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Abstract
The multi-longitudinal mode high-spectral-resolution lidar (MLM-HSRL) is an effective technique for detecting atmospheric optical characteristics of aerosols. Due to the excessive longitudinal mode numbers, the current MLM-HSRL cannot obtain a well spectral suppression effect, which seriously affects the retrieval accuracy of the optical characteristic parameters. In this paper, a new index called Longitudinal Mode Rejection Ratio (LMRR) has been proposed to evaluate the spectral suppression effect of the MLM-HSRL; a novel mismatch error and mode control (MEMC) technique is proposed to improve the spectral suppression effect of the MLM-HSRL, which contributes to developing the scientific potential of the MLM-HSRL for aerosol remote sensing. Based on our self-developed MLM laser, through controlling the longitudinal mode frequency-pulled shift of the MLM laser, adjusting the total mismatch error, and reducing the longitudinal mode numbers, we realize the LMRR index improved from about 5 to over 30, and the working stability of the system is also promoted by decreasing the longitudinal mode numbers. The experiment well improves the spectral suppression effect and verifies the effectiveness of the proposed MEMC technique. To the best of our knowledge, for the first time, the study addresses the conundrum of the lower spectral suppression effect for the MLM-HSRL. This work would help to provide a powerful support for the high-precision, long-term, and stable operation of the MLM-HSRL in the future.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-spectral-resolution lidar (HSRL) is an active remote sensing instrument for atmospheric detection, which is able to implement the vertical distribution profiles of the atmosphere [1–3]. Based on retrieval of the atmospheric backscatter echo signals, HSRL could obtain the aerosol optical characteristic parameters, and could further help to realize the investigation on aerosol properties [4,5]. Traditional HSRL mostly utilizes the injection-seeded single-longitudinal mode laser as the transmitter, which makes the system vulnerable, bulky and high cost [1,6]. Recently, HSRL utilizing a multi-longitudinal mode (MLM) laser as the transmitter with an interferometer as the spectral discriminator, called the MLM-HSRL, has been developed as an emerging technique [7]. Since it is unnecessary to demand the single frequency of the laser, MLM-HSRL has advantages of cost-effectiveness, easy implementation, and strong adaptability, which compensates the drawbacks of the traditional HSRL to a great extent.
In order to achieve high-precision, durable and stable aerosol detection of the MLM-HSRL, the crucial issue is to obtain a precise spectral discrimination, which can be called as a good spectral suppression effect (SSE). To the best of our knowledge, so far, only NASA has carried out an evaluation of the SSE for the single-longitudinal mode HSRL with an injection-seeded Nd:YAG laser [8]. Distinguished from the single-longitudinal mode HSRL, there exists significant differences of the MLM-HSRL in implementation. Because of utilizing an MLM laser as the emission source, the MLM-HSRL must perform perfectly spectral match between the MLM laser spectrum and the periodical spectral function of the interferometer in order to guarantee a good SSE. However, it is not easy to achieve this goal, because it is difficult to simultaneously and precisely regulate the interferometer and the MLM laser to achieve both oscillating frequencies aligned to each other. In the past five years, Jin et al. and Gao et al. have built an MLM-HSRL system based on a Mach-Zehnder interferometer (MZI) as the spectral discriminator with the commercial MLM laser [9,10]. Conversely, the scheme has following aspects to be further improved: (1) The resonator of the commercial MLM laser is relatively long, which yields dozens of oscillating longitudinal modes (LMs), thereby increasing difficulties to match with the periodical spectral function of the interferometer. (2) It is arduous to precisely adjust the parameters of the commercial MLM laser, thereby reducing the accuracy of the spectral match between the MLM laser and the interferometer. (3) The laser linewidth of the commercial MLM laser is about 30 GHz, which partly decreases the monochromaticity of the laser source and will make a decline of the interference contrast, thereby causing a low SSE. Additionally, Cheng et al. proposed an MLM-HSRL based on a compact field-widened Michelson interferometer (FWMI), which makes the free spectral range ($FSR$) of the FWMI to several gigahertzes. This may broaden the LM interval of the MLM laser to match with the $FSR$, so that it will theoretically decrease the possibility of numerous LM oscillation, and reduces the challenges of the spectral match for the MLM-HSRL [7,11]. However, no experiments have validated the theory and evaluated its practical SSE until now. Consequently, MLM-HSRL has rarely been reported possibly due to lacking a general approach to evaluate and improve its SSE.
