Open Access
Add to BibSonomy
Abstract
Tunable light sources are a key enabling technology for many applications such as ranging, spectroscopy, optical coherence tomography, digital imaging and interferometry. For miniaturized laser devices, whispering gallery resonator lasers are a well-suited platform, offering low thresholds and small linewidths, however, many realizations suffer from the lack of reliable tuning. Rare-earth ion-doped lithium niobate offers a way to solve this issue. Here we present a single-frequency laser based on a neodymium-doped lithium niobate whispering gallery mode resonator that is tuned via the linear electro-optic effect. Using a special geometry, we suppress higher-order transverse modes and hence ensure single-mode operation. With an applied voltage of just 68 V, we achieve a tuning range of 3.5 GHz. The lasing frequency can also be modulated with a triangular control signal. The freely running system provides a frequency and power stability of better than $\Delta \nu = {20}\;\textrm{MHz}$ and 6 %, respectively, for a 30-minute period. This concept is suitable for full integration with existing photonic platforms based on lithium niobate.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
For many applications such as e.g., frequency-modulated light detection and ranging (LIDAR) [1,2], biomedical imaging such as optical coherence tomography (OCT) [3,4] and trace-gas spectroscopy [5,6] the key component are tunable lasers providing stable single-frequency lasing plus fast and wide tuning range. Reducing the footprint of such devices by wafer-based manufacturing processes promises a lower power consumption and lower cost. One way to accomplish this task is to employ optical microresonators. They are characterized by a high quality factor ($Q$-factor), a small mode volume and a large free spectral range. Additionally, they provide the possibility of designing the transverse mode spectrum which ensures single-mode lasing.
These properties can be used to passively stabilize lasers via self-injection locking [7–10]. In Ref. [9], a compact on-chip system with a small linewidth was realized. It can be linearly tuned as fast as 12 PHz s−1. However, the tuning range of the system is limited by the locking bandwidth of the external resonator to the laser chip, which is about 1 GHz. In contrast to the self-injection technique, it is also possible to generate laser light directly from microresonators fabricated out of active laser media. The properties of microresonators described in the introduction before enable a low pump threshold and narrow linewidth. Such systems have been proposed and demonstrated in a large variety of material platforms [11,12]. For example, ultra-low threshold lasing of a titanium doped sapphire whispering gallery laser has been shown recently [13].
Whereas single frequency operation and wafer-scale fabrication in most systems is possible, changing the laser frequency often remains challenging. While approaches like temperature tuning or mechanical stress can achieve response times in the millisecond or microsecond range, linear electro-optic tuning offers even faster performance [14,15]. Lithium niobate (LN), as a non-centro-symmetric crystal, offers the possibility of influencing the refractive index $n$ by the linear electro-optic effect, the Pockels effect. In addition, large non-linear coefficients and a wide transparency range make LN an attractive material for many applications [16–19].
Additionally, rare-earth doped lithium niobate can serve as a laser material platform. A wide range of active components has been experimentally demonstrated on this platform, such as amplifiers and lasers [20–26]. The outstanding optical performance as well as the possibility of doping LN makes it a promising candidate to realize monolithic tunable laser sources. In Ref. [24] an electro-optically tunable erbium-doped lithium niobate microring laser has been demonstrated. However, the laser possesses multi-mode operation during the tuning and the electro-optical tuning efficiency suffers from the small spatial overlap between the optical mode and the electric control field. Furthermore, the electro-optic tuning behavior of such a microresonator laser has never been analyzed in detail. In this work, we demonstrate an electro-optically tunable single-frequency laser based on a neodymium-doped lithium niobate microresonator, which provides a four-level system. In order to ensure a high excitation efficiency, we resonantly pump the whispering-gallery resonator (WGR). Using extraordinarily polarized light, i.e., polarized parallel to the $c$-axis, has two advantages: Firstly, the absorption cross-section of the Nd-ions for the pump light is higher than that for ordinarily polarized light [27], resulting in a more efficient excitation scheme. Secondly, for electro-optic tuning of the lasing frequency, we can make use of the Pockels coefficient $r_{33}$ which is in our case the largest accessible electro-optic (EO) coefficient of lithium niobate, requiring lower voltages.
