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Abstract
In this paper, the effects of optical power factors like laser power, the powers of the laser beams in the two arms of the optical system, and the power of the photodetector on laser-linewidth measurements are studied. From the experiments, it can be found that when the average optical input power for the photodetector is about 50% of its linear saturation power, the measured laser line width is a minimum. When the optical powers of the laser beams in the two arms are equal in short-delay self-homodyne system, the measured laser line width is narrowest. In the low output power range of the laser, its line width decreases with the increase in optical power. By comparing experiments, it can also be clear that the conventional measurement method is seriously affected by different noise types, which causes the measured line width to become wider and not change even if the laser linewidth changes. However, based on the short-delay coherent envelope method, the measured coherent envelope changes significantly when the laser line width changes slightly, and its corresponding laser-linewidth values are also clearly visible. It confirms the low noise and high resolution of the short-delay self-homodyne coherent-envelope laser-measurement method. The outcomes of this study can provide helpful information for precision ultra-narrow laser-linewidth measurements.
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1. Introduction
Laser research typically focuses on generating ultra-narrow (frequency range), ultra-fast, and ultra-high power light sources. Using laser-linewidth compression [1–5] and laser-frequency stabilization [6–9], the spectral linewidth has already been narrowed to about ∼1 Hz. However, the conventional characterization method used for laser line widths cannot accurately determine the true linewidth because of several types of noise introduced during the detection [10–14]. Thanks to improvements in science and technology, the line width of lasers will likely become narrower in the future, which means it is crucial to find a more accurate laser-linewidth measurement method.
The original value of the spectral line width can be described by the Schawlow-Townes expression [15], and if self-heterodyne, the spectral line shape can be a Lorentzian spectrum [16]. Half of the full-width-at-half-maximum (FWHM) of the Lorentzian spectrum is defined as the laser line width. It shows that the line width is due to the phase change caused by spontaneous emission, and it is strictly inverse-proportional to the coherence time of the laser [12]. The instantaneous line width of narrow-linewidth lasers is challenging to measure because of the limited measurement time. However, suppose a narrow linewidth laser is used in an application such as distributed fiber-optic sensing [17–21], fiber-optic gyroscopes [22,23], hydrophones [24,25], and coherent optical communication [26–28]. In that case, the laser can continue to operate in the system for a significant period. Therefore, the continuous coherence characteristic of the CW laser, like the average laser line width, is also a critical parameter that we need to pay attention to, in addition to the instantaneous line width.
Furthermore, within a specific measurement time, the Lorentzian spectrum is affected by frequency jitter caused by different noise sources such as pump noise, acoustic noise, and vibration noise. The accumulation of these noises results in a Gaussian line shape [12,13], which is superimposed on a Lorentzian line shape (which represents the laser line width) to yield an even more complex spectral line shape (Voigt profile). Although researchers have proposed to extract the Lorentzian line width of a laser from the Voigt profile [29], the resulting measurement is not accurate enough. In addition, researchers have also proposed a method to suppress the effect of Gaussian noise. It can be done by shortening the delay time, which makes it possible to extract a more Lorentz line width [13,30–36]. However, the effect of critical factors during the measurement process on the laser linewidth measurement has not yet been studied. These factors also affect the accuracy of laser linewidth measurement.
This paper presents the effect of optical power on a laser-linewidth measurement using a self-homodyne system with a short delay. This approach considers the effect of laser output power, self-homodyne system power, and PD power on the laser-linewidth measurement. In this way, it is possible to determine the optimal power for each part of the measurement system and obtain the most accurate laser line width. In addition, this study also compares the measured spectral line shape of the laser and their corresponding laser line widths. These were obtained using the conventional long-delay measurement method and the short-delay measurement method with different input laser-line widths. It also highlights the high accuracy of the short-delay coherent envelope laser-linewidth measurement method.
2. System analysis
From the previous study of the short-delay systems [32–35], Short-delay system is more conducive to achieve precise measurement of ultra-narrow laser line width, because the sensitivity of the short-delay coherent-envelope method will increase as the line width decreases, which can provide sufficient measurement sensitivity and resolution for ultra-narrow laser linewidth measurement. In this paper, we believe a simple and compact short-delay self-homodyne (SDSH) system would be minimally affected by several types of noise and can enable a more accurate laser-linewidth measurement [35]. Therefore, the laser-linewidth measurement presented in this paper mainly relies on the SDSH coherent envelope method, which uses the envelope characteristics like the second peak-to-valley difference (△S) to characterize the laser line width. A laser-linewidth measurement with a self-homodyne system is shown in Fig. 1. The system can be divided into three modules: laser module, self-homodyne system module, and photodetector module. The self-homodyne system mainly consists of two optical couplers for laser beam splitting and beam combination. In addition, it has optical attenuators to adjust optical power and fiber optic delay lines. All fiber devices in the self-homodyne system are optical-polarization-maintaining devices. Finally, the double-arm combined laser enters the photoelectric detector module for photoelectric conversion. The spectrometer monitors the signal, and the obtained power spectrum from the spectrometer is used to fit the laser line width.
