Gain optimization of an erbium-ytterbium co-doped amplifier via a Si<sub>3</sub>N<sub>4</sub> photonic platform

Ziming Dong; Yuqing Zhao; Yitong Wang; Wei Wei; Lei Ding; Liqin Tang; Yigang Li

doi:10.1364/OE.503076

1. Introduction

In the 1980s, the invention of erbium-doped fiber amplifiers (EDFAs) contributed to groundbreaking advances in realizing long-distance optical communication on account of features including low nonlinearity, low-noise amplification, as well as wide gain covering the telecom C-band (1530-1560 nm) [1,2]. Subsequently, we have witnessed that compact erbium-doped waveguide amplifiers (EDWAs) have also evolved significantly on the basis of EDFAs [3,4]. Early researchers devoted to the realization of EDWAs on oxidized glass waveguide substrates, which suffered from high waveguide background loss, large device footprint, and incompatibility with contemporary photonic integrated circuits [5,6]. Nowadays, the above-mentioned limitations can be bypassed by the emergence of Si₃N₄ complementary metal oxide semiconductor (CMOS) compatible photonic integrated circuit platforms [7–10], which are promising candidates for the continued development of EDWAs. It offers a wider transparency window and lower temperature sensitivity than silicon, negligible two-photon absorption in the telecom band, and propagation loss as low as 3 dB/m.

Another critical task in designing and implementing erbium-doped devices lies in the selection of the host material. Various rare-earth host materials with suitable lanthanide solubility for compatible silicon photonic platforms are widely studied. There exist two main categories: amorphous materials, such as Al₂O₃ [11,12], Ta₂O₅ [13], TeO₂ [14], PMMA [15], and SU8 [16]; and crystalline materials, such as lithium niobate (LiNbO₃, LN) [17–21] and Si₃N₄ [22]. Among these, Al₂O₃ has proven to be an excellent platform for rare earth doping waveguide amplifiers due to its high transparency, high rare earth solubility, and moderate refractive index contrast for compact devices. Agazzi et al. first monolithically integrated erbium-doped Al₂O₃ (Er:Al₂O₃) layer into a silicon-on-insulator (SOI) chip to realize an on-chip optical amplifier with 7 dB signal enhancement (@1533 nm) on a 9.5 mm long waveguide pumped by 1480 nm beam [23]. To obtain higher gain, the Er:Al₂O₃ layer growth conditions were optimized to achieve a net internal gain of 13.7 dB/cm on a 2 mm long device pumped by 980 nm beam [24]. By mixing and integrating erbium-doped substrate materials into passive platforms, they exhibit the ability of optically emitting and amplifying, offering the possibility of on-chip integration of active devices such as high-performance lasers and amplifiers.

The challenge in realizing erbium-doped amplifiers based on photonic integrated circuits concerns the limited achievable gain owing to the doping concentration limitation deriving from cooperative upconversions [25]. This limitation requires Si₃N₄ waveguides with low propagation loss [26,27] and long waveguides to achieve high gain and output optical power. Recently, researchers have carried out numerous attempts to implement Er:Al₂O₃ waveguide amplifiers at the chip level in Si₃N₄ photonic integrated circuit platforms. To name a few, Rönn et al. converted a passive Si₃N₄ strip waveguide into an active waveguide amplifier with internal net modal gain by single-layer active layer deposition with a peak net gain of 2.82 dB/cm (@1533 nm) in a 1.2-mm-long waveguide pumped at 18 mW (@1480 nm) [28]. Mu et al. proposed a double-layer photonic platform to enable the monolithic integration of Er:Al₂O₃ on Si₃N₄ to obtain a high-gain optical amplifier. On a device with a spiral length of 10 cm, it has a net gain of 18.1 dB at 1532 nm under 976.2 nm pump excitation, with a gain bandwidth covering S, C, and L bands of more than 70 nm [29]. Chrysostomidis et al. obtained a gain of 1.44 dB/cm and achieved 480 Gbps WDM transmission in a 5.9 cm long device based on the above-mentioned double-layer structure [30]. However, insufficient pump efficiency plays an essential role in limiting the gain of EDWAs. The Yb³⁺ absorption cross section $({\sigma_{\textrm{12}}^{\textrm{Yb}}} )$ at 980 nm excitation is one order of magnitude larger than the Er³⁺ absorption cross section $({\sigma_{\textrm{12}}^{\textrm{Er}}} )$, and Yb³⁺ has been commonly added as a sensitizer to enhance the pump absorption efficiency of EDWAs [31,32]. Apparently, most of the reported works focus on experimental results of single-doped Er:Al₂O₃ amplifiers without providing systematic and comprehensive theoretical support for erbium-ytterbium co-doped Al₂O₃ (Er:Yb:Al₂O₃) waveguide amplifiers based on Si₃N₄ photonic integrated circuit platforms.

Herein, Er:Yb:Al₂O₃ amplifier with high gain performance based on Si₃N₄ waveguide has been achieved. The optimization design of the Si₃N₄ waveguide is carried out with the finite difference method combined with the overlap factor. A more accurate and comprehensive theoretical model of erbium-ytterbium co-doped is established, and the high-gain erbium-ytterbium co-doped waveguide amplifier is optimized with considering upconversions, energy transfer, amplified spontaneous emission (ASE) and propagation loss. When the Er³⁺ concentration is 3 × 10²⁰cm^-3 and the Yb³⁺ concentration is 3 × 10²¹cm^-3, the waveguide amplifier based on the optimized design exhibits a small-signal gain of more than 36 dB with 23 dBm input pump power. This work provides comprehensive theoretical support and optimization guidance for Er:Yb:Al₂O₃ amplifiers based on Si₃N₄ waveguides.

