Gain Characteristics of Hybrid Waveguide Amplifiers in SiN Photonics Integration with Er-Yb:Al₂O₃ Thin Film

Abstract

Integrated optical waveguide amplifiers, with their compact footprint, low power consumption, and scalability, are the basis for optical communications. The realization of high gain in such integrated devices is made more challenging by the tight optical constraints. In this work, we present efficient amplification in an erbium–ytterbium-based hybrid slot waveguide consisting of a silicon nitride waveguide and a thin-film active layer/electron-beam resist. The electron-beam resist as the upper cladding layer not only possesses the role of protecting the waveguide but also has tighter optical confinement in the vertical cross-section direction. On this basis, an accurate and comprehensive dynamic model of an erbium–ytterbium co-doped amplifier is realized by introducing quenched ions. A modal gain of above 20 dB is achieved at the signal wavelength of 1530 nm in a 1.4 cm long hybrid slot waveguide, with fractions of quenched ions f_q = 30%. In addition, the proposed hybrid waveguide amplifiers exhibit higher modal gain than conventional air-clad amplifiers under the same conditions. Endowing silicon nitride photonic integrated circuits with efficient amplification enriches the integration of various active functionalities on silicon.

1. Introduction

Erbium-doped fiber amplifiers (EDFAs) with low nonlinearity, low noise, wide gain, and coverage of telecommunication C-band and L-band are the basis of long-distance optical communication at present [1]. Erbium-doped waveguide amplifiers (EDWAs) [2] are an important complement to EDFAs, which have seen remarkable development in recent years [3,4,5,6]. Compared with EDFAs, EDWAs can utilize an optical waveguide structure to achieve high signal optical gain near the operating wavelength within a tiny size, attributed to its higher erbium concentration [7]. Therefore, EDWAs are capable of planar and three-dimensional integration with other optical waveguide devices, constituting a high-efficiency dense integrated optical system [8,9,10]. Taken together, EDWAs not only inherit the advantages of EDFAs but also possess the characteristics of low loss, compact size, high stability, and compatibility [11,12,13], which are key to promoting the development of photonic integrated circuits [14,15,16].

The integrated silicon nitride (SiN) photonic platform is an ideal candidate for the sustainable development of EDWAs [17], and it has a wider transparent window and lower temperature cross-sensitivity than silicon [18]. Moreover, in the telecom band, two-photon absorption is negligible, with propagation loss as low as 3 dB/m [19]. Amplifiers on SiN photonic integrated circuits have the function of light emission and amplification, which provides the potential to integrate active devices, including high-performance lasers [20] and amplifiers [21,22,23], on the chip. Erbium-doped amplifiers based on low-loss SiN waveguides are attractive active devices and have been widely deployed in applications such as optical communications, precision measurements, and integrated microcombs [24,25,26]. Recent advances have designed diverse SiN waveguide amplifiers to achieve gain performance [7,21,22,23,27].

Addressing the hurdles of efficient amplification in integrated SiN photonic platforms, alternative approaches involving host materials have gained prominence, with aluminum (Al₂O₃) standing out for its advantages relating to high transparency, high rare-earth solubility, and moderate refractive index contrast for compact devices. Although Al₂O₃ features various significant advantages, its point defects introduce characteristic absorption edges in the near-infrared spectral region [28,29]. This parasitic absorption directly competes with Er ions for pump beams (980 nm), reducing pump efficiency and limiting population inversion. Additionally, these point defects facilitate non-radiative relaxation channels for excited Er ions, leading to their energy being released to the defects in the form of lattice vibrations. This induces a decrease in the fluorescence quantum efficiency of the telecommunication bands, ultimately reducing the net gain. Thus, Yb ions are usually added as sensitizers to enhance the pump absorption efficiency of EDWAs and to alleviate the concentration-quenching effect among erbium ions.

Nowadays, slot waveguides attract significant attention in the field of integrated optics [30,31,32]. This is because, compared to conventional ridge or strip waveguides [33], slot waveguides provide superior optical field confinement in the low-refractive-index slot region, enabling remarkable enhancement of light–matter interactions. This unique structure confines the optical field within a nano-scale slot, demonstrating great potential for fabricating high-performance integrated waveguide amplifiers. In a recent report, a slot waveguide amplifier formed by coating SiN waveguides with an atomic layer-deposited Er:Al₂O₃ film showed a high gain per unit length of 20.1 dB/cm [7]. Despite this great progress, only modest total gains have been obtained in waveguides with a length of less than 0.12 cm, limiting their practical use.