In this paper, our lidar research group from Zhejiang University puts forward a new Longitudinal Mode Rejection Ratio ($LMRR$) index to evaluate the SSE of the MLM-HSRL, which is utilized to overcome the conundrums hindering the MLM-HSRL development. We demonstrate a novel technique called mismatch error and mode control (MEMC) based on the $LMRR$ index, which employs the FWMI as the spectral discriminator. It is found that while we ensure the frequency locking between the MLM laser and the interferometer, the longitudinal mode frequency-pulled shift of the MLM laser, the LM numbers, and the spectral mismatch error between the MLM laser and the interferometer play important parts in restricting the $LMRR$ index improvement, thereby influencing the SSE of the MLM-HSRL. By increasing the magnitude of the $LMRR$ index and enhancing its stability through the experiment, we obtain a superior spectral match result and achieve the SSE improvement of the MLM-HSRL, which confirms the effectiveness of the MEMC technique. This work will be conducive to providing an approach for stimulating the scientific potential of the MLM-HSRL.
2. Method
2.1 Principle and error analysis of the spectral suppression effect
The principle of spectral suppression between the MLM laser and the FWMI is illustrated in Fig. 1. We utilize a Lorentzian gain curve to simulate the MLM laser spectrum (pink curve), and there are 5 LMs demonstrated in the simulation. The frequency difference between adjacent LM is the LM interval $d\nu $, which is mainly determined by the optical length of the laser resonator. The FWMI spectral function is a cosine curve (blue curve), which is periodical in the frequency domain. The frequency interval between two peaks (or valleys) of the FWMI periodical spectral function is the $FSR$, which mainly depends on the fixed optical path difference ($FOPD$) of the FWMI [11]. The frequency band between two adjacent valleys of the spectral function curve is the so-called suppression section.
Fig. 1. Schematic of spectral suppression between the MLM laser and the FWMI. (a) Schematic of the theoretically ideal spectral suppression. (b) The detailed diagram of the ideal spectral suppression. (c) The total mismatch error ${M_\textrm{E}}$. (d) The frequency-pulled mismatch error ${M_\textrm{p}}$.
Theoretically, when the FWMI resonant frequency is aligned to the central frequency of the MLM laser, which is generally called “frequency locking”, simultaneously, the FWMI and the MLM laser satisfy the condition that $FSR$ is equivalent to $d\nu $, the FWMI will generate the maximum destructive interference with each LM. Therefore, each LM intensity of the MLM laser will be rejected to the greatest extent by the FWMI spectral function in the corresponding suppression section, which produces an optimized SSE, as presented in the black circle of Fig. 1(a). The orange envelope curve in Fig. 1(b) clearly demonstrates the LM transmittance after the spectral suppression, which only has a small quantity of LM intensities remained. We define the $LMRR$ index as the ratio between the normalized rejected LM intensity ${I_\textrm{r}}$ and the normalized transmitted LM intensity ${I_\textrm{p}}$ by the FWMI, as shown in Eq. (1):
The $LMRR$ index is a dimensionless parameter and is of linear scale, it could represent the SSE of the MLM-HSRL through its magnitude and stability. When the index magnitude becomes larger, the level of spectral suppression becomes higher; when the index fluctuation becomes milder, the stability of spectral suppression becomes superior. According to Eq. (1), ${I_\textrm{p}}$ will reach its minimum at the greatest rejection by the FWMI, and the $LMRR$ index could attain to its peak at this time, which means the spectral discriminator has a superior suppression effect, and has a great possibility to get a high-precision retrieval. However, due to the spectral mismatch during the MLM-HSRL operation, the spectral discriminator is generally hard to obtain a satisfactory rejection, which increases the transmitted LM intensities, thereby declining the $LMRR$ index, and finally lowers the SSE of the MLM-HSRL.
