1. Introduction

With the rapid advances in fabrication process technology, the scale of silicon photonic integrated circuits has become unprecedentedly large and complex [1,2]. Together with the emergence of new applications such as light detection and ranging, where high power and extremely large number of emitters are required [3], integrated optical amplifiers have become very important components for silicon photonics. Erbium (Er)-doped optical amplifiers, which have been widely adopted in long-haul optical fiber communication systems, are promising candidates for such purpose since they show several advantages over other kinds of optical amplifiers, specifically semiconductor optical amplifiers (SOAs). Er-doped optical amplifiers can provide much higher output power than SOAs. Saturated output power well above 10 W has been achieved in commercial available Er-doped fiber amplifiers (EDFAs), while SOAs typically provide output power far less than 1 W. Compared with semiconductor materials used in SOAs, dielectric host materials used in Er-doped optical amplifiers usually exhibit much lower optical nonlinearities (e.g., the nonlinear refractive indices of optical fibers are several orders of magnitude smaller than those of SOAs [4,5]), which makes signal waveform distortion caused by nonlinear impairments significantly lower. Er-doped optical amplifiers also have great potential for ultrahigh speed optical signal amplification. 170 Gbit/s transmission has been demonstrated in an Er-doped waveguide amplifier [6], whereas the signal speed of SOAs has been limited to tens of Gbit/s due to the limitation of carrier lifetimes in semiconductors. Besides, Er-doped optical amplifiers thus show superior temperature properties than SOAs since the optical transition energies of Er ions barely changes against wide-range temperature variation, while on the contrary the bandgaps of semiconductor materials are very sensitive to temperature change [7].

Aiming for such on-chip applications, Er-doped waveguide amplifiers (EDWAs) have been demonstrated in several amorphous host materials, including a variety glasses [8], Al$_2$O$_3$ [9–14], TeO$_2$ [15]. However, the achieved optical gain in most of these devices is relatively low (within one-digital dB/cm), mainly due to the rather low Er concentration (typically well below 10$^{21}$ cm$^{-3}$) and small absorption/emission cross sections of Er$^{3+}$ ions in amorphous materials (typically on the order of 10$^{-21}$ cm$^2$) [8]. Rather long waveguides, on the order of several centimeters, are thus required to achieve usable optical gain. Currently, it is difficult to further increase the Er concentration in amorphous host materials due to factors such as Er clustering and limited Er solubility [8]. On the other hand, crystalline host materials do not have such limitations, and the absorption/emission cross sections are generally much larger [8]. EDWAs based on single-crystal materials, including Er-doped potassium double tungstate (KGd$_x$Lu$_y$Er$_{1-x-y}$(WO$_4$)$_2$) [16], erbium silicate [17,18], erbium chloride silicate nanowires [19], and Er-doped thin film lithium niobate [20–22], have been realized with optical gain typically one or two orders of magnitude larger than those of amorphous materials.

However, most of these materials are difficult to integrate on Si substrate because of their dedicated crystal growth methods. Compared to these materials, rare-earth oxides (REOs) appear to be the most promising candidates for Si-based integrated optical amplifiers [23–25]. The crystal structure of most REOs is cubic, and their lattice constants are well matched with that of Si [26], indicating that they can be epitaxially grown on Si substrate. REO thin films with different rare-earth elements have been successfully grown on Si substrate by several groups [27–35]. In these thin films, the Er concentration can be widely adjusted from parts per million to extremely high levels (e.g., 2.7$\times$10$^{22}$ cm$^{-3}$ in fully concentrated Er$_2$O$_3$), making them not only suitable for optical amplifiers but also a promising platform for emerging quantum-optical devices [36,37]. The optical properties of REO thin films have been investigated in the context of their strong photoluminescence and large absorption coefficient, indicating their potential for high-gain optical amplifiers. However, there has been no work reported for their device applications, most likely due to the difficulties of fabrication of waveguide structure. Very recently, we have combined (ErGd)$_2$O$_3$ thin films with a high-confinement horizontal slot waveguide structure for such purpose and verified their feasibility as practical photonic devices for the first time [38]. However, the propagation loss of the waveguides was rather large, on the order of 100 dB/cm, which hindered optical amplification.

