The nonlinear effects and applications of gain doped whispering-gallery mode cavities

Whispering-gallery mode (WGM) microcavities [1,2] describe the dielectric structure where light waves are confined by total internal reflection in the microstructure, and light is reflected back on the same optical path where they interfere constructively. During the past decades, the WGM microcavities have enabled the observation of various novel optical effects that are quite important for future integrated optical devices and networks. On the other hand, improving the performance of optical microcavity has become a focal point due to the demands of modern optics, quantum sciences, and laser technology for further development [3]. In the WGM cavities, due to the high refractive index of the microcavity medium, the total reflection and constructive interference of the light field would enhance the cavity field. Usually, the quality (Q) factor and mode volume (V) is often employed to characterize the performance of microcavity, where Q indicates the loss of the optical microcavity and V characterizes the spatial distribution of the light field. Compared with other optical microcavities, the Q-factor of the WGM microcavities would approach up to 10¹¹ [4]. Focusing on WGM microcavity, several novel applications have been developed in recent years, including nonreciprocal photon blockade [5], photonic chaos [6], ultrasonic sensors [7], electromagnetically induced transparency [8–10], etc.

Recently, in order to improve the performance of the WGM microcavities, various approaches have been proposed to enhance the interaction between light and matter, such as designing new microcavity structures, changing the coupling methods, seeking different materials, and so on. For example, the optical gain material is provided to further enhance the optical performance of WGM microcavity. Here the gain cavity may be classified into two groups based on the different mechanisms for producing gain (laser). One method is to use its inherent nonlinear effects to generate gain, including Raman and Brillouin scattering [11,12]. Another more common method is the active gain material which involves doping optical gain media in microcavities, such as rare earth ions [13–15], organic dyes [16], and quantum dots [17].

Compared with conventional microcavities, the gain cavity offers primarily two benefits. First, it may reduce the loss of the mode and enhance the performance of optical devices. It can achieve non-reciprocal optical storage with a lifespan of 10 μs [18]. In addition, it may reduce the dissipation of the cavity mode and increase the detection limit and sensitivity, which has significant sensing applications [19]. Here in this review, we outline the most recent advancements in gain-doped optical WGM microcavities. Moreover, we introduce the dynamics of the gain in WGM resonators, the integration of gain media into WGM microcavities with various shapes, and the fabrication and applications of the gain microcavities. The purpose of this paper is to summarize the recent development of WGM gain microcavities.

The active gain cavity generally refers to optical microcavity containing organic dyes, semiconductor quantum dots or rare earth ions, and other gain media. Optical gain is mainly achieved through the stimulated emission process of the gain particles. For the WGM microcavities doped with quantum dots, they are produced by the recombination of electrons and holes in semiconductors. On the other hand, for the rare earth ions represented by the typical three-level or four-level system, the gain process involves coherent amplification between different energy levels through the population inversion [20]. The medium in the cavity is pumped by the light field from the ground state to the excited state and generates gain through the transition between the energy levels [21,22]. Here this section mainly introduces their energy level distribution and gain generation mechanism.

The rare earth ions used for gain microcavity fabrication include erbium ion (Er³⁺), ytterbium ion (Yb³⁺), and holmium ion (Ho³⁺), etc. [23–25]. The energy levels and gain dynamics of these three ions are shown in fig. 1, respectively. Figure 1(a) depicts a schematic representation of the basic energy levels of Er³⁺, where N₁, N₂ and N₃ represent the population of Er³⁺ in the ground state, metastable state and excited state per unit volume, respectively. Obviously, the difference in the energy levels of erbium ions coincides with the 1550 nm band of optical communications [26]. We can pump erbium ions with 980 nm and 1480 nm wavelengths. When the pump light is 1480 nm, the erbium ion is first excited from the ground state $^{4}I_{15/2}$ to the $^{4}I_{13/2}$ state, and the erbium ion in the $^{4}I_{13/2}$ state will generally transmit back to the ground state again, releasing 1550 nm photons at the same time. When the pump light is around 980 nm, the erbium ions are first excited from the ground state $^{4}I_{15/2}$ to the $^{4}I_{11/2}$ state, and the erbium ion in the $^{4}I_{11/2}$ state will rapidly relax to the $^{4}I_{13/2}$ state. Finally, the $^{4}I_{13/2}$ state erbium ion transitions to the ground state and releases 1550 nm photons.

