Quantum noise auxiliary multi-channel broadband optical chaos generation device based on micro-ring resonant cavity

Abstract

The invention discloses a quantum noise auxiliary multi-channel broadband optical chaos generation device based on a micro-ring resonant cavity. The quantum noise auxiliary multi-channel broadband optical chaos generation device comprises a noise driving source, the micro-ring resonant cavity and a filtering and demultiplexing detection unit, a noise signal is preprocessed through an optical band-pass filter to form a narrow-band noise light source which is injected into the micro-ring resonant cavity; different frequency components in the noise light source are mutually coupled through a nonlinear effect and a dispersion effect in the cavity to form a wide-spectrum chaotic signal; the intra-cavity dynamic effect further enhances the complexity of the chaotic signal and broadens the spectrum of the chaotic signal of each comb tooth; considering that the pumping frequency component occupies most energy of the optical comb, in order to avoid interference, the pumping frequency component of the chaotic signal is filtered by the band elimination filter, and the optical comb signal subjected to filtering processing passes through the wavelength division demultiplexer, so that the chaotic signals with different central wavelengths are separated for subsequent analysis and application.

Description

Technical Field

[0001] The present invention belongs to the field of optical communication technology, and more specifically, relates to a quantum noise-assisted multi-path broadband optical chaos generating device based on a micro-ring resonator. Background Art

[0002] Chaotic lasers have been widely used in recent years in the fields of secure optical communications, random number generation, lidar, fiber optic sensing, reinforcement learning, and reserve pool computing due to their wide spectrum, high sensitivity to initial conditions, and noise-like characteristics. By applying external disturbances to semiconductor lasers, their output can enter a chaotic state. At present, the common methods for generating chaotic lasers based on semiconductor lasers mainly include external cavity optical feedback, external light injection, and photoelectric feedback.

[0003] However, the above-mentioned method of generating optical chaos based on semiconductor lasers has the following limitations:

[0004] First, due to the inherent relaxation oscillation characteristics of semiconductor lasers, most of the energy in the power spectrum of chaotic signals is concentrated near the relaxation oscillation frequency. This leads to the unevenness and bandwidth limitation of the chaotic signal power spectrum, thus limiting the transmission rate of secure communication systems and the resolution of radar detection.

[0005] Second, in the chaotic laser generation scheme based on the optical feedback structure, the external cavity feedback will cause the autocorrelation curve of the chaotic signal to have a spike at the feedback delay position that is significantly higher than the surrounding value. This spike is called the time delay signature (TDS). The existence of TDS may leak the feedback delay parameters, thereby threatening the security of the confidential communication system.

[0006] Third, these methods can usually only generate single-channel chaotic signals, which makes it difficult to meet the needs of large-scale parallel signal processing, such as wavelength division multiplexing chaotic secure communication and chaotic laser-based radar three-dimensional imaging.

[0007] In order to solve the problem of limited bandwidth of chaotic signals, researchers have proposed a variety of improvement schemes, including asymmetric dual-path feedback structure, parallel coupled microring resonator feedback structure, phase modulation cascade dispersion element, wide spectrum signal injection and laser network coupling, to improve the bandwidth of chaotic signals. Although these schemes can extend the effective bandwidth to tens of GHz, they are usually difficult to break through the 50 GHz limit due to device performance limitations. In addition, these methods are still limited to generating single-channel chaotic signals and cannot meet the needs of multi-channel parallel applications.

[0008] The time delay signature (TDS) problem mainly comes from the feedback delay time determined by the length of the external cavity. The time delay characteristics caused by this linear feedback can be suppressed by optimizing the feedback loop. To solve the TDS problem, scholars have proposed some improvement measures, including using fiber Bragg gratings or chirped fiber gratings to replace traditional feedback mirrors, introducing dispersion modules in the feedback loop, and hiding TDS through multiple feedback paths. However, these methods are mainly aimed at the optimization design of single-channel chaotic signals and cannot meet the needs of large-scale parallel signal generation.