2. Structure design and simulation

2.1 Characterization of Er:Yb:Al₂O₃-Si₃N₄ waveguides

Figure 1 provides a schematic illustration of the designed waveguide amplifier structure. A diagram of a waveguide Er:Yb:Al₂O₃ based on Si₃N₄ platform is depicted in Fig. 1(a). The combined signal-pump beam is coupled into/from the passive Si₃N₄ waveguide via a tapered lens fiber. Combined with the active Er:Yb:Al₂O₃ layer, the Si₃N₄ waveguide can act as an integrated optical amplifier. The input signal beam gets amplified, while the pump beam attenuates simultaneously. Figure 1(b) presents the simplified cross-section at the central axis of the waveguide amplifiers, where the width (W_r) and height (H_r) of the passive waveguide and the height (H_g) of the active layer are indicated. The single-mode confinement conditions are determined by both the waveguide size and the refractive index of the waveguide and the surrounding medium. Single-mode field simulations at the pump and signal wavelengths are performed with the finite-difference method. Figures 1(c) and (d) demonstrate the effective refractive index’s $({{n_{\textrm{eff}}}} )$ dependence on W_r at 980 nm and 1550 nm, respectively, where the Si₃N₄ waveguide aspect ratio is set to be 1:1. With W_r in the range of 0 to 0.8 µm, the signal beam is transmitted in single-mode propagation. And the pump beam is transmitted in single-mode propagation when W_r is less than 0.5 µm. The electric field distributions of the fundamental quasi-transverse electric (TE) mode at $\lambda$= 980 nm and $\lambda$= 1550 nm are simulated, as shown in Fig. 1(e). The electric field distributions of the fundamental TE-mode illustrate that the signal and the pump beams are penetrated out of the waveguide. Obviously, on account of the reduced refractive index contrast between Er:Yb:Al₂O₃ (n ∼ 1.604) and Si₃N₄ (n ∼ 1.997) compared to the Si waveguide, the guided optical modes are penetrated out of the Si₃N₄ waveguide in the active Er:Yb:Al₂O₃ layer.

Fig. 1. Schematic illustration of the Er:Yb:Al₂O₃-Si₃N₄ waveguide amplifier structure. (a) Diagram of the Er:Yb:Al₂O₃-Si₃N₄ waveguide structure. The blue and green pulses represent signal and pump waves, respectively. (b) Description of waveguide structure parameters. (c) The $({{n_{\textrm{eff}}}} )$ dependence on the Si₃N₄ waveguide width (W_r) with height-to-width aspect ratios of 1 for the pump at 980 nm and (d) the signal at 1550 nm. (e) The simulated fundamental TE-mode for the waveguide.

Download Full Size | PDF

2.2 Optimization of Er:Yb:Al₂O₃-Si₃N₄ waveguides

To evaluate the ability to confine the light in the Si₃N₄ waveguide, TE-mode inside the waveguide region for the signal and pump wavelengths are calculated in combination with the overlap factors $(\Gamma )$, which represent the efficient utilization of the energy. The $\Gamma $ for TE-mode in the active region (A) is expressed as

(1)$$\Gamma = \frac{{n_{\textrm{eff}}^g}}{{n_A^g}}\frac{{\int\!\!\!\int_A {\varepsilon {{|{E({x,y} )} |}^2}dxdy} }}{{\int\!\!\!\int_\infty {\varepsilon {{|{E({x,y} )} |}^2}dxdy} }}$$

where $E({x,y} )$ represents the electric field of the fundamental TE-mode for the given cross-section, $\varepsilon$ is the permittivity of the given waveguide material, and A represents Er:Yb:Al₂O₃ active region. $n_{\textrm{eff}}^g$ is the effective group index of the TE-mode and $n_A^g$ is the group index of the active region. The effect of the inhomogeneous doping of erbium-ytterbium ions can be neglected here.

In order to obtain the value of $\Gamma $, it is necessary to calculate the effective mode index of the fundamental TE-mode for the corresponding waveguide cross-section as a function of the wavelength. After that, the group index of the TE-mode is calculated according to the definition ${n^g}(\lambda ) = n(\lambda )- \lambda {{dn} / d}\lambda$. Figure 2(a) shows the refractive index profile of the TE-mode in the wavelength range of 600∼1600 nm. The group index of the TE-mode is 2.088 at 980 nm and 2.042 at 1550 nm. Likewise, the group index of the active region is computed by the refractive index of Er:Yb:Al₂O₃ from Ref. [33], as shown in Fig. 2(b). The group refractive index of Er:Yb:Al₂O₃ is 1.619 at 980 nm and 1.610 at 1550 nm.

Fig. 2. Refractive and group index profiles of the TE-mode and Er:Yb:Al₂O₃ in the wavelength range of 600∼1600 nm. (a) Effective mode index and effective group index of the fundamental TE-mode for the studied waveguide cross-section. (b) Refractive index and group index of Er:Yb:Al₂O₃.

Download Full Size | PDF

The calculated $\Gamma $ as a function of H_r for the pump beam at 980 nm and the signal beam at 1550 nm for the fundamental TE-mode is illustrated in Fig. 3(a), where W_r and H_g are 0.5 µm and 0.2 µm, respectively. $\Gamma $ of pump beam decreases from 0.36 to 0.24 as H_r increases from 0.3 to 0.8 µm. $\Gamma $ of signal beam increases rapidly to the maximum value and then decreases slowly as H_r increases from 0.3 to 0.8 µm. At H_r of 0.5 µm, $\Gamma $ of signal beam reaches a maximum value of 0.39, which is used for further calculations. Figure 3(b) shows $\Gamma $ in a function of W_r for the pump beam at 980 nm and the signal beam at 1550 nm, where H_g is 0.2 µm. $\Gamma $ decreases from 0.53 to 0.14 as W_r increases from 0.3 to 0.8 µm for pump beam. When W_r is 0.4 µm, $\Gamma $ of pump beam is calculated to be 0.38, which is higher than the maximum value of 0.36 at 980 nm in Fig. 3(a). For the signal beam at 1550 nm, $\Gamma $ increases from 0.38 to 0.42 as W_r increases from 0.3 to 0.4 µm, while $\Gamma $ decreases to 0.26 as W_r continues to increase to 0.8 µm. With an optimized W_r of 0.4 µm, the calculated $\Gamma $ of TE-mode versus H_g is given in Fig. 3(c). As H_g increases from 0.1 to 0.3 µm, $\Gamma $ increases from 0.25 to 0.45 for the pump beam at 980 nm, and $\Gamma $ increases from 0.15 to 0.62 for the signal beam. Here, the appropriate H_g can be selected as required. Combined with the above analysis, it is apparent that reducing the size of the Si₃N₄ waveguide and increasing the thickness of the Er:Yb:Al₂O₃ in a certain scale facilitate the penetration of the guided optical mode out of the Si₃N₄ waveguide into the active Er:Yb:Al₂O₃ region. Therefore, the optimized H_r, W_r and H_g are 0.5 µm, 0.4 µm and 0.2 µm, respectively. The overlap factors for the TE-mode are 0.38 and 0.42 for the pump beam at 980 nm and the signal beam at 1550 nm, respectively.