While the MLM-HSRL is working, the state of the MLM laser resonator will change and causes the alteration of $d\nu $,which destroys the equality condition between $d\nu $ and $FSR$, and thus makes a spectral mismatch between the MLM laser and the FWMI. The mismatch bias is defined as the total mismatch error ${M_\textrm{E}}$, ${M_\textrm{E}}$ will lead the oscillating LM frequency deviated from the theoretical LM frequency, as shown in Fig. 1(c), and ${M_\textrm{E}}$ could be expressed as:
It should be noted that the $FSR$ keeps a constant while the MLM-HSRL is operating. In Eq. (2), $d\nu ^{\prime}$ is the operated LM interval, ${\nu _q}$ is defined as the cold-resonator LM frequency, which is closest to the central LM ${\nu _0}$ (${\nu _q}$ represents the first LM to the positive side of the central LM), and ${\nu _{qm}}$ represents the operated LM frequency of this LM, which is shown as ${\nu _{q1}}$ or ${\nu _{q2}}$ in Fig. 1(c). If $d\nu ^{\prime} < FSR$, ${\nu _{qm}}$ corresponds to ${\nu _{q1}}$, and ${M_\textrm{E}}$ will be positive, whereas ${M_\textrm{E}}$ will be negative. ${M_\textrm{E}}$ mainly includes the LM frequency-pulled mismatch error ${M_\textrm{p}}$ and the system spectral mismatch error ${M_\textrm{s}}$, which can be further expressed as:
${M_\textrm{p}}$ is generated by the frequency pulling effect of the gain medium [12]. The oscillating LM frequency ${v_q}^{\prime}$ is pulled towards the central LM frequency of the gain medium by ${M_\textrm{p}}$, which is shown in Fig. 1(d). Emphatically, ${\nu _{qm}}$ includes the frequency change introduced by ${M_\textrm{p}}$. For illustration, the brown arrow in Fig. 1(d) shows the pulling direction. Thus, ${M_\textrm{p}}$ could be given by:The system spectral mismatch error ${M_\textrm{s}}$ is yielded by the mismatch between the optical length of the MLM laser resonator and the $FOPD$ of the FWMI. As we mentioned above, the $FSR$ of the FWMI could be a constant, and the relationship between $FSR$ and $FOPD$ is shown as:
where c corresponds to the vacuum speed of light. Equation (6) indicates that the $FOPD$ of the FWMI can also be regarded as a constant while the MLM-HSRL is operating [11]. Thus, we could adjust the MLM laser resonator to match with the $FOPD$ in order to control ${M_\textrm{s}}$.2.2 Simulation of the spectral suppression effect
After expounding the principle and error analysis of the SSE, it is necessary to investigate the quantitative relationship between the mismatch error and the SSE. Figure 2 depicts the theoretical simulation results for the largest frequency shift $\Delta \nu $ caused by ${M_\textrm{p}}$, and the change of $LMRR$ with N. Nd:YVO4 is selected as the gain medium for simulation due to its wider fluorescence linewidth, which could better reduce the impact of ${M_\textrm{p}}$ on $LMRR$. The fluorescence linewidth of Nd:YVO4 is about 212 GHz (0.8 nm) [14], and each LM spectral width is assumed to be 300 MHz. According to Eq. (4), we could calculate ${M_\textrm{p}}$ is about 4.25 MHz. The LM numbers N are chosen from 3 to 81, which is because the commercial MLM laser may generate more than 80 LMs [10,15]. Except for introducing ${M_\textrm{p}}$, we do not add other parameters which might degrade the $LMRR$ index. Thus, this would be regarded as an ideal condition for the $LMRR$ evaluation. Figure 2 shows that $\Delta \nu $ increases linearly along with augmentation of N, which can be explained by Eq. (5). As for $LMRR$, it gradually declines from 50.5 to 35.4 with increasing of N. Interestingly, our study finds when N increase from 3 to 11, the variation of $LMRR$ is not significant, which only drops from 50.5 to 50.0. Hence, it is a relatively ideal study section while N are restricted within 11, which may almost neglect the effect of ${M_\textrm{p}}$ for the $LMRR$ variation, so that we could further evaluate the impact on the total mismatch error ${M_\textrm{E}}$ for the $LMRR$ index.