[0009] The researchers extended their research ideas to generate multiple chaotic signals at the same time to increase the number of chaotic entropy sources. The proposed technical solutions include: a method based on optoelectronic hybrid feedback and parallel filtering [Journal of Lightwave Technology, 2022, 40 (3), 751-761]; a long-cavity active Fabry-Perot laser solution [Journal of Selected Topics in Quantum Electronics, 2023, 29 (6), 1-7]; and a continuous wave laser using an external cavity laser with self-phase injection to achieve multi-channel chaotic signals [Opto-electronics Advances, 2022, 5 (5), 200026]. These studies explored the generation technology of multi-channel chaotic channels based on semiconductor lasers. However, the number of parallel chaotic channels generated by the above schemes is still limited, which is difficult to meet the needs of large-scale parallel signal processing.

[0010] In addition, Wang Xingjun's team at Peking University proposed a scheme to achieve hundreds of parallel chaotic outputs using a microring resonator under DC pumping [Nature Communications, 2023, 14(1), 4590]; Li Pu's team at Guangdong University of Technology proposed a scheme to achieve large-scale chaotic output using an add-drop microring resonator under DC pumping [Light: Science & Applications, 2024, 13(1), 66]. Although these schemes have made significant breakthroughs in the number of channels, the bandwidth of a single chaotic signal is limited to only about 1 GHz. In addition, due to the four-wave mixing effect, the chaotic signal has a certain correlation at the optical comb that is symmetric about the pump wavelength, making it difficult to fully meet the orthogonality requirements.

[0011] In summary, achieving the generation of large-scale parallel broadband chaotic signals and ensuring the orthogonality between different signals is still a technical problem that needs to be solved. Therefore, exploring a device that can generate multi-channel parallel broadband laser chaotic signals not only has important research value, but also has broad application prospects in the fields of secure communication and random number generation. Summary of the invention

[0012] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a quantum noise-assisted multi-channel broadband optical chaos generation device based on a microring resonator, which can effectively increase the number of channels and bandwidth of chaotic signals while reducing the correlation between signals, thereby providing a new way to generate large-scale parallel broadband optical chaotic signals.

[0013] To achieve the above-mentioned purpose of the invention, the present invention provides a quantum noise-assisted multi-channel broadband optical chaos generation device based on a micro-ring resonator, characterized in that it includes: a noise driving source, a micro-ring resonator and a filtering demultiplexing detection unit;

[0014] Among them, the noise driving source includes an erbium-doped fiber amplifier, an optical bandpass filter and a polarization controller, which are used to generate a narrowband noise signal as a driving source and inject it into the microring resonant cavity; the narrowband noise signal is subjected to a nonlinear effect in the microring resonant cavity, and a wide-range chaotic optical comb signal is output; the filtering and demultiplexing detection unit includes: an optical band-stop filter, a wavelength division multiplexer and a photodetector; the filtering and demultiplexing detection unit realizes the independent extraction of each comb tooth spectrum component in the chaotic optical comb signal, and then outputs it through photoelectric conversion.

[0015] The object of the invention of the present invention is achieved in this way:

[0016] The invention discloses a quantum noise-assisted multi-channel broadband optical chaos generating device based on a micro-ring resonator, comprising: a noise driving source, a micro-ring resonator and a filtering demultiplexing detection unit; the noise signal is pre-processed by an optical bandpass filter with a width of 30 GHz and a center wavelength consistent with the center wavelength of the micro-ring resonator to form a narrow-band noise light source, and then injected into the micro-ring resonator. After the noise light source enters the micro-ring resonator, different frequency components are coupled to each other through the nonlinear effect and dispersion effect in the cavity to form a chaotic signal with a wide spectrum. The dynamic effect in the cavity further enhances the complexity of the chaotic signal and broadens the spectrum of the chaotic signal of each comb tooth. Considering that the pump frequency component occupies most of the energy of the optical comb, in order to avoid its interference, the chaotic signal first passes through a band-stop filter with a center wavelength consistent with the center wavelength of the micro-ring resonator and a width of 50 GHz to filter out the pump frequency component. The optical comb signal after filtering is then separated by a demultiplexer to separate the chaotic signals of different center wavelengths for subsequent analysis and application.