Fig. 3. Optimizations of the waveguide with the overlap confinement factors for the pump beam at 980 nm and the signal beam at 1550 nm. (a) $\Gamma $ of the TE-mode dependence on H_r (W_r = 0.5 µm). (b) $\Gamma $ of the TE-mode as a function of W_r (H_r = 0.5 µm). (c) $\Gamma $ of the TE-mode as a function of H_g (H_r = 0.5 µm, W_r = 0.4 µm).

Download Full Size | PDF

3. Gain performance

3.1 Theoretical models

We model the optical gain by treating erbium-ytterbium as a multi-energy system describing the transition in the erbium-ytterbium co-doped energy level system comprehensively, as shown in Fig. 4. The lifetimes of the ⁴F_9/2, ⁴S_3/2, ²H_11/2, and ⁴F_7/2 energy levels of Er³⁺ are relatively short and have insignificant effects on the down-conversion luminescence at 1550 nm, therefore their radiative transitions can be relatively negligible. The cooperative upconversion effect and the cross-relaxation effect are mainly considered in this model. In conclusion, the energy level system is modeled with two energy levels of Yb³⁺ and five energy levels of Er³⁺, ignoring the dashed line to indicate the energy level. Yb³⁺ is excited by the pump beam from the ground state ²F_7/2 to the excited state ²F_5/2. The ²F_5/2 excited state of Yb³⁺ resonantly transfers energy to the ⁴I_11/2 level of Er³⁺. Due to the instability of the excited level ⁴I_11/2, Er³⁺ transits from the ⁴I_11/2 level to the metastable ⁴I_13/2 level in a nonradiative mode with a long millisecond lifetime. There is high population inversion between the ⁴I_13/2 level and the ground state ⁴I_15/2 level. Amplification of the signal beam is then achieved by the stimulated radiation.

Fig. 4. Scheme of energy level of Er³⁺/Yb³⁺ important transitions. Transitions labelled: (1) 980 nm pump; (2) Emission near 980 nm; (3), (4) and (5) Energy migration; (6) 1480 nm pump; (7) Cross-relaxation from ⁴I_9/2, ⁴I_13/2 and ⁴I_15/2; (8) Cooperative upconversion from ⁴I_13/2; (9) Cooperative upconversion from ⁴I_11/2; (10) Red emission at 665 nm; (11) Green emission at 545 nm; (12) Green emission at 520 nm; (13) 980 nm emission; (14) Emission near 1550 nm wavelength used for C-band optical amplification; Non-radiative relaxation are omitted for clarity.

Download Full Size | PDF

The simulations involve two sets of equations, one is the rate equation describing the overall dynamics of Er³⁺ and Yb³⁺ at each energy level. The other set is the propagation equations describing the evolution of the co-propagation and contra-propagation components of the signal, the pump and the ASE powers along the waveguide. The rate equations that govern the population dynamics including excited state absorption, cooperative upconversions and cross-relaxation upon pumping with 980 nm are given by

(2)$$ \begin{aligned} &\frac{{d{N_1}}}{{dt}}={-} ({K_{\textrm{tr}}}N_\textrm{2}^{\textrm{Yb}} + {R_{13}} + {W_{12}} + {C_{\textrm{cr}}}{N_4}){N_1} + ({A_{21}} + {W_{21}} + {C_{24}}{N_2}){N_2} + ({R_{31}} + {C_{35}}{N_3}){N_3}, \\ &\frac{{d{N_2}}}{{dt}}={-} ({A_{21}} + {W_{21}} + 2{C_{24}}{N_2}){N_2} + ({W_{12}} + 2{C_{\textrm{cr}}}{N_4}){N_1} + {A_{32}}{N_3}, \\ &\frac{{d{N_3}}}{{dt}} ={-} ({A_{32}} + {R_{31}} + 2{C_{35}}{N_3}){N_3} + ({K_{\textrm{tr}}}N_\textrm{2}^{\textrm{Yb}} + {R_{13}}){N_1} + {A_{43}}{N_4}, \\ &\frac{{d{N_4}}}{{dt}}={-} ({A_{43}} + {C_{\textrm{cr}}}{N_1}){N_4} + {C_{24}}N_2^2, \\ &\frac{{d{N_5}}}{{dt}}={-} {A_{54}}{N_5} + {C_{35}}N_3^2, \\ &{N_1} + {N_2} + {N_3} + {N_4} + {N_5}= {N_{\textrm{Er}}}, \\ &\frac{{dN_1^{\textrm{Yb}}}}{{dt}} ={-} R_{12}^{\textrm{Yb}}N_1^{\textrm{Yb}} + ({K_{\textrm{tr}}}{N_1} + A_{\textrm{21}}^{\textrm{Yb}} + R_{\textrm{21}}^{\textrm{Yb}})N_\textrm{2}^{\textrm{Yb}}, \\ &\frac{{dN_\textrm{2}^{\textrm{Yb}}}}{{dt}} ={-} ({K_{tr}}{N_1} + A_{21}^{\textrm{Yb}} + R_{21}^{\textrm{Yb}})N_\textrm{2}^{\textrm{Yb}} + R_{\textrm{12}}^{\textrm{Yb}}N_\textrm{1}^{\textrm{Yb}}, \\ &N_\textrm{1}^{\textrm{Yb}} + N_\textrm{2}^{\textrm{Yb}}= {N_{\textrm{Yb}}}, \end{aligned}$$

where ${N_i}({i = 1,2,3,4,5} )$ indicates the populations at the eight levels ⁴I_15/2, ⁴I_13/2, ⁴I_11/2, ⁴I_9/2 and ⁴F_7/2, respectively. Likewise, $N_i^{Yb}({i = 1,2} )$ indicates the populations at the two levels ²F_7/2 and ²F_5/2, respectively. ${K_{\textrm{tr}}}$ is the Yb³⁺-to-Er³⁺ energy-transfer coefficient. ${C_{\textrm{cr}}}$ presents the Er³⁺ cross-relaxation coefficient, while ${C_{24}}$ and ${C_{35}}$ are responsible for the first- and second-order cooperative upconversions, respectively. ${A_{ij}} = {1 / {{\tau _{ij}}}} $ is the decay rate from level i to level j, given by the inverse of the radiative life time (${\tau _{ij}}$). ${R_{ij}} = {{{\sigma _{ij}}I} / {h{\nu _p}}}$ is the transition rate of pump beam from state i to j, where ${\sigma _{ij}}$ is the transition cross section from state i to j. I is the optical intensity, h is Planck’s constant and ${\nu _p}$ is the photon frequency. ${W_{ij}}$ is the transition rate of signal beam from state i to j. ${N_{\textrm{Er}}}$ and ${N_{\textrm{Yb}}}$ represent the total Er³⁺ and Yb³⁺ concentration, respectively.

