1. Introduction

Coherent beam combination is a method that achieves a higher coherent radiation power than the upper limit of an optical amplifier. By superimposing two or more outputs from optical amplifiers or lasers with controlled relative phases a beam with combined power is obtained. Due to its beam-quality preserving feature [1,2] it is widely used in research fields that require stable high-power coherent radiations including atomic physics [3] and gravitational wave detection [4]. In general CBC is categorized in two schemes. One is the tiled-aperture scheme that interferes the input beams at far-field [5]. The scheme is free from the power limit associated with a combiner and, therefore, is advantageous in achieving high output power with multiple input beams. Successful combining of up to 218 semiconductor amplifiers using a diffractive optical element (DOE) in a tiled-aperture configuration was reported with a total output power of 38.5 W [6]. The other is the filled-aperture scheme that interferes the input beams at near-field using a combiner [7–9]. While spacial intensity inhomogeneity at near-field caused by finite numerical aperture limits the combining efficiency in the tiled-aperture scheme, the filled-aperture scheme is free from the inhomogeneity and, therefore, is advantageous in combining efficiency. There are a few implementations of the combiner in the filled-aperture scheme. One is a DOE in a filled-aperture configuration to combine multiple beams in free space. As many as 47 waveguide amplifiers were combined on a DOE with a combining efficiency of 87% and an output power of 40 W [7]. A second is a free-space beam splitter [10], and a third is a waveguide such as a fiber coupler [11,12]. In case of the free-space beam splitter the power limit can be shifted upward by making the spot size on the splitter larger, but good mode matching of the input beams has to be taken care of for high-efficiency combining. In case of the waveguide favorable combining efficiency can be achieved by well-defined spacial modes of the waveguides, but the available power is limited due to concentration of the power in small spot sizes. Another merit of the waveguide is that the whole setup can be constructed in a small footprint size.

The output power of various CBC implementations differs in applications. While powers as much as 400 W of CW coherent beams are achieved for gravitation wave detectors by CBC [4], CBC is applicable to generate coherent beams with powers below 1 W at specific wavelengths used in atomic physics, when sufficient power is not available with a single laser or optical amplifier. Our application is a coherent radiation at 729 nm for accessing the electric quadrupole transition ($^2{\rm S}_{1/2}-^2{\rm D}_{5/2}$) in a trapped calcium ion ($^{40}{\rm Ca}^+$). The transition with a lifetime of 1.1 s is used for experimental implementations of optical clocks [13–17] and quantum computers [18–21]. Ti:sapphire lasers and ECDLs amplified with a tapered amplifier, directly emitting a high-power beams at 729 nm, are usually used in the experiments. Typical power reported in publications is 200 mW [22] and 250 mW [18] in each implementation. Generation of a radiation at 1458 nm followed by SHG of 729 nm extends the use of $^{40}{\rm Ca}^+$ to network applications. An example is a network of $^{40}{\rm Ca}^+$ optical clocks, in which the 1458 nm radiation is delivered through optical fiber channels to the $^{40}{\rm Ca}^+$ clocks distributed at communication nodes. Quantum mechanical manipulations of $^{40}{\rm Ca}^+$ including Doppler cooling, sideband cooling and quantum gate operations, require a reasonably large Rabi frequency, which represents the speed of dynamics in the ion, to be in the range around 1 MHz [18–20]. The Rabi frequency depends on the power and the spot size of the 729 nm beam focused to the ions. In typical ion trap setups the Rabi frequency of 1 MHz is reported with a power around 200 mW [18,22,23]. Unfortunately, a coherent light source at 1458 nm delivering sufficient power to generate the power at 729 nm by SHG is not commercially available. Commercial fiber amplifiers and semiconductor amplifiers at 1458 nm are limited to a range around 100 mW in available power. Therefore, our goal is to provide a power more than 200 mW at 729 mm by SHG of coherently combined 1458-nm optical amplifier outputs seeded by a 1458-nm laser. The approach of coherent combining of semiconductor amplifiers at the fundamental wavelength for nonlinear conversion to a target wavelength was previously deployed to successful generation of a 2 W single-frequency radiation at 488 nm from three taper amplifiers at 976 nm [24]. Free-space beam splitters were used in contrast to our implementation.