To ensure single-mode operation, we make use of a so-called photonic belt resonator geometry, which suppresses higher-order transverse modes [28,29]. By this micrometer-sized structure, we can also prevent undesired self-frequency doubling given by fortuitous phase-matching with higher order modes [30]. In the following, we first elucidate the theoretical quantities such as the pump threshold and the influence of the Pockels effect on the resonance frequency. Then, we experimentally verify the single-frequency operation and analyze the stability of the laser. Finally, the tuning of this laser light source is demonstrated.
2. Theoretical considerations
The threshold power $P_\mathrm {th}$ for lasing with a four-level system in a microresonator can be determined by [31],
Let us consider e-polarized pump light with $\lambda _\mathrm {p} = {813}\;\textrm{nm}$. With $\sigma _\mathrm {em} = 1.8{\times}10^{-19}\;\textrm{cm}^{2}$ [27], $\tau = {100}\;\mathrm{\mu}\textrm{s}$, $V_\mathrm {p} = 1{\times}10^{6}\;\mathrm{\mu}\textrm{m}^{3}$, $n=2.15$, $Q_\mathrm {l}=6\times 10^6$ and $\eta =1$ we obtain $P_\mathrm{th}\;\approx\;{0.3}\;\textrm{mW}$.
We can also estimate the introduced shift of the lasing frequency $\nu _\mathrm {l}$ by an external electric field $E_z$. The resonance frequency of the WGR, being identical with the possible laser frequency $\nu _\mathrm {l}$, can be estimated by [32]
for the major radius of the microresonator $R$, the azimuthal mode number $m$, the vacuum speed of light $c$ and the refractive index of the bulk material $n_\mathrm {l}$ at the lasing wavelength.From Eq. (5) it is clear that either changing the radius $R$ or the refractive index $n_l$ will change the eigenfrequency. Since lithium niobate possesses the Pockels effect, the lasing frequency can be changed by applying an external voltage to the crystal. The refractive index is modified according to
for $r$ the Pockels coefficient and $E_\mathrm {z} =U_\mathrm {c}/d$ the electric field resulting from the control voltage $U_\mathrm {c}$ divided by the thickness $d$ of the WGR. Combining Eqs. (5) and (6), the change of the eigenfrequency $\Delta \nu _\mathrm {l}$ can then be expressed as We neglect the contribution of the piezo-electric effect to the frequency change since it is an order of magnitude smaller than the Pockels effect [33]. However, the piezo-electric effect may cause long term drifts of the lasing frequency when a dc-bias voltage is applied [34,35]. Using Eq. (7) we can make an estimate for the expected frequency tuning range. Assuming $U_\mathrm {c} = {62.5}\;\textrm{V}$ and a thickness $d$ of 250 µm which results in an electric field strength of $E_z = {250}\;\textrm{V}\;\textrm{mm}^{-1}$, a Pockels coefficient $r_{33} = {25}\;\textrm{pm}\;\textrm{V}^{-1}$ [36] and a lasing frequency of $\nu _\mathrm{l} = {276.15}\;\textrm{THz}$, we determine the frequency shift to be $\Delta \nu\;\approx\;{4.0}\;{GHz}$.3. Experimental methods
The microresonator is fabricated from a commercially available single-domain congruent $z$-cut lithium niobate (LiNbO$_3$) wafer of 250 µm thickness doped with nominally 0.4 mol % neodymium (Nd) and 5.1 mol % magnesium oxide (MgO) (Yamaju Ceramics Co. Ltd.). To provide a low resistance electrical connection, the $+z$ and $-z$-sides of the wafer are coated with a 250-nm-chrome layer. To cut a resonator blank out of the wafer, we use a femtosecond laser with a repetition rate of 60 kHz and a wavelength of 343 nm. The average power was 1 W. To ensure a sufficient mechanical and electrical connection, the crystal blank is soldered to a brass post using low temperature soldering tin.