In the waveguide, the spatial distributions of the signal, pump and ASE can be described with a set of propagation equation given by

(3)$$ \begin{aligned} \frac{{d{P_\textrm{s}}(z )}}{{dz}} &= {P_\textrm{s}}(z ){\Gamma _\textrm{s}}[{{\sigma_{21\textrm{s}}}{N_2}(z )- {\sigma_{\textrm{12s}}}{N_1}(z )} ]- {P_\textrm{s}}(z ){\alpha _{\textrm{0s}}}, \\ \frac{{d{P_\textrm{p}}(z )}}{{dz}} &= {P_\textrm{p}}(z ){\Gamma _\textrm{p}}[{\sigma_{\textrm{21p}}^{\textrm{Yb}}N_2^{\textrm{Yb}}(z )- \sigma_{\textrm{12p}}^{\textrm{Yb}}N_1^{\textrm{Yb}}(z )- {\sigma_{\textrm{13p}}}{N_1}(z )} ]- {P_\textrm{p}}(z ){\alpha _{0\textrm{p}}}, \\ \frac{{dP_{\textrm{ASE}}^\textrm{ + }(z )}}{{dz}} &= P_{\textrm{ASE}}^\textrm{ + }(z ){\Gamma _{\textrm{ASE}}}[{{\sigma_{\textrm{21,ASE}}}{N_2}(z )- {\sigma_{\textrm{12,ASE}}}{N_1}(z )} ]+ mh{\nu _j}\Delta {\nu _j}{\Gamma _{\textrm{ASE}}}{\sigma _{\textrm{21,ASE}}}{N_2}(z )\\ &- P_{\textrm{ASE}}^ + (z ){\alpha _{\textrm{0,ASE}}}, \\ \frac{{dP_{\textrm{ASE}}^\textrm{ - }(z )}}{{dz}} &={-} P_{\textrm{ASE}}^\textrm{ - }(z ){\Gamma _{\textrm{ASE}}}[{{\sigma_{\textrm{21,ASE}}}{N_2}(z )- {\sigma_{\textrm{12,ASE}}}{N_1}(z )} ]- mh{\nu _j}\Delta {\nu _j}{\Gamma _{\textrm{ASE}}}{\sigma _{\textrm{21,ASE}}}{N_2}(z )\\ &+ P_{\textrm{ASE}}^ - (z ){\alpha _{\textrm{0,ASE}}}, \end{aligned}$$

where ${\Gamma _\textrm{s}}$, ${\Gamma _\textrm{p}}$ and ${\Gamma _{\textrm{ASE}}}$ indicates the overlap factors of the signal, pump and ASE respectively. ${\alpha _{\textrm{0s}}}$ and ${\alpha _{\textrm{0p}}}$ are the waveguide background losses for the signal and pump, respectively. m is the number of guided modes propagating at the signal wavelength. The ASE noise can be calculated by discretizing the continuous absorption and emission spectrum of Er³⁺ into M frequency gaps of width $\Delta {\nu _j}$ and center frequency ${\nu _j}({1,2,\ldots ,M} )$. In simulations, the population densities maintain the dynamic equilibrium considered in this system. The modal gain (G) characteristics under uniform doping and steady-state conditions are analyzed by using simulations based on Eqs. (2) and (3), and it is expressed as

(4)$$G = 10\lg \left[ {\frac{{{P_\textrm{s}}(z )}}{{{P_\textrm{s}}(0 )}}} \right] - \alpha$$

where ${P_\textrm{s}}(z )$ and ${P_\textrm{s}}(0 )$ are the output powers of the signal beam excited and not excited by the pump beam, respectively. $\alpha$ is the propagation loss, including absorption loss (${\alpha _\textrm{a}}$), scattering loss (${\alpha _\textrm{s}}$) and bending loss (${\alpha _\textrm{b}}$). ${\alpha _\textrm{s}}$ is proportional to the Er³⁺ absorption cross section (${\sigma _\textrm{a}}$) given by ${\alpha _\textrm{a}} = {\sigma _\textrm{a}}\Gamma {N_{\textrm{Er}}}$, in which ${\sigma _\textrm{a}}$ is the absorption cross-section of Er³⁺ at the signal wavelength (1550 nm) and ${N_{\textrm{Er}}}$ is Er³⁺ concentration. Therefore, the propagation loss of the waveguide experienced by the signal alone can be expressed as

(5)$$\alpha = ({{\alpha_\textrm{a}} + {\alpha_\textrm{s}} + {\alpha_\textrm{b}}} )L$$

where L is the waveguide length and ${\alpha _s}$ is evaluated at 0.9 dB/cm in Ref. [33]. The noise figure (NF) can then be computed by

(6)$$NF = 10\lg \left[ {\frac{1}{{G(z )}} + \frac{{P_{\textrm{ASE}}^\textrm{ + }(z )}}{{G(z )h{\nu_s}\Delta {\nu_s}}}} \right]$$

3.2 Numerical modelling of optical amplification in Er:Yb:Al₂O₃-Si₃N₄ waveguide

Schematic representation of a typical 90° waveguide bend in a rectangular spiral is displayed in Fig. 5(a). With a radius of 300 µm, all bends are identical. Insets indicate the normalized mode profile for the TE-mode. Figure 5(b) shows the bending loss as a function of the radius. As the radius increases, the bending loss decreases exponentially. The bending loss is less than 0.12 dB/cm at the radius greater than 200 µm. When the radius is 300 µm, the bending loss is approximately 0.008 dB/cm. Figure 5(c) compares the propagation loss under different Er³⁺ concentrations according to Eq. (5). The Er³⁺ concentration of 1 × 10²⁰cm^-3, 2 × 10²⁰cm^-3, 3 × 10²⁰cm^-3 and 4 × 10²⁰cm^-3 with the waveguide length of 1 cm correspond to propagation losses of 1.284 dB/cm, 1.668 dB/cm, 2.052 dB/cm and 2.436 dB/cm, respectively.