Here, we propose and demonstrate a low-loss waveguide platform based on the concept of bound states in the continuum [39]. By engineering the geometric parameters (width) of the waveguide, we were able to achieve propagation loss of less than 5 dB/cm in waveguides with cross-section area of 462 nm $\times$ 1080 nm at a wavelength of 1445.8 nm. This is, to the best of our knowledge, the lowest loss for Si-based REO waveguides. Furthermore, through pump-probe measurements, we have also observed optical signal enhancement in the telecommunications band from these waveguides upon optical pumping, with peak enhancement as large as $\sim$16 dB/cm. The results indicate the high potential of our material platform for Si-based optical amplifiers.

2. Device design

Figure 1(a) shows a cross-section schematic diagram of the proposed waveguide structure, in which a cap layer is deposited on top of REO layer on silicon-on-insulator (SOI) substrate and patterned into a strip-loaded configuration. Here, we chose silicon nitride (SiN) as the cap layer material due to its low material loss in the telecommunication band and well-established fabrication process. With such a configuration, etching of REO is not required, which significantly simplifies the fabrication process.

 

Fig. 1. (a) Cross-section schematic diagram of the proposed SiN/REO/SOI strip-loaded waveguide. (b) Calculated leakage loss $\alpha _\textrm {leakage}$ and mode confinement factor $\Gamma _\textrm {REO}$ of fundamental TM modes of waveguides with different widths. The thicknesses of layers of Si, REO, and SiN are 72, 90, and 300 nm, respectively. The wavelength is 1536 nm. (c) Calculated leakage loss spectra of waveguides with widths of 1.15 and 2.35 $\mu$m. (d) Schematic diagram showing light propagation along the waveguide. Majority component of TM mode is bound within the waveguide core, while minority component is coupled with the left- and right-outgoing TE radiative modes at the edge of the waveguide. At BIC widths, both left and right radiative waves exhibit destructive interference. (e) and (f) Mode profiles of the waveguides with widths of 1.15 and 1.70 $\mu$m, respectively. Minority E$_x$ and majority E$_y$ components of electric field are plotted, both of which are normalized to corresponding E$_y$ maximum.

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The operation polarization was chosen to be transverse magnetic (TM), since the lateral optical confinement of the TM waveguide mode is much stronger than that of the transverse electric (TE) mode. The waveguide modes were calculated by a finite element mode solver implemented in COMSOL Multiphysics, with perfectly matched layer boundary condition. Due to the relatively low refractive index of SiN, the waveguide is inherent leaky in TM polarization. As one can see in the mode profiles show in Fig. 1(f), although the majority E$_y$ component is well confined in the waveguide core, the minority E$_x$ component shows oscillation behavior in the slab area outside the waveguide core, which is the source of the leakage loss. This is because the propagation constant of the TM mode lies in the continuum of radiative TE modes, and the TM mode is coupled with the TE radiative modes at the edges of the waveguide, resulting in lateral outward leakage radiation. The same behavior has been widely observed in similar low-contrast waveguides [40–42]. Inspired by recent theoretical and experimental demonstrations of low-loss photonic waveguides with bound states in the continuum (BIC) [43,44], we applied a similar design strategy to our material platform. The lateral radiation originating from the two edges of the waveguide (two radiation channels) exhibits a phase difference related to the waveguide width. If the two radiation channels are out of phase, destructive interference between them occurs and lateral leakage loss vanishes (schematically shown in Fig. 1(d)); that is, the TM mode is completely decoupled from the continuum of TE modes. We therefore expected that the lateral leakage loss exhibits strong dependence on waveguide width, which is verified from the simulation results shown in Fig. 1(b). During the mode calculation, complex effective refractive indices could be obtained from the mode solver, in which the imaginary parts correspond to the waveguide loss. Indeed, we noticed that loss vanishes at some specific widths, which are referred to BIC widths hereafter. The mode profile at the BIC width of 1.15 $\mu$m in Fig. 1(e) shows that both E$_x$ and E$_y$ components are well confined in the waveguide core, which is completely different from that of a leaky waveguide (1.70-$\mu$m-wide) [Fig. 1(f)]. We also noticed that the propagation loss was wavelength-dependent, as shown in Fig. 1(c). This is a direct consequence of the interference mechanism of BIC. However, the optical bandwidth in which loss increases by 3 dB/cm is larger than 100 nm, which is broad enough to cover both pump and signal lasers simultaneously.