In this work, we present a hybrid SiN waveguide amplifier via integration with an erbium–ytterbium co-doped aluminum oxide (Er-Yb:Al₂O₃) layer and an upper cladding. The upper cladding-covered waveguide has tighter optical confinement in the vertical cross-section direction. According to accurate and comprehensive Er-Yb co-doped amplification dynamics modeling, the hybrid waveguide amplifier is carefully optimized with quenched ions. A modal gain of above 20 dB at the signal wavelength of 1530 nm pumped by 980 nm can be achieved when the erbium ion concentration is 3 × 10²⁰ cm⁻³ and the ytterbium ion concentration is 2.4 × 10²¹ cm⁻³. This work provides theoretical support and optimization guidance for Er-Yb:Al₂O₃-cladded amplifiers based on SiN waveguides.

2. Structure Design and Simulation Optimization

2.1. Characterization of the Hybrid Slot Waveguide

A schematic diagram of the cladded amplifier based on the Er-Yb co-doped hybrid slot waveguide is provided in Figure 1a. On the silicon dioxide substrate, two adjacent high refractive index contrasting passive SiN waveguides create a slot region, which is filled with an active Er-Yb:Al₂O₃ layer. The top PMMA layer acts as an upper cladding layer to further enhance the amplifier performance and protect the hybrid slot waveguide against damage. The working principle of the Er-Yb co-doped amplifier during stimulated emission is shown in the dashed box. Employing a 980 nm laser as the pump source is primarily due to the fact that the absorption cross section of Yb ions at this wavelength is larger than that of Er ions. The excited Yb ions transfer energy to the neighboring Er ions, contributing to a high power conversion efficiency. The input signal beam is amplified, while the pump beam is simultaneously attenuated in this process. Figure 1b shows a simplified cross section of the slot waveguide amplifier at the central axis. The key design parameters affecting waveguide performance are the slot waveguide width (W_slot), the slot waveguide height (H_SiN), and the SiN waveguide width (W_SiN). To be more accurate in the model calculations, the refractive indices of PMMA, Er-Yb:Al₂O₃, SiN, and SiO₂ need to be known as a function of the wavelength. The refractive indices of these materials are obtained from references [34,35,36,37], and then the group refractive indices of each material are calculated by definition n_g(λ) = n(λ) − λdn/dλ, as exhibited in Figure 1c. Based on the above, Figure 1d demonstrates the calculated effective mode index and the effective group index of the fundamental transverse electric (TE) mode corresponding to the hybrid waveguide cross section at the same wavelength range. Before optimization, the TE and transverse magnetic (TM) fundamental mode electric field distributions of the waveguide at λ = 980 nm and λ = 1530 nm are calculated by setting W_slot = 150 nm, H_SiN = 500 nm, and W_SiN = 500 nm, as depicted in Figure 1e. The electric field distribution of the fundamental mode indicates that both polarizations can be confined within the waveguide cross section. However, the TE mode is more confined to the slot region of the active gain medium. Therefore, to obtain the highest possible gain, only the TE mode is investigated in subsequent calculations.

2.2. Optimization of the Hybrid Slot Waveguide

An essential feature of hybrid slot waveguide design is the effect on beam propagation by the slot waveguide width. In order to enhance the light interaction with the active layer, a hybrid slot waveguide amplifier was designed based on the finite element method, and the structure is further optimized according to the electric field mode distribution. The mode confinement factor Γ and the effective mode area A_eff in the active region of the waveguide are calculated as accurately as possible by considering the material dispersion and modal component contribution [7].