Fig. 5. Er:Yb:Al₂O₃-Si₃N₄ waveguide loss characterization. (a) Illustration of a typical 90° waveguide bend in a rectangular spiral. Insets show the electric field distribution of TE-mode. (b) Bending loss as a function of the radius for the signal beam at 1550 nm. The inset shows an enlargement of the bending loss for radius from 200 to 300 µm. (c) Propagation loss dependence on waveguide length with Er³⁺ concentration of 1 × 10²⁰cm^-3, 2 × 10²⁰cm^-3, 3 × 10²⁰cm^-3 and 4 × 10²⁰cm^-3.

Download Full Size | PDF

Based on the atomic rate equation and the optical power transmission equation, the gain characteristics of the erbium-ytterbium co-doped optical waveguide amplifier are simulated. The device size, ion doped concentration, signal and pump beam power can be optimized to simplify the fabrication of the actual devices. Table 1 summarizes the parameters used to calculate the gain characteristics.

Table 1. Parameters utilized in simulations of gain in an Er:Yb:Al₂O₃-Si₃N₄ waveguide.

View Table | View all tables in this article

The ratio of Yb³⁺ to Er³⁺ concentration (Yb:Er) is a pivotal factor affecting modal gain of Er:Yb:Al₂O₃-Si₃N₄ waveguide amplifiers. Figure 6(a) shows modal gain versus waveguide length for different Yb:Er ratios with a pump power of 200 mW. A maximum modal gain of 21.5 dB can be obtained in a 2.5 cm long waveguide with Yb:Er of 9:1, which is higher than the peak value of 19 dB with Yb:Er of 1:1, due to the more efficient pump absorption with Yb:Er of 9:1. The modal gain for different Yb:Er ratios decreases slightly by about 2 dB with increasing waveguide length from 2.5 to 5 cm. The reason for this decrease can be attributed to the need for higher pump power in the longer waveguides, not only as a result of the increase in gain medium length but also as a consequence of the decrease in pump efficiency. Figure 6(b) presents the simulated modal gain as functions of the Er³⁺ concentration and the Yb:Er ratio in a 5 cm long waveguide. The modal gain increases and then decreases as the Er³⁺ concentration increases at a fixed Yb:Er ratio. The cause of the decrease is the increase in absorption loss as a consequence of the increase in ion concentration. The modal gain gradually increases as the Yb:Er ratio increases at a fixed Er³⁺ concentration. To be more specific, the highest mode gain of 17 dB is obtained with Er³⁺ concentration of 2 × 10⁻²⁰cm^-3 at Yb:Er of 1:1 and the maximum modal gain of 21 dB is obtained with erbium concentration of 3 × 10⁻²⁰cm^-3 at Yb:Er of 10:1.

Fig. 6. Modal gain characterization of the Er:Yb:Al₂O₃-Si₃N₄ waveguide amplifier for -15 dBm input signal at 1550 nm. (a) Modal gain versus waveguide length for different Yb:Er ratios with Er³⁺ concentration of 3 × 10²⁰cm⁻³. (b) Calculation of modal gain under various Er³⁺ concentrations and Yb:Er ratios.

Download Full Size | PDF

The modal gain in function of the pump power for variable signal powers has also been calculated, as shown in Fig. 7(a). The modal gain reduces from 26.7 to 12 dB as the signal power increases from -20 to -5 dBm. The explanation for this is that when the signal power is small, some of the excited state Er³⁺ are consumed so that the signal beam can be fully amplified over the entire waveguide length, and when the signal power is large, stimulated emissions deplete the excited state Er³⁺, thus reducing the gain. The noise figures at various input signal powers and pump powers for a forward pumping scheme are shown in Fig. 7(b). As the pump power increases from 10 to 22 dBm, the noise figure gradually decreases from >14 dB to 8 dB at 10 dBm input signal power. When the signal power is reduced to -10 dBm, the noise is less than 4 dB as the pump power increases.

Fig. 7. Modal gain and noise figure characterization of the 5 cm long Er:Yb:Al₂O₃-Si₃N₄ waveguide amplifier. (a) Modal gain for signals at 1550 nm doped with 3 × 10²⁰cm⁻³ Er³⁺ concentration at Yb:Er of 10:1. Colored areas indicate mode gain and sources of loss. (b) Noise figure under various pump powers and input powers at 1550 nm.

Download Full Size | PDF

The amplifier has a broad mode gain from 1530 to 1570 nm at small signal powers, with maximum modal gain peaked around 1550 nm, as shown in Fig. 8(a). The modal gain characteristics of the amplifier are further calculated in the 5 cm long waveguide with different Er³⁺ concentrations at Yb:Er of 10:1, and compared with the model neglecting ASE and waveguide loss, as shown in Fig. 8(b) and (c). The modal gain the with consideration of ASE and propagation loss is shown in Fig. 8(b). A maximum modal gain of 36.4 dB can be obtained with Er³⁺ concentration of 3 × 10²⁰cm^-3 at -30 dBm signal power. It can be observed easily that the gain provided by the amplifier decreases with increasing signal powers due to the depletion of excited state Er³⁺ by stimulated emissions resulting from high power signals. In contrast, Fig. 8(c) shows the modal gain up to 48 dB with 4 × 10²⁰cm^-3 Er³⁺ concentration and -30 dBm input signal power, regardless of amplified spontaneous radiation and loss.

Fig. 8. Modal gain performance of the waveguide amplifier at the pump power of 23 dBm. (a) The small signal gain values at different signal wavelengths. (b) Mode gain considering spontaneous emission and propagation loss. The small inset shows the gain at -30 dBm input signal power. (c) Mode gain ignoring ASE and propagation loss.

Download Full Size | PDF

Figure 9 presents the simulated modal gain as functions of the pump power and the waveguide length. An optimized waveguide length of 3 cm can be found for an Er:Yb:Al₂O₃-Si₃N₄ amplifier with Er³⁺ concentration of 3 × 10²⁰cm⁻³ and Yb³⁺ concentration of 3 × 10²¹cm⁻³, capable of providing an optical modal gain exceeding 36 dB and with a power pump of around 23 dBm (∼200 mW). Further increases in modal gain can be achieved by deploying higher pump powers or reducing losses. Nevertheless, the further increase of the waveguide length would not significantly contribute to a higher modal gain, as the signal re-absorption by Er³⁺ can take place in the presence of the pump depletion and attenuation in longer waveguides.

Fig. 9. Calculation of modal gain under various pump powers at 980 nm and different waveguide lengths for -30 dBm input signal at 1550 nm. The red dot denotes the optimized waveguide length and pump power in the Er:Yb:Al₂O₃-Si₃N₄ waveguide amplifier.