We further calculated optical confinement factors in REO thin films from the mode profiles following the definition in [45], and the results are shown in Fig. 1(b). With a rather thin REO layer (< 100 nm), an optical confinement factor of $\sim$18$\%$ can be readily achieved. For coupling waveguides to single-mode fiber, we utilized grating couplers (GCs). Since the waveguide loss is strongly dependent on its width, a straight GC combined with a long adiabatic taper, as normally used in Si photonic circuits, is not appropriate here. Instead, short focusing GCs were chosen. Furthermore, apodized GCs with uniform periods and linearly varied filling factors were designed to optimize coupling efficiency. Through these optimizations, peak coupling efficiency of larger than 30$\%$ can be achieved by a numerical analysis. Besides, GCs were designed to be operated only with TM polarization. The polarization extinction ratio (ratio of TM polarization coupling efficiency to TE one) was calculated to be $\sim$30 dB, which is large enough that the effect of cross-polarization-coupled TE component on the measurement of TM transmission can be safely ignored.

3. Fabrication and measurement results

Using high purity Gd and Er metal sources and O$_2$ plasma, we grew an approximately 100-nm-thick (Er$_x$Gd$_{1-x}$)$_2$O$_3$ layer with Er composition x = $\sim$9.2$\%$ (measured by energy-dispersive X-ray spectroscopy, corresponding to a concentration of 2.33$\times$10$^{21}$ cm$^{-3}$) on SOI (111) substrate by molecular beam epitaxy. The single-crystal nature of the grown thin films was confirmed by transmission electron microscopy. The light emission properties of the thin films were characterized by room-temperature photoluminescence (PL) and time-resolved PL measurements. Intense light emission in the telecommunications band was observed, as shown in Fig. 2(a), with several well-isolated narrow peaks corresponding to Stark-split optical transitions between first excited state $^4$I$_{13/2}$ and ground state $^4$I$_{15/2}$ of Er$^{3+}$ ions. The details of the identification of these transitions and energy diagram can be found in our previous work [32,38]. Figure 2(b) shows PL decay of the strongest emission peak around 1536 nm. The PL signal decays rapidly in the first 2 ms in a non-exponential way, and slowly in the following stage in a single-exponential way. We also noticed that the former non-exponential decay was strongly dependent on the pump laser power: The higher the pump power, the faster the former non-exponential decay. Considering rather high Er concentration in the thin film, this non-exponential decay is most likely due to some power-dependent non-radiative processes, e.g., energy-transfer upconversion. On the other hand, the latter single-exponential decay was found to be almost independent on the pump power, indicating a pure radiative process. We thus fit the decay curve in the latter regime by an exponential function and obtained radiative lifetime of $\sim$2.35 ms. This lifetime is among the longest in materials with similar Er concentrations [15,16,19,46–48], thus confirmed the high crystal quality of our thin films.

 

Fig. 2. (a) Typical room-temperature PL spectrum of (ErGd)$_2$O$_3$ thin film excited with a 1462-nm pump laser. (b) Time-resolved PL decay curve of the strongest emission peak around 1536 nm shown in (a), with a peak pump power of 1.7 mW. The blue curve indicates experimentally measured data; the orange curve is the exponential fitting.