Figure 2a represents the dependence of the confinement factor (solid curve) and the effective mode area (dashed curve) on W_slot for the TE mode at λ = 980 nm and λ = 1530 nm, respectively. It can be seen that the confinement factor gradually increases as W_slot increases. When W_slot exceeds 150 nm, the confinement factor remains almost constant at about 0.19 at 980 nm, and the confinement factor exceeds 0.25 at 1530 nm. Notably, the growth rate of the mode confinement factor for the TE mode decreases significantly when W_slot exceeds 150 nm. Continuing to increase W_slot beyond 200 nm, the mode confinement factor exhibits a slight decline at 980 nm and increases by 0.02 at 1530 nm. Furthermore, the effective mode area dependence on W_slot illustrates that the effective mode area of the fundamental TE mode is less than 1 μm² at both signal and pump wavelengths with W_slot less than 150 nm. In general, a small effective mode area facilitates the slot waveguide amplifier to achieve net gain at a low saturated input power. Therefore, in combination with the above analysis, optimized W_slot = 150 nm is selected for further study.

Another key feature of the SiN waveguide design is its cross-section dimensions. H_SiN and W_SiN are simultaneously globally optimized to engineer the confinement factor and effective mode area of the fundamental TE mode. Aiming at a pump wavelength of 980 nm and a signal wavelength of 1530 nm, the ranges of H_SiN and W_SiN are both set from 100 nm to 500 nm, ensuring the existence of the fundamental TE mode. Here, it should be noted that the following comparative analysis is conducted based on the same size. Figure 2b shows the confinement factor and the effective mode area as functions of H_SiN at λ = 980 nm and λ = 1530 nm, respectively. Clearly, with the increase in H_SiN, the constraint factor increases and then decreases, while the effective mode area varies insignificantly at 980 nm. The difference is that the confinement factor gradually increases while the effective mode area progressively decreases as H_SiN increases at 1530 nm. When H_SiN exceeds 400 nm, the confinement factor remains at about 0.25 and the effective mode area remains at around 1.05 μm². This is attributed to the fact that the larger height-to-width ratio of the SiN waveguide alleviates the mode leakage in the hybrid slot waveguide to enable the mode field to be more intensively confined in the waveguide. As a result, optimized H_SiN = 400 nm is selected for further study. The confinement factor and the effective mode area of the TE mode versus W_SiN at the two wavelengths are depicted in Figure 2c. As expected, the trend in the confinement factor and the effective mode area for the TE mode at 980 nm is approximately the same as in Figure 2b. It is also worth noting that the confinement factor increases and then decreases with increasing W_SiN at 1530 nm, probably owing to the reduction in the ratio of the slot area to the whole cross section, which permits the light field to enter inside the SiN strip from the slot. Moreover, the effective mode area firstly decreases and then slightly increases with increasing W_SiN at 1530 nm, reaching almost a minimum value of about 1 μm² for the effective mode area at W_SiN = 300 nm. In SiN-based integrated photonic circuits, the desire is to achieve a higher possible confinement factor with a smaller effective mode area. Therefore, we chose W_SiN = 300 nm as the optimized device parameter for the slot waveguide.

Taking the designed hybrid slot waveguide structure as the basis, the effects of the upper cladding materials on the modal characteristics are evaluated by performing calculations of the mode confinement factors and electric field distributions. Figure 3a,b demonstrates the pronounced effect of the refractive index value of the upper cladding on the confinement factors at λ = 980 nm and λ = 1530 nm. It can be seen that as the upper cladding refractive index value varies from 1.0 to 1.6, the confinement factors at both wavelengths exhibit a tendency to increase and then decrease. The difference can be described as the confinement factor achieving a maximum at λ = 980 nm when the upper cladding index value is 1.56, while the confinement factor decreases sharply at λ = 1530 nm when the upper cladding index value exceeds 1.47. The reason for this phenomenon may be the minimized refractive index difference ∆n between the upper cladding material and the active gain medium. In addition, the insets in Figure 3 indicate the electric field distributions of the hybrid slot waveguide for the upper cladding materials of air, PMMA, and SU-8 at the corresponding wavelengths. On the whole, the variation in upper cladding material has a greater effect at λ = 980 nm than at λ = 1530 nm. As shown in Figure 3b, PMMA as the upper cladding of the hybrid slot waveguide confines a greater area of the optical field to the active region than air and SU-8 as the upper cladding materials. Therefore, PMMA can be selected as the upper cladding material for the hybrid slot waveguide amplifier.