Download Full Size | PDF

Table 2 summarizes the latest works on integrated optical amplifiers, including planar amplifiers based on Er-doped waveguide cores or coatings. The Er:Yb:Al₂O₃-Si₃N₄ waveguide amplifier demonstrated in this paper compared with some previous works in terms of the doping concentration, the waveguide length and the gain. The results indicate that the gain of our optimized amplifier exhibits superior gain performance. It is envisaged that our work could provide a guidance for large-scale integration of various active functions on silicon.

Table 2. Comparison with reported on-chip erbium-doped optical waveguide amplifiers.

View Table | View all tables in this article

4. Conclusion

In conclusion, the design of an erbium-ytterbium co-doped alumina amplifier based on the low-loss Si₃N₄ waveguide is elaborately optimized. The optimized height and width for Si₃N₄ are 0.5 µm, 0.4 µm, respectively. And the Er:Yb:Al₂O₃ film thickness is optimized to 0.2 µm. The overlap factors for TE-mode are calculated to be 0.38 and 0.42 at 980 nm and 1550 nm, respectively. What’s more, an accurate and comprehensive theoretical model of the multi-energy system of the erbium-ytterbium co-doped waveguide amplifier is constructed. Rate equations and propagation equations are solved, and the gain characteristics corresponding to different signal powers, pump powers, ion concentrations, and lengths are numerically achieved. The model demonstrates the modal gain up to 36 dB with 3 cm waveguide length when the signal power and the pump power are -30 dBm and 23dBm, Er³⁺ and Yb³⁺ concentration are 3 × 10²⁰cm^-3 and 3 × 10²¹cm^-3, respectively. The combined results reveal that the high-gain erbium-ytterbium co-doped amplifier model provides a theoretical support and guidance for developing monolithic integrated active and passive photonic components based on the Si₃N₄ platform.

Funding

National Key Research and Development Program of China (2020YFB1805801); National Natural Science Foundation of China (No.12034010).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data available from the authors upon reasonable request.

References

1. S. Poole, D. Payne, R. Mears, et al., “Fabrication and characterization of low-loss optical fibers containing rare-earth ions,” J. Lightwave Technol. 4(7), 870–876 (1986). [CrossRef]

2. R. J. Mears, L. Reekie, I. Jauncey, et al., “Low-noise erbium-doped fibre amplifier operating at 1.54 µm,” Electron. Lett. 23(19), 1026–1028 (1987). [CrossRef]

3. J. D. B. Bradley and M. Pollnau, “Erbium-doped integrated waveguide amplifiers and lasers,” Laser Photonics Rev. 5(3), 368–403 (2011). [CrossRef]

4. P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: the previous 20 and the next 20 years,” Opt. Express 26(18), 24190–24239 (2018). [CrossRef]

5. G. Nykolak, M. Haner, P. Becker, et al., “Systems evaluation of an Er/sup 3+/-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5(10), 1185–1187 (1993). [CrossRef]

6. K. Hattori, T. Kitagawa, M. Oguma, et al., “Erbium-doped silica-based waveguide amplifier integrated with a 980/1530 nm WDM coupler,” in Optical Fiber Communication Conference (Optica Publishing Group, 1994), paper FB2.

7. J. Riemensberger, N. Kuznetsov, J. Liu, et al., “A photonic integrated continuous-travelling-wave parametric amplifier,” Nature 612(7938), 56–61 (2022). [CrossRef]

8. J. Liu, G. Huang, R. N. Wang, et al., “High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits,” Nat. Commun. 12(1), 2236 (2021). [CrossRef]

9. D. J. Moss, R. Morandotti, A. L. Gaeta, et al., “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013). [CrossRef]

10. J. S. Levy, A. Gondarenko, M. A. Foster, et al., “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). [CrossRef]

11. S. A. Vázquez-Córdova, M. Dijkstra, E. H. Bernhardi, et al., “Erbium-doped spiral amplifiers with 20 dB of net gain on silicon,” Opt. Express 22(21), 25993–26004 (2014). [CrossRef]

12. J. D. Bradley, M. C. e Silva, M. Gay, et al., “170 Gbit/s transmission in an erbium-doped waveguide amplifier on silicon,” Opt. Express 17(24), 22201–22208 (2009). [CrossRef]

13. A. Z. Subramanian, G. S. Murugan, M. N. Zervas, et al., “High index contrast Er:Ta₂O₅ waveguide amplifier on oxidised silicon,” Opt. Commun. 285(2), 124–127 (2012). [CrossRef]

14. H. C. Frankis, H. M. Mbonde, D. B. Bonneville, et al., “Erbium-doped TeO 2-coated Si 3 N 4 waveguide amplifiers with 5 dB net gain,” Photonics Res. 8(2), 127–134 (2020). [CrossRef]

15. M. Zhang, G. Hu, S. Zhang, et al., “Gain characteristics of the hybrid slot waveguide amplifiers integrated with NaYF₄:Er³⁺ NPs-PMMA covalently linked nanocomposites,” RSC Adv. 10(19), 11148–11155 (2020). [CrossRef]

16. H. Gao, H. Li, G. F. R. Chen, et al., “3D printed and spiral lithographically patterned erbium-doped polymer micro-waveguide amplifiers,” Sci. Rep. 11(1), 21292–21298 (2021). [CrossRef]

17. Y. Liang, J. Zhou, Z. Liu, et al., “A high-gain cladded waveguide amplifier on erbium doped thin-film lithium niobate fabricated using photolithography assisted chemo-mechanical etching,” Nanophotonics 11(5), 1033–1040 (2022). [CrossRef]

18. M. Cai, K. Wu, J. Xiang, et al., “Erbium-Doped Lithium Niobate Thin Film Waveguide Amplifier With 16 dB Internal Net Gain,” IEEE J. Sel. Top. Quantum Electron. 28(3), 1–8 (2022). [CrossRef]

19. J. Zhou, Y. Liang, Z. Liu, et al., “On-chip integrated waveguide amplifiers on Erbium-doped thin film lithium niobate on insulator,” Laser Photonics Rev. 15(8), 2100030 (2021). [CrossRef]

20. X. Yan, Y. Liu, J. Wu, et al., “Integrated spiral waveguide amplifiers on erbium-doped thin-film lithium niobate,” arXiv, arXiv:2105.00214 (2021). [CrossRef]

21. Z. Chen, Q. Xu, K. Zhang, et al., “Efficient erbium-doped thin-film lithium niobate waveguide amplifiers,” Opt. Lett. 46(5), 1161–1164 (2021). [CrossRef]