A natural approach of CBC at 1458 nm would be to use fiber-based optical components considering that a variety of products for optical communications are available in the wavelength region. We consider, therefore, filled-aperture CBC in waveguides in the above mentioned categories. A power of 200 mW at 729 nm would need a power of several hundred mW as the input of SHG. A CBC scheme to allow a combination of much more than two optical amplifiers is necessary. Some of the previously reported CBC implementations of more than three optical amplifiers or lasers are shown in Fig. 1. The CBC scheme shown in Fig. 1(a) combines $N$ input beams in a $N\times N$ coupler in a single stage, but it requires replacing of the coupler whenever an input beam is added [12]. Four erbium-doped fiber lasers are successfully combined in a 4$\times$4 25%:25%:25%:25% fused fiber coupler with a combination efficiency of 95.6%. In the CBC scheme shown in Fig. 1(b) a next amplifier is added to the total beam combined in the previous stage. It allows combination of $N$ amplifiers in $N-1$ stages with 2$\times$2 couplers with $(1/N)$: $(1-1/N)$ ratios, which need custom fabrication [25]. Successful CBC of three erbium-doped fiber amplifiers at 1560 nm in two CBC stages with a combination efficiency of 95.7% is demonstrated [25]. The CBC scheme shown in Fig. 1(c) can be constructed by cascading CBC with 2$\times$2 50%:50% couplers, although the scaling is restricted to $N=2^M$ ($M$:integer) input beams [11]. $M$-stage CBC is required for combining $N$ amplifiers. Four erbium-doped fiber lasers are successfully combined in a two-stage CBC with a combination efficiency of 95% [11]. We follow the approach shown in Fig. 1(c) to implement and operate a setup with eight input beams in three stages, and to estimate scaling to further stages based on the measured parameters.

 

Fig. 1. Previously reported CBC schemes for combining more than three optical amplifiers or lasers (a) by using a $4\times 4$ 25%:25%:25%:25% fused fiber coupler [12], (b) by cascading of 2$\times$2 1/2:1/2 and 1/3:2/3 couplers [25], (c) by cascading of 2$\times$2 50%:50% couplers [11].

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In this manuscript we report three-stage CBC of eight 120-mW SOAs seeded by an ECDL at 1458 nm in fiber couplers. A distinct feature of our setup is that the simple design based on off-the-shelf optical components allows easier access to scaling. Although the number of amplifiers combined in the setup is limited to much smaller numbers compared to those constructed with dedicated devices [6,7], we believe that our approach can provide a simpler way to implement a CBC setup with manageable number of ready-made amplifiers. An overview of our design is depicted in Fig. 2(c) as is described in details in the next section. In our design two outputs from two SOAs are combined in a 2$\times$2 50%:50% fiber coupler in the first stage. The combined beam leaves from one of the two ports of the fiber, which is called ’bright port’ with proper relative phase control of two input beams. Two combined beams generated in two such first-stage setups are then sent to the second stage, which is constructed identical to the first stage except the input beams. This second stage is then followed by the third stage in the same manner. The design should allow scaling to CBC of $2^M$ SOAs, where $M$ is the number of the CBC stages. The first experimental issue is the combining efficiency $\eta$ at each stage. If we assume a same efficiency $\eta$ in each stage, the total combining efficiency depends on $\eta ^M$. Since it shows exponential decrease considering that $\eta < 1$, reasonably high combining efficiencies at all stages are necessary for the multi-stage scaling to work. Another experimental issue is the control on the $2^M-1$ optical phases of SOAs. The output from a bright port of the fiber coupler depends on the relative phase of the two input beams. In our multi-stage CBC $2^M-1$ relative phases have to be properly managed for the output of all SOAs to interfere constructively and to reach the bright port of the last fiber coupler. Another practical issue is access to optical components. Scaling requires a large number of optical components, and use of custom optical components would prohibit it by longer lead times and higher costs. We demonstrate that these issues can be addressed in our experimental setup including three stages ($M$=3), eight SOAs, and seven feedback loops. As a direct application of the 1458-nm beam generated by the three-stage CBC we demonstrate successful generation of an output power of 239 mW at 729 nm by SHG in a nonlinear crystal. In addition, characterization of the three-stage CBC setup gives an averaged value of the combining efficiency at a single stage. It gives an insight into scaling to further stages including up to 32 SOAs.