[0017] At the same time, the quantum noise-assisted multi-channel broadband optical chaos generation device based on the micro-ring resonator of the present invention also has the following beneficial effects:

[0018] (1) The width of the optical bandpass filter should be less than or equal to the resonant frequency range of the microring resonator to ensure that each frequency component can effectively induce nonlinear effects in the microring resonator, thereby achieving efficient generation of chaotic signals.

[0019] (2) The width of the optical band-stop filter should be greater than or equal to the width of the narrowband noise signal to ensure that the effective bandwidth of the chaotic signal in each channel can be accurately calculated and to avoid the pump frequency interfering with other chaotic signals.

[0020] (3) The channel bandwidth of the demultiplexer should be larger than the line width of each chaotic comb tooth, and it is necessary to ensure that each channel passband contains only one chaotic comb tooth, so as to achieve effective separation of parallel chaotic signals.

[0021] (4) Significant improvement in bandwidth: The present invention successfully increases the chaotic signal bandwidth of each comb tooth to 30 GHz, which is more than 10 times the bandwidth improvement compared to the traditional DC pumping scheme, greatly meeting the needs of high-speed signal processing.

[0022] (5) Low correlation and high orthogonality: Compared with the DC pumping scheme, the present invention effectively reduces the correlation of chaotic signals between channels. The signal cross-correlation between channels is about 0.05, which significantly improves the orthogonality between signals and ensures the stable output of independent channels.

[0023] (6) Reduced pumping threshold: The quantum noise-assisted pumping mechanism of the present invention makes the average power density threshold required to excite the chaotic light comb lower than that of the DC pumping scheme, further reducing the system power consumption and energy requirements.

[0024] (7) Noise width optimization: Appropriately increasing the spectral width of the injected noise can effectively improve the effective bandwidth of the chaotic signal and provide a feasible way to flexibly control the system bandwidth. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a structural diagram of a quantum noise-assisted multi-channel broadband optical chaos generation device based on a micro-ring resonator of the present invention;

[0026] Figure 2 (a) Spectrum of the chaotic light comb driven by noise; (b1)-(b4) Time domain waveforms corresponding to the wavelengths of four different comb teeth.

[0027] Figure 3 Effective bandwidth distribution of chaotic signals in 24 channels near the central wavelength under noise driving.

[0028] Figure 4 (a) The peak value of the cross-correlation function of chaotic signals in 8 channels under DC pumping; (b) The peak value of the cross-correlation function of chaotic signals in 8 channels under quantum noise driven pumping.

[0029] Figure 5(a1)-(a5) Spectral evolution diagrams of the chaotic light comb under DC pumping as the pump power increases; (b1)-(b5) Spectral evolution diagrams of the chaotic light comb under quantum noise driven pumping as the pump power increases.

[0030] Figure 6 The average effective bandwidth of the comb chaos signal varies with the ASE noise width. DETAILED DESCRIPTION

[0031] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0032] Example

[0033] In this embodiment, if Figure 1 As shown, the present invention is a quantum noise-assisted multi-channel broadband optical chaos generation device based on a micro-ring resonant cavity, comprising: a noise driving source, a micro-ring resonant cavity and a filtering demultiplexing detection unit;

[0034] The noise driving source includes an erbium-doped fiber amplifier 1, an optical bandpass filter 2 and a polarization controller 3;

[0035] Erbium-doped fiber amplifier 1: Erbium-doped fiber amplifier (EDFA) is used to directly amplify its internal broadband spontaneous emission (ASE) noise and provide broadband noise driving signal for the system.

[0036] Optical bandpass filter 2: The central wavelength matches the central wavelength of the microring resonator, and the bandwidth is set to 30 GHz. Optical bandpass filter 2 selects a narrowband noise signal with a spectral width of 30 GHz from the ASE noise amplified by the EDFA, and injects it into the microring resonator as a driving source to excite the nonlinear effect in the cavity. In this embodiment, an incoherent noise driving source is used to drive the microring resonator. Since the coherence of the excited optical comb depends on the coherence of the pump signal, the correlation between the multi-channel chaotic signals is effectively reduced, so that the chaotic signals of each comb tooth show orthogonality.