22. Y. Liu, Z. Qiu, X. Ji, et al., “A photonic integrated circuit-based erbium-doped amplifier,” Science 376(6599), 1309–1313 (2022). [CrossRef]

23. L. Agazzi, J. D. Bradley, M. Dijkstra, et al., “Monolithic integration of erbium-doped amplifiers with silicon-on-insulator waveguides,” Opt. Express 18(26), 27703–27711 (2010). [CrossRef]

24. M. Demirtaş and F. Ay, “High-gain Er³⁺:Al₂O₃ On-chip waveguide amplifiers,” IEEE J. Sel. Top. Quantum Electron. 26(5), 1–8 (2020). [CrossRef]

25. P. G. Kik and A. Polman, “Cooperative upconversion as the gain-limiting factor in Er doped miniature Al₂O₃ optical waveguide amplifiers,” J. Appl. Phys. 93(9), 5008–5012 (2003). [CrossRef]

26. X. Xu, T. Inaba, T. Tsuchizawa, et al., “Low-loss erbium-incorporated rare-earth oxide waveguides on Si with bound states in the continuum and the large optical signal enhancement in them,” Opt. Express 29(25), 41132–41143 (2021). [CrossRef]

27. J. Liu, A. S. Raja, M. H. P. Pfeiffer, et al., “Double inverse nanotapers for efficient light coupling to integrated photonic devices,” Opt. Lett. 43(14), 3200–3203 (2018). [CrossRef]

28. J. Rönn, W. Zhang, A. Autere, et al., “Ultra-high on-chip optical gain in erbium-based hybrid slot waveguides,” Nat. Commun. 10(1), 432 (2019). [CrossRef]

29. J. Mu, M. Dijkstra, J. Korterik, et al., “High-gain waveguide amplifiers in Si₃N₄ technology via double-layer monolithic integration,” Photonics Res. 8(10), 1634–1641 (2020). [CrossRef]

30. T. Chrysostomidis, I. Roumpos, K. Fotiadis, et al., “480 Gbps WDM Transmission Through an Al₂O₃:Er³⁺ Waveguide Amplifier,” J. Lightwave Technol. 40(3), 735–743 (2022). [CrossRef]

31. C. Strohhöfer and A. Polman, “Absorption and emission spectroscopy in Er³⁺-Yb³⁺ doped aluminum oxide waveguides,” Opt. Mater. 21(4), 705–712 (2003). [CrossRef]

32. C. Strohhöfer and A. Polman, “Relationship between gain and Yb³⁺ concentration in Er³⁺–Yb³⁺ doped waveguide amplifiers,” J. Appl. Phys. 90(9), 4314–4320 (2001). [CrossRef]

33. D. B. Bonneville, H. C. Frankis, R. Wang, et al., “Erbium-ytterbium co-doped aluminium oxide waveguide amplifiers fabricated by reactive co-sputtering and wet chemical etching,” Opt. Express 28(20), 30130–30140 (2020). [CrossRef]

34. M. Zhang, J. Yin, Z. Jia, et al., “Gain Characteristics of Polymer Waveguide Amplifiers Based on NaYF₄:Yb³⁺, Er³⁺ Nanocrystals at 0.54 µm Wavelength,” J. Nanosci. Nanotechnol. 16(4), 3564–3569 (2016). [CrossRef]

35. P. Zhou, S. Wang, X. Wang, et al., “High-gain erbium silicate waveguide amplifier and a low-threshold, high-efficiency laser,” Opt. Express 26(13), 16689–16707 (2018). [CrossRef]

36. T. Sun, Y. Fu, X. Zhang, et al., “Gain enhancement of polymer waveguide amplifier based on NaYF₄:Er³⁺, Yb³⁺ nanocrystals using backward pump scheme,” Opt. Commun. 488, 126723 (2021). [CrossRef]

37. M. Zhang, W. Zhang, F. Wang, et al., “High-gain polymer optical waveguide amplifiers based on core-shell NaYF₄/NaLuF₄: Yb³⁺, Er³⁺ NPs-PMMA covalent-linking nanocomposites,” Sci. Rep. 6(1), 36729 (2016). [CrossRef]

38. P. Xiao and B. Wang, “Design of an erbium-doped Al₂O₃ optical waveguide amplifier with on-chip integrated laser pumping source,” Opt. Commun. 508, 127709 (2022). [CrossRef]

39. S. Tao, J. Yan, H. Song, et al., “Modeling and simulation of erbium-ytterbium co-doped optical waveguide amplifiers with dual-wavelength pumping at 980 nm and 1480 nm,” J. Phys. D. Appl. Phys. 56(34), 344003 (2023). [CrossRef]

Parameter	Symbol	Value
Er³⁺ concentration	$N_{Er} (c m^{- 3})$	(1∼4) × 10²⁰	This Work
Yb³⁺ concentration		(1∼4) × 10²¹	This Work
Er³⁺ absorption cross-section (1550 nm)	$σ_{12s} (c m^{2})$	8.95 × 10⁻²¹	[34]
Er³⁺ emission cross-section (1550 nm)	$σ_{21s} (c m^{2})$	9.83 × 10⁻²¹	[34]
Er³⁺ absorption cross-section (980 nm) $N_{Yb} (c m^{- 3})$	$σ_{13p} (c m^{2})$	2.58 × 10⁻²¹	[35]
Yb³⁺ absorption cross-section (980 nm)	$σ_{12p}^{Yb} (c m^{2})$	1.2 × 10⁻²⁰	[35]
Yb³⁺ emission cross-section (980 nm)	$σ_{21p}^{Yb} (c m^{2})$	1.2 × 10⁻²⁰	[35]
ASE absorption cross-section	$σ_{12,ASE} (c m^{2})$	6 × 10⁻²¹	[36]
ASE emission cross-section	$σ_{21,ASE} (c m^{2})$	4 × 10⁻²¹	[36]
Er³⁺ emission lifetime on level ⁴I_13/2	$τ_{21} (ms)$	5	[35]
Er³⁺ non-radiation lifetime on level ⁴I_11/2	$τ_{32} (ms)$	0.1	[35]
Er³⁺ non-radiation lifetime on level ⁴I_9/2	$τ_{43} (μ s)$	1	[35]
Yb³⁺ emission lifetime on level ²F_5/2	$τ_{21}^{Yb} (ms)$	2	[35]
First order cooperative up-conversion coefficient	$C_{24} (c m^{3} s^{- 1})$	4.1 × 10⁻¹⁷	[37]
Second order cooperative up-conversion coefficient	$C_{35} (c m^{3} s^{- 1})$	4.1 × 10⁻¹⁷	[35]
Er³⁺ cross-relaxation coefficient	$C_{cr} (c m^{3} s^{- 1})$	3.4 × 10⁻¹⁶	[37]
Overlap factor of the signal	$Γ_{s}$	0.42	This Work
Overlap factor of the pump	$Γ_{p}$	0.38	This Work
Propagation loss	$α_{0p} (dB/cm)$	nearly 0	This Work

