Polarization-dependent gain characterization in x-cut LNOI erbium-doped waveguide amplifiers

4.1 Absorption loss under different polarizations

In order to accurately estimate the internal net gain of the EDWA, it is essential to properly evaluate the waveguide loss, mainly including the erbium absorption loss and propagation loss caused by waveguide sidewall roughness. Based on the preceding J–O analysis, TE modes propagating in x-cut Er:LNOI waveguides correspond to two distinct polarization states of the Er³⁺ ions. Due to the anisotropic crystal field, these polarizations exhibit different absorption and emission cross sections, which in turn lead to polarization-dependent absorption losses. The absorption loss α a b s λ due to Er³⁺ is related to the absorption cross section, as described by the following expression [38]:

where Γ λ is the optical mode confinement factor in the Er:LNOI waveguide, N _d is the Er³⁺ concentration in Er:LNOI, and σ a b s λ is the absorption cross section. The absorption loss described above represents the intrinsic absorption, defined under the assumption that all erbium ions remain in the ground state, which corresponds to the case where the signal power is near zero [29]. However, in practical measurements of absorption losses or gain characterization of EDWAs, the input signal power to the erbium-doped waveguides is never zero, and the actual absorption loss will be reduced due to excitation of erbium ions and corresponding depletion of the ground-state population. As a result, the total loss in the EDWA depends not only on the polarization state and signal wavelength but also on the input signal power.

We first characterized the coupling and propagation losses of EDWAs at 1,580 nm using the cut-back method, where the absorption of Er³⁺ ions is negligible [27], [34]. The experimental setup is illustrated in Figure 4(a), mainly consists of a C-band tunable laser source (TSL-550), a polarization controller, and an optical power meter (MPM-210H). This approach was adopted instead of using a ring resonator, since the x-cut Er:LNOI platform is polarization sensitive and a resonator cannot reliably distinguish the losses of α- and π-polarizations. To further minimize the potential influence of residual absorption, the source output power was set to 0 dBm during the measurement.

Figure 4:

Characterization of polarization-dependent absorption loss in the EDWA. (a) Experimental setup for measuring the optical total loss. (b) Measured transmission losses at 1,580 nm for two polarizations with varying waveguide lengths, used to extract facet coupling and propagation losses. (c) Small-signal absorption loss spectra across the entire C-band for two EDWA devices with identical geometry but different TE mode polarization states. (d) The loss versus input power at different wavelengths for both polarization states. (e) Measured absorption and emission cross sections of two polarization states under 1,480 nm pumping, with the uncertainty envelopes derived from the cut-back fitting method.

EDWAs with different lengths but the same polarization were measured on the same chip, ensuring that process variations between chips do not affect the results. Figure 4(b) shows the insertion loss versus waveguide length for both α- and π-polarizations. By linear fitting, the facet coupling losses were determined to be 4.88 ± 0.07 dB and 4.59 ± 0.12 dB per facet, and the propagation losses were 0.29 ± 0.01 dB/cm and 0.28 ± 0.02 dB/cm for the α- and π-polarizations, respectively. The small variations indicate that the extracted losses are highly consistent across waveguides of different lengths. Given that the designed device is capable of supporting both pump and signal wavelengths, the subsequent analysis approximates their facet coupling and propagation losses to be identical. For each polarization state, the fitted average values are employed in the calculations.

Then the absorption loss for each polarization can be obtained by subtracting the propagation loss from the on-chip total loss.

To determine the absorption loss under different polarization states, we performed C-band absorption loss measurement on two EDWAs with identical structures but different TE mode polarization orientations – corresponding to distinct erbium dipole alignments (α-polarization and π-polarization). We controlled the above setup via computer to form a rapid wavelength-sweeping measurement system for measuring the output power of the EDWAs across various signal wavelengths.

Figure 4(c) shows the absorption spectra for both polarization states with the source power set to −30 dBm. It is evident that the α-polarized EDWA exhibits significantly higher loss than the π-polarized one. Further comparison with the σ-polarization in z-cut devices shows that the absorption loss of the α-polarization at the peak wavelength of 1,531 nm is also substantially greater than that of both the σ- and π-polarizations.