Fig. 1. Schematic diagram of an SDSH system. ISO: Isolator. C1 and C2: Optical couplers (50/50). VOA1 and VOA2: Variable optical attenuator. DF: Delay fiber (32.25 m). PD: Photodetector. ESA: Electrical spectrum analyzer. PM: Power meter.
The laser used in the experiment was manufactured by YOKOGAWA (DFB-LD at 1550 nm), and the output power could be adjusted (8.2 dBm–14.2 dBm). The measured laser line width was about ∼26 kHz, and the optimal delay-fiber length was 32.25 m per the following Ref. [35]. Therefore, the length of the delay fiber used in the self-homodyne system was fixed at 32.25 m. The type of PD used in the experiment was an amplified photoreceiver (PDA1020) manufactured by Insight Inc. The output voltage corresponding to the input optical power of PD is shown in Fig. 2. It can be seen that the linear saturation power of PD is about 90 µW.
3. Experimental results and discussion
To explore the effect of the PD's receiving power on the laser-linewidth measurement, we fixed the output power of the laser at 8.2 dBm (6.6 mW). Adjusting the VOAs of the two arms of the homodyne system can change the optical power of the laser beam, entering the PD through two arms consistently. Moreover, adjusting the VOAs can also change the total optical power of the laser beam entering the PD from 0 µW to 90 µW. The linear saturation power of PD is about 90 µW as shown in Fig. 2. For example, to ensure that the total power of the laser beam entering the PD is 50 µW, it is necessary to adjust the two VOAs in such a way that the laser power of the beam reaching the PD through each arm, is 25 µW.
Figure 3(a) shows that different coherent envelope spectra were obtained from the different PD power measurements. Figure 3(b) shows different fitted line widths (blue curve), derived from second peak-to-valley difference (△S) values (red curve) obtained from Fig. 3(a), using the SDSH method, corresponding to different power values received by the PD. It can be seen that when the received power of the PD was 1µW, the measured value of the laser line width was 490.0 kHz. When the received power of PD was 1 µW–10 µW, the measured value of the laser linewidth decreased with increasing optical power entering the PD. When the optical power at the PD is 10 µW–50 µW, the measured value for the laser linewidth tends to be flat, about 24 ± 1 kHz. When the optical power continues to increase, the measured value of the laser linewidth increases gradually.
Fig. 3. (a) Output power spectra corresponding to different total power values received at the PD. (b) Fitted line widths (blue curve), derived from second peak-to-valley difference (△S) values (red curve) from (a), using the SDSH method, corresponding to different power values received by the PD.
Figure 3 shows that the detection power of the PD module has a particular impact on the measurement of the laser linewidth. If the detected power is small, the impact of PD module noise (mainly background noise), including PD noise and ESA noise, is more significant. Therefore, the laser power entering the PD detector must be large enough to reduce the effect of PD module noise and obtain a more accurate laser linewidth. For example, the detection power of the PD, which is used in this experiment, must exceed 10 µW. On this premise, the effect of PD module noise on the measurement system can be ignored, which ensures that the measured laser linewidth is closer to its actual value. When the detection power exceeds 50 µW, the laser-linewidth measurement results become larger. It is because, after two laser beams are combined, the peak power can exceed the threshold of the photodetector. This results in a voltage distortion in the electric output signal of the PD. When the voltage of the electric output signal reaches the maximum value of the detector, it can no longer increase with increasing optical input power leading to an inaccurate detected value. Moreover, an increase in the laser power increases the DC component, the amplitude of the measurement envelope is reduced under a constant signal-to-noise ratio (SNR) of the PD module. So, PD module with high SNR and low background noise can obtain more precise coherent envelope and detected laser line width.
According to the previous description, the PD detection power of the self-homodyne system should preferably be lower than 50% of its threshold power. For example, when the PD power used in this paper was 45 µW, the lowest measured laser linewidth was 23.82 kHz (8.2 dBm laser output power). The latter can be used as the best detection power of the system.
