that we can achieve C < 13 fF for L_EAM < 100 μm, which is the target range for our PhC-EAM. One of the reasons for such low capacitances is the air-bridge structure resulting in a low fringe capacitance, which has not been used for the previous EAMs. The capacitance per unit length for the Si-based EOMs fabricated on SOI substrates has >0.2 fF/μm¹⁰ and that for the previous InP-based EAMs having a large waveguide cross section should be much higher. On the other hand, our InP-based PhC with an air bridge structure has as small as 0.13 fF/μm. Since the air-bridge region is limited to the small PhC region, there should not be a significant problem on the future electrical integration.

The fabrication process of our PhC EAM is the same as that reported in Ref. 19. An InGaAsP layer with a photoluminescence peak wavelength at 1.45 μm and a designed width of 400 nm was embedded in an InP-PhC slab with a = 420 nm and 2r = 200 nm. A lateral p-i-n junction was formed by employing Zn diffusion and Si ion implantation for the p- and n-type doping, respectively. PhC airholes were formed by electron-beam lithography and Cl₂-based dry etching. After metallization, an InAlAs sacrificial layer was etched to form an air-bridge structure. The length of the EAM was varied as L_EAM = 35, 70, and 105 μm.

We measured the static characteristics in the electrical and optical responses for an applied DC voltage V_DC. Figure 4(a) shows I-V curves, indicating a reverse bias differential resistance (dV/dI) of more than 1 GΩ and an above-threshold forward bias dV/dI of 490, 230, and 210 Ω for L_EAM values of 35, 70, and 105 μm, respectively. This suggests that the DC energy consumption due to the leakage current is negligible (a few hundred pA) when the modulator operates with a reverse bias or under a sub-threshold forward bias condition. Figure 4(b) shows the transmission spectrum for a 70-μm-long device. The vertical axis indicates the on-chip insertion loss, which excludes the fiber-to-waveguide coupling loss and the input/output waveguide propagation loss (totally about −11 dB) by normalizing with the loss of the reference waveguide. This spectrum exhibited a steep cutoff on the longer wavelength side (λ = 1540 nm) due to the PhC waveguide band structure, as described in Fig. 2(a). The insertion loss of around 5 dB in the λ = 1510–1540 nm wavelength range was probably caused due to the optical coupling loss between the input/output waveguides and the PhC-EAM and increased at shorter λ due to the intrinsic absorption. The group index n_g was evaluated with a time-of-flight measurement²⁴ by injecting a 17-ps-wide optical pulse. To this end, the reference InP-PhC waveguide was measured (for example, n_g = 4 at 1530 nm), and thereafter the relative delay and subsequent n_g for the EAM were estimated at each wavelength. The measured n_g spectrum is also shown in Fig. 4(b), which indicates n_g ∼ 5 at a wavelength λ < 1530 nm and n_g increases as the wavelength of light approaches the cutoff wavelength, as also seen in the simulated results in Fig. 2(c). To evaluate the static optical response, the transmission spectra for different device lengths were measured as shown in Fig. 4(c). All the spectra are normalized by that at V_DC = +0.5 V, which is close to the built-in voltage of +0.7 V and exhibited the maximum optical transmission. These relative extinction spectra exhibit a wavelength dependency where a shorter wavelength has stronger extinction, which suggests that the optical modulation is actually caused by the FKE. The spectra exhibit the broadband operation with a wavelength range of more than 40 nm. The extinction at λ = 1500 nm is relatively high while keeping the insertion loss below 10 dB (see Fig. 4(b)) and is plotted as a function of V_DC in Fig. 4(d). The modulation efficiencies per voltage η_EAM were 7.7, 5.3, and 2.8 dB/V for lengths L_EAM of 105, 70, and 35 μm, respectively. The spectra in Fig. 4(c) also reveal extinction enhancement at λ > 1540 nm, which actually implies the slow-light effect that is expected from the n_g characteristic in Fig. 4(b). However, the optical coupling loss of this slow-light range was large. Since an appropriate design for obtaining n_g ≥ 20 with a fairly low coupling loss and low dispersion has been reported,²⁵ our device still has a room for an even higher η_EAM and/or shorter L_EAM than the present device by adopting such design optimization.

The PhC-EAM was dynamically driven by applying an AC signal voltage combined with a DC bias voltage via a bias tee. For this measurement, we used an RF probe with a 50 Ω termination to realize impedance matching with the signal generator and thus eliminate the signal back reflections and accurately estimate the applied voltage across the EAM. For all the following measurements, the wavelength and power of the incident light were fixed at 1.53 μm and 0 dBm, respectively.