To further study the power-dependent saturation behavior, we selected several representative wavelengths and measured the absorption loss as a function of input signal power, as presented in Figure 4(d). As the input power increases, the absorption loss gradually decreases, eventually saturating when approximately half of the erbium ions are excited, at which point the net absorption becomes zero. When the input signal power is as small as −30 dBm, the absorption loss no longer increases, approaching the intrinsic Er³⁺ absorption loss. The reason is that the absorption loss is proportional to the population of Er³⁺ remaining in the ground state when the absorption cross section is significant. As the signal power increases, more ions are excited, resulting in a reduced ground-state population and hence lower absorption loss. At 1,531 nm, the intrinsic absorption loss is 8.03 dB/cm for the α-polarization and 4.40 dB/cm for the π-polarization. At 1,550 nm, the values are 1.87 dB/cm and 1.22 dB/cm, respectively, indicating that the α-polarization consistently exhibits higher absorption loss than the π-polarization.

According to the McCumber’s theory, the absorption cross section and emission cross section obey the fundamental relation [35]:

where T is the temperature, h is the Planck’s constant, k is Boltzmann’s constant, and ε is the excitation energy related to temperature. In this study, T = 300 K and ɛ = 6,517 cm⁻¹, which are consistent with the parameters reported in Ref. [35].

Therefore, based on the saturated absorption spectra of the two polarizations shown in Figure 4(c), we calculated the actual transition strength, absorption cross section, and emission cross section using Eqs. (6), (8), and (10), respectively.

Table 2 presents a comparison between the experimental transition strengths and the theoretical calculations. It can be observed that the transition intensity for α-polarization is larger than that for π-polarization, which is consistent with the theoretical trend. Meanwhile, the experimental values are generally lower than the theoretical ones, which may be attributed to the fact that the measured absorption spectrum does not fully cover the entire transition range. Nevertheless, the deviations between the experimental and theoretical results for both polarizations fall within the error range reported in the literature [30], indicating the validity and reliability of the results.

Figure 4(e) shows the absorption and emission cross sections over the entire C-band, together with their corresponding uncertainties. The uncertainties were evaluated based on the facet and propagation loss variances obtained from the cut-back fitting method. Using standard error propagation, it was found that the uncertainties of the absorption cross sections for both polarizations are below 1.9 × 10⁻²² cm², while those of the emission cross sections are below 1.17 × 10⁻²¹ cm². Particularly around 1,530 nm and 1,550 nm, these uncertainties are negligible.

Moreover, both the absorption and emission cross sections of the α-polarization are consistently larger than those of the π-polarization across the C-band. At the peak wavelength of 1,531 nm, the absorption and emission cross sections of the α-polarization are approximately 1.8 times those of the π-polarization, highlighting the significant polarization-dependent difference. In particular, at 1,550 nm, the σ _abs and σ _em of the α-polarization are 0.50 × 10⁻²⁰ cm² and 0.73 × 10⁻²⁰ cm², respectively, while those of the π-polarization show lower values of 0.33 × 10⁻²⁰ cm² and 0.48 × 10⁻²⁰ cm². The test results show that the absorption cross section at 1,580 nm is nearly zero, which further supports the validity of treating the loss at 1,580 nm as the propagation loss.

The theoretical prediction is consistent with our experimental results and also agrees with previous findings reported in Er³⁺-doped LiNbO₃ bulk crystals [34], [39].

4.2 Signal enhancement and internal net gain

The measured differences in absorption and emission cross sections suggest that the gain performance of the EDWA should also be polarization-dependent. To verify this, we experimentally characterized the gain for both polarization states. First, we fabricated a series of α-polarized and π-polarized EDWAs with varying lengths on the same chip to evaluate the optimal gain length. The experimental setup is shown in Figure 5. The signal light is from a C-band tunable laser and the pump light is from a 1,480 nm laser diode. The pump light and signal light are combined via an input wavelength division multiplexer (WDM) and then coupled into the EDWA chip through the lensed fiber. The output WDM is used to inject backward pump light and extract the amplified signal light, which is then fed into an optical spectrum analyzer (OSA) for spectral measurement. Both signal light and pump light are adjusted to TE₀₀ mode by polarization controllers (PC) to minimize propagation loss. Notably, under 1,480 nm pumping, the entire EDWA becomes uniformly illuminated by green upconversion fluorescence, visually verifying both the active erbium distribution and effective light confinement within the fabricated waveguides.

Figure 5:

Experimental setup to characterize the gain of the EDWA. The digital camera photograph of the excited EDWA chip is shown in the center.