The laser output power was set to a constant value of 8.2 dBm to see the effect of double-arm optical-path power on the laser-linewidth measurement. Moreover, the optical power of the laser beam entered PD through the upper arm with the 32.25 m delay-fiber was fixed at 22.5 µW by adjusting VOA2. The optical power of the lower arm entering the PD was gradually increased from 0 µW to 70 µW by adjusting VOA1. Figure 4(a) shows the coherent envelope spectra for optical powers entering the PD from the lower arm. Figure 4(b) shows the fitted line widths using the SDSH coherent envelope method from the detected coherent envelope curves in Fig. 4(a).
Fig. 4. (a) Output power spectra corresponding to optical powers entering the PD from the lower arm of the self-homodyne system. The optical power of the laser beam entering PD from the upper arm was set to a constant value of 22.5 µW. (b) Different fitted line widths, obtained from (a) using the SDSH method, corresponding to the optical powers that enter the PD from the lower arm. (c) Output power spectra corresponding to optical powers entering the PD from the lower/upper arm of the self-homodyne system. The total optical power of the laser beam entering PD was set to a constant value of 45 µW. (d) Different fitted line widths, obtained from (c) using the SDSH method, corresponding to the ratio of the optical power values of one arm (P lower/upper arm power) to the total detected power (P total detected power = 45 µW).
Furthermore, it can be seen that when the lower arm power changed from 0 µW to 1 µW, the measured laser-linewidth decreased rapidly with increasing optical input power. The main reason for this is that when the optical power was 0–1 µW, the noise of the measurement system was mainly affected by PD module noise. With increasing the optical power of the arm, the effect of PD module noise on the self-homodyne system decreases rapidly, and the measured laser-linewidth also decreases rapidly. When the lower arm power changed from 1 µW to 22.5 µW, the measured laser linewidth decreased gradually, and the minimum laser linewidth was measured at 22.5 µW, 23.82 kHz. The main reason for this is that when two signals are correlated, their correlation characteristics can be highlighted only when the energy of the two signals is equal. The premise for deriving the coherent envelope formula is that the powers of both arms are equal. Therefore, when the self-homodyne system is used to measure the laser linewidth, the optical power of the laser beams in the two arms should be consistent for the measured value of the laser linewidth to be closer to its true laser linewidth. When the lower arm power exceeded 22.5 µW, the measured value of laser linewidth increased with increasing power. It is because when the total power measured by the homodyne PD detector exceeded 50 µW, its peak power could exceed the threshold of the PD. It can result in the piezoelectric distortion of its electric output signal and inaccuracy of the measured laser linewidth fitted using the power spectrum. Note that when the voltage of the electric output signal reaches the maximum value of the detector, it can no longer increase with increasing the input optical power.
The laser output power was also set to a constant value of 8.2 dBm to explore further the effect of double-arm optical-path power on the laser-linewidth measurement. The total optical detected power of PD was fixed at 45 µW by adjusting the VOA1 and VOA2. Figure 4(c) shows the coherent envelope spectra for optical powers entering the PD from the lower/upper arm. For example, When the optical power of the laser beam entering the PD from one arm is 1µW, the optical power of the laser beam entering the PD from the other arm is 44 µW. Figure 4(d) shows the fitted line widths from the detected coherent envelope curves in Fig. 4(c). The abscissa of Fig. 4(d) is the ratio of the optical power values of one arm (P lower/upper arm power) to the total detected power (P total detected power = 45µW). From Fig. 4, it can be seen that when the total detected power is constant with a value of 45 µW, which is lower than 50% of the PD threshold power, the measured value of laser linewidth is determined by the lower power arm.
Moreover, with the increase in the ratio of P lower/upper arm power/ P total detected power = 45µW, the measured value of laser linewidth decreases. Therefore, it can be concluded that if the optical powers of the laser beams in the two arms are close, the measured value of laser linewidth is small. When the optical powers of the two arms are equal to 50% each, the measured value of laser linewidth is narrowest, approaching its real linewidth.
The laser output power gradually increased from 8.2 dBm (6.6 mW) to 14.2 dBm (26.3 mW) to explore the effect of laser power on the laser linewidth. In addition, a set of coherent envelope data was recorded every 1dBm - see Fig. 5(a). Before data recording, the VOA of each arm was adjusted so that the optical power reaching the PD through each arm was 22.5 µW. Figure 5(b) shows different fitted line widths corresponding to the laser output powers obtained using the power spectra from Fig. 5(a) using the SDSH coherent envelope method. It can also be seen from the figure that the measured laser linewidth gradually decreased with increasing laser output power. When the laser power increased to 14.2 dBm, the measured value of the corresponding laser linewidth reached its minimum (14.38 kHz). The main reason for this phenomenon is that when the laser driving power increases, the stimulated radiation increases, ultimately increasing the output laser power. Then, the real linewidth of the laser itself becomes narrow in the low power range of 8.2 dBm–14.2 dBm in this experement.
