Electro-optic tuning of a single-frequency ultranarrow linewidth microdisk laser

Abstract. Single-frequency ultranarrow linewidth on-chip microlasers with a fast wavelength tunability play a game-changing role in a broad spectrum of applications ranging from coherent communication, light detection and ranging, to metrology and sensing. Design and fabrication of such light sources remain a challenge due to the difficulties in making a laser cavity that has an ultrahigh optical quality (Q) factor and supports only a single lasing frequency simultaneously. Here, we demonstrate a unique single-frequency ultranarrow linewidth lasing mechanism on an erbium ion-doped lithium niobate (LN) microdisk through simultaneous excitation of high-Q polygon modes at both pump and laser wavelengths. As the polygon modes are sparse within the optical gain bandwidth compared with the whispering gallery mode counterpart, while their Q factors (above 10 million) are even higher due to the significantly reduced scattering on their propagation paths, single-frequency lasing with a linewidth as narrow as 322 Hz is observed. The measured linewidth is three orders of magnitude narrower than the previous record in on-chip LN microlasers. Finally, enabled by the strong linear electro-optic effect of LN, real-time electro-optical tuning of the microlaser with a high tuning efficiency of ∼50  pm  /  100  V is demonstrated.


Introduction
Broad transparency window and high piezoelectric, acoustooptic, second-order nonlinear, and electro-optic (EO) coefficients characterize crystalline lithium niobate (LN) as the "silicon in photonics." [1][2][3][4][5][6][7] Recent breakthroughs in the nanofabrication technology on thin-film LN platforms 4 gave birth to a variety of integrated photonic devices such as high-performance EO modulators, 8,9 broadband optical frequency combs, [10][11][12] and high efficiency frequency converters. [13][14][15] To build a monolithic integrated photonic system on an LN chip, the capacity of microlaser fabrication on this platform is essential. The high EO coefficient of LN ensures that such lasers outperform all other on-chip counterparts in broad range and real-time wavelength tunability. However, similar to silicon, LN itself does not provide optical gain for lasing. Therefore, to functionalize LN, doping of the gain medium is necessary. In particular, to make lasers operating at widely needed telecom wavelengths, the erbium ion (Er 3þ ) is a favorable choice of dopant. [16][17][18][19][20][21][22] More importantly, to enable many applications and outperform silicon counterparts, such lasers should operate at a single frequency with an ultranarrow linewidth and fast wavelength tunability. [23][24][25][26][27] According to the Schawlow-Townes theory, the laser fundamental linewidth is quadratic inversely proportional to the undoped cavity Q factor. [28][29][30] Therefore, increasing the Q factor will quadratically reduce the linewidth of a microlaser. The highest Q factors demonstrated to date are those of whispering gallery mode (WGM) microcavities where light confinement is achieved by continuous total internal reflection at the smooth resonator periphery. 31 However, the dense WGMs within the optical gain bandwidth would easily lead to multifrequency lasing in a microcavity. To reduce the number of modes, attempts have been made to reduce the microcavity size, 23 which inevitably increases the radiation loss and decreases the mode volume, leading to a reduction of both the Q factor and optical gain in the microcavity. Consequently, the pump threshold increases while the laser power remains low.
The polygon-shaped modes in large LN microdisks have demonstrated high Q factors due to reduced scattering losses on their propagation paths. 32 In this work, by exciting polygon modes and avoiding the dense WGMs, we demonstrated single-frequency lasing in large Er 3þ -doped LN microdisks with an ultranarrow linewidth. EO tuning of the laser wavelength was realized with a high linear tuning efficiency of 50 pm∕100 V.