Zoom In Zoom Out Reset image size

The energy levels diagram of ytterbium ions [27] is shown in fig. 1(b). The structure consists only of the ground state $^{2}\mathrm{F}_{7/2}$ and excited state $^{2}\mathrm{F}_{5/2}$, and the two states are separated by about $10000\ \text{cm}^{-1}$. It has great potential in high-efficiency lasers due to its advantages of no excited state absorption and quenching effect [28]. The absorption band of Yb³⁺ is between 800 and 1064 nm. The Yb³⁺ ions are very suitable as an activator of other rare earth ions. For example, in Er:Yb-doped lasers, Yb³⁺ can effectively absorb 980 nm pump laser, and then transfer energy to Er³⁺ in the ground state and excite them to $^{4}I_{11/2}$ state. Next, these Er³⁺ in the $^{4}I_{11/2}$ state will quickly transition to the $^{4}I_{13/2}$ state, so the reverse energy conversion from Er³⁺ to Yb³⁺ is suppressed. The energy level diagram of Ho³⁺ ions is shown in fig. 1(c), which has mainly two pump absorption bands, with central wavelengths of $1.15\ \mu \text{m}$ and $1.95\ \mu \text{m}$, respectively. Therefore, it can be used for lasers with the spectral range above ${\sim }2\ \mu \text{m}$ as the center and has the characteristics of high efficiency. The operating band with the spectrum is in the high transmission atmospheric window [29].

Here we choose the gain of Er³⁺ as an example, the gain of Er³⁺ to the total energy of the microcavity is mainly contributed by the transitions from the excited to the ground state in $\Delta t$ time [30],

$$\begin{equation} \Delta E=\phi_{p} \sigma_{p}^{a} \cdot N_{3} V_{\textit{neff}} \cdot \hbar \omega_{p} \cdot \Delta t, \end{equation} \tag{ 1 }$$

here, $V_{\textit{eff}}$ is the effective mode volume, $\sigma_{p}^{a}$ denotes the absorption cross-section of the pump laser and $\phi_{p}$ represents the flux of the photons, which could be expressed as

$$\begin{equation} \phi_{p}=\frac{\Delta N}{\Delta s \Delta t}=\frac{|a_{p}|^{2} c}{\hbar \omega_{p} V_{\textit{eff}} n}, \end{equation} \tag{ 2 }$$

where $|a_{p}|^{2}$ represents the total energy of the pumped light in the microcavity. $\omega_{p}$ is the resonant frequency of the pump laser, and ℏ is the reduced Planck constant. Therefore, the gain of this process can be expressed as

$$\begin{equation} g=\lim_{\Delta t \rightarrow 0} \frac{\Delta E}{\Delta t|a_{p}|^{2}}=\frac{c}{n_{p}} \sigma_{p}^{a} N_{3}, \end{equation} \tag{ 3 }$$

where n is the effective refractive index, and c is the speed of light.

As depicted in fig. 1(d), the majority of organic compound materials are capable of realizing the population inversion of particles emitted by excitation through the quasi-four-level system $(E_{1},\ldots, E_{4})$ [16]. Similar to the transition dynamics of rare earth ions, visible light can excite organic dyes from the ground state to the excited state, after which they are rapidly vibrated and cooled to the lowest sublevel of the excited state. The laser can then pass the level of vibrational excitation from the transition to the ground state and relax to the lowest level of the excited state.