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To fabricate the waveguide devices, a 300-nm-thick SiN layer was deposited and patterned to simultaneously form the strip-loaded waveguide structure and GCs in one step of electron beam lithography and reactive ion etching [49]. Figure 3(a) shows a typical scanning electron microscope (SEM) image of the waveguide, together with a magnified view of the GC. The transmission of waveguides was then measured by using wavelength-tunable lasers. Due to the existence of strong visible upconversion from Er$^{3+}$ ions in the waveguides, it is possible to directly observe the lateral leakage and its dependence on waveguide width. As shown in Fig. 5 in the Appendix, the brightness of lateral-leakage-induced green upconversion is strongly dependent on waveguide width, and it features a minimum for 1.14-$\mu$m- and 1.20-$\mu$m-wide waveguides. This is well consistent with our simulation results, and indicates that these two widths are close to the BIC width for the wavelength of 1536 nm.

 

Fig. 3. (a) SEM image of a fabricated waveguide, together with magnified view of GC section. (b) Extracted propagation loss spectra of waveguides with width of 1.08, 1.14, and 1.20 $\mu$m. Solid curves indicate loss spectra; dashed curves are calculated leakage loss spectra without consideration of Er$^{3+}$ ion absorption. For W = 1.08 $\mu$m, solid curves with different colors (blue and orange) were measured by two tunable lasers with different wavelength ranges. The inset shows the insertion loss of waveguides with different lengths at a wavelength of 1445.8 nm, at which lowest propagation loss is obtained. By linear fitting of these data, propagation loss of 4.70$\pm$2.05 dB/cm is extracted.

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The precise propagation losses of waveguides with width of 1.08, 1.14, and 1.20 $\mu$m were characterized by using the standard cut-back method, which measures the transmittance of waveguides with different lengths. To avoid exciting ground state population of Er$^{3+}$ ions, the launched laser power was kept low enough ($\sim$60 $\mu$W prior to waveguide coupling). Around this power range, the transmittance of the waveguides doesn’t change against the launched power. The extracted propagation loss spectra are shown in Fig. 3(b), together with corresponding calculated leakage loss spectra without consideration of Er$^{3+}$ ion absorption. The background of the experimental spectra agrees very well with simulation results, with a lower shift corresponding to passive losses other than leakage, such as residual scattering loss induced by roughness of layer interfaces and waveguide sidewalls and leakage loss towards the SOI substrate due to its rather thin buried oxide layer (2 $\mu$m). These results indicate that BIC occurs at different waveguide widths for different wavelengths, which is a consequence of its interference cancellation mechanism. A minimum loss of 4.70$\pm$2.05 dB/cm at 1445.8 nm for 1.08-$\mu$m-wide waveguide is obtained, which is two orders of magnitude lower than those of Si/REO/SOI horizontal slot waveguides previously reported [38] and is on the same order to that of state-of-the-art silicon waveguides [50,51]. Our waveguide structure is thus a highly promising platform for REO-based active photonic devices, as well as for photonic devices based on other functional materials heterogenously integrated on Si [52,53]. Besides, Er$^{3+}$ ion absorption corresponding to Stark-split optical transitions between $^4$I$_{13/2}$ and $^4$I$_{15/2}$ manifolds can be clearly observed as dips in the loss spectra, whose wavelengths are well consistent with those of peaks in the PL spectrum shown in Fig. 2(a). The deepest dip around 1536 nm corresponds to the lowest transition of Er$^{3+}$ ions at $C_2$ crystalline symmetry site [38]. From the dip depth we obtain that the Er$^{3+}$ ion absorption is larger than 35 dB/cm, indicating a large potential optical gain.

