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Abstract
In this study, the focus is on continuously tuning an external cavity diode laser equipped with an antireflection-coated laser diode over a 14.8 GHz range, 4.5 times larger than the free spectral range, using only injection current sweeps. In contrast, the absence of antireflection coating led to a tuning range of only one-fifth of the free spectral range, accompanied by hysteresis on mode hops. Theoretical analysis of this observed hysteresis suggests that broad tuning can be achieved when the longitudinal modes of the solitary laser diode are eliminated through the antireflection coating.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Tunable lasers with frequency control in the vicinity of atomic transitions with narrow linewidths are essential for conducting experiments such as laser cooling and atom manipulation in the field of atomic physics [1]. Recently, laser cooling of atoms has been applied to precision measurements, including clocks [2,3], magnetometers [4], and gravimeters [5,6], and the operation must be as stable as possible in these applications. A major cause for the unintentional stoppage of the operation is the mode hops of lasers, due to which a frequency lock to an atomic transition does not work. Therefore, decreasing the mode hops of lasers in the long term is essential.
External cavity diode lasers (ECDLs) are the commonly used tunable lasers in atomic physics applications because of their compactness and low cost [7,8]. Several types of ECDLs with optical components for wavelength selection, such as reflective grating [8–16], Bragg grating [17–20], microresonators [21], and interference filters (IFs) [10,22–27], have been developed. Several studies have been conducted to improve the performance of ECDLs in terms of their short-term stability [9,10,17–21], long-term stability [11–13,18,19,22–26], and tunability [10,14–16,27]. Among these, long-term stability is essential for eliminating unintentional mode hops during operation. ECDLs with an IF inserted into the external cavity (IF-ECDL) for improving their long-term stability are structurally insensitive to misalignment because a cat’s eye configuration, in which the laser light is focused on both ends of the external cavity, can be quickly adopted [22]. However, all ECDLs except for reflective-grating ECDLs generally have the limitation of a relatively narrow continuous tuning range (CTR) because synchronizing the wavelength selected by the optical component with the frequency of the longitudinal modes determined by the length of the external cavity is difficult. By contrast, in ECDL systems that employ reflective gratings, the grating serves dual functions: as an output coupler and a wavelength selector. Synchronization is attainable through the adoption of a carefully designed geometrical layout that facilitates grating movement. Consequently, continuous tuning over a range greater than 10 THz has been realized [14]. More recently, a continuous tuning range of 1.7 THz was achieved in the IF-ECDL, in which variation in the angle of the IF was synchronized with the length of the external cavity independently of the location of the rotation pivot for frequency scanning [27]. In conventional IF-ECDLs, the CTR is not strongly considered; however, their long-term stability is pursued as an advantage. Therefore, the IF does not move; that is, the selected wavelength remains unchanged when the laser frequency is scanned by actuating an output coupler. Consequently, the CTR is constrained by the external cavity's free spectral range (FSR), usually in the realm of a few gigahertz. This limitation applies when the longitudinal mode having the highest gain is consistently chosen among modes that are uniformly spaced at intervals equal to the FSR.
IF-ECDLs have also been developed as laser sources for atomic fountain primary frequency standards by our group [28], wherein continuous operation for a month or longer is required. To render them mechanically more robust, all the optical components are fixed, and any position adjusters are removed [23]. The frequency was tuned by changing the injection current into a laser diode (LD), which leads to variations in the refractive index and, thus, the optical length of the active layer of the LD, whereas, in the commonly used IF-ECDLs, the frequency is generally scanned by displacing an output coupler with a piezo actuator. In the ECDLs proposed in this study, although the CTR was degraded to one-fifth of the FSR of the external cavity when the output facet of the LD was not coated with an antireflection (AR) material, the unintentional mechanical variation in the length of the external cavity was strongly suppressed. Thus, the frequency variation under free running is dominated by atmospheric pressure [23] and is largely suppressed by installing the ECDL in a housing sealed from the outside [24]. When focusing on frequency lock associated with an atomic transition, elevated passive stability enhances the robustness of the frequency lock. On the other hand, a reduced CTR equates to a limited locking range. Consequently, an overly narrow CTR can compromise the frequency lock, even though expanding the CTR is not an immediate objective. In actual use, the benefit provided by the mechanical robustness surpasses the defect owing to the small CTR. In the laboratory under a well-controlled environment, unintentional mode hops occurred only once per approximately 5 months in the ECDLs used for our atomic fountain, which has been tried to operate continuously day and night. The mode hop was attributed to not mechanical vibration but the frequency drift exceeding the locking range.