3. Amplification Performances

3.1. Dynamic Modeling

Optical gain is modeled by treating Er-Yb co-doped as a multi-energy-level system, which generally well describes the population of five energy levels of Er and two levels of Yb [27]. At elevated Er ion concentrations, the quenched phenomenon arises due to energy migration and cross-relaxation interactions among neighboring ions. These processes result in the shortened lifetime of the excited-state ions and a reduced probability of stimulated emission, thereby leading to a decline in optical gain. Consequently, investigating the influence of fractions of quenched ions f_q on gain characteristics is of significant practical importance for the optimization and performance enhancement of optical waveguide amplifiers. The dynamical behavior of quenched ions can also be described by our previous work [27], in which the total density N_Er and the excitation energy-level lifetime τ_ij of Er ions are replaced by f_qN_Er and τ_q, respectively. The total modal gain is obtained by summing the active ions (1 − f_q)N_Er and the quenched ions f_qN_Er in the steady-state dynamic response.

The spatial evolution of signal, pump, and spontaneous amplifier noises in a given waveguide can be described by a set of propagation equations:

$$\begin{gathered} {\displaystyle \frac{d{P}_{\mathrm{s}}(z)}{dz}}=P_{\mathrm{s}}(z){\mathrm{\Gamma }}_{\mathrm{s}}\left[{\sigma }_{21\mathrm{s}}{N}_2(z)-{\sigma }_{12\mathrm{s}}{N}_1(z)\right]-P_{\mathrm{s}}(z){\alpha }_{0\mathrm{s}} \\ {\displaystyle \frac{d{P}_{\mathrm{p}}(z)}{dz}}=P_{\mathrm{p}}(z){\mathrm{\Gamma }}_{\mathrm{p}}\left[{\sigma }_{21\mathrm{p}}^{\mathrm{Yb}}{N}_2^{\mathrm{Yb}}(z)-{\sigma }_{12\mathrm{p}}^{\mathrm{Yb}}{N}_1^{\mathrm{Yb}}(z)-{\sigma }_{13\mathrm{p}}{N}_1(z)\right]-P_{\mathrm{p}}(z){\alpha }_{0\mathrm{p}} \\ \begin{array}{ll}{\displaystyle \frac{d{P}_{\mathrm{ASE},\mathrm{f}}(z,{\nu }_j)}{dz}}=& P_{\mathrm{ASE},\mathrm{f}}(z,{\nu }_j){\mathrm{\Gamma }}_{\mathrm{ASE}}\left[{\sigma }_{21,\mathrm{ASE}}{N}_2(z)-{\sigma }_{12,\mathrm{ASE}}{N}_1(z)\right]\\ & -P_{\mathrm{ASE},\mathrm{f}}(z,{\nu }_j){\alpha }_{0,\mathrm{ASE}}+mh{\nu }_j\Delta {\nu }_j{\mathrm{\Gamma }}_{\mathrm{ASE}}{\sigma }_{21,\mathrm{ASE}}{N}_2(z)\end{array} \\ \begin{array}{ll}{\displaystyle \frac{d{P}_{\mathrm{ASE},\mathrm{b}}(z,{\nu }_j)}{dz}}=& -P_{\mathrm{ASE},\mathrm{b}}(z,{\nu }_j){\mathrm{\Gamma }}_{\mathrm{ASE}}\left[{\sigma }_{21,\mathrm{ASE}}{N}_2(z)-{\sigma }_{12,\mathrm{ASE}}{N}_1(z)\right]\\ & +P_{\mathrm{ASE},\mathrm{b}}(z,{\nu }_j){\alpha }_{0,\mathrm{ASE}}-mh{\nu }_j\Delta {\nu }_j{\mathrm{\Gamma }}_{\mathrm{ASE}}{\sigma }_{21,\mathrm{ASE}}{N}_2(z)\end{array} \end{gathered}$$

(1)

in which α_0s and α_0p are the waveguide background losses for the signal and pump, respectively. The ASE noise can be calculated by discretizing Er ion continuous absorption and emission spectra into M frequency strips with width Δν_j and center frequency ν_j (j = 1, 2, …, M), where m is the number of guided modes propagating at the signal wavelength.

The parameters in the modeling used to calculate the gain characteristics, which are extracted from references [38,39,40,41,42,43,44,45], are given in

Table 1. Parameters of an Er-Yb-based hybrid slot waveguide.