[0037] Polarization controller 3: The polarization controller is used to adjust the polarization state of the light injected into the microring resonator. Since the microring resonator is a polarization-dependent device, the polarization state needs to be adjusted before the noise light source enters the cavity to ensure the best coupling efficiency. Specifically, by observing the output power, when the power reaches the maximum value, the polarization state of the injected light is the TE state, and the coupling efficiency is the highest at this time.

[0038] The micro-ring resonant cavity 4 is used to receive the narrow-band noise signal. The narrow-band noise signal is transmitted in the micro-ring resonant cavity according to the formula: The nonlinear effect, dispersion effect and frequency interaction are carried out to make all frequency components within the resonance peak resonate in the cavity, thereby outputting a wide range of chaotic optical comb signals.

[0039] Where BPF[·] represents the output optical field after ASE noise is amplified by EDFA and passes through the optical bandpass filter; E randn (t) is the random amplitude of the ASE noise light field after EDFA amplification; randn(t) is the phase noise of the ASE noise light field after EDFA amplification; t R is the time it takes for the light field to travel back and forth in the microring resonator; E(t,τ) is the light field evolving in the cavity, t is the slow time describing the evolution of the electric field envelope in the cavity, and τ is the fast time traveling at the group velocity in the resonator; α 0 is the total loss in the microring resonator; δ 0 is the frequency detuning between the pump light and the microring resonator; β 2 is the second-order dispersion in the microring resonator; L is the cavity length of the microring resonator; γ is the nonlinear coefficient in the microring resonator; θ is the power transmission coefficient between the straight waveguide and the microring resonator; is the driving term of the input light field;

[0040] In this embodiment, the microring resonator directly generates a chaotic Kerr optical frequency comb during the excitation process, without going through the evolution process from the primary optical comb to the secondary optical comb and then to the chaotic state. In addition, due to the lack of coherence of the noise driving signal, although the conversion efficiency is lower than that of the DC pumping method, the chaotic signal on each comb tooth has better orthogonality. As the power of the pump noise signal increases, the spectral linewidth of each optical comb tooth is significantly broadened, thereby increasing the effective bandwidth of the chaotic signal.

[0041] The filtering demultiplexing detection unit further comprises: an optical band-stop filter 5, a de-wavelength division multiplexer 6 and a photodetector 7;

[0042] Optical band-stop filter 5: The central wavelength of the optical band-stop filter (OBPF) is consistent with the central wavelength of the microring resonator, and the bandwidth is set to 50 GHz. Since the bandwidth of the pump narrowband noise signal is 30 GHz and its power is tens of dBm higher than the excited optical comb signal, in order to avoid the interference of the pump noise signal on the subsequent chaotic signal performance analysis, an optical band-stop filter is required to filter out the pump frequency component in the spectrum.

[0043] De-wavelength division multiplexer 6: De-wavelength division multiplexer (DWDM) is used to separate the filtered chaotic optical comb signal into multiple chaotic signals with different central wavelengths, and each channel corresponds to the central wavelength of a comb tooth. This process realizes the independent extraction of the spectral components of each comb tooth in the chaotic optical comb, providing a basis for the subsequent analysis of the performance parameters of a single comb tooth chaotic signal.

[0044] Photodetector 7: The photodetector (PD) converts the chaotic optical signals of each channel output by the demultiplexer into corresponding electrical signals. These electrical signals can be directly used for subsequent performance analysis and processing.

[0045] Figure 2 (a) shows the spectrum of the chaotic light comb excited in the microring resonator under the ASE noise drive with an average power density of 23.5dBm and a width of 30GHz. It can be observed from the figure that under the quantum noise-assisted pump drive, the system can still excite a chaotic light comb that is symmetrical about the central wavelength. Since the free spectral range (FSR) of the microring resonator is set to 50GHz, a chaotic light comb tooth will be generated every integer multiple of the free spectral range. Further analysis shows that the spectral coverage of the chaotic light comb is closely related to the pump power. As the pump power increases, the excited spectral range gradually widens.