To investigate the operation speed, we carried out measurements to determine the fall time (90%–10% of optical power) and the rise time (10%–90%) of a modulated optical signal. The light was modulated by a 200-ps-wide rectangular electrical pulse, for which V_pp was changed in the 0.5–3.5 V range by fixing the forward voltage for the low absorption state V_low at +0.5 V and varying the reverse voltage for the high absorption state V_hi from −3 V to 0 V, as shown in Fig. 5(a). As shown by the modulated optical output in Fig. 5(a), the rectangular voltage pulse is clearly transferred to the output light. Figure 5(b) summarizes the rise time τ_r and fall time τ_f of the modulated optical pulse as a function of V_pp. The incident rectangular voltage pulse intrinsically has rise and fall times of τ_r0 = 9 ps and τ_f0 = 11 ps, respectively. Therefore, τ_r and τ_f were estimated by subtracting τ_r0 and τ_f0, respectively, from the measured values. Both τ_r and τ_f were shorter than 20 ps (the minimum value was only 10 ps) at V_pp = 0.5–2.0 V for any L_EAM. This encourages us to drive the modulator at an operation bandwidth of 25 GHz or more. The lack of dependence on L_EAM in this V_pp range suggested that the operation speed is not limited by the RC time but by the carrier traveling time. Considering the carrier (hole) drift velocity of 5 × 10⁴ m/s²⁶ and assuming a depletion width of 0.5 μm, the carrier traveling time would be 10 ps, which agrees with the experimental result. Figure 5(b) also indicates that τ_r becomes longer for L_EAM = 35 and 70 μm at V_pp > 2 V. This can be explained as follows. Strong optical absorption and carrier generation occur with a reverse voltage. However, the carrier extraction is slowed at a reverse-to-forward transition in voltage, which results in carrier screening and consequently long τ_r. This process should be more pronounced for shorter L_EAM and higher V_pp because they induce a higher carrier density for a constant optical input power. This is also suggested by the static response in Fig. 4(d), showing that modulation saturation occurs at a lower voltage for shorter L_EAM. On the other hand, this slowing does not occur at a forward-to-reverse transition in voltage because the electrical field and carrier extraction become stronger during the transition. These situations affect the behavior of τ_r and τ_f, but a transition time of less than 20 ps and a modulation contrast exceeding 3 dB are still maintained for V_pp < 2 V. This implies that the narrow p-i-n junction width (that is, a narrow depletion width) for our PhC-EAM is effective for providing fast carrier extraction.

Next, the operation bandwidth for a device with L_EAM = 70 μm was obtained by measuring the small-signal frequency response and the eye diagram. For the small-signal measurement, the response was measured in the 100 MHz–60 GHz frequency range with an input RF power of 9 dBm and different DC bias voltages. A modulated optical signal collected from the device was fed into a network analyzer that converted the optical signal to an electrical signal with an inbuilt detector. The measured frequency response is shown in Fig. 6(a). This indicated that the 3-dB bandwidth is around 28 GHz when there is no DC voltage or a reverse voltage of −0.5 V, which supported the expectation based on a rectangular pulse measurement. On the other hand, a forward bias voltage of +0.5 V results in a bandwidth of just a few GHz and reduces the output RF signal. This is because an optical modulation was induced by the carrier injection.

Figure 6(b) shows the eye diagram obtained for an output optical signal from the EAM. A non-return-to-zero (NRZ) voltage signal with a 2³¹ − 1 pseudo-random bit sequence (PRBS) and a bit rate of 40 Gbit/s was applied to the modulator. The modulated optical signal was amplified with an erbium-doped fiber amplifier (EDFA), detected by a 70-GHz high-speed photodetector, and observed with a sampling oscilloscope. The voltage for the low absorption state V_low was kept at +0.5 V and V_pp was varied in the same way as in Fig. 5. Unfortunately, due to the large coupling loss of −11 dB between the input/output waveguide and optical fiber, the detected signal suffered significantly from the amplified spontaneous emission noise of the EDFA and the intrinsic electrical noise of the high-speed oscilloscope. However, the eye diagrams for V_pp ≥ 1.0 V exhibit a clear eye opening. The modulation efficiency was 3 dB/V for the L_EAM = 70 μm device. Although the wavelength in the dynamics measurement was limited to longer than 1530 nm due to the gain band of the EDFA, the modulation efficiency should be higher for λ = 1500 nm, as discussed in the static response, which was 5.3 dB/V. Another device with L_EAM = 105 μm, which had a lower insertion loss of 3 dB and the same rise/fall time as the L_EAM = 70 μm device, provided a clearer eye diagram, as shown in Fig. 7. The eye opening for 40 and 56 Gbit/s signals was clearly observed for V_pp = 2.0 V. These dynamics successfully demonstrated the fast modulation speed that was realized thanks to both the short carrier traveling time and the high RC bandwidth.