Parameter	Symbol	Value
Er concentration	NEr	3 × 1020 cm−3
Yb concentration	NYb	2.4 × 1021 cm−3
Lifetime of state 4I13/2	τ21	5 ms
Lifetime of state 4I11/2	τ32	0.1 ms
Lifetime of state 4I9/2	τ43	1 μs
Lifetime of state 2F5/2	${\tau }_{21}^{\mathrm{Yb}}$	2 ms
Lifetime of quenched ions	τq	1 μs
Er pump absorption cross section	σ13p	2.58 × 10−21 cm2
Er signal emission cross section	σ21s	9.83 × 10−21 cm2
Er signal absorption cross section	σ12s	8.95 × 10−21 cm2
Yb pump emission cross section	${\sigma }_{21\mathrm{p}}^{\mathrm{Yb}}$	1.2 × 10−20 cm2
Yb pump absorption cross section	${\sigma }_{12\mathrm{p}}^{\mathrm{Yb}}$	1.2 × 10−20 cm2
ASE emission cross section	σ21,ASE	4 × 10−21 cm2
ASE absorption cross section	σ12,ASE	6 × 10−21 cm2
First order CUC coefficient	C24	4.1 × 10−17 cm3s−1
Second order CUC coefficient	C35	4.1 × 10−17 cm3s−1
Cross-relaxation coefficient	C14	3.4 × 10−16 cm3s−1
Fraction of quenched ions	fq	0, 15%, 30%
Pump propagation loss	α0p	2.3 dB/cm
Signal propagation loss	α0s	0.6 dB/cm

.

3.2. Numerical Simulation of Optical Amplification

The amplification dynamics in PMMA-clad and air-clad amplifiers with different fractions of quenched ions f_q have been elaborately investigated. Modal gain as a function of waveguide length is first simulated for both waveguide amplifiers with different fractions of quenched ions, f_q = 0%, 15%, and 30%, as shown in Figure 4a. It can be clearly seen that the PMMA-clad amplifier obtains a higher modal gain than the air-clad amplifier at the same fractions of quenched ions. To be more specific, the PMMA-clad amplifier obtains a maximum modal gain of 19.5 dB, which is higher than that of the air-clad amplifier, at 18.1 dB, when the waveguide length is 1.5 cm in the absence of quenched ions. By further increasing the waveguide length to 2 cm, the modal gain of both amplifiers decreased slightly by about 1.5 dB, which can be attributed to insufficient pump power. In contrast, the maximum modal gains obtained by the PMMA-clad amplifier and air-clad amplifier are 10.6 dB and 9.2 dB, respectively, at the waveguide length of 1 cm for f_q = 30%. This indicates that the presence of quenched ions greatly reduces the optical gain owing to their detrimental absorption of the pump and signal power without contributing to the inversion gain. For a fixed waveguide length of 1 cm, the dependence of the modal gain on the pump power at an input signal power of −30 dBm can be seen in Figure 4b. For both amplifiers, the level of modal gain increase becomes slow and tends to saturate when the pump power exceeds 30 mW. It is worth noting that the larger the fractions of quenched erbium ions, the higher the pump power required to obtain net modal gain.

Furthermore, modal gain as a function of the input pump and signal powers under different fractions of quenched erbium ions is calculated for air-clad and PMMA-clad waveguide amplifiers. As shown in Figure 5, the fractions of quenched erbium ions exhibit a significant effect on the modal gain of the waveguide amplifiers. The ‘0’ gain plots in the gain maps are represented by black lines, where the actual loss and gain regions are delimited. The comparison of the modal gains of the air-clad and the PMMA-clad waveguide amplifier in the absence of quenched erbium ions is given in Figure 5a,d. Both amplifiers have the same gain behavior with comparable gain values. According to the variation in the ‘0’ dB plots, the presence of quenched erbium ions significantly reduces the area of the actual gain region, as shown in Figure 5b,e. At the same signal power, to achieve identical modal gain, smaller input pump power is required for the PMMA-clad waveguide amplifier relative to the air-clad waveguide amplifier. Figure 5c,f shows modal gain assuming that 30% of the active erbium ions are rapidly quenched. Both amplifiers exhibit a further reduction in the actual gain area compared to f_q = 15%. Moreover, the PMMA-clad waveguide amplifier provides a larger maximum small-signal gain and actual gain area than the air-clad waveguide amplifier. The findings of this investigation reveal the potential contribution of the cladding materials to reducing the counteracting role of quenched erbium ions. Although a portion of input optical power in the PMMA-clad waveguide amplifier is guided outside the active region, leading to a decrease in the detrimental absorption of pump and signal powers by quenched erbium ions, this decrease can be compensated by a more uniform inversion along the entire length of the waveguide amplifier. In addition, the PMMA-clad waveguide amplifier confines a portion of the input pump power in the cladding material, which mitigates the excessive excitation of erbium ions. Thus, the energy transfer upconversion process is alleviated, allowing for higher modal gain.