Fig. 2. Simulation results of the frequency-pulled mismatch error ${M_\textrm{p}}$ influenced on the SSE with different LM numbers N.
In addition, the central frequency deviation ($CFD$) yielding in the frequency locking between the MLM laser and the FWMI will also affect the SSE. If the FWMI resonant frequency does not strictly align to the central frequency of the MLM laser, the FWMI rejection will also be decreased, thereby declining the $LMRR$ index. Cheng et al. have elaborately discussed $CFD$ in the bibliography [7], which is no need to intensively research here. Even so, as one of the constraints for the SSE improvement, we still evaluate the $CFD$ influence through the simulation.
Figure 3 demonstrates the simulation results of the $LMRR$ index influenced by ${M_\textrm{E}}$ and N with different $CFD$ values, we select four typical $CFD$ values of 0 MHz, 30 MHz, 50 MHz, and 100 MHz, which all represent the peak-valley (PV) value, corresponding to the subplot (a), (b), (c) and (d). In terms of Eq. (3), ${M_\textrm{E}}$ is mainly composed of ${M_\textrm{p}}$ and ${M_\textrm{s}}$, and they will both exist during the MLM-HSRL detection. In order to minimize the impact of ${M_\textrm{p}}$, the LM numbers are taken from 3 to 11, so that ${M_\textrm{E}}$ will be mainly affected by ${M_\textrm{s}}$ under this case. It is clear that by reducing ${M_\textrm{E}}$ and N, the $LMRR$ index will be improved, which represents the SSE improvement. As for $CFD$, the larger $CFD$ is added, the lower $LMRR$ will generate, this can be explained by the leakage of the LM intensities. There are some useful conclusions from the simulation results which could provide guidance for the experiment: According to Fig. 3(a), the optimized $LMRR$ is realized when $CFD$ and ${M_\textrm{E}}$ are both zero and the LM number is 3. We find that the allowable range of ${M_\textrm{E}}$ can be expanded by reducing N, for instance, even though ${M_\textrm{E}}$ reaches ±150 MHz, $LMRR$ can be more than 26.7 as the MLM laser operates in 3 LMs. From Fig. 3(b) and 3(c), the maximum values of $LMRR$ have dropped to 48.1 and 44.3, respectively, which is due to the $CFD$ increasing. If $CFD$ increases to 100 MHz, the maximum of $LMRR$ will further drop to 32.4. Although $LMRR$ is nearly constant up to 11 modes in Fig. 2 simulation, the introduced $CFD$ and ${M_\textrm{E}}$ will also cause an apparent change of $LMRR$ with the LM increasing. For example, as depicted in Fig. 3(d), when the LM numbers augment from 3 to 11, the $LMRR$ index sharply drops from 30.3 to 15.8, in the condition of 50 MHz ${M_\textrm{E}}$. With ${M_\textrm{E}}$ further increasing to 100 MHz, $LMRR$ will continuously drop to 6.4 at 11 LMs, which leads to a severe deterioration of the SSE. However, significantly, even if ${M_\textrm{E}}$ is up to ±150 MHz, the $LMRR$ indexes all exceed 20 at 3 LMs of four $CFD$ values, which could be an acceptable SSE for the MLM-HSRL detection [8].