The operation energy is one of the most important factors for optical modulators. Ref. 17 provides an analytical expression of the energy consumption in an EAM that runs with a reverse bias voltage and/or a sub-threshold forward bias voltage, and so here we estimated the energy consumption in a similar way. Since we envision that an EAM such as ours will be integrated to configure an on-chip photonic network, the large electrical pad with a parasitic capacitance of around 5 fF, which was used in our experiment, will not be required in final applications. In the present dynamics measurements (Sections III and IV), the EAM was driven with a 50-Ω termination that was used to precisely estimate the driving voltage across the EAM without signal reflection back to the pulse-pattern generator. It will also not be required when driving with a CMOS driver circuit appropriately designed for impedance matching. Therefore, the intrinsic energy needed for our EAM is estimated in this section. This energy is described in detail in Ref. 17 and also in the supplementary material. The intrinsic energy required for EAM originates from (i) the dissipation energy caused by charging and discharging the device capacitance (E_ch) and (ii) the energy consumption caused by the photocurrent flow under the external voltage (E_pc), and each contribution is estimated as follows.

The dissipation energy caused by the charging and discharging of device capacitance is given as E_ch = CV_pp²/4 (see Eq. (S1) in the supplementary material), where C is the capacitance and V_pp is the peak-to-peak signal voltage. Experimental C values have yet to be evaluated because they are too small to measure. Instead, we employed the theoretical device capacitance obtained with a 3-D FEM simulation (see Fig. 3(a)), which includes the fringe capacitance of the p/n-doped region but does not include that of the electrical pad. On the other hand, we experimentally evaluated the driving voltage for obtaining a modulation contrast of 3 dB, as shown in Fig. 8, in which all the PhC-EAMs with different L_EAM values clearly respond to the signal voltage at a bit rate of 40 Gbit/s. The theoretical device capacitance, the experimental driving voltage, and the estimated dissipation energy per bit caused by charging/discharging the capacitance for PhC-EAM lengths L_EAM = 35, 70, and 105 μm are approximately (C, V_pp, E_ch) = (5 fF, 2.0 V, 5.0 fJ/bit), (9 fF, 1.0 V, 2.2 fJ/bit), and (13 fF, 0.7 V, 1.6 fJ/bit), respectively.

The photocurrent flows under the external reverse voltage causes the energy consumption (E_pc). The detailed procedure is described in the supplementary material, and here we show the outline of the procedure. Since E_pc depends on the optical energy, both the required optical bit energy transmitted from the EAM (E_{bit_trans}) and the required input optical energy (E_opt) should be determined. Eq. (S2) in the supplementary material gives E_{bit_trans} = E_opt|η_low − η_hi|/2, where η_hi and η_low are the absorption efficiencies in the high and low absorption states of the EAM, respectively. We take the extinction ratio of 3 dB as shown in Fig. 8, which gives us (1 − η_hi)/(1 − η_low) = 0.5. We also measured the photocurrent, and η_hi/η_low = 3 was roughly estimated for the device with L_EAM = 105 μm. These two resulted in η_hi = 0.6 and η_low = 0.2. The same η_hi and η_low are assumed for L_EAM = 35 μm and 70 μm in the following estimation. With these results, the required optical energy was calculated as E_opt = 2E_{bit_trans}/|η_low − η_hi| = 5E_{bit_trans}. In estimating the photocurrent energy E_pc, Eq. (S4) in the supplementary material gives E_pc = (E_opt/2)(η_lowμ_low + η_hiμ_hi), where μ_hi and μ_low are the photocurrent dissipation multipliers given by μ_hi = −eV_hi/ℏω and μ_low = −eV_low/ℏω, and V_hi and V_low are the applied reverse voltages in high and low absorption states, respectively. In our experiment (Fig. 8), V_low = +0.5 V and ℏω/e = 0.81 V were fixed for all the devices and thereby μ_low = −0.6. On the other hand, V_hi was varied at −1.5, −0.5, and −0.2 V for L_EAM = 35, 70, and 105 μm, respectively, thereby leading to μ_hi = 1.9, 0.6, and 0.2, respectively. Although negative μ_low for the forward voltage state suggests the energy feedback into the voltage supply, this should not be counted because no recovery system is configured at present. Therefore, we need to include the energy only in the reverse voltage state, giving E_pc = E_optη_hiμ_hi/2. As a consequence, E_pc for L_EAM = 35, 70, and 105 μm are 0.57E_opt (= 2.9E_{bit_trans}), 0.18E_opt (= 0.9E_{bit_trans}), and 0.06E_opt (= 0.3E_{bit_trans}), respectively.

