Unifying optical gain and electro-optical dynamics in Er-doped thin-film lithium niobate platform

Domain: physics
Published: 2025-11-25
Editorial outcome: major_revision

Abstract
Modulation and amplification are two fundamental processes in optoelectronics. While discrete implementations have achieved widespread success, the challenge of monolithically integrating sufficient gain and electro-optic bandwidth remains a significant barrier, limiting optical systems’ miniaturization and scalability. We unify these two functions in the Er-doped thin-film lithium niobate (Er:TFLN) platform, achieving a record-high internal net gain of 38 dB in a 9.16-cm-long waveguide amplifier. Meanwhile, leveraging the host material’s strong Pockels effect, we realize ultra-wide-range electro-optic modulation with a bandwidth of 53 GHz and operation up to 170 GHz, fabricated alongside waveguide amplifiers using a zero-change process. Additionally, we validate this functional fusion through two signal processing scenarios: self-amplified digital signal encoding and pre-amplified broadband radio frequency front-end receiving, demonstrating improved signal recovery quality compared to off-chip gain. The modulation-amplification integration holds broad potential for increasing system complexity and network depth in applications such as optical interconnections, Lidar, and microwave photonics.

Introduction
Photonic integrated circuits hold immense potential for advancing modern infrastructure, from telecommunications to high-performance computing1. The integration of multiple functions on a single chip enables far greater system complexity and density compared to conventional bulk optics, as demonstrated in parallel optical interconnections2–6, optical phased arrays7–9, and optical computing engines10–12. However, large-scale optical system integration has primarily focused on the high-volume deployment of passive devices (e.g. optical I/O8, filters12–14, and interferometers11), while incorporating only a limited number of lossy active electro-optic (EO) devices to preserve a sufficient signal-to-noise ratio. Additionally, these systems are typically configured in parallel to prevent loss-induced level-by-level degradation10. These constraints limit on-chip data throughput and challenge the realization of high-depth on-chip networks for powerful and versatile system operation.

To mitigate link loss and address the bandwidth demands of on-chip optical systems, the monolithic integration of two fundamental functions-high optical gain and high-speed modulation-is essential on a photonic chip. Generally, to maximize the performance of different functions, appropriate material systems are selected individually based on their inherent characteristics15. For instance, III-V semiconductor optical amplifiers (SOAs)16–19 or rare-earth-doped waveguides with various host materials20–27 are used to generate optical gain, while materials with a strong Pockels effect28 or free-carrier dispersion29 are preferred for EO conversion. The combination of these two functions, however, continues to pose significant challenges in terms of both material properties and process complexity. Although Er-doped waveguide amplifiers with an internal net gain exceeding 30 dB, comparable to commercial standards, have been demonstrated on the SiN platform24 and Al2O3 platform26, the passive nature of these platforms impedes further monolithic manipulation of EO conversion. Combining amplification and modulation functions has been previously achieved on the III-V-silicon hybrid platform30, but additional fabrication processes, such as epitaxial regrowth, are required to integrate III-V functional layers with varying bandgaps, increasing both fabrication complexity and manufacturing difficulty. Furthermore, these systems still face challenges, including relatively high waveguide loss, inherent amplification noise, and signal distortion caused by nonlinear gain process in III-V material and nonlinear EO conversion in silicon-based systems17–19,31, which limits performance, especially in applications that demand high fidelity and low crosstalk.

In order to embed the amplification function into high-speed opto-electrical circuitry, Erbium-doped lithium niobate is a promising alternative. Compared to previous host materials (such as SiN, Al2O3) lacking fundamental properties and functions (such as Pockels effect for EO modulation or second-order optical nonlinearity), lithium niobate distinguishes itself through its diverse optical properties, including high refractive index contrast and pronounced EO effect32. Early explorations of combining optical gain and electro-optic effects in lithium niobate were reported in bulk platforms33. Recent breakthroughs in thin-film lithium niobate (TFLN) technology further enables stronger optical confinement and higher EO bandwidth compared to its bulk counterpart33. First developed in 2021, the Erbium-doped lithium niobate (Er:TFLN) waveguide amplifier already shows its potential for small signal enhancement34,35. However, the internal net gain and saturated output optical power have not yet simultaneously reached the ideal performance level36–38. More importantly, the study of EO dynamics in Er:TFLN still remains elusive, despite its host material, TFLN having achieved significant success in both high-frequency functionality and system implementations28,39.

In this work, we unify the ultra-high optical gain and sufficient electro-optical modulation capability on an Er:TFLN platform for the first time (Fig. 1). By employing a multimode waveguide design, the fabrication-induced background loss is reduced to 0.4 dB/cm. Leveraging the low background loss and optimized doping density, we achieve a significant improvement of the internal net gain as high as 38 dB in a compact 9.16-cm-long amplifier. The proposed amplifier also presents an on-chip saturated output power of over 14 dBm and a low noise figure of 4.7 dB. To the best of our knowledge, this is the highest internal net gain reported for integrated amplifiers, with critical parameters matching the performance of commercial erbium-doped fiber amplifiers (EDFAs). Meanwhile, we integrate a high-speed electro-optic modulator with the Er-doped amplifier for the first time, using a zero-change process that preserves the waveguide amplifier fabrication, achieving efficient electro-optical dynamics with a bandwidth of 53 GHz while maintaining high optical gain. Moreover, by using this monolithically integrated modulation-amplification function, both on-chip digital and analog signal processing are performed losslessly. The self-amplified Er:TFLN modulator performs a 50 Gbps signal transmission and a pre-amplified chip-based radio frequency (RF) front-end receives a frequency-chirped signal from 8 to 12 GHz. With the on-chip amplification scheme, the signal-to-noise ratio (SNR) degradation of the recovered signal is mitigated, resulting in an improvement compared to using an EDFA. Through modulation-amplification integration, our work unlocks promising prospects for integrated photonics, with the potential to enable more advanced functional modules, such as tunable and mode-locked lasers, while also facilitating deeper on-chip photonic networks due to enhanced signal integrity.

Results
Multifunctional co-design and basic performance
To unify optical amplification and electro-optical modulation, a carefully designed structure is developed to achieve a balanced performance for both functionalities in Er:TFLN. For optical amplification, the underlying process involves light-matter interactions, namely the stimulated absorption of pump light and the stimulated emission for signal light in Er3+ ions40. The Er3+ ion is doped during the crystal growing process (See Supplementary Note 2). Figure 2a depicts the photoluminescence (PL) spectrum of the Er:TFLN, exhibiting amplified photon emission via stimulated emission from Er3+ ions across 1520 to 1570 nm and a notable peak emerges around 1531.7 nm, with two minor peaks observed at 1543 nm and 1550 nm. The photoluminescence lifetime is measured to be 5.8 ms (See Supplementary Note 5), which indicates an ideal doping condition, comparable to the typical value in the commercial EDFA (@ 10 ms41).

