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Research on the Rationality of Standing Wave Supermode Microcavity Coupling

Due to its extremely high quality factor and small mode volume, the acoustic bar-mode optical microcavity can greatly enhance the intensity of light-matter interaction, so it has attracted extensive research interests in high-sensitivity sensing, nonlinear optics, miniature lasers, quantum optics, etc. The sound bar mode in the microcavity is a traveling wavemode, which supports a pair of degeneracic modes that propagate in opposite directions, i.e., clockwise mode A and counterclockwise mode A. In a perfect microcavity, the clockwise and counterclockwise modes have the same frequency and opposite directions of propagation, and they are orthogonal and do not interact. However, when scatterers or periodic modulation appear on the surface of the microcavity, there will be a coupling between the positive and negative propagation modes. When the coupling strength is greater than the loss rate of the cavity mode itself, it will cause a strong coupling between the forward and reverse propagation modes. At this time, two new standing wave modes are formed in the microcavity through the superposition of positive and negative propagation modes, also called optical supermodes, and the two optical supermodes are (a±a)/√2 respectively. The frequencies of the two optical supermodes are no longer degenerate, but rather split, and the magnitude of the cleavage depends on the strength of the coupling between the positive and negative propagation modes. Supermodel optical microcavities have been widely used in nanoparticle detection, stimulated Brillouin scattering, optical parametric oscillation, and microcavity optical comb dispersion control.

For the above-mentioned supermode microcavity applications, the coupling condition between the microcavity and the coupled waveguide plays a crucial role in the sensor detection limit and nonlinear optical process. For example, in the application of nanoparticle sensing, the frequency splitting caused by nanoparticles needs to be larger than the bus width of the supermodel, so the nanoparticle sensing needs to be carried out in an undercoupled state to effectively suppress the increase in line width caused by external coupling.

Recently, the team of Li Beibei, a distinguished researcher from the Institute of Physics of the Chinese Academy of Sciences/Beijing National Research Center for Condensed Matter Physics, used a supermode optical microcavity with edge periodic modulation to realize a pair of optical supermodes with mode cleavage, and made the mode cleavage amount just match the Brillouin phonon frequency in the microcavity, so as to achieve the double resonance condition of microcavity Brillouin scattering. By pumping at the high-frequency mode of this pair of optical supermodels, they achieved a narrow linewidth Brillouin phonon laser; By pumping at low frequency mode, strong photo-mechanical coupling is achieved. (Min Wang#, Zhi-Gang Hu#… Qi-Fan Yang*, Bei-Bei Li*, “Taming Brillouin Optomechanics Using Supermode Microresonators,” Phys. Rev. X 14, 011056 (2024))。 In this work, they were surprised to find that the bus width of the standing wave supermode is significantly more than twice its intrinsic loss rate in the near-critical coupling state, and that the optical supermode cannot reach the overcoupled state even when the external coupling rate is much larger than the intrinsic loss rate. These behaviors are significantly different from the traveling-wave sound bar pattern, which goes from undercoupling to critical coupling to overcoupling as the external coupling rate continues to increase. In addition, for the traveling-wave sound bar mode, the bus width in the critically coupled state is twice the intrinsic loss rate of the mode. This behavior can be characterized by the coupling degree of hypothesis, which characterizes the proportion of the optical mode in the microcavity coupled to the waveguide fundamental mode. Previous work has systematically studied the coupling degree in the traveling-wave echo wall mode in the silica microsphere cavity and the integrated silicon nitride microring cavity. The results show that the use of single-mode waveguides can generally effectively reduce the parasitic losses, so that the coupling degree can reach 1. However, there is still no research on the coupling rationality of the VSWR model.

Research on the Rationality of Standing Wave Supermode Microcavity Coupling

Figure 1(a) Schematic diagram of the loss channel of a VSW-wave supermode microcavity with periodic radius modulation. (b) Normalized transmission spectra of the optical mode, with a gradual increase in backscatter intensity (/2) from top to bottom, where the intrinsic loss rate κ/2 = 100 MHz for the mode. Inset: The distribution of the light field of two standing wave supermodes, with red and blue representing the positive and negative maxima of the electric field, respectively. (c) Normalized transmission spectra at different external coupling rates κ/2. The blue, red, orange, purple, and green curves correspond to = κ/κ= 0.01, 0.1, 1, 5, and 10, respectively (where κ/2 = 100 MHz, /κ= 10). (d) The normalized transmission spectral depth of the optical mode as a function of the bus width. The blue and green dots correspond to cases with strong backscatter (/κ = 10) and no backscatter (/κ = 0), respectively. The black dashed and solid fitted curves correspond to the ideal case of = 0.5 and = 1, respectively.