Waveguide materia	Active material	Erbium concentration (cm^-3)	Length (cm)	Gain (dB)	Year	Source
Si₃N₄	Er:Al₂O₃	4.9 × 10²¹	0.025	1.595	2019	[28]
Si₃N₄/Er:Al₂O₃	Er:Al₂O₃	1.65 × 10²⁰	10	18.1	2020	[29]
Er:Yb:Al₂O₃	Er:Yb:Al₂O₃	1.5 × 10²⁰	3	4.3	2020	[33]
Er:LiNbO₃	Er:LiNbO₃	1.9 × 10²⁰	3.6	18	2021	[19]
Si₃N₄/Er:Al₂O₃	Er:Al₂O₃	1.7 × 10²⁰	5.9	8.5	2022	[30]
Si/Er:Al₂O₃	Er:Al₂O₃	2.1 × 10²⁰	20	34	2022	[38]
Er:Yb:Polymer	Er:Yb:Polymer	5 × 10²⁰	7	40.6	2023	[39]
Si₃N₄	Er:Yb:Al₂O₃	3 × 10²⁰	3	35	2023	This Work

Parameter	Symbol	Value
Er³⁺ concentration	$N_{Er} (c m^{- 3})$	(1∼4) × 10²⁰	This Work
Yb³⁺ concentration		(1∼4) × 10²¹	This Work
Er³⁺ absorption cross-section (1550 nm)	$σ_{12s} (c m^{2})$	8.95 × 10⁻²¹	[34]
Er³⁺ emission cross-section (1550 nm)	$σ_{21s} (c m^{2})$	9.83 × 10⁻²¹	[34]
Er³⁺ absorption cross-section (980 nm) $N_{Yb} (c m^{- 3})$	$σ_{13p} (c m^{2})$	2.58 × 10⁻²¹	[35]
Yb³⁺ absorption cross-section (980 nm)	$σ_{12p}^{Yb} (c m^{2})$	1.2 × 10⁻²⁰	[35]
Yb³⁺ emission cross-section (980 nm)	$σ_{21p}^{Yb} (c m^{2})$	1.2 × 10⁻²⁰	[35]
ASE absorption cross-section	$σ_{12,ASE} (c m^{2})$	6 × 10⁻²¹	[36]
ASE emission cross-section	$σ_{21,ASE} (c m^{2})$	4 × 10⁻²¹	[36]
Er³⁺ emission lifetime on level ⁴I_13/2	$τ_{21} (ms)$	5	[35]
Er³⁺ non-radiation lifetime on level ⁴I_11/2	$τ_{32} (ms)$	0.1	[35]
Er³⁺ non-radiation lifetime on level ⁴I_9/2	$τ_{43} (μ s)$	1	[35]
Yb³⁺ emission lifetime on level ²F_5/2	$τ_{21}^{Yb} (ms)$	2	[35]
First order cooperative up-conversion coefficient	$C_{24} (c m^{3} s^{- 1})$	4.1 × 10⁻¹⁷	[37]
Second order cooperative up-conversion coefficient	$C_{35} (c m^{3} s^{- 1})$	4.1 × 10⁻¹⁷	[35]
Er³⁺ cross-relaxation coefficient	$C_{cr} (c m^{3} s^{- 1})$	3.4 × 10⁻¹⁶	[37]
Overlap factor of the signal	$Γ_{s}$	0.42	This Work
Overlap factor of the pump	$Γ_{p}$	0.38	This Work
Propagation loss	$α_{0p} (dB/cm)$	nearly 0	This Work

Waveguide materia	Active material	Erbium concentration (cm^-3)	Length (cm)	Gain (dB)	Year	Source
Si₃N₄	Er:Al₂O₃	4.9 × 10²¹	0.025	1.595	2019	[28]
Si₃N₄/Er:Al₂O₃	Er:Al₂O₃	1.65 × 10²⁰	10	18.1	2020	[29]
Er:Yb:Al₂O₃	Er:Yb:Al₂O₃	1.5 × 10²⁰	3	4.3	2020	[33]
Er:LiNbO₃	Er:LiNbO₃	1.9 × 10²⁰	3.6	18	2021	[19]
Si₃N₄/Er:Al₂O₃	Er:Al₂O₃	1.7 × 10²⁰	5.9	8.5	2022	[30]
Si/Er:Al₂O₃	Er:Al₂O₃	2.1 × 10²⁰	20	34	2022	[38]
Er:Yb:Polymer	Er:Yb:Polymer	5 × 10²⁰	7	40.6	2023	[39]
Si₃N₄	Er:Yb:Al₂O₃	3 × 10²⁰	3	35	2023	This Work

Gain optimization of an erbium-ytterbium co-doped amplifier via a Si₃N₄ photonic platform

Abstract

1. Introduction

2. Structure design and simulation

2.1 Characterization of Er:Yb:Al₂O₃-Si₃N₄ waveguides

2.2 Optimization of Er:Yb:Al₂O₃-Si₃N₄ waveguides

3. Gain performance

3.1 Theoretical models

3.2 Numerical modelling of optical amplification in Er:Yb:Al₂O₃-Si₃N₄ waveguide

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (2)

Equations (6)

Optics Express

Abstract

1. Introduction

2. Structure design and simulation

2.1 Characterization of Er:Yb:Al2O3-Si3N4 waveguides

2.2 Optimization of Er:Yb:Al2O3-Si3N4 waveguides

3. Gain performance

3.1 Theoretical models

3.2 Numerical modelling of optical amplification in Er:Yb:Al2O3-Si3N4 waveguide

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (2)

Equations (6)

Optics Express

2.1 Characterization of Er:Yb:Al₂O₃-Si₃N₄ waveguides

2.2 Optimization of Er:Yb:Al₂O₃-Si₃N₄ waveguides

3.2 Numerical modelling of optical amplification in Er:Yb:Al₂O₃-Si₃N₄ waveguide