 

Fig. 2. Overview of the CBC setup. (a)The first-stage CBC with 2 SOAs. (b)The fiber stretcher for controlling phase difference. A PZT element (drawn in yellow) changes the circumference of the acrylic reel. (c)Three-stage CBC setup including 8 SOAs.

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2. Construction of the CBC setup

Experimental implementation of CBC consists of preparation of identical coherent beams for combining, superposition of the beams and control of their relative phases. Fig. 2 depicts our experimental setup together with a laboratory-made fiber stretcher. The first-stage CBC consists of two SOAs and a 2$\times$2 fiber coupler as shown in Fig. 2(a). The relative phase of the two inputs is controlled with the fiber stretcher described in Fig. 2(b). The outputs from four first-stage CBC setups are then combined in the second stage CBC to two combined beams, and, finally, the two beams are combined in the third stage CBC as shown in Fig. 2(c).

As the laser source, we used a laboratory-made single-mode ECDL at 1458nm [26]. The laser consists of a gain chip (Thorlabs: SAF1093H) and a diffraction grating (Thorlabs: GR13-1210). It provides a 100 mW output to free space, and a 60 mW output through a polarization maintaining (PM) fiber after transmitted through three isolators and a fiber collimator. The isolation of a single isolator (Thorlabs: IO-4-1480-VLP) is 38 dB. In our experiment all fibers are PM fibers with FC/APC connectors on both ends. The linewidth of the ECDL was estimated by taking a beat note with another ECDL in a method described in ref. [27]. The 3 dB Lorentzian linewidth at 1 ms of the beat note spectrum was 11 kHz. The ECDL linewidth is estimated to be about 7.8 kHz assuming that those of the two ECDL are the same.

2.1 First-stage CBC

The first stage ($M$=1) CBC setup is shown in Fig. 2(a). First, for preparing the beams for the superposition the input power from the ECDL delivered through a fiber is split with a 1$\times$2 50%:50% PM fiber splitter for 1480 nm (Thorlabs: PN1480R5A1), and we find 49.5%:50.5% as the largest imbalance recorded in the inspection reports delivered with the products by the manufacturer. At 1458 nm the imbalance was found to increase to 43.6%:56.4% as the largest deviation in our measurement. Each split beam is then amplified in a SOA with input/output PM fibers (Thorlabs: BOA1410P). The SOA is temperature-controlled within $\pm$ 0.001 degree by a diode laser controller. The specifications of the fiber splitter are 1480 nm for the center wavelength, $\pm$15 nm for the bandwidth, 50%:50% for the splitting ratio, 10.5$\mu$m for the mode-field diameter and 0.3 dB for the excess loss. Although our target wavelength 1458 nm is outside of the specified bandwidth of the splitter, we confirmed by measurement of seven splitters that the transmission efficiency defined by sum of the two outputs divided by the input is distributed between 89% to 98%. The specifications of the SOA are 1410 nm for the center wavelength, 95 nm for the 3 dB bandwidth, 9.3$\mu$m for the mode-field diameter and 130 mW for the absolute maximum rating output power. Again, our wavelength 1458 nm is outside of the specified bandwidth of the SOA, but we confirmed by measurement of eight SOAs that an output power of 120 mW is obtained for input power of 5 mW to 7.5 mW at operating currents between 440 mA to 680 mA, which is below the absolute maximum current of 750 mW. A PM fiber adaptor (Thorlabs: ADAFCPM2) is used to all fiber-to-fiber connections including fiber splitters, couplers and SOAs.

Second, for superimposing the two amplified outputs we use a 2$\times$2 50%:50% PM fiber coupler (Thorlabs: PN1480R5A2) that has similar specifications as the fiber splitter described above except the number of inputs. The transmission efficiency defined by sum of the two output powers divided by the input power is distributed between 86% to 95% at 1458 nm. While one of the two output ports for the combined beams is called bright port, the other is called ’dark port’. A photo diode (PD) amplifier with 11 MHz bandwidth (Thorlabs: PDA20CS2) is attached to the dark port with 35 dB attenuators (Thorlabs: FA15T-APC (15 dB) and FA20T-APC(20 dB)) in between. Then the signal from the dark port is used for phase control. Output power from the bright port depends on the phase difference of the two input beams at the fiber coupler and it fluctuates due to fiber length change originating mainly from thermal and acoustic disturbances. The power at the bright port is often tapped and used for the phase control. However, we found that additional loss appearing by fiber connections when a 1$\times$2 99%:1% fiber splitter is inserted to the bright port for tapping. To detour the loss we use the dark port outputs for monitoring the phase difference.