Traditional organic fluorescent dyes include rhodamine, coumarin 6, fluorescein, ICG, and Nile red. They have good biocompatibility and are widely used in biosensors and laser [31–34]. In addition to the four-level system, scientists have also explored other ways to achieve organic gains, such as excimer state, excited-state intramolecular proton transfer state, charge transfer state, and thermally activated delayed fluorescence process [35–38].

Rare earth ion gain varies with glass composition. Rare earth ion doped glass products feature cheap manufacturing costs, a simple preparation technique, strong thermal stability, and high photoluminescence efficiency, and improve the gain cavity's optical performance. Quartz glass is the oldest and most used substrate. It has the advantages of fluorescence lifetime, high quantum efficiency, and mature production technology. People have obtained near-infrared laser emission in quartz glass, such as 1.1 μm (Yb³⁺-doped), 1.5 μm (Er³⁺-doped) and 2.0 μm (Ho³⁺-doped). For achieving visible and mid-IR lasers, researchers turned to glasses with additional components including silicate glass, phosphate glass, heavy metal oxide glasses, and non-oxide glass [39,40].

Among these glasses, the silicate glass [41] was the first laser glass (doped with Nb³⁺) discovered and is primarily used in the production of high-energy, high-power lasers. The second kind of glass is phosphate glass, which has a low nonlinear refractive index and good solubility for rare earths. It can realize $30\ \mu \text{W}$ low threshold laser in Er:Yb doped WGM microspheres [42] and achieve ultra-wide 700 GHz tunable range in C-band and L-band [43]. These two kinds of glass have good thermal stability and high mechanical strength, and their usage is second only to quartz glass. The research of heavy metal glass extends the laser to the mid-infrared band, such as tellurite [40], germanate [44], etc. The phonon energy of this kind of glass is lower than that of quartz glass, and its infrared transmission window is wide and has good thermal stability, so it has become a hot spot in the research of mid-infrared lasers. At present, the luminescence properties Dy³⁺-doped tellurite glass [40] and Er³⁺-doped germanate glass [44], at $2.9\ \mu \text{m}$ and $2.7\ \mu \text{m}$ have been studied, respectively. However, it is found that the phonon energy of non-oxide glasses such as fluoride glasses and chalcogenide glasses is lower than that of oxide glasses, which relatively reduces the probability of non-radiative relaxation in the matrix. People gradually began to study the gain and luminescence properties of rare earth ion doped non-oxide glasses. Recently, it was reported that a Ho³⁺/Tm³⁺ co-doped fluorozirconate glass microsphere laser can realize three-wavelength laser. As the 793 nm laser pump power grows, lasing occurs initially at $2.08\ \mu \text{m}$, followed by the cascade outputs at $1.50\ \mu \text{m}$ and $1.84\ \mu \text{m}$ [45]. Similarly, Raman laser at 1620 nm is obtained by using WGM Chalcogenide glass microresonators [46]. Besides glass materials, polymers can also easily be doped with gain materials to prepare WGM resonators. In particular, polymer-based WGMs [47] with high thermal optical coefficient and good biocompatibility have great advantages in improving sensitivity. In terms of biosensing, the Fluorol 7GA doped polymer microcavity exhibits a high refractive index sensitivity of $60.3\ \text{nm/RIU}$ [48]. Moreover, polymer WGM microcavities based on double microdisk coupling can realize single-mode lasers of photonic molecules (PM) in water [49]. Doping with rhodamine dye in a polymer microbottle resonator has successfully achieved a single-mode laser with spectral tunability >8 nm [50].