Fig. 5. (a) Measured power spectra corresponding to laser output powers with SDSH. (b) Fitted linewidths corresponding to laser output powers obtained by the power spectra from (a).
To further verify the accuracy of the coherent envelope linewidth measurement method, using an SDSH, the length of the delay fiber in the experimental system was changed from 32.25 m to 3 km. In other words, the measurement system changed into a conventional delayed self-homodyne laser-linewidth measurement system. We gradually increased the laser output power from 8.2 dBm to 14.2 dBm and recorded a group of power spectrum data every 1 dBm - see Fig. 6(a). Before recording the data, the double arm VOA was adjusted so that the optical power of the laser beam reaching the PD via two arms was 22.5 µW, eliminating the effects of the self-homodyne system module and PD detection module. Figure 6(b) shows different fitted laser line widths corresponding to different laser output powers obtained using the – 20 dB laser linewidth fitted from the measured power spectrum in Fig. 6(a).
Fig. 6. (a) Different measured power spectra correspond to different laser output powers for a conventional self-homodyne system. (b) Different fitted laser values corresponding to different laser output powers obtained using a –20 dB laser linewidth fit.
It can be seen from Fig. 6(a) that the conventional self-homodyne output power spectrum is easily affected by 1/f noise, low-frequency noise, and the suppression of low-frequency noise by ESA at low frequency. It causes a cut-off in the peak of the low-frequency power spectrum. In this case, the laser line widths, fitted using – 3 or – 20 dB, were not necessarily accurate. It was done in addition to using a – 20 dB laser linewidth fit – see Fig. 6(a) and (b). The measured value of laser linewidth was about 310 kHz. Figure 6(a) indicates that when the frequency exceeds 10 MHz, the higher the laser power, the lower the amplitude of the power-spectrum noise at the same frequency. Therefore, it can be roughly inferred from the power spectrum in Fig. 6(a) that the higher the laser output power is, the narrower the laser linewidth. In other words, the conventional self-homodyne method can only roughly compare the magnitudes of laser line widths for different output powers. It cannot accurately measure the linewidth. Therefore, even if the actual linewidth of the laser shown in Fig. 5 changes, the laser linewidth shows no evident change, as shown in Fig. 6(b).
It can be seen from Fig. 5 that when the laser power increases, the actual value of the laser linewidth can be narrow. The change law can be monitored using the SDSH coherent envelope method. Figure 6 also shows that even if the actual laser linewidth changes, the results obtained using the conventional self-homodyne system do not change significantly. The measured laser line widths are not necessarily accurate. It is because the 1/f noise introduced by the conventional method is much larger than the change in laser linewidth, which represents the limitation of the conventional self-homodyne laser-linewidth measurement. Therefore, based on a comparison of Fig. 5 and Fig. 6, the accuracy of the laser-linewidth measurement method with an SDSH coherent envelope can be verified.
4. Conclusion
This study investigated the effect of laser output power, self-homodyne double-arm power, and PD-detected power on the laser-linewidth measurement of an SDSH system. The following experimental results were found. 1) When the optical power entering the PD ranges from 10% to 50% of its linear saturated power and does not exceed SNR of the measurement system, the measured laser linewidth will closer to its actual value. 2) When the double-arm power of the self-homodyne system remains equal, their coherence characteristics can be highlighted, and the measured laser linewidth can be closer to the actual value. However, suppose the power difference between the two arms is too large. In that case, one optical signal may drown the other optical signal, which can lead to an inaccurate coherent envelope and an inaccurate laser linewidth fit. 3) The real laser linewidth can narrow with increasing optical power in the low output power range of the laser. By comparing the laser-linewidth measurement results of the SDSH and the conventional self-homodyne, the accuracy of the SDSH coherent envelope laser-linewidth measurement method was confirmed. The results of this study can serve as a reference for the precise measurement of laser linewidth. This method is expected to enable the precise measurement of ultra-narrow linewidth lasers.
Funding
Basic and Applied Basic Research Foundation of Guangdong Province (2022A1515011352, 2022A1515110203); Guangzhou Municipal Science and Technology Project (202201010523).
Acknowledgments
The authors acknowledge support by the Scientific Research Program of Guangzhou University.
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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