The total electrical energy consumption required for transmitting one bit of information is given by E_total = E_ch + E_pc. Based on the above estimations, E_total for L_EAM = 35, 70, and 105 μm are E_ch + 2.9E_{bit_trans}, E_ch + 0.9E_{bit_trans}, and E_ch + 0.3E_{bit_trans}, respectively. E_{bit_trans} should be eventually determined by the minimum acceptable optical energy at a photoreceiver end. As a reference, if considering the thermal noise limit for a CMOS-integrated p-i-n photoreceiver with a noise equivalent power (NEP) of 14 pA/Hz^0.5,²⁷ the minimum receivable optical energy per bit (that is, to obtain a signal-to-noise ratio of 144 for a bit error rate of 10⁻⁹ and a bandwidth of 20 GHz for accepting a bit rate of 40 Gbit/s in NRZ format) is around 0.5 fJ/bit. If applying this value for E_{bit_trans} (and hence E_opt = 2.5 fJ/bit), E_pc for L_EAM = 35, 70, and 105 μm are 1.5, 0.5, and 0.2 fJ/bit, respectively. Consequently, the total electrical energy consumption for L_EAM = 35, 70, and 105 μm would be E_total = E_ch + E_pc = 6.5, 2.7, and 1.8 fJ/bit, respectively.

In comparison, a SiGe-based EAM driven by the QCSE has exhibited the lowest reported E_ch (0.75 fJ/bit),^8,17 which is half of that in our PhC-EAM with L_EAM = 105 μm. However, E_total estimated in the same way is around 7 fJ/bit, which is dominated by the high E_pc due to the high reverse voltage (−4 V). On the other hand, our EAMs have no significant problem with regard to E_pc because our EAM operates with a lower reverse voltage in the modulation, that is, −0.2 V (see V_hi for the L_EAM = 105 μm device in Fig. 8) as the minimum value in this study, resulting in lower E_total than SiGe-based modulators.

For a more practical evaluation, we should also include the input optical energy and consider the on-chip insertion loss of the device in the total energy estimation. Our present device still has an on-chip insertion loss of 3 dB at the operation wavelength of 1.53 μm for the L_EAM = 105 μm device. If we simply take this loss as an increase in incident optical energy (that is, E_opt = 5.0 fJ/bit) and count all the electrical/optical energy contribution, the total energy becomes 7.0 fJ/bit. This total energy is still much lower than those of the above-mentioned SiGe-based EAM (>100 fJ/bit)⁸ and the Ge-based EAM having the previous lowest value (>15 fJ/bit),⁷ which were estimated in the same way.

We demonstrated an EAM based on an InGaAsP-embedded PhC waveguide that exhibits a low capacitance, low energy, and high-speed operation. A clear intensity modulation was observed for short lengths of 35, 70, and 105 μm with DC modulation efficiencies of 2.8, 5.3, and 7.7 dB/V, respectively. With regard to the dynamic response, rise/fall times of around 10 ps in the modulator transition were obtained and eye diagrams up to 56 Gbit/s were also successfully observed. Our 105-μm-long EAM with C = 13 fF V_pp = 0.7 V revealed a charging energy of only 1.6 fJ/bit, and the intrinsic total electrical energy consumption was 1.8 fJ/bit even when considering the photocurrent flow. This energy is lower than that of any other waveguide EAMs including SiGe-based ones. Even with the broad wavelength range of >40 nm for our device, the energy is close to the resonator type having the record-lowest energy of 1 fJ/bit.⁵ For the further energy reduction, the BH with a MQW core instead of a bulk core would be effective for the electro-absorption enhancement because of the exciton confinement. Hence it suggests its great potential for use as a small-footprint low-energy transmitter and photonic switch. Monolithic integration with PhC nanolasers¹⁹ that have a similar BH structure should be possible on the same InP-PhC platform, and even integration on silicon would be possible with a heterogeneous fabrication technique. This is attractive for constructing a dense nanophotonic functional architecture on a CMOS chip.

See supplementary material for supporting content.

We thank T. Tamamura, H. Onji, Y. Shouji, and K. Ishibashi for support in fabricating the device. We also thank T. Kakitsuka and K. Hasebe for fruitful discussions about the modulator characteristics. This work was supported by CREST (JPMJCR15N4), JST.