Using an uncoated LD, the longitudinal modes of a solitary LD influence the ECDL [29]. Because the solitary LD modes are unsynchronized with the ECDL modes, the CTR of an ECDL with an uncoated LD becomes narrow. AR coating on the output facet of an LD eliminates the unnecessary solitary LD modes and generally enhances the CTR of an ECDL [30]. Therefore, it is expected to improve the CTR to the limitation of the FSR and enable a semipermanent frequency lock by using an AR-coated LD for an ECDL. If a semipermanent frequency lock even out of a laboratory is realized, the atom physics application will be accelerated toward social use. For this purpose, a distributed Bragg reflector laser [31] and distributed feedback laser [32] are some of the most promising candidates as well. However, while they have the advantages of compactness and mechanical robustness, the short-term stability is substantially worse than that of an ECDL due to a short cavity length. For the narrow linewidth of an atomic transition, the requirement for a low noise in a current source is generally more stringent than that in the use of an ECDL.
Because of AR-coating, the CTR of the ECDL was increased by a factor of 4.5 times wider than the FSR in the present study. In addition, in other studies, a CTR of more than 10 times the FSR in an IF-ECDL [25] and a CTR slightly exceeding the FSR in a Bragg-grating ECDL [19] by sweeping the LD current have been reported. However, no in-depth investigations regarding wide CTRs have been performed.
In an IF-ECDL employing an uncoated LD, hysteresis on mode hops becomes evident when scanning the frequency by varying the LD current. This hysteresis reveals that the initially dominant mode remains favored, despite having a lower gain compared to its neighboring modes. If the longitudinal mode with the largest gain is not necessarily selected, the CTR can be wider than the FSR when unnecessary solitary LD modes are sufficiently eliminated using an AR-coated LD. For an LD without an external cavity, the hysteresis on the mode hops has been explained through nonlinear effects that suppress the gain of the adjacent modes [33]. The experiment to induce strong hysteresis by doping Te acting as saturable absorbers in the cladding layer of the LD was conducted [34]. However, thus far, no studies have focused on hysteresis in an ECDL. In contrast to an LD, optical components for wavelength selection may play an essential role in hysteresis in an ECDL.
In this study, the continuous frequency tuning of an IF-ECDL with an AR-coated LD significantly exceeding the FSR by only sweeping the LD current was performed. Moreover, the hysteresis of mode hops in an IF-ECDL with an uncoated LD was experimentally investigated. To explain the wide CTR, the extent of the broadening of the CTR of the IF-ECDL with an AR-coated LD was estimated from the observed hysteresis.
2. Experiment
Figure 1 shows the IF-ECDL used in the experiment, which is identical to that described in [23]. The ECDL comprised a Fabry–Perot-type LD, three lenses, a partial mirror (PM), and an IF. The first lens collimated the output from the LD, focused on the PM by the second lens, and collimated again by the third lens. The focal lengths were 4.51 mm, 18.40 mm, and 11.00 mm, respectively. An external cavity with a reflectance of 30% was created between the rear facet of the LD and the reflection surface of the PM. The setup was intentionally designed to achieve the given reflectance of the PM. In contrast, the reflectance of the rear facet of the LD was fortuitously found to be approximately the same (see Section 3). The IF used was a bandpass filter (BPF) with a transparence bandwidth of 0.3 nm at full width at half maximum (FWHM). The BPF was inserted between the first and second lenses. The central wavelength of the BPF depends on the tilt of the laser beam; therefore, the BPF was designed such that the central wavelength was tuned to 895 nm, which is the resonant wavelength of 133Cs D1 line, at an incident angle of 6°. The tilt of the BPF was adjusted such that the wavelength was near the atomic transition point. The optical length of the external cavity in terms of the refractive index of the vacuum was 46 mm, from which the FSR was calculated to be 3.3 GHz.