Then, using the same femtosecond laser, we shape the resonator using a computer-controlled lathe. The WGR has a major radius $R = {800}\;\mathrm{\mu}\textrm{m}$, resulting in a free spectral range (FSR) of 27.1 GHz. A schematic of the resonator is shown in Fig. 1). The optic axis is parallel to the axis of symmetry of the resonator. In the final step of the machining in order to improve the quality factor of the resonator, a single run of 2 min chemical mechanical polishing is done. The final shape after polishing was determined by a 3D Optical Profiler (Zygo NewView 9000). This way, we obtain a width $B$ of 5 µm and a height $H$ of 3.6 µm, see Fig. 1(b). This resonator design is inspired by the one in Ref. [28]. It considerably reduces the number of transverse modes and consequently the susceptibility to mode hops. We estimate with finite element method (FEM) simulation, that a true single-mode resonator requires $H\;\leq\;{2}\;\mathrm{\mu}\textrm{m}$ and $B\;\leq\;{2.5}\;\mathrm{\mu}\textrm{m}$ [37]. However, with our chosen waveguide geometry a stable single-frequency operation and mode-hop-free tuning should be possible. Because of the wedge-like geometry we need to consider a reduction of the electric field compared to that of a simple plate capacitor. It has been shown before, that the overlap between the externally applied electric field and the optical electric field is reduced depending on the size of the belt [37]. However, a small size of wedge is desired to suppress higher-order modes and therefore ensure single mode lasing and suppress undesired self-frequency doubling [30]. We compute the electric field distribution for our geometry of the microresonator by using an FEM simulation (COMSOL Multiphysics) based on the profile measured before. The resulting electric field strength $E_\mathrm {z}$ and the shape and area of the optical mode are shown in Fig. 1(b) . We obtain an average electric field strength $E_\mathrm {z}$ in $z-$direction in the area of the fundamental optical mode of 71 % compared with the electric field based on $E_\mathrm {z,0} =U_\mathrm {c}/d$.
Fig. 1. a) A 3D schematic of the microresonator. On $+z$- and $-z$-side of the resonator there are electrodes. On the bottom side of the microresonator you can see in orange the upper part of the brass post on which the resonator is mounted. b) FEM simulation of the electric field and the fundamental optical mode (shaded area) in the waveguide structure on the circumference of the resonator. The electric field strength $E_\mathrm {z}$ is compared with the electric field strength $E_\mathrm {z,0}$ according to the plate capacitor formula. The simulation is based on the coordinate measured with a 3D optical profiler.
The setup for the optical characterization consists of a pump laser, coupling optics and mechanics, a voltage source for the tuning, a protective housing and devices to characterize the properties of the emitted beam (Fig. 2). As a pump laser we use either a titanium sapphire laser or an $813$-nm single frequency laser diode. While both lasers are used for characterization, only the Ti:Sa laser is used as a pump laser in the electro-optic tuning experiments. The extraordinarily polarized pump beam is coupled resonantly into the microresonator via a rutile prism.
Fig. 2. A schematic of the measurement setup. The laser with $\lambda _\mathrm {l} = {813}\;\textrm{nm}$ is coupled via a rutile prism to the whispering gallery resonator (WGR). The polarization is controlled by a $\lambda /2$-wave-plate. The remaining pump light is filtered using a dichroic mirror (DM) and sent to a beam dump (BD). The lasing beam is split by a 50:50 beam splitter (BS) and further analyzed using a scanning Fabry-Pérot-Interferometer (FPI) and an optical spectrum analyzer (OSA).