Third, for controlling the phase difference of the input beams passive and active approaches are deployed. We constructed a cover made of 20 mm thick sound absorbing material on the fiber components arranged on a 300 mm $\times$ 300 mm aluminum breadboard surrounded by a 5 mm hardboard made of foam and plastic to reduce the thermal and acoustic disturbances. Feedback control on the phase difference is implemented by lock-in detection of the phase difference using a PZT-driven fiber stretcher and proportional-integral-differential (PID) control on it. The fiber stretcher shown in Fig. 2(b) consists of a 50 mm diameter reel machined out from a 10 mm thick acrylic plate, a PZT actuator with 16 $\mu$ m travel for 150 V (TOKIN: AE0505D16DF) and a PM fiber. Instead of using a fiber dedicated to the stretcher we use a 1.5 m input fiber with 0.9 mm diameter jacket attached to the SOA in order to avoid extra loss coming from additional fiber connections. The middle part of the fiber is wound on the reel six times. We observed phase travel of about 10$\pi$ for an applied voltage of 150 V to the PZT, which is smaller than the value calculated from circumference change of the reel due to loose contact of the fiber and the reel. The travel could be made larger by fastening a screw for pushing the PZT toward the reel to increase friction between the fiber and the reel. We found that too much force on the fiber degrades its transmission efficiency and, therefore, the screw adjustment was limited to a degree to result in the 10 $\pi$ phase travel. The mechanical resonance of the stretcher was found around at 2.5 kHz. A lock-in amplifier is used to detect the deviation of the phase difference from the value for the minimum output power from the dark port. The fiber stretcher PZT is dithered with a sinusoidal voltage in a frequency range around 1 kHz generated internally by the lock-in amplifier, and the PD signal is fed to the lock-in amplifier input to derive an error signal. The whole CBC system includes seven feedback loops, and proper selection of the dither frequencies and integration times of the lock-in amplifiers is important in establishing stable operation. The parameters are determined experimentally with the whole system operated. Intuitively, the feedback in the first stage should be established first and then those in the second and in the third stages should be established sequentially. The parameters for stable operation as the whole system were determined with the consideration and an additional policy that cross talk by harmonics should be avoided. The experimentally determined parameters are listed in Table 1. The dither frequencies and the integration times support the policies. The derived error signal is fed to an analog PID controller with 100 kHz bandwidth (Stanford Research System: SIM960). The whole system operated stably with I-action only. The output of the PID controller is added to the dither signal in a summing amplifier (Stanford Research System: SIM980) and sent to a high-voltage amplifier (Piezomechanik: SVR150) driving the stretcher PZT.

Table 1. Experimentally determined dither frequencies and integration times for phase locking of the three-stage CBC with 8 SOAs

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2.2 Second and the third stage CBC

The second stage (CBC6, $M$=2) combines two output beams from two first stage setups (CBC3 and CBC4, $M$=1) as is shown in the bottom half of Fig. 2(c). For this purpose the input from the ECDL is first split to two by an additional 1$\times$2 50%:50% PM fiber splitter. Two outputs of the splitter are delivered to the two first-stage setups. Two output fibers of the splitter are fixed to the breadboards and are covered with sound absorbing material to avoid additional acoustic and thermal fluctuation of the phases. Two outputs from bright ports of CBC3 and CBC4 are combined in an additional 2$\times$2 50%:50% PM fiber coupler. An additional PD (PD6) is attached to the dark port of the coupler with attenuators in between as in the first stage for detecting the phase difference between the outputs of CBC3 and CBC4. The error signal is derived with an additional lock-in amplifier and is fed to an additional PID controller for the phase control via a fiber stretcher (stretcher 6).

The third stage (CBC7, $M$=3) combines two output beams from two second-stage setups (CBC5 and CBC6 , $M$=2) in the same manner for the second stage as is shown in Fig. 2(c) The relative phase between CBC5 and CBC6 is detected with a photo diode labeled as PD7 and controlled via a fiber stretcher labeled as stretcher7. Although we demonstrate scaling up to three stages in the present report, extensions to $M$-stages with $2^M$ SOAs with larger number of $M$ should be implemented with identical optical components as used in the first stage. The use of off-the-shelf optical components is an advantage in the scaling.