Fig. 1. Schematic of the side view of the IF-ECDL. The yellow part represents the substrate that is sterically machined.
The LD, encased in a can package, and the PM were securely anchored to a substrate of sterically machined copper using screws. The fixation of these elements dictates the length of the external cavity. Following their placement, jigs that support the three lenses and the BPF were adhered to the substrate. Upon completion of the ECDL fabrication, all components become immobile, precluding any frequency tuning via component adjustment. Initial coarse frequency tuning was achieved by controlling the substrate’s temperature via a Peltier element; a thermistor embedded in the substrate served as the temperature monitor. Finally, fine-tuning of the laser frequency was executed by manipulating the LD current. In other words, the temperature of the substrate was changed so that the specific frequency to be tuned may have been included in the CTR. At the process of the tuning, no significant reduction in the CTR was observed. When scanning the frequency, the LD current was linearly varied by providing a triangular waveform from a direct digital synthesizer into the modulation port of the current controller.
Two IF-ECDLs were used in the experiment: (1) “ECDL-AR” with an AR-coated LD (Sacher, SAL-0920-060) and (2) “ECDL-UN” with an LD without AR coating (Thorlabs: M5-905-0100). Except for the LD chips, the structures of the ECDLs are almost identical. According to the datasheet, the typical and specification reflectance values of the output facet of the AR-coated LD are <5 × 10−5 and <5 × 10−4, respectively. The supplier emphasized the process of evaporation of the coating; thus, the spectral fringes generated by the longitudinal modes were observed, and the thickness of the coating was adjusted to minimize the fringes [35]. The evaporation process might be important for the expansion of the CTR. Hence, using an AR-coated LD with a similar specification of reflectance purchased from another supplier, the CTR of EDCL-AR was not significantly enlarged compared with that of ECDL-UN.
Moreover, two distinct variations existed in the IF-ECDL configurations utilized for this research, likely exerting a modest impact on the capability for continuous tuning. One difference was the housing: although the ECDL-UN was contained in a sealed housing to avoid the influence of variations in atmospheric pressure [24], the ECDL-AR was not contained. Sealed housing was considered unimportant in this study, as long-term measurements were not conducted. The other difference was the current controller for LDs (Thorlabs LDC202C for ECDL-AR, Vescent Photonics D2-105 for the ECDL-UN); owing to the difference in noise, the spectral linewidths were 200 kHz for ECDL-AR and 40 kHz for ECDL-UN.
To measure the variation in the frequency of ECDL-AR (ECDL-UN), a beat signal was obtained using ECDL-UN (ECDL-AR) as a reference laser. The frequency of the beat signal was measured using a frequency counter. Figure 2 shows the frequency variation in ECDL-AR as a function of the LD current. Here, the LD current was linearly varied with a rate of 2.5 mA/s. The laser frequency was continuously tuned over a range of 14.8 GHz, 4.5 times larger than the FSR, at a rate of −0.12 GHz/mA. Notably, the minimum LD current providing the frequency data was close to the threshold current for laser emission (65 mA). In contrast, the maximum LD current was determined to avoid damage to the LD. No mode hops were observed over the entire range of the LD currents used in the experiment. No hysteresis was observed concerning the LD current.