The pump-probe method was then used to measure optical gain in waveguides with width of 1.08 $\mu$m, which show minimum propagation loss near the pump wavelength we used. The measurement configuration is shown in Fig. 4(a). A 1462 nm pump laser with a maximum output power of $\sim$500 mW and a wavelength-tunable probe laser were combined by a wavelength division multiplexing coupler, and launched into the waveguide. A short-pass filter in the pump line and a long-pass filter after the waveguide output were used to spectrally divide the pump and probe lasers. Moreover, the probe laser was AC-modulated by an electro-optic modulator and the detected output signal from the waveguide was fed into a lock-in amplifier so that the influence of amplified spontaneous emission could be eliminated. Figure 4(b) shows the output spectra of the waveguide with a length of 1.2 mm, when the pump laser was turned on (with a power of 230 mW prior to waveguide coupling) and off. Considering measured coupling efficiency of grating couplers of $\sim$14.4$\%$ at pump wavelength, the on-chip pump power is $\sim$33 mW. It is clearly observed that the output around 1536 nm was significantly increased upon pumping, demonstrating signal enhancement (SE). This indicates that the population in $^4I_{13/2}$ state is increasing, which is a sign of the onset of optical gain. The extracted SE spectrum, which is defined as the ratio of waveguide output with and without pumping, is shown in Fig. 4(c). A broadband SE from 1510 to 1560 nm was obtained, with several pronounced peaks. These peaks are well consistent with the optical transitions observed from the light emission and absorption spectra. Therefore, the SE obtained here indeed originates from Er$^{3+}$ ions in the thin film. A peak enhancement of $\sim$16 dB/cm was obtained around 1536 nm. It is much larger than those of most amorphous or polycrystalline host materials [48,54], as well as some of single-crystal host materials with lower Er concentrations [16,47].

 

Fig. 4. (a) Pump-probe measurement setup for measuring optical signal enhancement in the waveguides. VOA: variable optical attenuator. PC: polarization controller. EOM: electro-optic modulator. WDM: wavelength division multiplexer. SPF: short-pass filter. LPF: long-pass filter. DUT: device under test. PD: photodetector. (b) Output spectra of the waveguide with and without pumping. The waveguide length is 1.2 mm, and pump power is 234.5 mW. (c) Extracted SE spectrum. (d) Pump power dependence of SE at 1536 nm for waveguides with different lengths of 0.6, 1.2, and 2.4 mm.

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We also performed SE measurements under different pump powers. The results for waveguides with different lengths of 0.6, 1.2, and 2.4 mm are plotted in Fig. 4(d). The SE increases against pump power, however, the achieved SE under the maximum available pump power is still not large enough to compensate the total loss (Er$^{3+}$ ion absorption and passive propagation loss) indicated in Fig. 3(b). One of the possible reasons is that the absorption efficiency of the pump laser we used is rather low. It is found that SE per unit length almost does not change at all against waveguide length, which is a sign that the pump laser has not been efficiently absorbed in the waveguides. Otherwise, SE per unit length would have significantly decreased against waveguide length since pump laser would have been quickly depleted at the initial segment of the waveguide. We deduce that the modal absorption coefficient at the pump wavelength (1462 nm) is only $\sim$2.84 dB/cm and large amount of pump power was not absorbed by Er$^{3+}$ ions. This can be significantly improved by using pump laser with an optimized wavelength that consistent exactly with rather narrow optical transitions of Er$^{3+}$ ions. Furthermore, the modal absorption coefficient can be increased by increasing optical confinement factor.