Fig. 3. Simulation results of the SSE evaluation with respect to the total mismatch error ${M_\textrm{E}}$ and the LM numbers $N$ under different central frequency deviation $CFD$. (a) 0 MHz $CFD$, (b) 30 MHz $CFD$, (c) 50 MHz $CFD$, and (d) 100 MHz $CFD$. Note that the black dot lines represent the contour lines of $LMRR$.
2.3 MEMC technique
From the simulation, it is clear that the LM numbers are tightly associated with the magnitude of $LMRR$, and decreasing the LM numbers will compensate the spectral mismatch (${M_\textrm{E}}$ and $CFD$) in a certain degree. In addition, different LM numbers could also introduce the LM competition to varying degrees, and thus affect the laser stability [16]. We discover that the LM competition could change the intensity of each LM randomly, and causes LM intensity changing over time, which brings about a real-time variation of the spectral suppression level. This will induce fluctuation of the $LMRR$ index, thereby affecting the SSE of the MLM-HSRL. Therefore, it is vital to control the LM numbers to minimize the LM competition for keeping the $LMRR$ stability. Consequently, appropriate LM numbers must be selected to promote the stability and magnitude of the $LMRR$ index, simultaneously, we also need to take into account the range of the total mismatch error ${M_\textrm{E}}$ and make sure the $CFD$ within a certain limits to realize the SSE improvement of the MLM-HSRL. That is why we call this method as the MEMC technique.
3. Experiment
3.1 Experimental system
In order to better understand the MEMC technique, we establish a self-developed MLM laser and construct a proof-of-principle experimental system. The schematic of the self-developed MLM laser is demonstrated in Fig. 4(a). Nd:YVO4 is utilized as the gain medium for the experiment. The employed Nd:YVO4, with 3 × 3 × 10 mm3, a-cut and 0.3%-doped is end-pumped by a fiber-coupled diode laser. The pump laser is collimated and focused into Nd:YVO4 by a coupler. Cr4+:YAG is employed as the passive Q-switch, the initial transmittance ${T_\textrm{0}}$ of the Cr4+:YAG is 30.9% with 2.6 mm thick. Cr4+:YAG can extinguish several oscillating LMs during the establishment of a pulsed laser, which plays a natural LM selection role for the MLM laser [17]. The resonator is designed as a parallel plane cavity with an optical length of 50 mm, corresponding to the LM interval of 3 GHz, which would match with the $FSR$ (3 GHz) of the FWMI. The front surface of Nd:YVO4 is coated with 1064 nm high-reflective film as the resonator rear mirror. The oscillating laser outputs from the plane mirror as the output coupler (OC) with 30% reflectivity, the OC is fixed on a flexible frame. The flexible frame is mounted on a micro displacement stage (MDS), which could adjust the laser resonator length. The arrows in Fig. 4(a) represent the moving directions of the Cr4+:YAG and the MDS. The whole set MLM laser is fixed on a baseplate of invar material with low thermal expansion coefficient to guarantee the structural stability. We measure the pulse energy of the MLM laser is 0.4 mJ, the repetition rate is 10 Hz, and the pulse width is around 20 ns.
Fig. 4. (a) Schematic of the self-developed MLM laser. LD, laser diode; OC, output coupler; MDS, micro displacement stage. (b) Proof-of-principle experimental system for verifying the MEMC technique. BS, beam splitter; PZT, piezo-electric transducer; CCD, charge-coupled device; FPE, Fabry-Perot etalon.