The effective doping of the gain medium into the microcavity is essential to the fabrication of active gain cavities, such as using the sol-gel technology [51], Van de Graaff accelerator [52], and direct melting of rare earth ion doped optical fiber [53]. The flow chart of the three methods is shown in fig. 2. The first method is to coat the microcavity with doped rare earth ion thin films by sol-gel technology. As shown in fig. 2(a), there are three key steps in this process: After mixing raw materials such as tetraethyl silicate and isopropanol, rare earth ions are added. By putting the microsphere cavity into the solution, then the microspheres were removed from the solution and annealed. Repeat this process 2–3 times, the microspheres could be obtained with the rare earth ions coating. Based on this method, Yang and Vahala [51] reported the laser with a threshold of $28\ \mu \text{W}$ and the single-mode laser output power is as high as $10\ \mu \text{W}$. This method is also suitable for preparing on-chip microtoroid cavities [39], which has the advantages of adjustable doping concentration and uniform distribution of rare earth ions.

Zoom In Zoom Out Reset image size

The second method is to inject rare earth ions into the WGM microcavity by using the Van de Graaff accelerator. The preparation process is shown in fig. 2(b), the erbium ion beam is electrostatically scanned through the aperture of $5 \times 5\ \text{mm}^{2}$, while the microsphere rotates slowly around the stem axis [52]. Erbium ions are uniformly implanted into the microspheres in this way, and then thermally annealed to obtain doped microspheres with a quality factor higher than 10⁷. Besides, this method is also applicable to the microdisk cavity with a thin-layer disk structure, whose bottom is usually a microcylindrical structure. Er³⁺ ions can be doped into the silica microdisk by 2 MeV ion implantation at room temperature. This method can accurately control the distribution of ions in the disk so that Er³⁺ overlaps with WGM. It has obtained laser emission at 1550 nm band, and its pump threshold is 43 pW [54].

The third method is to prepare single-mode fiber doped with rare earth ions directly (fig. 2(c)). This method first etches the fiber with hydrofluoric acid to expose the doped ions to the air and then melts them with a fiber fusion machine or a carbon dioxide laser to obtain microspheres of the required size. Early Nd³⁺ doped microspheres were formed by melting at the end of quartz wire in this way [53]. Microspheres can also be prepared by directly melting vertically placed Er³⁺/Yb³⁺ co-doped glass rods with a laser [55]. It is noteworthy that the preparation of microbubble cavities can be improved in the direct treatment of doped fiber. Based on this, a new thermo optical tuning method is realized, which can tune the laser mode only by letting the airflow through the cavity. Wind speed measurement can be achieved by using this principle (fig. 3), which allows the flow rate to be calibrated with a flow sensitivity as high as 72 GHz/sccm.

Zoom In Zoom Out Reset image size

Certainly, there are also some other ways to prepare the gain cavity. For bulk glass, it can be melted or crushed. The molten glass droplets are collected on rotating plates or quenched with liquid nitrogen, which have been used to prepare Er³⁺-doped and Nb³⁺-doped lasers. The crushed glass powder is formed by the surface tension through the microwave plasma torch flame [56–58]. This method is suitable for mass production of microsphere cavities, but the requirements for temperature and environment are relatively high.

Ultralow threshold lasers

The optical cavity can significantly improve the performance of light-matter interaction. Based on the gain medium in the microcavity, it is possible to create lasers at relatively low pump power. The low threshold lasers with a threshold of 2 to $3\ \mu \text{W}$ are achieved in WGM microcavities and even deformable cavities doped with Er³⁺, Tm³⁺, Yb³⁺, Ho³⁺ [27,28,60]. As previously mentioned, Yb³⁺ can be used as a sensitizer for Er³⁺ to prepare Er³⁺/Yb³⁺ co-doped single-mode or multi-mode lasers with 1550 nm wavelength [13]. The increase of pump power will reduce the output power of the laser due to the diversity of energy levels in the gain medium.