Another important issue limiting SE might be population loss caused by energy-transfer upconversion (ETU) in our materials with rather high Er concentration. Indeed, as we have mentioned above, intense green light emission was observed from the waveguides upon optical pumping. Pump-power-dependent PL decay also confirmed the existence of ETU. A rough estimation through fitting PL decay with Zubenko’s model [55,56] indicates that the macroscoptic ETU parameter $W_{ETU}$ is as high as 1.8$\times$10$^{-17}$ cm$^3$/s. This is two orders of magnitude larger than that of amorphous Al$_2$O$_3$:Er$^{3+}$ [56], and one order of magnitude larger than that of single crystal KGd$_x$Lu$_y$Er$_{1-x-y}$(WO$_4$)$_2$ [57], both with doping concentration one order of magnitude lower. One of the most feasible ways to mitigate this effect is to reduce the Er concentration in REO thin film since $W_{ETU}$ decreases significantly as the Er concentration decreases. Although reducing it will also reduce the potential material gain, we can compensate for this by increasing the optical confinement factor and thus the modal gain. Through simulation, we confirmed that the confinement factor can be readily increased from 18$\%$ to 56$\%$ if we increase the REO thin film thickness to 270 nm. Even a higher confinement factor can be achieved by replacing the SiN cap layer with materials with a higher refractive index, such as Si [38]. With such a large confinement factor of 56$\%$, the Er concentration can be reduced to $\sim$7.5$\times$10$^{20}$ cm$^{-3}$ while keeping the modal absorption unchanged. Achieving such a relatively low concentration requires more precise control on the deposition rate of Er, which can be realized by using Knudsen cell instead of electron beam evaporator currently used. Reducing Er concentration can have another advantage that the lattice mismatch between (Er$_x$Gd$_{1-x}$)$_2$O$_3$ and Si is further reduced so that thicker layers can be grown with high quality. Provided that optical gain of 5.9 dB/cm has already been demonstrated from a similar thin film material Er:(Gd,Lu)$_2$O$_3$ grown on Y$_2$O$_3$ substrate with an even lower doping concentration of 1.61$\times$10$^{20}$ cm$^{-3}$ [47], we expect that optical gain of two-digital dB/cm should be achievable with a higher Er concentration as in our case. However, unlike these single crystal host materials demonstrated so far, with thick films and specific crystal substrates required [16,47], our platform is fully compatible with mature Si photonics technology. As we recently demonstrated, high Q-factor microring resonators can be easily adapted on our platform [58]. Therefore, compact on-chip lasers become possible as long as net optical gain is achieved.

4. Conclusion

In conclusion, we demonstrated large optical signal enhancement from low-loss waveguides by using Er-incorporated REO ((ErGd)$_2$O$_3$) thin films epitaxially grown on SOI substrate as the active medium. Based on the concept of bound states in the continuum, SiN/REO/SOI multilayer strip-loaded waveguides with low propagation loss could be realized by adjusting waveguide width. A minimum propagation loss of 4.70 dB/cm was achieved in waveguides with cross-section area of 462 nm (thickness) $\times$ 1080 nm (width) at a wavelength of 1445.8 nm. The proposed low-loss waveguide structure may also be applicable to other functional materials for heterogeneously integrated Si photonics. By combining high-quality single-crystal REO thin films and low loss waveguide platform, broadband optical signal enhancement ranging from 1510 to 1560 nm was achieved upon optical pumping. The peak signal enhancement is as large as 16 dB/cm, which is limited by the low pump laser absorption efficiency and strong energy-transfer upconversion. With optimization of the pump laser wavelength, waveguide confinement factor, and Er concentration, we expect that signal enhancement can be largely increased further and optical gain of two-digital dB/cm can be achieved. By combining such active medium with high Q-factor microring resonators based on our low-loss waveguide platform, Si-based lasers can also be envisioned. Our results therefore pave the way for the realization of high-gain monolithic-integrated optical amplifiers and lasers on Si.

Appendix

Figure 5 shows images taken with an overhead microscope by using a visible CMOS camera when a 1536-nm laser was launched into the waveguides with widths ranging from 0.96 to 1.44 $\mu$m. In addition to bright green light emission in the waveguide core area, green light can also be observed on both sides of the waveguide core, which corresponds to lateral leakage of the 1536-nm laser during propagation along the waveguide. From the brightness of such green light emission, we thus can qualitatively characterize the magnitude of leakage loss of the waveguide at 1536 nm.

 

Fig. 5. Microscope images of waveguides with widths ranging from 0.96 to 1.44 $\mu$m with pump from the left input fiber with a 1536-nm laser. The left upper image is under light illumination. All others were taken while illumination light was turned off, with gain and exposure time of the camera kept the same.

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Funding

Japan Society for the Promotion of Science (19H02207, 19H02636, 20H00357).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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