Figure 4(b) demonstrates the proof-of-principle experimental system for verifying the MEMC technique of the SSE improvement. Since our self-developed MLM laser generates 1064 nm output laser, we need to double the laser frequency to 532 nm for the experiment by KTP outside the resonator. The output beam first propagates through an attenuator to decrease the light intensity, and then the beam diameter is expanded by an expander. Later, the beam is divided into two paths through a beam splitter (BS) with a transmission-reflection ratio of 9:1. The transmitted light directly enters the FWMI to generate a double-beam interference. The interference light is converged into a charge-coupled device (CCD1) by a focusing lens to collect the interference spectra of the FWMI, the spectra are ultimately sent to computer for analysis. By analyzing the interference spectra, the computer drives the actuator to generate a feedback signal which could regulate the three-axis piezo-electric transducer (PZT). The PZT tunes the length of the FWMI air arm to create the optimized destructive interference for the following evaluation of the $LMRR$ index. The reflected light travels through a 532 nm Fabry-Perot etalon (FPE) to generate multi-beam interference. The FPE is employed to measure the LM spectral characteristics of the MLM laser, which is 2 mm thick with silver film coated. The interference light is converged through another focusing lens and collected by CCD2 to image the LM interference fringes. Finally, the images are sent to computer for LM spectral analysis.
3.2 LMRR measurement
In the experiment, we first make sure the frequency locking between the central frequency of the MLM laser and the FWMI during the whole experiment. The specific method can refer to the bibliography [18], and $CFD$ would be controlled by this means. We estimate that $CFD$ is less than 100 MHz. Next, we start to calculate $LMRR$, Fig. 5 shows the specific measuring approach of the $LMRR$ index.
Firstly, tune the three-axis PZT which controls the length of the FWMI air arm to precisely adjust the $FOPD$, so that we could obtain the optimized destructive interference, the step precision of the PZT is 1 µm. Then, nearby the destructive interference position, periodically scan the PZT to observe the interference fringes on CCD1 from destructive to constructive interference for at least 1 period, and consecutively collect the scanning interference spectra. After the interference spectra transmitted to computer, we normalize the interference light intensities, which are shown in Fig. 5 as the violet measuring points. To improve the measurement accuracy, we need to conduct multiple periodical scanning for reducing the random errors, and also slow down the scanning speed of the PZT so as to collect the interference spectra as many as possible in each scanning period. Next, we fit the measuring points according to the cosine function, it can be seen that the blue curve has well fitted with the sample results, which is regarded as the practical calibration transmittance curve of the FWMI. The light intensities of the measuring points are relatively stable while the PZT is scanning, which could guarantee the accuracy of the $LMRR$ measurement. Calculate the normalized light intensity of the lowest point for the transmittance curve as ${I_\textrm{r}}$, we could obtain the $LMRR$ index according to Eq. (1). The calculated $LMRR$ in Fig. 5 is 24.
In order to realize the real-time measurements of the $LMRR$ index, on the premise of maintaining the frequency alignment between the central frequency of the FWMI and the MLM laser, continuously collect the normalized light intensities of the destructive interference, we could calculate $LMRR$ based on the measured FWMI transmittance curve in real-time. If the spectral matching condition between the MLM laser and the FWMI changes, such as altering ${M_\textrm{E}}$ and the LM numbers, it is essential to re-measure the normalized light intensity of the lowest ${I_\textrm{r}}$ of the transmittance curve following the above steps. After that, we could further calculate the $LMRR$ index.
3.3 Experiment of the spectral suppression effect improvement
Since we have introduced the method of $LMRR$ measurement, we start to regulate the MLM laser for $LMRR$ improvement. Due to employing Cr4+:YAG as the passive Q-switch with natural LM selection, and utilizing Nd:YVO4 as the gain medium with wider fluorescence linewidth, ${M_\textrm{p}}$ has been well restricted, thus, ${M_\textrm{s}}$ is approximately equal to ${M_\textrm{E}}$ at this time. Figure 6 shows the experimental results for the $LMRR$ magnitude improvement by adjusting ${M_\textrm{E}}$. As illustrated in Fig. 4(a), inch the MDS along the bi-directional arrow (the direction of the laser oscillating) so as to adjust the optical length of the laser resonator, we could control ${M_\textrm{E}}$ in this way. By analyzing the interference light intensities from CCD1, we could judge the MDS moving direction whether makes ${M_\textrm{E}}$ decrease. While ${M_\textrm{E}}$ is optimized from 150 MHz to 30 MHz, the $LMRR$ magnitude gradually elevates from around 5 to over 30. It is regarded as quite an ideal SSE for the MLM-HSRL that $LMRR$ reaches 30 [8]. For realizing ${M_\textrm{E}}$ within 30 MHz, the optical path mismatch between the FWMI and the MLM laser should be controlled no more than 0.5 mm, which is considered to be a relatively loose index for implementation.