For efficient amplifiers in the integrated Er:TFLN platform, the background loss, especially the scattering loss, emerges as the primary limiting factor compared with their fiber-based competitor. Integrated waveguides typically exhibit orders of magnitude higher propagation loss compared with fibers, leading to higher loss of pump light and decreased net gain of signal light. To suppress the scattering loss, we implement a 3-μm width × 600-nm height multimode waveguide to decrease the interaction between the optical field and the etched sidewalls. Meanwhile, the multimode waveguides with larger mode area could provide higher gain and saturation power42. Another loss factor is from the bending region, limiting the minimum bending radius and the compactness. Different from the ridge waveguide in previous work, with relatively large bending radii of about several hundreds of μm to ensure pure single mode propagation over long delay lines35,37, the optical amplifier is formed by strip waveguide with a fully-etching process, as shown in Fig. 1b. The strip waveguide supports a tighter light confinement for small bend radius and small waveguide gaps for compact structures. Figure 1c shows a bend region of a square spiral. The gap between adjacent waveguide is set to 7 μm with negligible coupling. The minimal bend radius is set to 170 μm. The adiabatic bend design is adopted here43 for quasi-single-mode transmission with compact size. For more details about amplifiers design, see Supplementary Note 1. Figure 2b shows the measured loss of amplifiers with different lengths with the off-chip input signal power of 30 μW. The background loss coefficient is estimated as 0.4 dB/cm by linearly fitting the total losses of different waveguide lengths at 1600 nm, where the absorption of Er3+ ions is ignorable (See Supplementary Note 3). The coupling loss is estimated as the average of intercepts at different wavelengths, which is ~6.7 dB/facet.

Based on the developed amplifier, the electro-optical modulation functionality is integrated using a traveling wave electrode patterned on a 900-nm-thick gold (Au) layer. Instead of the conventional design with the electrode coplanar to the waveguide, we position the electrode above the the waveguide by depositing a oxide layer, as shown in Fig. 1d. This design reduces optical propagation losses by minimizing the interaction between the light field and the electrode44. Simultaneously, microwave losses are reduced by distancing the microwave field from the Silicon substrate with high index. Figure 2c illustrates the relationship between the simulated optical and microwave propagation losses as a function of the thickness of the oxide layer between the electrode and the waveguide. It shows that as the thickness of the oxide layer between the substrate and the electrode is ⩾1 μm, both optical loss and microwave loss are maintained at low levels. Figure 2d presents the simulated VπL of single-drive modulation under different oxide layer thicknesses and electrode gaps45. As the electrode spacing increases, the interaction between the applied electrical field and the optical field decreases. To ensure low levels of optical and microwave losses while achieving high modulation efficiency, the electrode gap and oxide layer thickness are set to 3.5 μm and 1 μm, respectively. Figure 1e shows a photo of a phase modulator with 8-mm-long electrode. The carrier-to-first sideband (FSB) intensity equalization technique31 is used to determine the half-wave voltage. As depicted in Fig. 2e, when the peak-to-peak voltage Vm of the applied radio frequency field reaches 8 V, the modulated spectrum exhibits equal intensities between the carrier and the first sidebands. The modulation efficiency can be then estimated as L Vm/0.457, yielding 3.1 V·cm for push pull modulation (See Supplementary Note 9).

High-gain optical amplification
Benefiting from the low background loss coefficient, the designed amplifier features an impressive amplification performance. In experiment, a continuous-wave laser at 1531.7 nm is used as the signal light to access the gain factor. To maximize the amplifying performance, the bidirectional pumping scheme24 is adopted here, with the experimental setup depicted in Fig. 3a. A pump laser at 1480 nm is employed, which is equally split and injected into the waveguide amplifier from both facets. To accurately extract the gain performance, the powers of output and input signal are directly measured and compared in the spectra recorded by an optical spectrum analyzer (OSA), where the pump power interference can be eliminated due to the inherent wavelength selectivity of the OSA. The internal net gain is thereby obtained from the fiber-to-fiber power difference, meanwhile considering the coupling loss and the insertion loss from the fiber-based measurement link (e.g., the wavelength division multiplexer).

To evaluate the amplification, the internal net gain with the varying pump power under a small input signal (off-chip −39.6 dBm) is measured, as shown in Fig. 3b. The gain factor increases much slower with the pump power, as the pump power >80 mW compared with that in the low pump power region (0~20 mW). Significantly, the highest on-chip net gain under 115 mW off-chip pump power is around 38 dB at 1531.7 nm (with the consideration of 2.9 dB fiber link loss and 6.7 dB/facet coupling loss, as shown in Fig. 3b) in the 9.16 cm waveguide amplifier, corresponding to an average gain of 4.1 dB/cm. The gain spectrum is depicted in Fig. 3d by estimating gain factors at different signal wavelengths. For most of the band from 1530 nm to 1565 nm, the gain factor is above 20 dB. The achieved gain factor not only rivals that of commercial EDFAs but also represents the highest internal net gain reported to date for waveguide-based amplifiers (See Supplementary Note 8). Higher pump power of larger than 115 mW could further increase the gain before saturation, while the measurement of such performance is presently affected by the parasitic lasing24, resulting from the internal reflection between the chip facets (See Supplementary Note 7).

The saturation output power is another essential property for practical systems-level deployments, representing the maximum output capacity of the amplifier. For the waveguide amplifier, the gain factor should decrease as the increasing input signal power due to the gain saturation, under a fixed pump power. The on-chip saturation output power of the waveguide amplifier is defined as the on-chip signal power at which the internal net gain is equal to zero. Figure 3e illustrates the off-chip amplified signal on the OSA with a peak power of 5.9 dBm, as the off-chip input signal power is −1.0 dBm, where an ultra-high signal enhancement of 69.6 dB is evidenced. Considering the coupling loss and the off-chip link loss, the internal net gain is still over 23 dB. This result implies that the on-chip saturation output power greatly exceeds 14 dBm. Figure 3e is also utilized for extracting the noise figure, an essential factor for assessing signal-noise ratio degradation, based on the optical source subtraction method (See Methods)41. The noise figure is measured to be 4.7 dB, closed to that of a commercial EDFA.