The residual pump light and the generated laser light are separated using a dichroic mirror and sent to a beam dump. The generated laser light is split into two arms to be further analyzed either using a scanning Fabry-Pérot-Interferometer (FPI) or an optical spectrum analyzer (OSA). The FPI has a FSR of 1.5 GHz and is scanned by multiple FSRs during the experiment. The linewidth of the FPI is 10 MHz. The OSA (Yokogawa AQ6370D) is used to measure the absolute frequency and to resolve a larger frequency range. It has a resolution of 15 GHz. To maintain similar conditions for all experiments, the WGR is housed in an acrylic glass cover. Measurements begin after a period of a few minutes to allow the system to attain thermal stability, since no temperature controller is active for the experiments. For the electro-optic control of the resonance frequency a copper wire is bonded onto the top of the WGR while the bottom is connected to the brass post. The control signal from the function generator is amplified by a 10 volt-per-volt high−voltage amplifier with a maximum output of 150 V. Using this setup, we determine the quality factor at the lasing wavelength. Therefore, we scan the laser across the mode of the WGR, record the transmission spectrum and measure the linewidth $\delta \nu _\mathrm {FWHM}$ of the Lorentzian-shaped transmission curve. Based on $\delta \nu _\mathrm {FWHM}$ we determine the quality factor of $Q_\mathrm {l}=6\times 10^6$. Our estimation of the oscillation threshold assumes that the round-trip loss for the pump light is smaller than one. We have determined the absorption loss of the resonator material at 813 nm to $\alpha _\mathrm{p} = {0.6}\;\textrm{cm}^{-1}$ leading to 30 % round-trip loss.
4. Results and discussion
When the resonator is excited with extra-ordinarily polarized light at only $P_\mathrm {p} = {4\pm 0.5}\;\textrm{mW}$ laser excitation is clearly visible and emission of 1086 nm wavelength light is observed in both emission directions. This power value is higher than the estimated before, the difference stemming mainly from the unknown prism-to-resonator coupling strength during the laser operation.
As can be seen in Fig. 3(a) we observe only a single emission peak at the expected frequency $\nu _\mathrm {l} = {276.15}\;\textrm{THz}$; the entire measurement covers a frequency range of 450 GHz. The peak position corresponds to $\lambda _\mathrm {l} = {1085.6}\;\textrm{nm}$.
Fig. 3. Characterization of the emitted laser light. a) The recorded spectra of the optical spectrum analyzer (OSA) and in b) of the scanning Fabry-Pérot-Interferometer (FPI). The inset in b) shows a false-color picture recorded with a beam profile camera.
For higher spectral resolution we launch the generated laser light into the scanning FPI. The recorded spectrum can be seen in Fig. 3(b). Since only one peak is visible in the free spectral range, added to the fact that we scan over the entire 430-GHz gain bandwidth of Nd:MgO:LN [38], we verify single frequency operation. By fitting a Lorentzian function to the transmission peak, we determine a linewidth of the transmitted laser light similar to the linewidth of the FPI of 10 MHz, indicating that the measurement is equipment-limited.
The inset in Fig. 3(b) shows a false-color image of the beam profile, taken after collimating the beam with a 40-mm bi-convex lens. It shows a TEM$_{00}$-like shape, another clear indication of single mode operation.
For measurement of power and frequency stability, an additional beam splitter and a photodiode are placed in front of the FPI. First, we couple about 12 mW of pump light into the resonator, leading to a lasing power of $P_\mathrm {l} = {340}\;\mathrm{\mu}\textrm{W}$. The result is shown in Fig. 4 where the upper part shows the frequency stability and the lower one, the power stability for a 30 min period. The lasing frequency $\nu _\mathrm {l}$ shows a drift of about ${20}\;\textrm{MHz}$ and the output power of the laser fluctuates within $\pm$ 6 % with a slight downward slope. A shift of the lasing frequency by 20 MHz by the thermo-optic effect in Nd:LiNbO$_3$ happens already for temperature changes in the mK range [39]. Our current experimental setup provides temperature stability on the level of some mK. Thus, it is straightforward to conclude that the observed frequency shift is caused mainly by temperature variations. However, there might be contributions of other effects as well, e.g., pyroelectric or piezoelectric [34,35].