Fig. 6. Experimental results for the SSE improvement by adjusting the total mismatch error ${M_\textrm{E}}$.
The representative results of the MLM laser spectra measured by the FPE are presented in Fig. 7. The FPE could help to conduct the frequency domain analysis of the MLM laser. We evaluate the spectral width of each oscillating LM is approximately 300 MHz. Combined with computer software, the FPE interference patterns have been entirely collected for LM analysis during the experiment. There exist 3 interference fringes in each period of the laser spectra, which indicates that the MLM laser operates in 3 LMs. We could apparently observe the LM intensity variation of the MLM laser comparing Fig. 7(a) with 7(b), the intensities of different LMs are discrepant according to the spectral distribution. Although the MLM laser operates in 3 LMs, each LM (marked serial number 1,2,3 in Fig. 7) continuously changes its intensity with time, which could be explained by the LM competition phenomenon.
Fig. 7. Experimental demonstration for the MLM laser spectral distribution measured by the FPE. Note that there are 3 LMs in this case, (a) and (b) show the LM competition.
The LM competition is tightly associated with the LM numbers, which both affects the magnitude and stability of the $LMRR$ index. As depicted in Fig. 4(a), by rotating the Cr4+:YAG along the direction of the arc arrow, the angle between Cr4+:YAG and the optical axis of the oscillating laser will be changed, so that the residual absorption loss of the laser resonator will be modulated while Cr4+:YAG is rotating [19]. This could partly regulate the laser threshold, thereby controlling the oscillating LM numbers. By twirling Cr4+:YAG, the oscillating LM numbers are varied from 9 LMs to 3 LMs, and $LMRR$ has been measured in real-time as shown in Fig. 8 during the experiment.
We have calculated the mean square error ($MSE$) of $LMRR$ for different LM numbers in Fig. 8. As the LM numbers decrease from 9 LMs to 3 LMs, the $MSE$ of $LMRR$ reduces from 1.35 (9 LMs) to 0.53 (3 LMs), which means the $LMRR$ stability enhanced about 2.5 times. It is remarkable that no matter the MLM laser operates in 3, 5, or 9 LMs, $LMRR$ exists no fierce plunge and stays over 20, which indicates that each suppression section of the FWMI produces relatively stable spectral suppression with the corresponding LM, so that $LMRR$ could maintain its stability. According to the experimental results, when the LM numbers reduce, the stability of $LMRR$ is enhanced, which could be attributed to the weakening of the LM competition because of the LM numbers reduction. Consequently, we can conclude from the experiment that the LM competition among different LM numbers will evidently change the stability and magnitude of $LMRR$, for example, the variation of 3, 5, and 9 LMs, and also the output laser linewidth will be changed while the variation of the different LM numbers. Obviously, due to the fixed LM interval, the more LM numbers, the wider output laser linewidth. However, the LM competition among the same LMs does not generate significant change on $LMRR$, such as the case of the LM competition demonstrated in Fig. 7. Moreover, the current experiment could acquire the most desirable SSE at 3 LMs, which is consistent with the simulation results in Fig. 3.