The parallel gradient descent method and [28] the single-detector electronic-frequency tagging method [29], both with a single photo detector on the final bright port, are usually deployed as the phase control method of CBCs with multiple inputs. In our experiment we constructed the whole setup by incrementing single CBC setups. Thus the seven photo diodes installed on the dark ports remain in the final setup, and this redundant construction is used to control the whole setup due to the historical reason. We consider that the standard locking methods with a single photo diode could be implemented to the present setup without problems.

3. Experimental results

The operation of the three-stage CBC system including 8 SOAs was optimized by first adjusting the first-stage CBCs (CBC1 to CBC4), then the second-stage CBCs (CBC5 and CBC6) and finally the third-stage CBC (CBC7). The adjustment includes compensation of the imbalances of the 1$\times$2 50%:50% fiber splitters for inputs, operating currents of the SOAs and compensation of the imbalances of the 2$\times$2 50%:50% fiber couplers. Finally, the parameters for the phase lock were determined to establish stable operation of the whole system.

In our three-stage CBC seven 1$\times$2 fiber splitters are used, and the input to each SOA is delivered through three of them as shown in Fig. 2(c). Allocation of the seven splitters was experimentally determined to minimize the input power differences to the SOAs. The 2$\times$2 50%:50% fiber couplers for CBC have imbalance in the coupling ratios to the two ports with a measured ratio of 42.1%:57.9% as the largest deviation for 1458 nm. The imbalance gives some power escaping from the dark ports and degrades the combining efficiency. The currents of two SOAs coupled to a coupler were adjusted again so that the power in the dark port becomes minimized, while the sum of the SOA outputs keeps 240 mW. This imbalance compensation is applicable to the first stage only. Care was taken to allocated 2$\times$2 couplers with ratios nearer to 50%:50% to the second and the third stages. Allocation of the 2$\times$2 couplers was experimentally determined so that the powers escaping from the dark ports became minimum.

The error signals derived with the parameters are sent to the PID controllers, in which only gains for I-action have non-zero values. Stable operation observed with the lock parameters is shown in Fig. 3. Fluctuating output power at free running is brought to stable operation after the start of the locking operation at 300 s. Here the power was measured with a calibrated photodiode-based power meter (Thorlabs: S132) connected to a digital console (Thorlabs: PM100D) with a signal filtering bandwidth of 15 Hz. To avoid saturation of the power meter head the output port of the last CBC was connected to a 1$\times$2 75%:25% fiber splitter, and the power coupled out from the 25% port was measured. The ratio of tapped power at the 25% port and the total power was calibrated at lower input powers prior to the experiment. An output power of 723 mW at 1458 nm was obtained without notable degradation with longer time operation. The obtained power should be enough for generating a power more than 200 mW at 729 nm by SHG. Operation for extended periods is reported later in this section.

 

Fig. 3. Time evolution of the three-stage CBC output power in the free-running and the phase-locked operation. In the first 300 seconds the whole system was operated without active control. At 300 second the phase lock has started. Stable operation is observed in the locked state.

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Without the active locking of the relative phases as shown in the left half of Fig. 3 the output power fluctuates randomly and it is difficult to measure the output powers. Stable operation of the whole setup enables measurement of the output powers of the first-stage($M$=1, 2 SOAs), the second-stage($M$=2, 4 SOAs) and the third-stage ($M$=2, 8 SOAs) CBC. The measured powers and the ratios to a single SOA are listed in Table 2. The fluctuation of the combined power measured with the power meter at 1 second sampling period was 1.0% peak-to-peak, and 0.14% rms for 9000 seconds. The present limitation of the fluctuation comes presumably from infidelity of the seven looking loops due to insufficient optimization of the locking parameters. Further optimization with wider range of the parameters might reduce it.

Table 2. Output powers at 1458 nm of the multi-stage CBC, those of the second harmonic generation at 729 nm and ratios to a single SOA.