The spectrum of the beat signal was observed using a spectrum analyzer. Through the whole range where the experimental data shown in Fig. 2 were given, the noise was dominated by the spectrum analyzer, and the main signals were observed. In most LD current ranges, a single longitudinal mode was obtained, as shown in Fig. 3(a), which is the spectrum at an LD current of 130.0 mA. The sidemode suppression ratio was >42 dB. However, particularly at approximately 88.5 mA and 167.5 mA, a few side modes were observed. As the spectra around either of the LD currents had the same characteristics, only the spectrum at 88.5 mA is shown in Fig. 3(b). The power of the maximal side mode was 10.7 dB lower than that of the carrier mode. The modes were equally separated by 2.9 GHz, differing to some extent from the FSR, 3.3 GHz. Despite the excitation of side modes, the capability for continuous tuning of the carrier frequency remained unaffected. A frequency differential of 9.9 GHz was observed between the laser carriers operating at LD currents of 88.5 mA and 167.5 mA. The power of the maximal side mode was reduced to 20 dB below the power of the carrier at LD currents of 88.5–2.0 mA and 88.5 + 3.1 mA, as well as at LD currents of 167.5–1.3 mA and 167.5 + 2.3 mA. Notably, no problems were observed while obtaining a single mode near a specific atomic resonance; even if the side modes accidentally appeared when the carrier frequency was tuned to the desired frequency, a single-mode oscillation was obtained at that frequency by adjusting the LD current and temperature. However, single-mode oscillations were not acquired over a wide range of 14.8 GHz, even when the temperature was changed.
Fig. 3. Frequency spectra of the beat signal at LD currents of (a) 130.0 mA and (b) 88.5 mA in ECDL-AR.
Subsequently, the frequency of ECDL-UN was measured by increasing or decreasing the LD current with a rate of 0.2 mA/s. Figure 4 shows the variations in the laser frequency as a function of the LD current, where the blue and red lines indicate the cases in which the LD current increased and decreased, respectively. Compared with that of ECDL-AR, the CTR of ECDL-UN was considerably reduced, and mode hops appeared. Subsequently, the hysteresis of the laser frequency was observed every approximately 2.7 mA of variation concerning an increase and a decrease in the LD current. First, consider the strong hysteresis found in the range of the LD current between 80 mA and 85 mA. The symbols A–F in Fig. 4 represent the mode hops. In the following, I and f with a subscript of A–F are the LD current and frequency at the symbols, respectively. Notably, no mode hops occurred when the LD current was swept between IC = 81.05 mA and IF = 84.34 mA, as indicated in Fig. 4, after selecting the ECDL mode. Therefore, the CTR was ${f_\textrm{C}} - {f_\textrm{F}} = 0.67\; \textrm{GHz}$. If no hysteresis had been observed, the CTR would have been ${f_{\textrm{C}/\textrm{D}}} - {f_{\textrm{E}/\textrm{F}}} = 0.47\; \textrm{GHz}$, where fC/D and fE/F are the frequencies at LD currents of (IC + ID)/2 = 81.31 mA and (IE + IF)/2 = 84.05 mA, respectively. Therefore, the CTR increased by a factor of 1.4 owing to hysteresis. For the hysteresis found between 78 mA and 82 mA, the CTR with the hysteresis and the CTR assuming no hysteresis were 0.58 GHz and 0.47 GHz, respectively; for the hysteresis found in the range between 83 mA and 88 mA, they were 0.55 GHz and 0.45 GHz, respectively. The difference in the CTRs with the hysteresis may be attributed to the deviation of the laser frequency from the central frequency of the BPF with a bandwidth of 100 GHz at FWHM.
Fig. 4. Frequency variations of ECDL-UN as a function of the LD current, where the blue and red lines indicate the cases of increasing and decreasing the LD current, respectively. The symbols A–F represent the LD currents and frequencies at which mode hops occurred. Note that the blue line partially disappears owing to its overlapping with the red line. This indicates that the frequencies in the cases of increasing and decreasing LD current were extremely close to each other to resolve the lines.