Recently, an interesting phenomenon has been observed in Er³⁺/Yb³⁺ co-doped fluosilicate glass microspheres. This glass material provides Er³⁺ with a low phonon energy environment, and visible green light is observed. With the increment of the pump power, the color of the luminous emission changed to yellow-green, and then yellow-red [61]. It is found that 1550 nm laser can also be generated in microcavity by using the amplified spontaneous emission (ASE) light source. Compared with tunable pump light, ASE pump source has polarization in all directions to excite WGM in Er³⁺/Yb³⁺ co-doped SiO₂ microsphere cavity (fig. 4(a)). Therefore, the laser generated by ASE pump source will not be affected by the change of vibration and temperature which is more suitable for practical applications [62]. Besides, Gain microcavities are also used to prepare high-power lasers. The erbium-doped aluminosilicate microspheres prepared by sol-gel method have a laser power of up to $0.45\ \text{mW}$ [63]. A laser with a wavelength of $2\ \mu \text{W}$ can be generated in Er³⁺-doped SiO₂ microspheres with a laser power of $0.222\ \text{mW}$ [64]. The optical path of double microsphere coupling is shown in fig. 4(b). Since the emission field generated by the first microsphere cavity is coupled to the second microsphere, when the laser modes in the two cavities overlap and resonate at the same time, the laser can be enhanced and accompanied by higher conversion efficiency and narrower linewidth [65].

Zoom In Zoom Out Reset image size

In terms of tunable laser, the gain cavity doped with rare earth ions also has better performances, such as the tunable range up to $17.3\ \text{GHz}$ [26]. Based on the improved sol-gel method, it is easy to prepare an all-optical tunable high-Q microbubble laser [66]. As shown in fig. 4(c), a spherical end was designed in the conical region of the microbubble, and iron oxide nanoparticles were coated on its surface. Iron oxide nanoparticles with excellent photothermal properties could be used to realize all-optical tuning of laser wavelength in the range of $4.4\ \text{nm}$ by controlling the axial light into heat energy. Interestingly, phosphate glass microspheres with Yb³⁺/Er³⁺ co-doping have photorefractive properties. The researchers measured the laser blueshift by UV irradiation and obtained a laser power of $90\ \mu \text{W}$ at $1568.3\ \text{nm}$ [67]. Due to the unique advantages of microbubble cavities, the design of rare earth ion doped microbubble lasers has been theoretically analyzed recently [68].

Optical sensing

The gain microcavity could be used for optical ultrasensitive sensing due to the strong light-matter interaction. The microbubble cavity with a hollow structure is very suitable for detecting the change of refractive index through liquid flow. When a liquid with refractive index varying from 1 to 1.5 is injected into the Er³⁺/Yb³⁺-doped microbubble cavity, the WGM wavelength has a red shift of approximately $0.3\ \text{nm}$ [69]. Er³⁺/Yb³⁺ co-doped tellurite spheres were placed in three organic solvents with different refractive indices [70], which are methanol $(n = 1.3284)$, acetone $(n = 1.3586)$ and isopropanol (IPA) $(n = 1.3772)$. The detection sensitivity is $7.7\ \text{nm/RIU}$ by the change of resonance displacement and refractive index. The author found that tellurite spheres with a high refractive index are more suitable for detecting nanoparticles smaller than 50 nm. It is worth noting that dye-doped polymer microcavities have great potential for refractive index sensing. The microgoblet cavity doped with laser dye is integrated onto the microfluidic chips, and its refractive index sensitivity reaches $10.56\ \text{nm/RIU}$ [72].

Furthermore, doping Er³⁺/Yb³⁺ in different glasses has been widely used for temperature sensing [73]. The WGM resonance in the Er³⁺/Yb³⁺ co-doped glass microspheres was analyzed at different temperatures in the range of 290–380 K, and a resonance shift of $4.7\ \text{pm K}^{-1}$ has been achieved [74]. For Yb³⁺/Pr³⁺-doped phosphate microsphere temperature sensor [71], the temperature uncertainty of WGM displacement is $0.4\ \text{K}$, which is $0.3\ \text{K}$ higher than that of LIR technology (fig. 5). Recently, an erbium-doped microsphere laser placed in an open microcavity of fiber [75] has been reported, with a laser threshold of $0.033\ \text{mW}$. By this special system, the author observed the temperature sensitivity of the gain microlaser is $33.3\ \text{pm/}^{\circ}\text{C}$, which is significantly better than that of a conventional WGM resonator.