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3.1 Combining efficiency

It is important to characterize the combining efficiency of our system to get an insight into scaling. Combining efficiency $\eta$ of a single-stage CBC with output $P^{\rm comb}$ from $N$ inputs is defined as

Experimentally the averaged single-stage combining efficiency can be characterized by measuring the ratio of output beam power to the input beam powers. The single-stage combining efficiency was measured with seven CBCs (CBC1 to CBC7). The averaged value was found to be 89.5$\pm$4.2%, where the error is the standard deviation. If we write the combining efficiency as the product of the overall transmission efficiency $\eta _t$ and that due to the splitting ratio $\eta _s$ as ($\eta _t$ , $\eta _s$), it is (90.0% , 99.4%). The averaged combining efficiencies of the first, second, third stages described in the same manner are 88.2% (88.8%, 99.4%), 88.6% (89.1%, 99.4%), 96.4% (97.0%, 99.4%), respectively. We note that the combiner with the largest overall transmission is used in the third stage and, therefore, the value is larger than those of the other stages. The combining efficiencies are within the range of the specified efficiency of the fiber couplers. Other sources of additional loss were not found in our experiment.

3.2 Long-term operation

In our design of $M$-stage CBC 2$M$-1 phase differences have to be controlled for continuous operation. With the increase of the stage number $M$, the chance of running out of the lock operation increases. One of the sources is the arrival of the PZT voltages at the operating limits. To address this problem we implemented re-lock functionality by software control which monitors the PZT voltages during the lock operation, switches off the PID controllers when they reaches to the limits, and restarts them after a moment. To characterize long-term operation and the re-lock functionality of the three-stage CBC, we monitored the CBC output and PZT voltages for more than three days. The observation was done in a room with active temperature control of $\pm 1.0$ degree Celsius. Figure 4(a) shows the time evolution of the output power, while those of the PZT voltages are shown in Fig. 4(b). No notable degradation of the output power, nor interrupt of the lock for more than 3 days (72 h) was observed. The stable period supports most of the standard experiments with trapped ions lasting for hours. The change in power was 1.58 mW (rms), which is less than 1% of the total power of 723 mW. In Fig. 4(b) it is found that one of the PZT voltages traveled over the operating range of 0 V to 150 V at 74 h and that the re-lock functionality restarted the lock successfully. The optical components of the CBC setups are mounted on aluminum breadboards, and the breadboards are floated thermally from the optical table via insulating rubbers. Gradual increase of all PZT voltages shown in Fig. 4(b) could be presumably due to temperature increase of the breadboards. Difference in the actual packaging of each CBC might be responsible in the different slopes of the voltage increase. We note that PZT voltage change in spike shapes are synchronized with the room temperature spikes measured with a sensor placed on the optical table. Extension of the stable period might be achieved by improvement of the packaging so that all CBC setups show smaller PZT travel as seen with CBC4 and CBC6 in Fig. 4(b).

 

Fig. 4. (a) Time evolution of CBC output with 8 SOAs. (b) Time evolution of PZT voltages applied to fiber stretchers. Black dotted lines indicate the operating range of PZT. When voltage exceeds the operating range, re-lock functionality is activated by software.

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The bandwidth of the feedback to the phase difference is limited to below 2.5 kHz due to mechanical resonance of the laboratory-made fiber stretcher. Our result suggests that proper isolation of the optical components from environmental perturbations using sound-absorbing materials and PID feedback with proper locking parameters lead to stable servo operation for days even with a feedback bandwidth limited to a low frequency. We note that the standard locking methods [28,29] with a single photo diode could be implemented to the present setup without problems.

3.3 Application to second harmonic generation

As an application of the 1458 nm radiation generated by the three-stage CBC we used a PPLN (periodically-poled lithium niobate) waveguide module (NTT Electronics: 0729-000-A-B-C) to generate a coherent radiation at 729 nm by SHG in an experimental setup shown in Fig. 5. The PPLN module has an input PM fiber, and the output fiber of the three-stage CBC was directly connected to it. The generated 729-nm radiation is emitted from the PPLN waveguide to free space, and the spacial mode profile looks nearly a Gaussian. For each input power of 1458 nm the phase matching temperature was adjusted to the maximum output of the 729-nm radiation. No notable change in the phase matching temperature was found up to the input of 723 mW. The generated power at 729 nm by inputs from a single SOA, CBC of two SOAs, four SOAs and eight SOAs is plotted in Fig. 6. A 239 mW radiation at 729 nm was generated from a 723 mW fundamental power at 1458 nm. The obtained 729 nm power is comparable with those generated by Ti:S lasers and amplified ECDLs. The generated powers are summarized also in the third column of Table 2 together with the ratio to that with a single SOA. While the fundamental power is increased to 6.0 times by three-stage CBC from a single SOA, the second harmonic power at 729 nm is increased to as much as 16.2 times from that of a single SOA. Our example shows that the increase in available power brings more dramatic effects in applications with a nonlinear process.