The signal enhancement G _se of the EDWA is quantified by measuring the output signal power difference between the pumped and unpumped states, expressed as:

where P _on and P _off represent the output signal power with and without pumping. This value provides an intuitive representation of the extent of signal enhancement under pumping conditions; however, the internal net gain should be regarded as the primary metric for evaluating actual amplifier performance.

The internal net gain is then obtained by subtracting the total loss from G _se, expressed as:

The net gain calculation method employed in this work is widely adopted for the characterization of erbium-doped lithium niobate waveguide amplifiers [23], [24], [25], [26], [27], [28], [29]. Unless otherwise specified, all gain values discussed herein refer to the on-chip internal net gain.

Figure 6(a) describes the internal net gain versus EDWA length for both polarization states under the same sufficient pump power excitation with a fixed on-chip input signal power of −5 dBm (all power values referenced to on-chip levels). The α-polarized and π-polarized configurations achieve nearly identical maximum net gains of 9.87 dB and 10.04 dB at their respective optimal waveguide lengths of 9.71 cm and 11.71 cm. Furthermore, we investigated the relationship between input signal power and gain characteristics. Figure 6(b) shows the internal net gain and output power as a function of input signal power for both polarization states at their respective optimal waveguide lengths. As the input signal power increases, the population inversion decreases, causing the internal net gain to gradually reduce. At first glance, the gain performance of the two polarization states appears similar, showing no significant polarization-dependent behavior. However, it’s worth noting that waveguide lengths for the α-polarization and π-polarization are different. As a result, their gain per unit length and signal enhancement are not directly equivalent. As shown in Figure 6(c) and (d), with an input signal power of approximately −15 dBm, the α-polarized EDWA exhibits 32.01 dB signal enhancement with 3.3 dB/cm unit gain, while the π-polarized EDWA reaches 25.77 dB signal enhancement with 2.2 dB/cm unit gain. According to the rate equation model, the net absorption rate of the pump and the net stimulated emission rate of the signal are both proportional to the absorption and emission cross sections. Therefore, α-polarization can achieve a higher population inversion within a shorter waveguide length, resulting in a larger gain coefficient than π-polarization and consequently a shorter optimum gain length.

Figure 6:

On-chip gain performance of the EDWA under different polarization states. (a) Internal net gain of α-polarized and π-polarized EDWAs with varying waveguide lengths under a fixed input signal power of −5 dBm at 1,550 nm. (b) Internal net gain and output signal power versus input signal power at 1,550 nm for both polarization states. (c) and (d) Spectra of the output signal power with and without pump at the maximum gain point for (c) α-polarization and (d) π-polarization. Insets show photos of the device with pump applied.

To further investigate the evolution of signal gain with increasing pump power under different polarizations, we measured the gain evolution as a function of on-chip pump power under different input signal power levels at 1,550 nm and conducted model-based analysis using the experimental data.

As shown in Figure 7(a) and (b), the results show that under small-signal conditions, the α polarization, due to its larger stimulated absorption cross section and higher energy transfer up-conversion coefficient, tends to experience insufficient population inversion at high pump power, where the inversion becomes difficult to sustain and saturation occurs earlier, leading to a rapid gain roll-off. In contrast, under high input signal power, the strong signal significantly depletes the excited-state population, which makes the system more dependent on the pump. In this regime, although the α polarization still has a larger stimulated absorption cross section, it can maintain a relatively stable population inversion at high pump powers, and thus does not exhibit the same gain degradation observed in the small-signal regime.

Figure 7:

Amplifier performance under different pump power levels. Measured (scatters) and simulated (curves) internal net gain with respect to the on-chip pump power at three input signal powers for (a) α-polarization and (b) π-polarization; along with the measured on-chip output signal power for (c) α-polarization and (d) π-polarization.

For the π-polarization, due to its relatively smaller stimulated absorption cross section and lower energy transfer up-conversion coefficient, it can maintain a more stable population inversion under small-signal conditions, resulting in smoother gain growth at low to moderate pump powers. However, when the input signal power is high, the signal significantly depletes the inversion, making the system more reliant on strong pumping to replenish the excited-state population. Although the pump power increases, the π-polarization exhibits a relatively smaller absorption cross section for the pump light, and the longer propagation length further reduces the effective pumping efficiency. As a result, even under high pump powers, it is difficult to maintain sufficient population inversion, leading to gain saturation and eventual decline.