Active Microdisk Fabrication
The fabrication process of the microdisk begins from the preparation of an Er 3þ -doped Z-cut LN thin-film wafer by ion slicing. The doping concentration of Er 3þ is 1% (mole fraction). The fabrication flow of the microdisk resonators mainly consists of four steps. First, a chromium (Cr) thin layer was coated on the LN thin-film wafer and then patterned into microdisks using femtosecond laser micromachining. The removal of the Cr thin film with a high spatial resolution was achieved by femtosecond laser ablation. Second, the microdisk pattern was transferred from the Cr layer to the LN thin film via chemomechanical polishing. Third, the microelectrodes were fabricated on the Cr layer again using the space-selective femtosecond laser ablation. Finally, the silica layer underneath the LN disk was partially undercut to form the supporting pedestals for supporting the LN thin-film microdisks. The details of the fabrication can be found in Refs. 17 and 33. An optical micrograph of the fabricated microdisk integrated with electrodes is shown in the inset of Fig. 1 (bottom right). The distance between the microelectrodes is 35 μm. The zoom-in scanning electron microscope (SEM) image of the fabricated microcavity without microelectrodes is also shown in the inset of Fig. 1 (bottom middle), which consists of an Er 3þ -doped LN microdisk with a thickness of 700 nm and a diameter ∼29.8 μm, indicating an ultrasmooth surface. The microdisk is supported by a thin silica pedestal (with a diameter of ∼8 μm) on the LN substrate. The principal dielectric axes x; y of LN are illustrated in the inset of Fig. 1.

Experimental Setup
The experimental setup is illustrated in Fig. 1. A narrow-linewidth tunable diode laser (Model: TLB-6719, New Focus, Inc.) Fig. 1 The experimental setup for lasing and polarization measurement. A variable optical attenuator (VOA) was used to tune the input power into the Z -cut microdisk. TM and TE represent transverse magnetic and transverse electric polarization states, respectively. Inset: SEM image of the microdisk (without electrodes) and optical micrograph of the microdisk integrated with Cr electrodes. was used as the pump light source, and the pump laser wavelength was tuned to be resonant with a specific transverse electric (TE) polarized cavity mode around 968 nm. The laser was coupled to the microdisk via a tapered fiber with a waist size of 2 μm. The position between the tapered fiber and the microdisk was adjusted by a three-dimensional (3D) piezo stage with a 20-nm resolution. An optical imaging system consisting of a microscope objective lens with a numerical aperture (NA) of 0.42, long-pass filters (Thorlabs, Inc., Model: FELH1100), and an infrared (IR) charge-coupled device (CCD) was used to monitor the coupling system from the top and capture the intensity profile of the lasing modes around 1550-nm wavelength. To capture the intensity profiles of the pump mode and upconversion fluorescence signal in the microdisk, a visible CCD and a set of long-pass filters and short-pass filters (Thorlabs, Inc., Model: FEL800 and FES800) were used to take the place of the IR CCD and long-pass filters in the optical micrograph system for blocking the upconversion fluorescence, and combination of the pump light and the lasing signal, respectively. The generated emission from the microdisk was coupled out by the same tapered fiber and sent into either an optical spectrum analyzer (OSA for short, YOKOGAWA, Inc., Model AQ6370D, detection range: 600 to 1700 nm) or a fiber spectrometer [Ocean Optics, Inc., Model USB2000+ (VIS-NIR), detection range: 350 to 1000 nm] for spectral analysis. Meanwhile, the polarization states of the pump and lasing modes were checked via a precalibrated wire grating polarizer (WGP) by collecting the signals scattered from the edge of the microdisk. The resolutions of the OSA and the spectrometer were set as 0.01 and 1.5 nm, respectively.

Polygon Mode Formation
When the relative position between the tapered fiber and the center of the microdisk was adjusted to 13.37 μm [inset in Fig. 2(c)], the single-mode laser peaking at 1546-nm wavelength was observed in TE polarization, as shown in Fig. 2(a). The IR CCD captured the top view of the lasing mode in Fig. 2(b), which displays a square pattern in the microdisk. The large overlap between the lasing mode pattern and those of the pump mode at 968 nm and the upconversion fluorescence at ∼550-nm wavelengths [shown in Fig. 2(b)], ensures that conventional high-density WGMs circulating around the circumference of the disk cannot be efficiently excited. The relatively large free spectral range (FSR) of 11.5 nm facilitates singlemode lasing within the gain bandwidth of Er 3þ . Figure 2(d) confirms that the laser exhibits a side mode suppression ratio of 37.0 dB. The output power of the laser signal as a function of the pump power is plotted in Fig. 2(e), indicating a lasing threshold of merely ∼25 μW. The maximum output power of the microlaser was measured as 2 μW (i.e., −27.0 dBm) when the dropped pump power was 20 mW. For comparison, we also pumped the microdisk to exhibit a conventional WGM at the pump laser wavelength of 971.5 nm, giving rise to the multiple-mode lasing shown in Fig. 2(f).