[0046] Figure 2 (b1)-(b4) respectively show the time domain waveforms of the chaotic signals corresponding to four comb teeth selected from the optical comb. By observing the time domain waveforms, it can be seen that compared with the chaotic optical comb generation scheme of the traditional continuous light pumping, the effective bandwidth of the chaotic signal of each comb tooth in the present invention has been significantly improved. In the traditional DC optical pumping scheme, the effective bandwidth of each chaotic comb tooth is usually limited to about 1 GHz; while the quantum noise assisted pumping scheme proposed in the present invention successfully increases the effective bandwidth of the chaotic signal at each comb tooth to about 30 GHz.

[0047] A larger effective bandwidth is of great significance for achieving higher-speed physical random number generation and higher-resolution radar detection. This shows that the quantum noise-assisted pumped chaotic optical comb scheme proposed in this invention has made a significant breakthrough in bandwidth performance and meets the needs of high-performance chaotic entropy sources in practical applications.

[0048] Figure 3 The effective bandwidth of the chaotic signal at 24 comb teeth near the central wavelength is further demonstrated. As can be seen from the figure, the effective bandwidth of the chaotic signal at each comb tooth is significantly improved, reaching about 30 GHz. Compared with the solution in the literature [Journal of Lightwave Technology, 2024, 42 (24), 8730-8738], the solution of the present invention shows better wavelength insensitivity, ensuring the uniformity and stability of the bandwidth performance of each comb tooth signal.

[0049] Figure 4 (a)-(b) shows the peak value relationship of the cross-correlation function between the DC pumping scheme and the selected example channel in the scheme of the present invention. Figure 4(a) It can be seen that under DC pumping, the correlation of chaotic signals between comb teeth is greater than 0.1, and comb teeth symmetrical about the central wavelength (such as CH1 and CH5, CH2 and CH6, CH3 and CH7, CH4 and CH8) have higher correlation. This phenomenon is because the symmetrical comb teeth are generated by the same four-wave mixing process, and the four-wave mixing meets the phase matching condition. The spectrum of the comb teeth on both sides has a high similarity, which leads to an increase in signal correlation.

[0050] Figure 4 (b) shows the cross-correlation characteristics of the eight comb teeth chaotic signals driven by quantum noise. As can be seen from the figure, the correlation of chaotic signals between comb teeth in this scheme is reduced to about 0.05. This phenomenon is attributed to the random distribution of the frequency and phase components of narrowband noise, which effectively destroys the original coherence between comb teeth, thereby significantly reducing the correlation between signals.

[0051] Figure 5 (a1)-(b5) show the evolution of the output state of the microring resonator under DC pumping and narrowband noise pumping. (a1)-(a5) are the evolution diagrams of the microring resonator output under DC pumping with the change of pump power. The pump power is set to 110mW, 130mW, 150mW, 180mW, and 200mW respectively. With the increase of pump power, the comb teeth symmetrical about the central wavelength are gradually excited, and the covered wavelength range is also expanded. From the time domain waveform of a single comb tooth, when the pump power reaches 200mW, the output signal shows a chaotic state. It can be determined that the power threshold for exciting the chaotic optical comb under DC pumping conditions is 200mW.

[0052] (b1)-(b5) show the spectral evolution of the microring resonator output as the pump power changes under narrowband quantum noise pumping. Since the pump light is a narrowband noise source with a width of 30GHz, the average power density is used to describe the size of the pump power. Among them, Figure (b5) corresponds to the chaotic state output, and the average power density threshold is 9.8dBm, which is significantly lower than the power threshold required for DC pumping to excite the chaotic light comb. Set the average power density to P, Figures (b1)-(b4) respectively show the evolution of the microring resonator output spectrum when the pump power is 0.1P, 0.2P, 0.3P and 0.8P.

[0053] Compared with the DC pumping scheme, narrowband quantum noise pumping can also excite a light comb with a wider wavelength range. However, unlike the light comb excited by DC pumping, which shows symmetry about the central wavelength, the light comb under quantum noise pumping shows strong inhomogeneity. This phenomenon is mainly attributed to the randomness and narrowband characteristics of the driving signal, which makes the nonlinear coupling between different modes more complicated, making the dynamic behavior of each comb tooth more independent.