Broadband electro-optic conversion
With the designed modulation region on the high-gain optical amplifier, we present, to the best of our knowledge, the first demonstration of broadband modulation characteristics on Er:TFLN through pump on/off experiments to validate high-fidelity signal integrity. Figure 4a shows a photo of an intensity modulator based on the Mach–Zehnder interferometer with the electrode length of 8 mm. The signal light is injected from the left side, while the pump light is injected from both sides, as done during the gain characterization process. The RF field is applied on the electrodes from the same side as the signal (See Supplementary Note 11). As the signal light passes through the modulation region, it is modulated and amplified simultaneously. Figure 4c displays the measured EO responses with and without the pump light, where the 3-dB bandwidth is measured as 53 GHz (with pump). Notably, the amplification provides a 6 dB enhancement of the modulated signal without degrading the modulation process. To further prove the unity of amplification and modulation, a digital signal transmission experiment is performed using a high-speed on-off keying (OOK) signal of 50 Gbps applied to the signal light. Figure 4d, e show the detected signal with and without the pump light. With amplification, the higher EO response results in a clearer eye diagram due to partial loss compensation of the measurement link, improving subsequent digital signal extraction and processing.

The above EO response enhancement is limited by the device length of 8 mm. To boost the enhancement with the high-gain amplifier, an amplifier of a 6-cm-long spiral is added after the modulation region, as depicted in Fig. 4b. Two electrodes are positioned on both sides of the straight waveguide to form a phase modulator. Unlike the intensity modulator, it is difficult to directly measure the EO response profile for a phase modulator. Instead, the optical spectra with and without the pump light are given in Fig. 4g–j, as the applied RF signal tuned from 20 GHz to 170 GHz. With the extended optical amplifier, the optical signal enhancement is ~30 dB. As the modulation frequency increases, the power difference between the modulated sideband and the optical carrier decreases from −20 dB to −38 dB due to the reduced EO response at high frequencies. Detailed EO response measurements of the phase modulator from 10 GHz to 170 GHz are provided in Supplementary Note 11.

Analog radio frequency (RF) receiving with pre-amplification
To verify the capability of Er:TFLN in real-world applications, the developed chip with both amplification and modulation is used for analog RF receiving system. The schematic is shown in Fig. 5a and detailed experimental setups are given in Supplementary Note 12. A frequency modulated continuous wave (FMCW), chirped between 8 GHz and 12 GHz at a repetition rate of 800 kHz, is applied to the phase modulator, acting as an RF signal to be received. The FMCW signal is loaded on the optical carrier and amplified through the developed modulator and amplifier. After the Er:TFLN chip, a band pass filter (BPF) is employed to suppress the lower sideband, converting the phase-modulated signal to an intensity-modulated signal. The filtered optical signal is detected by a photodetector, converting it back into an RF signal. The detected RF signal is recorded in the frequency domain (depicted in Fig. 5b–d) with an electric signal analyzer and in the time domain with an oscilloscope. Using the short-time Fourier transform, the spectra are recorded, revealing the instantaneous frequency chirping over time, as shown in Fig. 5e–g.

When the input signal light is at 1600 nm without the pump light, the on-chip loss decreases the optical power to −15.0 dBm, resulting in a detected SNR of less than 9 dB, as depicted in Fig. 5b. The low SNR prevents the extraction of the instantaneous frequency. With the pump light, the output signal at 1550 nm is boosted to −4.2 dBm, resulting in a SNR of 30 dB. A clear FMCW signal can be recovered, as shown in Fig. 5f. For comparison, an undoped TFLN phase modulator is adopted to receive the same RF signal and then amplified by a commercial EDFA. The RF power, input optical power and amplified power level are set the same as the previous setup. The recovered RF signal in this configuration shows an SNR of 22 dB. Interestingly, the proposed approach can recover the signal with an increase in SNR than utilizing conventional fiber optics. This can be attributed to the position of the amplifier in the system, besides the difference in insertion loss. When using the on-chip amplifier with the pump light, the signal is modulated and amplified simultaneously, allowing the signal to maintain a high power level with low amplifier noise. In contrast, the EDFA amplification occurs after significant insertion loss from the undoped TFLN chip, which degrades the modulated signal and makes it drown into background noise. Although the EDFA can boost the weakened optical signal, the low input power results in a higher level of amplified spontaneous emission noise.

Methods
Fabrication process
The Er:LN is formed with the erbium oxide doping during the growth of the LN crystal, ensuring uniform Er3+ ion distribution60. A 3-inch Er:LN wafer is exfoliated and transformed onto the silicon dioxide substrate, resulting in the Er:TFLN. Then, the wafer is patterned using electron beam lithography (EBL) and etched via inductively coupled plasma-reactive ion etching (ICP-RIE)61,62 or EBL. A SiO2 layer is deposited as protection. Without changing the aforementioned fabrication process, a 900-nm-thick Au layer is deposited on the SiO2 surface by electron beam evaporation (EBE). Finally, the electrodes are formed using the lift-off method.

Loss rate calculation
The loss rate is measured by the intercept method. Without the pump light, the optical powers are measured at two points: before the input of the waveguide amplifier and after the output. The difference between these two power measurements is referred to as the total loss (IL), which includes coupling loss (Lc), waveguide background loss (Lb), and waveguide absorption loss (La). The relation between the absorption loss and the length of the amplifier can be expressed as:
La=α(λ)·l (1)
where λ is the wavelength of the signal light and α denotes the absorption loss rate which is the function of λ. Similarly, considering the scattering loss as the primary contribution to the Lb, the relation between Lb and l can be expressed as:
Lb=s·l (2)
where s indicates the scattering loss rate. Thus, IL can be expressed as:
IL=[α(λ)+s]·l+Lc (3)

Photoluminescence spectrum measurement
The photoluminescence (PL) spectrum was acquired using a fluorescence spectrometer (MicroSpec IR) equipped with a long-pass optical filter (Thorlabs FELH1500; cut-on wavelength: 1500 nm). The sample was pumped by a 1480 nm laser source (PSU-III-LED1480). The added optical filter suppressed residual pump scattering at 1480 nm, ensuring signal fidelity below 1500 nm.