Fig. 4. Stability of the emission frequency and power of the free running system. The frequency is recorded by tracking the peak position of the scanning Fabry-Pérot-Interferometer (FPI). The power of the lasing is measured using an additional photodiode placed behind a 50:50 beam splitter in front of the FPI.
To demonstrate wavelength tuning, we apply a voltage that increases linearly in 10 s to a maximum value of 70 V. Such a slow ramp helps to mitigate thermal effects that originate from the change of the in-coupled power stemming from the shift of the resonance frequency. The shift in peak position on the scanning FPI while increasing the voltage results in a measure for the change of the lasing frequency $\nu _\mathrm {l}$ as shown in Fig. 5. The maximum frequency shift we could obtain was 3.5 GHz. If we increase the voltage further we cannot observe lasing anymore. It is likely that the pump mode frequency is then shifted so far from resonance that we decouple the resonator from the pump light.
Fig. 5. Electro-optic tuning of the WGR-laser: Frequency shift $\Delta \nu _\mathrm {l}$ of lasing frequency vs. applied voltage. The dashed line represents a linear fit to the data.
The magnitude of the observed lasing frequency shift corresponds to the GHz-broad resonances of the WGR, due to the strong absorption of the pump light. We observe a non-linear tuning with deviations of $\pm{200}\;\textrm{MHz}$ from the expected linear behavior. By applying a voltage to change the lasing frequency, we also change the pump detuning and thus the amount of in-coupled pump light. Since we use a pump power of several mW, it is likely that light induced thermal effects influence the frequency tuning characteristic. Changes of the resonance frequency of hundreds MHz with a few mW in-coupled light at a wavelength where much less absorption is present have already been observed before, supporting our interpretation of the data [39,40]. The frequency shift amounts to 3.5 GHz at 68 V. According to the electric field strength obtained by the FEM simulation, we calculate an expected tuning range of 3.1 GHz only. However, the Pockels coefficients for Nd:MgO:LiNbO$_3$ are not precisely known which makes it difficult to compare the theoretically expected value with the measured ones.
Finally, we quantify the tunability of the presented system for smaller tuning ranges but for higher tuning speeds. To do so, we apply a triangular voltage sweep to the resonator with a frequency of 11.25 Hz. Here, we can change the resonance frequency faster since we reduce the tuning range and consequently the change of the in-coupled pump power is smaller which reduces thermo-optic effects. The electric control signal and the resulting frequency shift can be seen in Fig. 6. By applying 15 V to the electrode we observe a frequency shift $\Delta \nu ={0.85}\;\textrm{GHz}$ on the rising side resulting in a tuning rate of ${57}\;\textrm{MHz}\;\textrm{V}^{-1}$. On the rising side of the first triangle we extract from the linear fit $R^2= 0.99$ and on the falling side $R^2= 0.95$, indicating a high linearity of the observed frequency shift. The long-term drift of the center frequency within a a time window of 30 s is 15 MHz. This value is higher than the drift obtained in the stability measurement. However, in contrast to Fig. 4, a dynamic situation is present, induced by the triangular voltage signal applied to change the laser frequency. The formerly mentioned dc drift of lithium niobate as well as by light-induced thermal effects can cause such long-term drifts.
Fig. 6. Electro-optic tuning of the WGR-laser on the millisecond time scale. In the top plot we show the applied control voltage $U_\mathrm {c}$ on the electrodes. In the bottom the recorded frequency shift $\Delta \nu _\mathrm {l}$ is displayed. The dash-dotted lines are linear fits to the recorded data.