Mode Structure Measurements
In principle, WGMs feature ultrahigh Q factors based on the nature of total internal reflection. In reality, however, these modes suffer from the inevitable surface roughness introduced during fabrication, as their optical pathways overlap with the periphery of the cavity. The polygon modes have their main propagation paths away from the boundary yet preserve the total internal reflection condition at the bouncing points. Thus, polygon modes can have competitively high Q factors over those of WGMs. This was proved experimentally based on an undoped microdisk that had the same geometry as the microlaser.

Linewidth Characterization
With such a high Q factor, a laser based on the polygon mode can have an ultranarrow linewidth based on the relationship between the laser linewidth and the Q factor of an undoped cavity. 32 As shown in Fig. 4(a), we measured the linewidth by heterodyning two independently pumped single-mode microlasers. 34 Since the two microdisks have the same diameter, a relative lasing frequency difference of ∼1 MHz can be achieved by adjusting the pump powers. [16][17][18][19]22 The two laser signals were photo-mixed with a 3-dB optical directional coupler and converted to electrical signals with a balanced photodetector for spectral analysis in the radio frequency (RF) domain, as illustrated in Fig. 4(a). Here, a polarization controller was used at the output of one of the microlasers to ensure the two laser signals were of the same polarization state when photo-mixing. The Lorentzian-shaped power spectrum of the beat note signal was captured by a real-time spectrum analyzer (RSA for short, Tektronix RSA5126B) with a resolution bandwidth of ∼1 Hz. Figure 4(b) shows the RF spectrum around 1 MHz when the output powers of both microlasers were ∼2 μW. The full width at half maximum of the detected signal was measured as 643 Hz. Accordingly, the linewidth of the microlaser was 322 Hz, assuming that the microdisks were identical. The power spectral density of the frequency noise was also recorded by the spectrum analyzer in the phase noise analysis mode, as shown in   . 4(c). At the high-frequency range (>0.5 MHz), the frequency noise is almost flat around 196.5 Hz 2 ∕Hz, indicating a linewidth of 309 Hz, which is consistent with the result shown in Fig. 4(b). The linewidth of the microlaser as a function of the output power was further characterized. The inverse linear dependence of the linewidth versus output power agrees well with the Schawlow-Townes formula, [28][29][30] suggesting our microlaser linewidth is quantum noise limited. The measured linewidth is three orders of magnitude narrower than the previous record in on-chip LN microlasers. [16][17][18][19][20][21][22] In addition, the tuning of the microlaser as a function of the pump power in the MHz range can be resolved from the beat note signal captured by the RSA, which has been provided in the Supplementary Material. Here, the tuning efficiency agrees well with the results measured by the OSA.

Real-Time Wavelength Tuning
For the sake of application, the ability of wavelength tuning is usually required, especially for lasers with an ultranarrow linewidth. The wavelength of an LN microlaser can be tuned via temperature or pump power control. [16][17][18][19]22 The pump power tuning based on the combined significant photorefractive and thermo-optic effect is a spontaneous yet limited way. 22,35,36 As shown in Figs. 5(a) and 5(b), when the pump power dropped to the cavity increased from 1.92 to 20.00 mW, the laser wavelength shifted from 1545.633 to 1545.866 nm, corresponding to a wavelength tuning rate of 12.3 pm∕mW (i.e., 1.54 MHz∕μW). To achieve a fast wavelength tuning, the EO-based mechanism is the more favorable way, enabled by the strong linear EO effect of LN. 4 To introduce a refractive index change in the microdisk via the EO effect, a bias was applied between the circular microelectrode on the microdisk and the plane electrode integrated into the LN-on-insulator (LNOI) surface using two metal probes. The microelectrode integrated on the microdisk possesses a radius of 5 μm, as shown in the inset of Fig. 1. The electric potential and the electric field distribution are plotted in Figs. 5(c) and 5(d), respectively. The electric field distributed in the microdisk is mainly oriented in the radial direction. When the applied voltage was 1 V, the electric field strength was ∼2.08 × 10 4 V∕m in the mode volume. Here, the EO coefficient r 22 (6.8 pm∕V) was utilized, and the details of the electrode design can be found in the Supplementary Material. 37,38 Figures 5(e) and 5(f) show the EO performance of the microlaser. When the voltage was tuned from −300 to 300 V, the lasing wavelength was redshifted from 1545.716 to 1546.017 nm, indicating a high linear tuning efficiency of 50 pm∕100 V, which roughly agrees with the theoretically calculated value of 80 pm∕100 V. 37 To access the largest EO coefficient r 33 (30.9 pm∕V), an X-cut LNOI substrate and TE polarized modes should be utilized. External wires can be directly integrated on the chip using air-bridge wiring 37 in future work.