Figure 6a exhibits modal gain as a function of input signal power at a pump power of 20 dBm. It can be seen that for the same configuration, the higher the fractions of quenched erbium ions, the smaller the modal gain. As the input signal power increases, the modal gain provided by both amplifiers gradually decreases. The reason for this phenomenon may be the depletion of excited-state erbium ions by the stimulated emissions from high power signals. In addition, the PMMA-clad waveguide amplifier has a higher small-signal modal gain than the air-clad waveguide amplifier, while at high power signals the modal gains obtained by both amplifiers are pretty close to each other, taking into account the presence of quenched erbium ions. It is pleasing to note that the PMMA-clad waveguide amplifier maintains a modal gain of over 10 dB at f_q = 30%. The derived noise figures at various input pump powers for a forward pumping scheme are shown in Figure 6b. The noise figure of both amplifiers decreases as the pump power increases with different fractions of quenched ions. When the pump power is lower than 13 dBm, with higher fractions of quenched ions for both amplifiers, the noise figures are smaller, and the PMMA-clad waveguide amplifier noise is smaller than the air-clad noise at the same fractions of quenched ions. As a result, increasing the pumping power enables the device to achieve a larger modal gain and lower noise figure.

Based on the above study, we further explore the performance of the PMMA-clad hybrid waveguide amplifier with fractions of quenched ions f_q = 30%. The calculated modal gain versus input pump power and waveguide length is given in Figure 7. For a PMMA-clad hybrid waveguide amplifier with an Er concentration of 3 × 10²⁰ cm⁻³ and Yb concentration of 2.4 × 10²¹ cm⁻³, an optimized waveguide length of 1.4 cm can be found that is capable of delivering more than 20 dB of modal gain with a power pump of around 25 dBm. Modal gain is further increased by applying a higher input pump power or reducing propagation losses, but a further increase in waveguide length would not improve the modal gain significantly. This is primarily due to the fact that erbium signal reabsorption is more likely to occur in longer waveguides.

A comparison of recently reported erbium-doped waveguide amplifiers is presented in

Table 2. Comparison with recently reported erbium-doped waveguide amplifiers.

Waveguide /Active Material	Active Region Length (cm)	Erbium Concentration (cm−3)	Gain (dB)	Method	Reference
SiN/Er:Al2O3	0.12	4.9 × 1021	1.98	Exp.	[7]
SiN/Er:TeO2	6.7	2.5 × 1020	5	Exp.	[22]
SiN/Er:Al2O3	0.16	3.88 × 1021	3.13	Exp.	[23]
Si/Er:Polymer	1.5	1.3 × 1021	5.78	Theo.	[46]
Er:LiNO3	3.6	1.9 × 1020	18	Exp.	[4]
Er:LiNO3	2.58	7.2 × 1019	16	Exp.	[47]
Si/Er:TeO2	4	2.2 × 1020	15.21	Theo.	[32]
Er:Yb co-doped	1	1.644 × 1021	18.77	Theo.	[44]
HSQ/Er:Al2O3	9.31	2.5 × 1020	14.4	Exp.	[3]
SiN/Er:Al2O3	1.4	3 × 1020	20	Theo.	This work

. The table compares integrated amplifiers with various material platforms in terms of the active material, active region length, erbium doping concentration, and gain. The proposed hybrid waveguide amplifier presents a strategy for high-efficiency on-chip amplification. This provides an avenue for the development of active devices based on passive SiN photonic platforms.