Internal net gain calculation
The internal net gain refers specifically to the on-chip optical power amplification within the Er:TFLN waveguide itself, calculated by accounting for all passive losses except input/output coupling. This value represents the pure amplification within the waveguide, excluding coupling losses and link loss. It is defined as:
Gnet = (Pout(off-chip) - Pin(off-chip)) + Lcoupling + Llink (4)
where Pout(off-chip) is the optical power measured after the chip (e.g., −17.6 dBm at 1531.6 nm in Fig. 3b), Pin(off-chip) is the input power launched into the chip (e.g., −39.6 dBm in Fig. 3b), Lcoupling is the total input/output fiber-chip coupling loss with a value of 13.4 dB, Llink is the insertion loss of the fiber links and devices (mainly induced by the wavelength division multiplexers) amounting to 2.9 dB.

Amplification measurement
In experiment of internal net gain and saturation output power test, a continuous-wave laser (EXFO T100S-HP) at 1531.7 nm is used as the signal light to access the gain factor. To maximize the amplifying performance, we use the bidirectional pumping scheme. A 1480 pump laser (PSU-III-LED1480) is equally split and injected into the waveguide amplifier from both facets. Meanwhile, the polarization and the power of the signal light is controlled through a polarization controller (Thorlabs FPC560) and an optical attenuator (Thorlabs V1550A). To accurately extract the gain performance, the powers of output and input signal are directly measured and compared in the spectra recorded by OSA (YOKOGAWA AQ6370C), where the pump power interference can be eliminated due to the inherent wavelength selectivity of the optical spectrum analyzer.

Noise figure extraction
The noise figure is measured by optical source subtraction method41, which can remove the source spontaneous emission (SSE) noise from the total noise emitted by the erbium amplifier. An optical spectrum analyzer is employed to capture the spectra of both the input signal light and the amplified signal light. The optical gain G at the optical frequency v, the noise power of the input light (PSSE), and the output power (Pout) within an optical bandwidth (B0) are determined from the obtained optical spectra. The noise figure follows the expression:
NF = Pout - GP SSE + 1 / GhvB0 (5)
To avoid overestimating the noise figure, the OSA resolution bandwidth is set to the finest value of 0.02 nm. Because the OSA sensitivity limits the noise power extraction under low signal powers, the noise property is characterized under a high-power input signal as a representative example. From the power difference at the signal wavelength (Fig. 3e), an off-chip optical net gain is calculated as 6.9 dB. The noise powers, recorded as Pout=−53.5 dBm and PSSE=−80.1 dBm within the resolution bandwidth of the OSA, are determined from the noise floors measured at wavelengths 0.3 nm distant from the signal peak. Substituting the measured results into the Eq. (5) yields a noise figure of 4.7 dB.

Modulation measurement
For the bandwidth test, a vector network analyzer (Keysight PNA-X Network Analyzer N5247B) with its plug-in 67-GHz lightwave component analyzer (Keysight LCA Optical Receiver N4372E) is used to measure the EO S21 transmission. In the data transmission experiments, the high-speed OOK signal with a standard pseudo-random binary sequence (PRBS) pattern is generated by a bit pattern generator (SHF12104A). The signals are amplified by a commercial driver (SHF S807C) which Vpp=2 V and then injected into the modulator, working under the push-pull configuration. At the receiving end, a 50 GHz photodiode (PD, Coherent HPDV2120R) is used to receive the optical signal. Digitized data are collected using an 80-GSa/s real-time oscilloscope with an analogue bandwidth of 62 GHz (Keysight DSA-X 96204Q). More details about the experimental setup are given in Supplementary Note 10.

For the amplification experiment with broadband modulation, the RF generator (Keysight N5222B+N5292A) loads signals ranging from 10 GHz to 110 GHz onto the modulator and the modulated spectra are recorded with a OSA (YOKOGAWA AQ6370C). For higher frequency signals (110–170 GHz), a frequency multiplier (SGFE06) is used to up-convert the signal frequency generated by KEYSIGHT E8257D before it is applied to the modulator (See Supplementary Note 11).