3. Discussion
In the following, the wide CTR of ECDL-AR is evaluated from the experimentally observed hysteresis in ECDL-UN. For the highly reliable evaluation, the types of LDs used in the ECDLs are preferred to be the same except for AR coating, but that was not the case. Moreover, because the strength of the hysteresis in ECDL-UN depends on the range of the LD current, the CTR of ECDL-AR theoretically estimated depends on which current range hysteresis in ECDL-UN is chosen for the analysis. Therefore, the following analysis may be rough to a certain extent. Nevertheless, whether the wide CTR of ECDL-AR significantly beyond the FSR can be explained by the hysteresis in ECDL-UN or not should be important. From this perspective, the hysteresis in ECDL-UN in the current range between 80 mA and 85 mA, which was the strongest in the hysteresis observed in the experiment, is used in the following analysis.
Figure 5(a) provides a schematic representation of the transmittance spectra for the BPF, solitary LD modes, and ECDL modes, under the ECDL-UN scenario. In this context, laser medium gain was disregarded, as its spectrum significantly surpassed the BPF transmittance in width and was consequently considered uniform. Within ECDL-UN, the BPF selected one of the solitary LD modes, given that its FSR was approximately half of the FWHM of the BPF’s transparency bandwidth. Fluctuations in the LD current led to corresponding shifts in the frequencies of both solitary LD and ECDL modes; these shifts were attributed to changes in the active layer’s refractive index. Due to the minor contribution of this active layer to the external cavity’s optical length, the rate of frequency change in solitary LD modes was 16-fold greater than in ECDL modes. As a result, each alteration of the solitary LD mode frequencies by an FSR triggered a mode hop in ECDL modes.
Fig. 5. Schematic of the transmittance of the BPF, solitary LD mode, and ECDL modes in the cases of (a) ECDL-UN after the LD current is decreased, and (b) ECDL-AR. In (b) the pink lines represent the initial ECDL modes, and red lines represent the ECDL modes after the LD current is decreased.
The transmittance spectrum of solitary LD modes with a Fabry–Perot cavity is given as,
Initially, the midpoint of the two successive ECDL modes was assumed to match the center of the solitary LD mode, whose frequency was denoted as νs0. In particular, the frequencies of the two ECDL modes are νs0 ± fFSR/2, where fFSR is the FSR of the external cavity. Here, the transmittances of the solitary LD mode at ECDL modes on the positive and negative sides are denoted as $S_{\textrm{LD}}^ + $ and $S_{\textrm{LD}}^ - $, respectively, and the larger values of $S_{\textrm{LD}}^ + $ and $S_{\textrm{LD}}^ - $ are denoted as $S_{\textrm{LD}}^\textrm{L}$. When the LD current is decreased (increased), $S_{\textrm{LD}}^ + $ ($S_{\textrm{LD}}^ - $) becomes larger than $S_{\textrm{LD}}^ - $ ($S_{\textrm{LD}}^ + $) because the solitary LD modes shift in the positive (negative) direction significantly faster than ECDL modes, as shown in Fig. 5(a). When the central frequency of the solitary LD mode changes to νs0 + δ by varying the LD current, the proportion of the difference between $S_{\textrm{LD}}^ + $ and $S_{\textrm{LD}}^ - $ to $S_{\textrm{LD}}^\textrm{L}$, $\alpha \equiv ({S_{\textrm{LD}}^ +{-} S_{\textrm{LD}}^ - } )/S_{\textrm{LD}}^\textrm{L}$ is given as,
Because the refractive index of the active layer of a solitary LD varies linearly with the LD current [36], the optical lengths of the active layer and external cavity change linearly with the LD current. Although the frequency variation of ECDL-UN under continuous tuning was nonlinear with the LD current, as shown in Fig. 4, the discrepancy may be attributed to the frequency pulling induced by the solitary LD mode and BPF. The hysteresis frequency range, defined as the range of the central frequency of the solitary LD mode where the relation between the oscillation mode and the sign of α(δ) is broken as described above, is given from the experimental result as follows:
Thus, once the ECDL mode on the positive (negative) side is selected as an oscillation mode under the condition of α(δ) > 0 (< 0), it continues to be chosen even when −αmax < α(δ) < 0 (0 < α(δ) < αmax). Incorporating the value $\delta = \mathrm{\Delta }{f_\textrm{h}}/2$ into Eqs. (2) and (3), and using Eq. (1), ${\alpha _{\textrm{max}}} \simeq 0.020$.