Zoom In Zoom Out Reset image size

Other nonlinear effects and applications

The gain medium in the WGM microcavity can significantly reduce the loss of signal light through gain compensation, resulting in gain nonlinearity. An optical isolator is implemented in an Er³⁺-doped microcavity, where the nonlinearity caused by gain saturation greatly suppresses the signal loss, making it have significant unidirectional optical transmission characteristics and very low insertion loss [76]. Gain compensation of rare earth ions is used to overcome surface scattering in passive cavities. In the fluoride glass microspheres doped with Er³⁺, the slow light effect is introduced by coherent oscillation, so that the photon lifetime is as high as $2.5\ \text{ms}$ [77]. Additionally, $\mathcal{P}\mathcal{T}{\text{-symmetric}}$ systems can be constructed based on the gain and dissipation of the cavity, which is conducive to further study of nonlinear effects. Recently, chaotic phenomena can be effectively controlled in a $\mathcal{P}\mathcal{T}{\text{-symmetric}}$ structure which consists of a YIG sphere coupled with Er/Yb-doped microsphere [78].

Measuring the lifetime of gain ions is an important issue in the field of quantum information and nanophotonics, which is conducive to further understanding and improving the performance of photonic and quantum devices. Recently, it has been reported that the gain lifetime can be characterized by time-resolved stimulated emission in the microtoroid cavity [20] and the experimental device is shown in fig. 6. Two tunable laser diodes with linewidth less than 200 kHz provide pump laser (1430 nm) and probe signal (1550 nm) to the microtoroid cavity with $Q \sim 10^{6}$. The authors observed the evolution of optical gain by tuning the probe signal and the lifetime can be characterized simultaneously by measuring the linewidth of the mode. The calculated gain lifetime to erbium ion is estimated to be $5.1\ \text{ms}$. They also used this device to realize the optical thermal control of the gain [79]. By changing the incident frequency and scanning speed of signal light, the gain of erbium ions is successfully adjusted, which has strong robustness to pump laser.

Zoom In Zoom Out Reset image size

For the WGM microcavity, the two most important parameters are the resonance frequency and the dissipation rate. The dissipation rate of cavity mode can be effectively controlled by using gain competition, and the resonance evolution of the probe signal can be controlled while the pump remains unchanged [80]. Furthermore, recent studies have shown the parameter design of passively mode-locking (ML) gain lasers [81]. It is found that the threshold of passively mode-locking is related to the gain and dispersion. Weak anomalous dispersion promotes ML operation with limited gain. A $300\ \mu \text{m}$ microtoroid gain cavity with the Q-value slightly higher than 10⁷ is conducive to mode-locking. All optical, pump assisted and thermal tuning of high-Q WGM resonance can be achieved in Er³⁺/Yb³⁺ co-doped quartz microspheres [82].

In summary, the WGM microcavities play an important role in the field of nanophotonics and quantum information. Through the gain doping, the interaction between the optical field and solid material could be enhanced, and the loss of optical signals could be compensated. Here in this review, we discussed the dynamics of the passive and active gain cavities. The recent progress of applications using gain microcavities is also discussed. With the progress of fabrication technologies on the nanoscale, the optical gain cavities based on the WGM mode could have more potential applications in optical communication, aerospace, and quantum information science.

The authors gratefully acknowledge the support from the National Natural Science Foundation of China through Grant No. 62131002, and the Fundamental Research Funds for the Central Universities (BNU). The authors declare no conflicts of interest.

Data availability statement: All data that support the findings of this study are included within the article (and any supplementary files).