For the signal modulation and amplification test, the Arbitrary Waveform Generator (AWG, Micram Instruments 10002) generates a 200 mV chirped signal ranging from 8 GHz to 12 GHz. The EDFA (AEDFA-PA-35-B-FA) is used to compare with the developed EDWA. (See Supplementary Note 12).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The work demonstrates optical gain and intensity and phase modulation in erbium-doped thin film lithium niobate waveguides. High gain is shown at 1531nm (38 dB) and low noise figure (4.3 dB). RF operation up to 170 GHz is shown, including demonstrations of broadband electro-optic conversion and analog RF receiving with an 8-12 GHz FMCW signal, both using an amplified on-chip waveguide. The combination of high gain with low noise and high-speed electro-optic modulation on a monolithic thin film lithium niobate chip is novel and of interest to the integrated photonics community. Below are some comments to be addressed:\n- The prior art has not been fully addressed, specifically bulk lithium niobate chips. See the work of Sohler et al., (for example Suche et al., IEEE Photonics Technology Letters 7, 505, 1995, where phase modulation and erbium gain are both shown on a lithium niobate chip). It is also suggested to change the title accordingly, e.g. specifically referring to thin film lithium niobate, or LNOI.\n- The doping is quite high and might introduce extra background loss. How does the loss compare to undoped LNOI MM waveguides?\n- Why is the coupling loss so high? Can’t inverse tapers be used to get significantly lower coupling loss?\n- Fig. 3b is missing the pump/no signal spectrum (i.e. ASE) to properly assess the gain and proper pump background/ASE in the gain calculation\n- It shows that an optimal balance is achieved with low optical loss and minimal microwave loss as the oxide layer thickness is set to 1 μm -> is this true? Isn’t it a bit better at > 1µm?\n- Page 5: “Highest gain…” The gain is impressive but highly wavelength dependent (as shown in Fig. 3c). Most applications (WDM systems, tunable lasers, etc.) require amplification over a broad wavlength range. A better wording might be highest single wavelength gain. Table 1 in the supplementary material should also include the wavelength the gain is measured at and pump wavelength for better comparison. More importantly, the high gain in this system at the peak emission wavelength should be justified. Is this typical for lithium niobate? If so, why? Under 1480nm in-band pumping of Er, the inversion is lower and the gain is usually flatter. See for example ref [24] where the gain is lower near 1530nm.\n- Page 5: it is stated that the gain saturates, but higher pump power could provide more gain which seems to be contradictory\n- More details on the parasitic lasing, at what pump powerand gain it sets in, etc. should be provided.\n- The saturation output power of the waveguide amplifier…on-chip signal power.” This statement seems to be describing external stauration, so the on-chip part is confusing in the explanation.\n- Fig. 5: What is the 100 kHz showing in the inset of Fig. 5a. This should be stated in the caption. There are several sidebands in Fig. b that should be explained, especially in terms of the levels indicated in the SNR measurements. It should also be stated and/or shown where the EDFA is in the setup figure.\n- The lifetime is compared to commercial silica fiber amplifiers, but what about lithium niobate? Is the lifetime similar to prior lithium niobate measurements and what is expected in theory for this host? The higher n host would typically lead to a shorter lifetime.\n- The noise figure measurement needs more justification: Was the noise figure measurement qualified with a commercial amplifier? This should be stated to ensure the method is accurate here. The measurement of noise 0.4 nm from the peak would seem to underestimate the noise figure, given ASE would be strongest at the peak where the gain is measured.\n- The cross-sections in Fig. S5 look abnormal and perhaps mixed up in the legend. The shape seems strange particularly compared to the gain with 3 peaks in Fig. 3c (and see gain spectra with 3 peaks in Brinkman IEEE Journal of Quantum Electronics 30, 2356, 1994). It looks like the blue cross section is not tending to 0 around 1600nm as expected from the gain measurement and there is perhaps a systematic DC offset due to the measurement method.\n- Conclusion:\no highest gain should be qualified as single wavelength\no again details of the parasitic lasing are mentioend but not explained\no 1400nm – Nd, is 1.3um band meant? And has gain been shown in Dy-doped lithium niobate? (normally specialized low phonon host materials are required)\no slow light -> what about the high losses usually associated with such waveguides, which would affect the gain?\n- Some additional details would help in a several places", "reviewer_including": "no Providing the typical bend radius of ridge lithium niobate waveuigde in the text for easy comparison\no What is the signal and pump polarization used? What is the polarization dependent (TE vs. TM) loss and gain?\no Page 3: distancing the microwave field from the high index layer – lithium niobate? Why?\no What are the fits in Fig. 3? (should state in caption). Also, high input signal power -> state power\no Page 6: a signal enhancement of 30 dB is given but what is the gain?\n- Formatting:\no Figure 1 is somewhat redundant, and doesn’t add much to what is already shown in the other panels. It is suggested to remove it or to improve the overall presentation by adding it as a part a panel in figure 1 (the current part a figures can be shifted to the right).\no Parts i – iv are listed out of order in fig. 2\no “Mod.” short form unnecessary in Fig. 4/caption\n- The wording should be adjusted in some places to adhere to normal scientific style, examples are below:\no “impressive performance” in abstract\no “electro-optic operation” in abstract – be specific\no “unprecedented” in abstract\no Page 3: fatal blocks\no Page 3: indidcating additional loss of pump light\no Page 3: Delicate adiabatic\no Fig. 3 caption: intensely pumped\no Page 4: which is intutitve -> remove\no Generally, the net gain dynamically changes… -> too general/obvious – consider rewording\no Page 6: delicately\no Etc.\n- The manuscript requires another careful check of English, some examples are below:\no Fig. 2 caption: an sine wave\no Page 3: is adopt\no Fig. 3 caption: Optical spectra of signals output\no Page 4: As the electrode apart\no Page 4: A optical spectrum analyzer\no Page 7: analogy RF\no continuous wave (FMCW) -> word missing\no in frequency domain\no the spectroscopy is obtained\no the increasement\no Etc.", "reviewer_2": "Dear Authors,\nDear Editor,\nI have carefully read and analyzed the paper titled “Unifying Optical Gain and Electro-Optical Dynamics in Er-doped Lithium Niobate Platform” and the supplementary information provided with the manuscript.\nThe authors describe in detail the fabrication, design, and characterization of a photonic chip that utilizes a thin-film erbium-doped lithium niobate layer. The photonic chip contains both an amplitude modulator used for on-off keying (with a length of 8 mm) and a phase modulator used for FMCW style modulation, combined with a 6 cm long amplifier spiral. In figure 2, the modulator design is discussed together with a photoluminescence spectrum from the waveguide. In figure 3, the amplification of a single laser line is presented and discussed. In figure 4, the authors present the modulator devices together with the results of a 50 Gbps on-off keying system experiment. It also includes optical spectra of a high-RF-frequency phase-modulated optical carrier. Finally, in figure 5, the modulation of a laser line with an FMCW signal is presented. In the discussion, ways for further improvement of the performance metrics are given and possible future applications are presented. In the supplementary information, the authors present additional technical details on the measurements they performed and the simulations that were used for the device design.