4. Discussion
Further research indicates that the MLM laser is likely to produce high-order transverse modes and will introduce new transverse mode frequency intervals, which will also make the spectral mismatch between the FWMI and the MLM laser, so that it may decline the $LMRR$ index. Actually, we have already considered this conundrum while design the MLM laser, which could be resolved in terms of the following approaches: (1) Employ the architecture of plane parallel cavity to reject the transverse mode oscillation. (2) Restrain the spot size of the oscillating laser. (3) Control the thermal effect of the gain medium. These three strategies will help us effectively avoid the adverse impact on the high-order transverse modes.
For the proposed MEMC technique, there is no doubt that a smaller ${M_\textrm{E}}$ is always preferred. If ${M_\textrm{E}}$ is smaller, the magnitude of $LMRR$ will be larger, so that we could obtain a preferable SSE. The experiment has achieved ${M_\textrm{E}}$ of 30 MHz, which is practical to implement. For further reducing ${M_\textrm{E}}$, we need to simultaneously improve the tuning precision for the optical length of the laser resonator and the $FOPD$ of the FWMI. By reducing the LM numbers, we acquire a high and stable $LMRR$, therefore, it is a good choice to make the MLM laser operate in a small quantity of LM numbers, such as 3 LMs.
The experiment has achieved the SSE improvement for the MLM-HSRL, which could well verify the theory and simulation. However, there still exists discrepancy between the simulated $LMRR$ and the experiment, which might be attributed to the following aspects:
First of all, the wavefront distortion of the FWMI will reduce $LMRR$ in a certain degree. It is inevitable to introduce the wavefront distortion during the FWMI development process of the film coating and the interference arm fabrication, which will yield imperfect destructive interference, thereby degrading $LMRR$. If a better approach can be employed to elevate the wavefront fabrication accuracy of the FWMI, we shall acquire a better experimental result.
Secondly, the step precision for the employed PZT of the FWMI is 1 µm, which is relatively inferior for the displacement resolution, so that it is difficult to precisely adjust the $FOPD$ to the optimal position of destructive interference, thereby reducing $LMRR$. If we replace the PZT with higher displacement resolution, such as 0.1 µm or less, we will obtain a preferable destructive interference, thereby optimizing the experimental results.
Additionally, although $CFD$ is less than 100 MHz in the experiment, it is still a bit larger for realizing an excellent spectral match. $CFD$ is controlled based on the technique of the pulse laser frequency locking between the FWMI and the MLM laser. However, the frequency locking precision needs to be improved due to the immature technique. If $CFD$ could be further optimized to a smaller value, a higher $LMRR$ will also be implemented.
In the application of the MLM-HSRL, the spectral discriminator needs to reject the Mie scattering signal. Because of the spectral width of the Mie scattering signal is close to the LM spectral width, hence, a higher $LMRR$ indicates a better rejection of the Mie scattering signal.
5. Conclusion
In summary, we propose a new $LMRR$ index to evaluate the SSE of the MLM-HSRL, and demonstrate a novel MEMC technique that can improve the SSE of the MLM-HSRL. The experiment has verified the principle and simulation, which confirms the feasibility and effect-iveness of the technique. We also discuss the approaches to further optimize the experimental results. The technique will shortly after apply to the MLM-HSRL for aerosol detection, which could better stimulate the scientific potential of the MLM-HSRL. Besides, the scheme can be employed in the interferometer with periodical spectral function such as MZI and Fabry-Perot interferometer (FPI), and could also extend to the ultraviolet band. Furthermore, the scheme is beneficial to enhance the robustness of the MLM-HSRL operating in the harsh environments, especially for the future construction of the airborne and spaceborne MLM-HSRL.
Funding
Key Research and Development Program of Zhejiang Province (2020C01106); National Natural Science Foundation of China (41775023, 41805108); Excellent Young Scientist Program of Zhejiang Provincial Natural Science Foundation of China (LR19D050001); Young Scientist Fund of National Natural Science Foundation of China (61905212); Scientific Research Projects of Zhejiang Administration for Market Regulation (20200103).
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.
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