[0054] Figure 6 The trend of the average effective bandwidth of the chaotic signal of the four comb teeth changing with the driving noise width is shown. The average power density of the injected quantum noise is the threshold power density (9.8dBm) required to excite the chaotic light comb, and the spectral width of the injected quantum noise is gradually adjusted from 5GHz to 50GHz. It can be seen from the figure that with the increase of the ASE noise width, the effective bandwidth of a single comb tooth gradually increases from 4GHz to about 7GHz. This phenomenon shows that after more frequency components are injected into the microring resonator, more modes can be excited, thereby introducing stronger nonlinear interactions and effectively improving the bandwidth of the output chaotic signal.

[0055] In addition, the size of the pump power will also have a significant impact on the effective bandwidth of the chaotic signal. As the pump power increases, the nonlinear effect in the cavity gradually increases, thereby further expanding the output chaotic signal bandwidth. Therefore, in practical applications, by optimizing the pump power and the spectral width of the driving noise, a higher bandwidth chaotic optical signal output can be achieved.

[0056] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A quantum noise-assisted multi-channel broadband optical chaos generation device based on a microring resonator, characterized in that: include: Noise driving source, micro-ring resonator and filter demultiplexing detection unit; The noise driving source further comprises an erbium-doped fiber amplifier, an optical bandpass filter and a polarization controller; The erbium-doped fiber amplifier EDFA is used to directly amplify the broadband spontaneous emission ASE noise inside it, and provide a broadband noise driving signal for the entire device; The optical bandpass filter is used to filter out a narrowband noise signal with a spectrum width of 30 GHz and covering the resonance peak range of the microring resonant cavity from the ASE noise amplified by the EDFA, and inject it into the microring resonant cavity as a driving source to stimulate the nonlinear effect in the cavity; The polarization controller is used to adjust the polarization state of the light injected into the microring resonator, and then observe the output power. When the power reaches the maximum value, the polarization state of the injected light is the TE state, at which time the best coupling efficiency is achieved, and the narrowband noise signal E with the adjusted polarization state is obtained. pump =BPF[E randn (t)×e j2π×randn(t) ]; The micro-ring resonant cavity is used to receive a narrow-band noise signal. The narrow-band noise signal is transmitted in the micro-ring resonant cavity according to the formula: The nonlinear effect, dispersion effect and frequency interaction are carried out to make all frequency components within the resonance peak resonate in the cavity, thereby outputting a wide range of chaotic optical comb signals. Where BPF[·] represents the output optical field after ASE noise is amplified by EDFA and passes through the optical bandpass filter; E randn (t) is the random amplitude of the ASE noise light field after EDFA amplification; randn(t) is the phase noise of the ASE noise light field after EDFA amplification; t R is the time for the light field to travel back and forth in the microring resonator; E(t,τ) is the light field evolving in the cavity, t is the slow time describing the evolution of the electric field envelope in the cavity, and τ is the fast time traveling at the group velocity in the resonator; α0 is the total loss in the microring resonator; δ0 is the frequency detuning between the pump light and the microring resonator; β2 is the second-order dispersion in the microring resonator; L is the cavity length of the microring resonator; γ is the nonlinear coefficient in the microring resonator; θ is the power transmission coefficient between the straight waveguide and the microring resonator; is the driving term of the input light field; The filtering demultiplexing detection unit further comprises: an optical band-stop filter, a wavelength division demultiplexer and a photoelectric detector; Wherein, the optical band-stop filter is used to filter out the pump frequency component in the chaotic optical comb signal; The demultiplexer is used to separate the filtered chaotic optical comb signal into multiple chaotic signals with different central wavelengths, and each channel corresponds to the central wavelength of a comb tooth; The photoelectric detector is used to convert the chaotic optical signals of each channel output by the de-wavelength division multiplexer into corresponding electrical signals for output.

2. According to the quantum noise-assisted multi-path broadband optical chaos generation device based on microring resonator according to claim 1, the central wavelength of the optical bandpass filter is consistent with the central wavelength of the microring resonator.

3. According to the quantum noise-assisted multi-path broadband optical chaos generation device based on microring resonator in claim 1, the width of the optical band-stop filter is greater than or equal to the width of the narrowband noise signal.

4. According to the quantum noise-assisted multi-channel broadband optical chaos generation device based on a microring resonator as described in claim 1, the channel bandwidth of the demultiplexer is greater than the line width of each chaotic comb tooth.

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