\nThe results presented in the paper are interesting and highly relevant given the fast-moving field of photonic integration, with many recent advances in both thin-film lithium niobate and rare-earth doped waveguides. Moreover, the figures that present the results are highly detailed and very well thought through, with great attention to visual clarity. In general, the paper presents interesting results with excellent graphics.\nMy main comment is that the writing is sometimes not fully clear, and in many sentences, hard-to-understand phrasing is used. I would recommend that the authors try to rewrite the text to improve this issue. Some examples of the language issues:\nPage 3: Fig. 2. a(iii) “Pseudo color picture images…” — it is my understanding that this is a false-color SEM image?\nPage 3: “… is the most fatal blocks compared with…”\nPage 3: “… height of 600 nm is adopt to decrease …”\nPage 3: “…waveguide with a fully-etch process…”\nMoreover, in general, I would comment that the way the text is written can be improved to make the technical results clearer.\nI would recommend the manuscript for publication with several, in my opinion mandatory", "reviewer_improvements": "n1. Can the authors clarify why this electrode geometry was chosen exactly? If I understand correctly, the lithium niobate modulators realized in 2018 had a much smaller VpiL (see for example https://doi.org/10.1038/s41586-018-0551-y).\n2. Given that the performance of the amplifier relies also on the in- and outcoupling, can the authors comment on why facets with relatively high losses were used?\n3. What are PC fibers? (Fig. 3 a)\n4. Please clarify what you mean exactly by net internal gain when you first introduce the term in the text. What exactly does this include and exclude?\n5. In most of the experiments, measurements are performed with and without pump. It is sometimes unclear to me what conclusions can be taken from this. As erbium is a 3-level system, the signal will be heavily absorbed when there is no pump present. Therefore, comparing the signal strength with and without the pump laser does not provide information on amplification. Can the authors clarify what model they use exactly to infer the amplification from these experiments?\n6. Can the authors clarify what exactly they expect for the EO S21 as shown in Fig. 4(c)? As I understand it, this just implies that the light was amplified. Or is it expected that the pump would somehow influence the shape of the EO S21?\n7. Please add a very detailed set-up description to the supplementary information where the exact power level is described at each point in your set-up, so it is easier to understand how the numbers used are calculated.\n8. I think for the experiments shown in Fig. 3(f) and Fig. 4, the comparison of with and without pump is not very relevant. When not pumped, the 6 cm spiral will strongly absorb the signal light. The correct comparison would be with and without the amplifier waveguide if the authors want to demonstrate amplification. Can the authors comment on how they would improve this experiment to extract the amplification from the spiral? Moreover, the change in SNR with and without pump in Fig. 5(b) is also not relevant, as without pump the signal is absorbed by the amplifying waveguide. I would ask the authors to explain why they chose this approach.", "reviewer_3": "The authors present what they believe to be the first integrated modulator-amplifier in LNOI, a material platform that has garnered significant attention in recent years due to its excellent modulation capabilities. The integration of modulation and amplification opens the door to promising developments, such as lossless modulators and other advanced photonic building blocks. However, the reviewer remains uncertain about the platform’s potential for developing complex PICs, as suggested by the authors. The need for erbium doping necessitates circuit-wide pumping, which could be undesirable and lead to unnecessarily high power consumption. That said, this concern is speculative and will only be clarified with further research.\nOverall, the reviewer finds the work presented in this manuscript worthy of publication in Nature Communications, particularly after addressing the comments outlined below, which aim to further enhance the quality of the paper.\nIn the abstract the authors mention the NF of 4.3 dB, which is really good. Please, specify whether this is internal or external (fiber-to-fiber).\nPage 1 second column: please, clearly state that the 30dB of net gain in reference 24 is “internal” net gain. Overall, please try to be very concise and specify whether a gain is internal or fiber-to-fiber. The same with the powers, state very clearly whether they are on-chip or off-chip. This will enhance the readability of the paper and the understanding of the reported measurements. Adding to this comments, the authors mention the 30 dB in reference 24 as the highest internal net gain reported (or one of the highest), while as they show in the Table comparing the different erbium amplifiers in the supplementary materials, Bonneville et. Al, have shown an even higher internal net gain. Maybe rewrite a bit the sentence to include both references.\nIn Page 2 first paragraph the authors write: “Furthermore, these systems still face challenges, including relatively high waveguide loss, inherent amplification noise, and significant nonlinearity, which limits performance, especially in applications that demand high fidelity and low crosstalk”. Please, compare the non-linearity and expected performance between the silicon platform and the LNOI platform. The LNOI is highly non linear. Please, explain why the LNOI is expected to behave in a better way in terms of non linear effects, signal distortion and power handling.\nIn Page 2 second paragraph, the authors refer to other materials with limited optical properties. It would be good to specify which material the authors refer to and also what lack of properties they refer to. The LNOI is proposed as a great material thanks to it high n and EO coefficient. What about the non linear properties (chi2 and chi3), which can lead to signal distortion etc? Als what about the power handling? Please, comment.\nThe authors report a background loss of 0.4dB/cm, and they mention that it is very low. However, it is much higher than in other amplifier materials (see ref. to the Liu et al Science paper). Please, comment.\nAt the end of the introduction the authors propose this platform as a better platform for complex PICs. However, as I mentioned above, the necessity to having to pump the whole system can lead to an excessive power consumption. Also, as systems get larger and more complex, it adds complexity to ensure a good level of pumping all along the devices. It would be good if the authors revise this claim and sharpen the application space for the building block proposed in the manuscript.\nIn the second page second column, the authors mention the erbium concentration of 0.5% mol. Would it be possible to convert it also to at.% and ions/cm3? Those are two metrics that used int eh EDFA literature and it will facilitate the reader to compare different amplifier designs easier. Also, how was the concentration of erbium measured?\nThe authors mention: “… exhibiting stimulated radiation of Er3+ ions”. The erbium ions are not stimulated emitted, what is emitted are photons. It would be good to rephrase the sentence.\nFigure 2(c): please, add the PL spectrum from 1460nm (or below that even) to 1640nm (at least). This will enable to see the full range of emission of the erbium ions.\nFigure 2(f): Why is the signal at 1600nm? Can you please add the signal in the C-band (eg. 1532nm or 1550nm?).\nPage 3 paragraph 1: the lifetime was “ calculated”. However, this introduces too many unnecessary errors. It would be desirable to directly measure the lifetime. Please, add this experimental measurement to the manuscript.\nThe authors write: “ For efficient amplifiers in the integrated Er:LNOI platform, the background loss, especially the scattering loss, is the most fatal blocks compared with their fiber-based competitor. “. The words: “fatal blocks” are not very understandable.