Figure 7(c) and (d) shows the on-chip output power as a function of on-chip pump power. At an input signal power of 9.1 dBm, the α-polarized device achieves a maximum on-chip output power of 21.18 mW, and the π-polarized counterpart reaches 17.82 mW. However, based on the observed trend of the output power curves, it can be expected that under increased pump power, α-polarization still has the potential to further enhance output power, exhibiting a higher saturation gain limit. This higher saturation gain limit and pump demand are attributed to a faster inversion depletion rate in the α-polarization, resulting from its larger absolute absorption cross section coupled with stronger excited-state absorption and upconversion.

5.1 Polarization-dependent gain performance and mechanism

The measured absorption and emission cross sections exhibit a pronounced disparity between α- and π-polarizations. At the peak wavelength of 1,531 nm, the cross sections for α-polarization are 1.8 times greater than those for π-polarization. More notably, at the standard telecommunication wavelength of 1,550 nm, the absorption and emission cross sections were quantified as 0.50 × 10⁻²⁰ cm² and 0.73 × 10⁻²⁰ cm² for α-polarization, compared to 0.33 × 10⁻²⁰ cm² and 0.48 × 10⁻²⁰ cm² for π-polarization, respectively.

This substantial difference in cross sections directly leads to divergent amplifier gain performance. The higher cross sections of the α-polarization result in a higher gain coefficient of 3.3 dB/cm, allowing it to achieve optimal amplification in a shorter device length of 9.71 cm. In contrast, the π-polarization, with its lower gain coefficient of 2.2 dB/cm, requires a longer interaction length of 11.71 cm to attain comparable gain levels. Consequently, under high input signal power conditions, the α-polarized amplifier delivers a superior maximum unsaturated output power of 21.18 mW, outperforming the 17.82 mW achieved by the π-polarized device.

These performance discrepancies originate fundamentally from the crystalline anisotropy of the x-cut LNOI substrate, which strongly influences the transition strengths of the Er³⁺ ions. Judd–Ofelt theoretical calculations confirm that the transition strength for α-polarization is significantly higher than that for π-polarization. This directly predicts the larger cross sections observed experimentally and provides a rigorous physical explanation for the enhanced gain and output performance of the α-polarization across the C-band.

5.2 Comparison with conventional z-cut platform

To evaluate the implications of our platform choice, we compare the performance of our x-cut amplifier with the well-established z-cut platform in Table 3. The comparison reveals a clear trade-off: while z-cut EDWAs generally yield higher absolute net gain and output power [24], [25], [26], [28], [29], their performance is largely isotropic. In contrast, the x-cut platform provides a decisive new degree of freedom – polarization-dependent gain – as demonstrated in this work. More importantly, it offers superior electro-optic (EO) and nonlinear optic (NLO) compatibility due to facile access to the dominant r₃₃ and d₃₃ coefficients, which is a fundamental requirement for future densely integrated photonic circuits.

5.3 Advancements beyond prior work on x-cut LNOI

Having contextualized the x-cut platform against the z-cut standard, we now highlight the specific advancements of our work within the emerging field of x-cut Er:LNOI amplifiers.

As summarized in Table 4, pioneering studies by Luo et al. [40] and Xue et al. [27] successfully demonstrated the feasibility of achieving optical gain on this platform. However, their analyses were not designed to resolve the fundamental polarization-dependent characteristics inherent to the x-cut orientation.

Our work provides the first comprehensive, polarization-resolved analysis of transition strength, gain, cross sections, and saturation properties on this platform. This dataset provides the indispensable foundation for designing sophisticated, polarization-aware functional devices on this platform.

5.4 Conclusion and outlook

In summary, this work systematically investigated the polarization-dependent gain characteristics of EDWAs on the x-cut LNOI platform. Guided by J–O theory, we analyzed the variations in Er³⁺ transition strength and rate-equation parameters for different polarizations, revealing the underlying mechanism of how crystal orientation and polarization state affect device performance. Experimental validation confirmed significant differences in absorption/emission cross sections and gain coefficients between α- and π-polarizations, leading to distinct trends in optimal gain length, gain saturation, and output performance. A maximum unsaturated output power of 21.18 mW is achieved under 1,480 nm pumping in a 9.71 cm-long α-polarized EDWA, indicating the potential for even higher output power with increased pump power. This study provides the first comprehensive insight into polarization-selective amplification in x-cut Er:LNOI and establishes both theoretical and experimental foundations for designing efficient, fully integrated EDWAs, paving the way for large-scale photonic integration on a unified photonic platform.