In order to systematically study the coupling behavior of standing wave super-mode microcavities, the team recently designed and fabricated super-mode optical microcavities, and systematically studied their coupling degree and imagination. By designing periodic modulation with an amplitude of the nanometer at the edge of the microcavity, the light field in the microcavity can be backscattered, so that the clockwise and counterclockwise propagation modes of the microcavity are strongly coupled, resulting in mode splitting (Fig. 1(a)). The frequency difference between the two standing wave supermodes is twice the backscatter intensity, so it gradually increases as the backscatter intensity increases (Fig. 1(b)). As the external coupling rate increases, the linewidth of the transmission spectrum of the supermodel gradually increases, and the depth gradually decreases, but the overcoupling region cannot be reached (Fig. 1(c)). For the traveling wave echo wall mode without backscattering, when the fiber cone diameter satisfies the single-mode condition, there is no parasitic loss caused by the higher-order mode, and the coupling degree can reach 1, but for the standing wave supermode with strong backscattering, the coupling degree can only reach 0.5 (Fig. 1(d)).

Research on the Rationality of Standing Wave Supermode Microcavity Coupling

Fig.2. Characterization of silica supermode optical microcavities. (a) Top: Scanning electron microscope (SEM) image of an optical microcavity. Middle: Locally enlarged view of periodic modulation at the edges. Bottom: Optical microscope image of a supermode microcavity coupled to a tapered fiber. (b) and (c) are the normalized transmission (blue) and reflection (orange) spectra of the TE (b) and TM (c) modes of supermode microcavities, respectively. (d) and (e) are fine scanning transmission (blue) and reflectance (orange) spectra of the labeling patterns in the black boxes in (b) and (c), respectively.

Research on the Rationality of Standing Wave Supermode Microcavity Coupling

Fig.3. Coupling degree measurement of silica supermode microcavity. (a, b), evolution of the normalized transmission (a) and reflection (b) spectra of the high-frequency TE target mode (₊), where =0.02, 0.17, 1.08, 3.39, 5.22. (c), the normalized resonant transmission depth of mode ₊ is a function of the bus width with a like-mindedness of 0.5, where /κ = 135. (d, e), the evolution of the normalized transmission (d) and reflectance spectrum (e) of the non-target mode, where =0.02, 0.16, 0.99, 3.26, 5.38, where the backscatter is zero. (f), the normalized resonance transmission of the non-target mode is a function of the bus width with a like-for-likeness of 1, where /κ= 0.

In this work, a series of Silica supermode optical microcavities with a radius of only 20 μm and edge periodic modulation quantities ranging from 10 nm to 30 nm were designed and fabricated (Fig. 2(a)), and the cleavage of the modulated optical supermodes was about GHz. For optical modes where the number of angular patterns does not match the number of edge modulation periods, there is no strong backscatter, so these modes are still traveling-wave echo wall patterns (Figure 2(c)). The degree of coupling probability can be characterized by measuring the transmission and reflection spectra of the VSWC and traveling-wave echo wall modes at different external coupling rates (Figure 3). The experimental results show that for the standing wave supermodel with strong backscattering, there is a strong reflection spectrum, and its coupling degree can only reach about 0.5, while for the traveling wave echo wall mode, the reflection spectrum intensity is almost 0, and the coupling degree can reach 1. These results are in good agreement with the theoretical results. In addition, the transmission and reflection spectra of standing wave supermodes with different backscattering intensities were measured experimentally, and their coupling probabilities were statistically calculated (Fig. 4). The experimental results also show that in the absence of other parasitic losses, the coupling degree of the traveling wave echo wall mode without strong backscattering can always reach 1. As long as the large to strong backscattering condition is, no matter what the value of / is, the coupling degree of the standing wave supermode can only reach 0.5. This is due to the strong backscattering in the cavity that scatters half of the energy in the microcavity to the back, and this part of the backastigmatism is not collected, thus causing the equivalent parasitic loss. The coupling degree of =0.5 provides a convenient way to adjust the bus width while maintaining critical coupling, and is expected to be used in applications such as controlling the bandwidth of photosensors, implementing bandwidth-adjustable optical filters, and optimizing phase matching conditions for photon-phonon interactions.

Research on the Rationality of Standing Wave Supermode Microcavity Coupling

Fig.4 Experimental results of the coupler degree of supermode and non-splitting mode with /κ.

The research results were published in the journal Photonics Research on July 15, 2024 under the title of "Coupling ideality of standing-wave supermode microresonators". Wang Min and Lei Yuechen, Ph.D. students from the Institute of Physics, Chinese Academy of Sciences, are the co-first authors, and Li Beibei, Distinguished Researcher of the Institute of Physics, Chinese Academy of Sciences, is the corresponding author. The above research work has been supported by the National Key R&D Program of China (2021YFA1400700), the National Natural Science Foundation of China (11934019, 12174438, 62222515, 91950118, 92150108), the Beijing Natural Science Foundation (Z210004), the Basic Research Young Scientist Program of the Chinese Academy of Sciences (YSBR-100), and the Basic Frontier Scientific Research Program of the Chinese Academy of Sciences ( ZDBS-LY-JSC003).

Edited by virens