\nAlthough the reviewer understands that larger cores will lead to higher gain, how is the multimode behavior handled in the rest of building blocks? Eg., MZI modulators? Mode conversion in the bends?\nReference 40: “ Gaafar, M. A. et al. Femtosecond pulse amplification on a chip. arXiv preprint arXiv:2311.04758 (2023).” Should be changed by the journal publication in Nature Communications.\nThe authors write: “ Figure. 2b shows the measured loss of amplifiers with different lengths with the off-chip input signal power of 4 mW”. The loss in erbium doped waveguides should be measured for very small launched signals, in the uW region, as otherwise variations in the ground state population will result in variation of the propagation losses. As the signal power increases, the losses should decrease till a saturable absorption. The same happens at the pump wavelength. It would be good to see the loss measured at very small signals and also the scan of the losses as a function of signal power and pump power till reaching saturation.\nIn page 3 the authors write: “ For moderate modulation efficiency, the electrode gap is set to 3.5 µm.” Why do they choose to go for “moderate” EO efficiency instead of “high” ?\nThe authors write: “ Generally, the net gain dynamically changes under different pump powers”. Does it not happen always? What case are the authors thinking about to say “Generally”? It would be good to explain in the manuscript.\nThe authors write: “ The internal net gain increases with the pump power, which is intuitive”. I believe this is not “intuitive” but represents the physics of the device.\nFigure 4 (f): On-chip or off-chip?\nThe authors write: “ Significantly, the highest on-chip net gain under 115 mW off-chip pump power is around 38 dB (with the consideration of 2.9 dB fiber link loss and 6.7 dB/facet coupling loss, as shown in Fig. 3b) in the 9.16 cm waveguide amplifier, corresponding to an average gain of 4.1 dB/cm”: please, indicate that it is at 1531nm (it is in the figure, but it would be good for clarity and precision to also write it in the text.\nIn figure 3( c), the gain saturates with pump power. However, in the text the authors mention that they can get more gain by pumping harder. It think it would be good to add an explanation.\nThe authors write: “ When the pump light is turned off, the on-chip loss decreases the output optical power to -27 dBm, resulting in a detected SNR of less than 5 dB, as depicted in Fig. 5b(i). The low SNR prevents the extraction of the instantaneous frequency. With the pump light, the output signal is boosted to -12 dBm, resulting in a SNR >15 dB. A clear FMCW signal is observed in Fig. 5c(ii). For comparison, the output signal without pump light is amplified to -12 dBm using a commercial EDFA” The reviewer is not sure whether this comparison makes sense: the SNR ratio increases when pumping. When not pumped, the losses of the circuit are high. It makes sense that the performance improves with pumping. In the opinion of the reviewers the good comparison should be with an undoped modulator in LNOI amplifier by an EDFA. Can this comparison be made/ Otherwise, the reviewer is not sure whether the proposed comparison by the authors is relevant.\nIn Figure S1d the authors show results from the erbium model. However, it is necessary to show how the model fits the experimental data to ensure that it is correct. Can the authors add a graph showing how the model fits the experimental data? Ideally for different amplifier lengths, signal powers and erbium concentrations.\nIn page 3 of the supplementary information, the authors mention parasitic lasing. Do they authors do anything to prevent it in the design?\nIn Figure S2 a Cr mask is used. In Figure S3 a PR mask is used. Why?\nIn Figure S4c, please keep increasing the signal power, since it is supposed to go to saturate at the background loss and it did not happen yet in the figure.\nIn Figure S5, why is the absorption cross-section in the C-band higher than the emission? Also, it would be good to extend the wavelength range to cover the spectrum till both ends of the PL band. Finally, why does the PL spectrum do not resemble a typical erbium emission/absorption cross-section spectrum? Please, add an explanation in the paper."}, "author_response": "Response to the report from the Referee #1\nGeneral comments: \"The work demonstrates optical gain and intensity and phase modulation in\nerbium-doped thin film lithium niobate waveguides. High gain is shown at 1531 nm (38 dB) and low\nnoise figure (4.3 dB). RF operation up to 170 GHz is shown, including demonstrations of broadband\nelectro-optic conversion and analog RF receiving with an 8-12 GHz FMCW signal, both using an amplified\non-chip waveguide. The combination of high gain with low noise and high-speed electro-optic\nmodulation on a monolithic thin film lithium niobate chip is novel and of interest to the integrated\nphotonics community. Below are some comments to be addressed.\"\nOur reply: We thank the reviewer for carefully reading our manuscripts and evaluating our work. We\nmade the point-by-point response according to your comments as follows.\nComment 1: \"The prior art has not been fully addressed, specifically bulk lithium niobate chips. See the\nwork of Sohler et al., (for example Suche et al., IEEE Photonics Technology Letters 7, 505, 1995, where\nphase modulation and erbium gain are both shown on a lithium niobate chip). It is also suggested to\nchange the title accordingly, e.g. specifically referring to thin film lithium niobate, or TFLN.\"\nOur reply: We thank the reviewer for raising this critical point. We have now expanded the discussion\nof prior work on bulk LiNbO in the revised manuscript and highlighted the key innovations of our study.\nmodulation in bulk waveguides. While such platforms inherently suffer from weak optical confinement,\nlimited electro-optic bandwidth, and high driving voltage. These constraints arise from the large\nwaveguide dimensions and low refractive index contrast of bulk LiNbO₃, which restrict both pump-signal\noverlap for efficient optical amplification and microwave-optical velocity matching for high-speed EO\nmodulation. In contrast, our work leverages thin-film Er-doped lithium niobate on insulator (Er:TFLN).\nSuch a compact platform enables submicron optical confinement and high-speed traveling-wave\nelectrodes for high optical gain and efficient wideband EO modulation.\nTo emphasize the innovation of Er:TFLN over bulk Er:LN , we have modified the description in the revised\nmanuscript:\n(Introduction, page 2) In order to embed the amplification function into high-speed opto-electrical\ncircuitry, Erbium-doped lithium niobate Er:LNOI31,32 is a promising alternative.……\n(Introduction, page 2)Early explorations of combining optical gain and electro-optic effects in lithium\nniobate were reported in bulk platforms33. Recent breakthroughs in thin-film lithium niobate (TFLN)\ntechnology further enables stronger optical confinement and higher E-O bandwidth compared to its\nbulk counterpart31.……\nFor enhanced descriptive rigor, we have revised all performance claims to explicitly qualify their\napplicability to thin-film LiNbO₃ platforms, avoiding generalizations that might conflate bulk and thin-\nfilm material properties. And following the reviewer's suggestion, we have revised the title to: \"Unifying\nOptical Gain and Electro-Optical Dynamics in Er-Doped Thin-Film Lithium Niobate Platform\" to\nemphasize this integrated platform.\n[33] Suche, H. et al. Er-doped Ti:LiNbO waveguide laser mode locked via loss modulation. IEEE\ncompare to undoped TFLN MM waveguides?