Next, the ECDL-AR was considered, wherein the solitary LD modes are negligible, as shown in Fig. 5(b). In this case, the ECDL mode was selected using the BPF. The frequency of one of the ECDL modes was assumed to initially match the center frequency of the transmittance of the BPF, and that laser oscillation occurred in the central ECDL mode. When the LD current is decreased, all ECDL modes shift in the positive direction, whereas the transmittance spectrum of the BPF is fixed. Therefore, although the transmittance of the BPF in the oscillation mode decreases, that of the ECDL mode on the negative side increases. When the LD current is increased, the opposite occurs. Applying the discussion regarding ECDL-UN to ECDL-AR, the oscillation mode was permitted to sustain in the case where $\beta \equiv ({T_{\textrm{BPF}}^{\textrm{max}} - T_{\textrm{BPF}}^{\textrm{osc}}} )/T_{\textrm{BPF}}^{\textrm{max}} \,<\, {\alpha _{\textrm{max}}}$, where $T_{\textrm{BPF}}^{\textrm{max}}$ and $T_{\textrm{BPF}}^{\textrm{osc}}$ are the transmittance of the BPF at its maximum and that at the oscillation mode, respectively. Using numerical value ${\alpha _{\textrm{max}}} \simeq 0.020$, the equation can be converted to $T_{\textrm{BPF}}^{\textrm{osc}}/T_{\textrm{BPF}}^{\textrm{max}}\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }0.980.$ From the transmittance spectrum of the BPF used in the experiment, the frequency range satisfying $\beta \,<\, {\alpha _{\textrm{max}}}$ was approximately estimated to be 16 GHz. Therefore, the experimental results of continuous frequency tuning over a range of 14.8 GHz significantly exceeding the FSR of the external cavity can be explained.
In the above discussion, αmax was derived not from a theoretical analysis but from the experimentally obtained hysteresis frequency range. Here, αmax may depend on the conditions of the specific ECDL. Therefore, adapting the discussion to quantitatively estimate the enhancement of the CTR of a general ECDL is difficult. For the generalization, a more profound theoretical analysis of hysteresis in an ECDL, which has not yet been focused on, will be needed. Here, in the external cavity based Fabry-Perot LD including no optical components for wavelength selection (e.g., a BPF), the laser frequency can be tuned by varying the power of the external optical injection, as reported in [37]. The phenomenon can be attributed to the nonlinear dynamics of period-one oscillation. These nonlinear dynamics might be indicative of the hysteresis observed in the present study.
4. Conclusion
In contrast to the CTR of conventional tunable lasers, in this study, by only sweeping the LD current, the CTR of the IF-ECDL was determined to be 4.5 times wider than the FSR of the external cavity by using an AR-coated LD to eliminate the solitary LD modes. However, when using an uncoated LD, hysteresis was observed in mode hops. Theoretical analysis starting from hysteresis explains the wide CTR of the IF-ECDL with an AR-coated LD.
In previous experiments [23,24], the mechanical robustness of the ECDLs was achieved at the expense of a narrow CTR, notably due to the absence of position adjusters and the use of an uncoated LD. This study effectively addresses that limitation. A substantially wide CTR of 14.8 GHz, as determined in this research, adequately meets the requirements for frequency locking under typical environmental conditions. For example, the CTR covers an atmospheric pressure range of 222 hPa according to the ratio between the laser frequency and the atmospheric pressure [23]. ECDLs with both mechanical robustness and wide CTRs are expected to be used for applications based on atomic physics, wherein lasers must be steadily frequency-locked to atomic transitions over the long term.
Funding
Innovative Science and Technology Initiative for Security (JPJ004596).
Acknowledgments
This study was supported by Innovative Science and Technology Initiative for Security Grant No. JPJ004596, ATLA, Japan. The author sincerely thanks S. Yanagimachi for his help in creating the setup for the data acquisition of the beat signal.
Disclosures
The author declares 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 author upon reasonable request.
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