5. Conclusion and outlook
In summary, we implement an electro-optically tunable laser based on a Nd:MgO:LN microresonator, showing stable single-frequency lasing centered around 1086 nm wavelength with a TEM$_{00}$-like beam profile. The lasing frequency can subsequently be tuned more than 3.5 GHz without mode-hops. This free-running WGR laser provides 6 % output power stability as well as ${20}\;\textrm{MHz}$ frequency stability without any feedback system for a period of 30 min. We have also demonstrated that using a triangular control signal leads to a corresponding linear shift of the lasing frequency, making the system useful as a possible light source for ranging and sensing, for example.
Since lithium niobate can be doped with other rare-earth ions such as praseodymium, tunable lasing could also be realized at visible wavelengths
A limitation of our demonstration is that resonant pumping limits the stable tuning range to the width of the pump mode. Furthermore, resonant pumping affects the tuning behavior, because less light is coupled into the resonator when a voltage is applied, which leads to a reduction in temperature and is most likely the origin of the nonlinear tuning behavior when the lasing frequency is tuned wide and slowly. One approach to tackle this issue is to employ a side-pumping scheme [41]. By doing so, even an inexpensive pump source like a 813-nm multi-mode laser diode can be employed. This ensures that the same pump power is always present during the electro-optic tuning. However, the quality factors achieved here were too low to use these schemes efficiently. Realizing this approach on an on-chip platform would push another limit: a smaller radius would lead to a larger FSR and hence larger tuning ranges would not be impeded by mode-hops, when only one longitudinal and transverse mode is present in the complete gain bandwidth of the laser material [41]. Furthermore, implementing this scheme in integrated photonic platforms based on lithium niobate will lead to an increase of the electric field strength using the same voltage as used in this demonstration by two orders of magnitude and thus will allow for wider tuning - we consider this work to be an important step towards inexpensive tunable light sources.
Funding
Gisela and Erwin Sick Fellowship.
Acknowledgments
The authors thank Jan Szabados and Nicolas Amiune for fruitful discussions on the manuscript. We acknowledge support by the Open Access Publication Fund of the University of Freiburg.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. H. Bostick, “A carbon dioxide laser radar system,” IEEE J. Quantum Electron. 3(6), 232 (1967). [CrossRef]
2. B. Behroozpour, P. A. M. Sandborn, M. C. Wu, and B. E. Boser, “Lidar system architectures and circuits,” IEEE Commun. Mag. 55(10), 135–142 (2017). [CrossRef]
3. Z. Yaqoob, J. Wu, and C. Yang, “Spectral domain optical coherence tomography: a better oct imaging strategy,” BioTechniques 39(6S), S6–S13 (2005). [CrossRef]
4. S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Technol. Lett. 16(1), 293–295 (2004). [CrossRef]
5. D. R. Bowling, S. D. Sargent, B. D. Tanner, and J. R. Ehleringer, “Tunable diode laser absorption spectroscopy for stable isotope studies of ecosystem–atmosphere co2 exchange,” Agric. Forest Meteorology 118(1-2), 1–19 (2003). [CrossRef]
6. M. Lackner, “Tunable diode laser absorption spectroscopy (tdlas) in the process industries–a review,” Rev. Chem. Eng. 23(2), 65–147 (2007). [CrossRef]
7. V. Vassiliev, V. Velichansky, V. Ilchenko, M. Gorodetsky, L. Hollberg, and A. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998). [CrossRef]
8. B. Sprenger, H. G. L. Schwefel, and L. J. Wang, “Whispering-gallery-mode-resonator-stabilized narrow-linewidth fiber loop laser,” Opt. Lett. 34(21), 3370–3372 (2009). [CrossRef]
9. V. Snigirev, A. Riedhauser, G. Lihachev, J. Riemensberger, R. N. Wang, C. Moehl, M. Churaev, A. Siddharth, G. Huang, Y. Popoff, U. Drechsler, D. Caimi, S. Hoenl, J. Liu, P. Seidler, and T. J. Kippenberg, “Ultrafast tunable lasers using lithium niobate integrated photonics,” arXiv preprint arXiv:2112.02036 (2021).