\"\nOur reply: We appreciate the reviewer's insightful question. It is true that the quite high doping leads\nto high absorption loss. In this manuscript, the propagation loss is attributed to two factors, one is the\nscattering loss due to the etching process and the other is the absorption loss of the doped Er3+ ions. To\nminimize the influence of the Er3+ absorption, we measured the propagation loss at 1600 nm, a\nwavelength where Er3+ ions exhibit negligible absorption. The measured loss coefficient is about 0.4\ndB/cm, comparable to the reported values for undoped TFLN waveguides (~0.33 dB/cm[R1]). Subtracting\nthe loss coefficient measured at 1600 nm, we can estimate the absorption loss at other wavelengths,\nas shown in the revised Fig. S4. The high doping leads to about 3~5 dB/cm loss under small-signal\nconditions, and the propagation loss decreases as the input optical power increase due to the saturation\neffect. The high absorption also indicates a high gain factor with the pump at these wavelengths.\n[R1]Li M, Chang L, Wu L, et al. Integrated pockels laser[J]. Nature communications, 2022, 13(1): 5344.\n(Fig. S4, Page S6)\nFig. S4. Passive characteristics of Er:TFLN waveguide amplifier. a, Experimental setup; PC, Polarization\ncontroller; Att., Attenuator; OSA, Optical spectrometer analyzer. b, Measured transparent spectrum of\nthe waveguide amplifier at low signal power; c, Measured loss factor of amplifiers under different input\npowers.\nComment 3: \"Why is the coupling loss so high? Can't inverse tapers be used to get significantly lower\ncoupling loss?\"\nOur reply: Thank you for your insightful comments. We do design an inverse taper considering an input\nmode diameter of 3 μm, with a simulated coupling loss of 0.8 dB/facet at 1530 nm (Fig. R1). While the\nestimated coupling loss in experiment is 3 dB/facet for lensed fibers with a mode diameter of 3 μm and\na numerical aperture (NA) of 0.25. The SEM of the fabricated edge coupler is depicted in Fig. R2. The\nlarger coupling loss may be due to unideal fabrication such as under/over-etching and minor chip-edge\nwear[R2]. In experiment, we find that the index mismatch between the fiber-air-chip facet leads to great\nreflection, resulting in severe parasitic lasing. Thus, we use UHNA7 fiber with index-matching gel to\nsuppress the reflection. The UHNA7 fiber has the same mode diameter as the lensed fiber but a larger\nNA of 0.41. The larger NA leads to a higher coupling loss of 6.7 dB/facet. The detailed selection of fibers\nto suppress the parasitic lasing can be found in \"Reply to Comment 8\".\nat the present setup, validating the high-performance amplification of the integrated Er:TFLN platform.\nWith advanced edge coupler designs[R3], the coupling loss could be down to <1 dB/facet in undoped\nTFLN, promising higher off-chip net gain in Er:TFLN platform.\n[R2] Mu X, Chen Z, Cheng L, et al. Effects of fabrication deviations and fiber misalignment on a fork-\nshape edge coupler based on subwavelength gratings[J]. Optics Communications, 2021"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have carefully reviewed the revised manuscript and response to reviewers. In my opinion, the authors have carried out a very careful and thoughtful revision of the manuscript and satisfactorily addressed almost all of my comments. However, there are still several remaining/additional comments for the revised manuscript and supplementary material that I believe are important to address before publication:\n- Perhaps I am missing it and it has been indicated somewhere, but for Fig. S7a, the pump power used to obtain that ASE spectrum should be indicated\n- *Most important: The gain equation outlined in the Methods section and response doesn't seem to be correct:\n-> It mixes power units (dBm) and relative power units (dB) - it works out ok but it should be slightly revised.\n-> Also the internal net gain should account for any on-chip loss. Therefore, as I understand it, the + L_link term should not be included in the G_net equation, and the reported internal net gain should be slightly (2.9 dB) lower (it doesn't affect the overall story, but the number should be correct). *But now as I read the corresponding description in the manuscript (page 5, bottom right), it seems to describe this as the fiber loss of the system, not the background loss as it seems to represent in the Methods description. It is important to clarify this.*\n-> Also, I know it is a bit picky, but since the coupling might change slightly and the L_coupling term is important in the gain calculation (effectively adding a lot of internal gain - 2*6.7dB=13.4 dB - when you add it into the equation because of the relatively high coupling loss), somewhere it should be stated how it was verified to be consistent for pump on and off measurements. Perhaps there is already a statement, but a single sentence ensuring consistency of the L_coupling term across gain measurements in the supplementary material would suffice.\n-> Check the added text in Methods - L_coupling is repeated\n- Fig. 1 caption - \"picture\": should perhaps indicate they are SEMs (perhaps this is indicated in the text though...I can see that simplifying language for an overview panel is helpful, just double check what is typical for such overview pictures)\n- Response to Comment 18.10: The absorption cross-section for a given dopant ion and transition is an ion and host material property and can typically only be changed slightly by changing the host material...if another method is suggested it should be indicated.\n- I believe it is important to clarify internal vs. external NF throughout because other recent works are referring to an external noise figure that accounts for fibre-chip coupling losses. The fiber-chip coupling loss is important for minimizing NF.\n- Is the ion concentration really exactly 10^20 cm^-3, or is it missing a number in front? 1x10^20 is relatively low for EDWAs and given the typical (actually slightly lower than silica) cross sections in Fig. S5 doesn't seem to match with the high gain.\n- Why are there thick bars for individual wavelengths in the PL spectrum in Fig. 2a? Also photo luminescence -> photoluminescence. And why does the spectrum cut off sharply before 1500nm - is this a setup artifact or truly the shape of the PL spectrum??? It does not seem to match the emission cross-sections in Fig. S5. This should be clarified. Furthermore, a statement with comparison to literature erbium-doped lithium niobate cross-sections should be included.\n- Supplementary note 12: chirp -> chirped; and what is the spiral waveguide length and why does it introduce significant loss if the background loss is only 0.4 dB/cm?", "reviewer_2": "Dear authors and editor,\nI have carefully reviewed the updated manuscript, supplementray information and response to the comments of the reviewers.\nMy concerns have been adressed by the authors and I find the manuscript almost ready for publication.\nI especially appreciate that the authors extended the supplementary information with detailed setup and power level descriptions of the relevant experiments clarifying conditions for the readers of the paper.\nIt is my opinion that the paper represents an a very relevant and detailed technical work with interesting experiments and photonic integrated circuit design.\nHowever, I do have a concern that the manuscript needs a final in depth review by the authors themselves to assure quality.\nFor example in the supplementary information on page 4 the authors calculate the density of the ions which they find to be 10^23 per cm^3: \"... is the Er3+ molar fraction, ρ=4.64 g/cm3 is the density of LiNbO3, M=147.9 g/mol is its molar mass, and NA =6.022×1023 mol−1\nis Avogadro’s constant. Substituting these values yields an Er3+ ion density of 1023 ions/cm3\n.\"\nThis is clearly not correct and a quick calculation yields approximately 9 x 10^19 cm-3 for the ion density. Please assure that this error is not propagated into the other parts of the manuscript, where the value for N_Er is not explicitly given.\nPending this minor correction and any associated updates, I recommend the manuscript for publication."}, "author_response": ""}, {"round": 3, "reviewer_comments": {"reviewer_1": "I really appreciate the authors' attention to detail and effort to address all the comments. I am satisfied with the responses and changes and reccommend that paper can be published", "reviewer_2": "Dear authors and editor,\nAfter examining the updated manuscript and the detailed response to the reviewers, I recommend this paper for publication."}, "author_response": ""}]

Decision letter