4. Discussion

The development of high-gain integrated waveguide amplifiers is critical for scaling photonic integrated circuits. We propose an efficient amplification scheme based on a hybrid slot waveguide consisting of SiN waveguides and a thin-film Er-Yb:Al₂O₃/electron-beam resist. By very carefully engineering the optical mode supported in such a hybrid waveguide, the PMMA-clad hybrid waveguide features higher single-mode conservation than conventional air/SU8-clad hybrid waveguides at 1530 nm. A comprehensive dynamic model of the Er-Yb co-doped amplifier is developed by introducing quenched ions. The results demonstrate that a PMMA-clad hybrid waveguide amplifier exhibits a modal gain of more than 20 dB.

The advantage of this hybrid waveguide based on a silicon nitride photonic platform enables the flexible engineering of the guided mode and the modal overlap between pump and signal beams and the active layer in a hybrid slot structure by changing the cladding material. Compared to conventional air/SU8-clad hybrid waveguides, the PMMA-clad hybrid waveguide features higher single-mode conservation. To better reflect actual conditions, a comprehensive dynamic model of Er-Yb co-doped amplifiers is further established by introducing quenching ions based on our previous research [27]. As expected, the PMMA-clad amplifier obtains a higher modal gain than the air-clad amplifier in the presence of quenched ions, in agreement with the results reported in Ref. [48]. Moreover, it is evident that the increase in the proportion of quenched ions significantly reduces the modal gain, owing to their deleterious absorption of pump and signal powers without facilitating the inversion gain, consistent with the results reported in Ref. [22].

Another advantage stems from the active material nanostructure design, which mitigates the concentration-quenching effect caused by pump depletion and energy transfer upconversion. Recent studies have shown that bidirectional energy cycling between Er ions and Yb ions is the primary factor contributing to pump depletion at high doping concentrations. Specifically, the reverse transfer from Er ions to Yb ions competes with forward sensitization, leading to the nonlinear quenching of red emissions [49]. To suppress energy transfer upconversion, an engineered core-shell nanostructure with an interfacial energy transfer layer was proposed. This strategy reduces losses due to energy transfer upconversion in high-concentration Er-Yb systems by isolating Er ion clusters [50].

In addition, the host material is a key factor affecting the performance of EDWAs. Al₂O₃ is a promising candidate host material due to its wide transparency window, high thermal conductivity, and excellent mechanical stability. However, the presence of intrinsic and extrinsic point defects in Al₂O₃ introduces characteristic absorption bands in the visible and even near-infrared regions [51,52,53,54]. These defects introduce parasitic absorption losses, compete with Er ions for pumping energy, and finally affect the gain performance of EDWAs. Although these point defects in Al₂O₃ trigger a marked challenge to the efficient amplification of EDWAs, using a co-doping strategy with sensitizers (e.g., Yb ions) to improve pump absorption efficiency and mitigate the concentration-quenching effect may be a feasible solution.

Despite the comprehensive theoretical scheme proposed, achieving efficient amplification in SiN-based photonic integrated circuits necessitates trade-offs among optical performance, thermal stability, and fabrication feasibility. Yet, although PMMA is essential in high-gain, low-cost erbium-doped waveguide amplifiers due to low optical losses and the ease of processing, thermal stability shortcomings limit its industrial applications. Exploring alternative cladding materials with enhanced thermal and environmental resilience while mitigating the potential negative impact on optical performance (e.g., by engineering composite cladding interfaces, exploring graded indices, or utilizing lower-index stable polymers) is a critical and valuable direction for future research in real-world applications. In addition, it could allow for the co-doping of other rare-earth ions such as neodymium and thulium, thereby providing optical gain in other wavelength regions.

5. Conclusions

In conclusion, we have theoretically proposed PMMA-clad hybrid waveguide amplifiers based on a SiN photonic platform, in which one can flexibly engineer the guided mode and the modal overlap between the pump and signal beams and active layer in a hybrid slot structure. An accurate and comprehensive dynamic model of an Er-Yb co-doped amplifier considering quenched ions is developed. A modal gain of above 20 dB can be achieved at 1530 nm within a 1.4 cm hybrid slot waveguide for an Er concentration of 3 × 10²⁰ cm⁻³ and a Yb concentration of 2.4 × 10²¹ cm⁻³ with fractions of quenched ions f_q = 30%. This work offers a strategy for designing high-gain waveguide amplifiers with a simple fabrication process and unveils the versatility of SiN-based photonic integrated circuits. It will enrich the building blocks in active platforms and pave the way for the development of on-chip high-efficiency amplification.