Numerical Modeling
The underlying physics behind the polygon modes can be further explained by performing a 2D finite element simulation using COMSOL. In our simulation, the extraordinary and ordinary refractive indices of LN used in the simulation are n e ¼ 2.1622 and n o ¼ 2.2393 for the pump wavelength and n e ¼ 2.1361 and n o ¼ 2.2113 for the laser wavelength. 39 To provide sufficient perturbation for polygon modes, a tapered fiber is placed on top of the disk and we use the effective index method to compute the effective refractive index of the fiber-disk overlap regime. 40,41 Figures 6(a) and 6(b) show the intensity profiles of the square mode and fundamental WGM at the pump wavelengths while Figs. 6(c), 6(f), and 6(i) display the square mode, fundamental, and high order WGMs, respectively. It is worth mentioning that within one FSR around each of the laser and pump wavelengths, multiple numbers of WGMs coexist but only the single square mode will appear due to the stringent requirement for polygon mode formation. We then compute the overlap factor Γ between different laser and pump modes defined by (1) Here,Î p andÎ l are normalized pump (I p ) and laser (I l ) intensities such thatÎ p;l ¼ I p;l ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi RRR The distributions of the integrand between different pump and laser modes are displayed in the rest of the subplots in Fig. 6. As shown, when the pump is in the square mode, its overlap factor with a square mode at the laser wavelength is Γ ¼ 0.86 [ Fig. 6(d)] while its overlap factor with the fundamental and high-order WGM can be as low as Γ ¼ 0.24 [ Fig. 6(g)] and Γ ¼ 0.34 [ Fig. 6(j)]. The significantly higher overlap coefficient ensures that only the square mode will have a sufficient optical gain for lasing. In addition, the FSR is larger than the gain bandwidth of Er 3þ . Therefore, the square mode at neighboring FSRs will not be excited either due to lower gain. Consequently, single mode operation can be achieved when the polygon mode is formed at the pump wavelength. In contrast, when a regular WGM is formed by the pump, multiple WGMs within the gain bandwidth may lase simultaneously as the Γ of the laser and pump WGMs are close in value [e.g., the overlap between the pump fundamental WGM and high order laser mode can be as high as Γ ¼ 0.53 (Fig. 6(k)]. Finally, it is also worth mentioning that the two-dimensional (2D) simulation will not allow the precise evaluation of the overall quality factor of the coupled cavity due to the unphysically large reflection incurred at the fiber-to-disk interfaces. The issue can be overcome with a full-wave 3D mode match method, which will be applied in future research. 40,41 Nevertheless, the 2D simulation results capture the essence of the polygon mode microlaser, which faithfully reproduces the main features of the observed microdisk laser mode as shown above.

Conclusions and Discussion
The formation of coherent polygon modes with ultrahigh Q factors has allowed for the realization of single-mode narrowlinewidth microlasers in single LN microdisks, which has significant implications for the miniaturization of optical systems in which highly coherent laser sources must be incorporated. To achieve a fully integrated EO tunable polygon mode microdisk laser, the suspended microdisk can be replaced with a microdisk sitting on the fused silica substrate to achieve better mechanical stability. A cladding layer of fused silica is then coated on the LNOI microdisk, which is flattened by polishing to support a coupling waveguide. Then, the fiber taper can be replaced with a waveguide lithographically fabricated on top of the fused silica cladding, and the polygon mode is formed by controlling the coupling location of the upper waveguide and lower LNOI microdisk, allowing for the construction of a fully integrated narrow-linewidth EO tunable polygon mode microdisk laser. Further exploration of the strong piezoelectric, acousto-optic, and second-order nonlinear properties of the LN will promote the performance and functionality of the single-mode microdisk laser in a straightforward manner without the necessity of heterogeneous integration.