10. M. Li, L. Chang, L. Wu, J. Staffa, J. Ling, U. A. Javid, Y. He, R. Lopez-rios, S. Xue, T. J. Morin, B. Shen, H. Wang, S. Zeng, L. Zhu, K. J. Vahala, J. E. Bowers, and Q. Lin, “Integrated pockels laser,”arXiv:2204.12078v1 (2022). [CrossRef]
11. M. Kuwata-Gonokami and K. Takeda, “Polymer whispering gallery mode lasers,” Opt. Mater. 9(1-4), 12–17 (1998). [CrossRef]
12. L. He, Ş. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7(1), 60–82 (2013). [CrossRef]
13. F. Azeem, L. S. Trainor, A. Gao, M. Isarov, D. V. Strekalov, and H. G. L. Schwefel, “Ultra-low threshold titanium-doped sapphire whispering-gallery laser,” Adv. Opt. Mater. 10(8), 2102137 (2022). [CrossRef]
14. C. S. Werner, W. Yoshiki, S. J. Herr, I. Breunig, and K. Buse, “Geometric tuning, spectroscopy using whispering-gallery resonator frequency-synthesizers,” Optica 4(10), 1205–1208 (2017). [CrossRef]
15. K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4-5), 269–281 (2014). [CrossRef]
16. Y. Jia, L. Wang, and F. Chen, “Ion-cut lithium niobate on insulator technology: Recent advances and perspectives,” Appl. Phys. Rev. 8(1), 011307 (2021). [CrossRef]
17. G. Poberaj, H. Hu, W. Sohler, and P. Günter, “Lithium niobate on insulator (LNOI) for micro-photonic devices,” Laser Photonics Rev. 6(4), 488–503 (2012). [CrossRef]
18. J. Lin, F. Bo, Y. Cheng, and J. Xu, “Advances in on-chip photonic devices based on lithium niobate on insulator,” Photonics Res. 8(12), 1910–1936 (2020). [CrossRef]
19. D. Zhu, L. Shao, M. Yu, R. Cheng, B. Desiatov, C. J. Xin, Y. Hu, J. Holzgrafe, S. Ghosh, A. Shams-Ansari, E. Puma, N. Sinclair, C. Reimer, M. Zhang, and M. Lončar, “Integrated photonics on thin-film lithium niobate,” Adv. Opt. Photonics 13(2), 242–352 (2021). [CrossRef]
20. C.-H. Huang and L. McCaughan, “980-nm-pumped Er-doped LiNbO3 waveguide amplifiers: a comparison with 1484-nm pumping,” IEEE J. Sel. Top. Quantum Electron. 2(2), 367–372 (1996). [CrossRef]
21. D. Brüske, S. Suntsov, C. E. Rüter, and D. Kip, “Efficient ridge waveguide amplifiers and lasers in Er-doped lithium niobate by optical grade dicing and three-side Er and Ti in-diffusion,” Opt. Express 25(23), 29374 (2017). [CrossRef]
22. D. Brüske, S. Suntsov, C. E. Rüter, and D. Kip, “Efficient Nd:Ti:LiNbO3 ridge waveguide lasers emitting around 1085 nm,” Opt. Express 27(6), 8884–8889 (2019). [CrossRef]
23. Z. Wang, Z. Fang, Z. Liu, W. Chu, Y. Zhou, J. Zhang, R. Wu, M. Wang, T. Lu, and Y. Cheng, “On-chip tunable microdisk laser fabricated on Er3+-doped lithium niobate on insulator,” Opt. Lett. 46(2), 380–383 (2021). [CrossRef]
24. D. Yin, Y. Zhou, Z. Liu, Z. Wang, H. Zhang, Z. Fang, W. Chu, R. Wu, J. Zhang, W. Chen, M. Wang, and Y. Cheng, “Electro-optically tunable microring laser monolithically integrated on lithium niobate on insulator,” Opt. Lett. 46(9), 2127–2130 (2021). [CrossRef]
25. W. Sohler, “Rare-earth-doped LiNbO3 waveguide amplifiers and lasers,” in Integrated Optical Circuits, vol. 1583K. K. Wong, ed., International Society for Optics and Photonics (SPIE, 1991), pp. 110–121.
26. M. George, R. Ricken, V. Quiring, and W. Sohler, “In-band pumped Ti:Tm:LiNbO3 waveguide amplifier and low threshold laser,” Laser Photonics Rev. 7(1), 122–131 (2013). [CrossRef]
27. T. Y. Fan, A. Cordova-Plaza, M. J. F. Digonnet, R. L. Byer, and H. J. Shaw, “Nd:MgO:LiNbO3 spectroscopy and laser devices,” J. Opt. Soc. Am. B 3(1), 140–148 (1986). [CrossRef]
28. A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Morphology-dependent photonic circuit elements,” Opt. Lett. 31(9), 1313–1315 (2006). [CrossRef]
29. I. S. Grudinin and N. Yu, “Dispersion engineering of crystalline resonators via microstructuring,” Optica 2(3), 221–224 (2015). [CrossRef]
30. S. J. Herr, Y. Folwill, K. Buse, and I. Breunig, “Self-frequency doubling in a laser-active whispering-gallery resonator,” Opt. Lett. 42(13), 2627–2630 (2017). [CrossRef]
31. S. J. Herr, K. Buse, and I. Breunig, “Led-pumped whispering-gallery laser,” Photonics Res. 5(6), B34–B38 (2017). [CrossRef]
32. I. Breunig, “Three-wave mixing in whispering gallery resonators,” Laser Photonics Rev. 10(4), 569–587 (2016). [CrossRef]
33. R. Weis and T. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37(4), 191–203 (1985). [CrossRef]
34. M. Xu, M. He, H. Zhang, J. Jian, Y. Pan, X. Liu, L. Chen, X. Meng, H. Chen, Z. Li, X. Xiao, S. Yu, S. Yu, and X. Cai, “High-performance coherent optical modulators based on thin-film lithium niobate platform,” Nat. Commun. 11(1), 3911 (2020). [CrossRef]
35. J. P. Salvestrini, L. Guilbert, M. Fontana, M. Abarkan, and S. Gille, “Analysis and control of the dc drift in linbo 3 based mach–zehnder modulators,” J. Lightwave Technol. 29(10), 1522–1534 (2011). [CrossRef]
36. E. D. A. Méndez, A. García-Caba nes, and J. Cabrera, “Wavelength dependence of electro-optic coefficients in congruent and quasi-stoichiometric LiNbO3,” Electron. Lett. 35(6), 498–499 (1999). [CrossRef]
37. Y. Minet, H. Zappe, I. Breunig, and K. Buse, “Electro-Optic Control of Lithium Niobate Bulk Whispering Gallery Resonators: Analysis of the Distribution of Externally Applied Electric Fields,” Crystals 11(3), 298 (2021). [CrossRef]
38. N. MacKinnon, C. J. Norrie, and B. D. Sinclair, “Laser-diode-pumped, electro-optically tunable Nd:MgO:LiNbO3 microchip laser,” J. Opt. Soc. Am. B 11(3), 519–522 (1994). [CrossRef]
39. M. Gorodetsky and A. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Top. Quantum Electron. 12(1), 33–39 (2006). [CrossRef]
40. J. Szabados, D. N. Puzyrev, Y. Minet, L. Reis, K. Buse, A. Villois, D. V. Skryabin, and I. Breunig, “Frequency comb generation via cascaded second-order nonlinearities in microresonators,” Phys. Rev. Lett. 124(20), 203902 (2020). [CrossRef]
41. S. J. Herr, K. Buse, and I. Breunig, “Tunable single-frequency lasing in a microresonator,” Opt. Express 27(11), 15351–15358 (2019). [CrossRef]