 

Fig. 5. Overview of the setup for second harmonic generation with CBC and PPLN.

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Fig. 6. Output characteristics of the wavelength conversion with a PPLN waveguide device. The points in red, blue, green and orange represent experimental data with one, two, four and eight SOAs, respectively. Black curve shows the fitting result.

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In order to estimate the scaling of the second harmonic generation we determined parameters in a theoretical formula describing the generated second harmonic power [31] using the measured data. The generated second harmonic power $P_{\rm out}^{2\omega }$ is given by

Our goal is to obtain a few hundred milliwatt of the 729-nm beam to be focused to a spot with a few tens of micrometer diameters. This would enable time evolution of the internal states of a $^{40}$Ca$^+$ with Rabi frequencies in MHz range. The obtained power of 239 mW at 729 nm with nearly a Gaussian shape fulfils the requirement. It has been confirmed that our multi-stage CBC system constructed with off-the-shelf optical components is an effective approach to this goal.

4. Discussion

Our goal was achieved with three stages, but further stages could be implemented for applications requiring more power. Stable control of the phase differences in further stages is a prerequisite for the extension, and we assume that it could be achieved by introducing a locking scheme more suitable for scaling like the LOCSET method mentioned in the previous section together with passively stabilized packaging as demonstrated with our 3-stage CBC. In order to obtain an insight into accessible powers in further stages the measured outputs of the multi-stage CBCs are plotted against the number of SOAs as shown in Fig. 7. The least square fit of the formula (3) to the measured data gives the averaged single-stage combining efficiency $\bar {\eta } = 90.6{\%}$ as the best parameter. The fitted curve shows reasonable agreement with the measured data. The fit parameter is in good agreement with the average of the measured single-stage combining efficiency of 89.5$\pm$4.2% This suggests that our multi-stage CBC setups can be characterized by the scaling model described by formula (3). The value obtained by the measurement is used to estimate the combined powers with four and five stages as plotted in Fig. 7. Additional curves with $\bar {\eta } = 100.0$% (ideal scaling) and $\bar {\eta } = 90.6$% (fitting) is plotted as comparison. The standard error of the measured efficiency ($\pm 4.2$%) gives uncertainty in the scaling estimation growing with the number of stages as represented by the gray area, which prohibits meaningful estimation over five stages. Experimental limit of the combined power comes from damage threshold of the fiber couplers. The quoted damage threshold of the couplers with fiber connectors used in our experiment is 1 W. It is understood from Fig. 7 that the number of the CBC stages accessible with the ready-made couplers and fiber connectors is limited to three (8 SOAs). In four-stage CBC (16 SOAs) the combined power is estimated to be 1.3 W for 120 mW SOA outputs, and reaches the damage threshold. Avoiding the damage would demand operation of SOAs with reduced drive currents, which would not exploit the full power of SOAs. Splicing of fiber-to-fiber connections is excluded in our approach to use off-the-shelf components only, and its use is considered for future reference. The damage threshold would be increased up to 5 W by splicing as is specified in the documentation of the fiber couplers [33]. In this case implementation more than five stages (32 SOAs) might be possible, which would generate a combined power more than 2.2 W. The $\bar {\eta }$ value might be improved by splicing, because loss due to fiber-to-fiber connection by splicing is generally smaller than that by connectors. This suggests that more combined power might be obtained by introduction of splicing.

 

Fig. 7. Combined powers in the experiment and the estimated powers with further stages. Measured values are plotted with red circles. The ideal scaling curve ($\bar {\eta }$=100.0%) is plotted in blue for reference. The scaling predicted with the best fit parameter ($\bar {\eta }$=90.6%) is plotted in black, while that predicted with the averaged single-stage efficiency ($\bar {\eta }$=89.5%) in red. The standard error of the averaged efficiency ($\pm 4.2$%) gives error in the scaling estimation as presented in the gray area. The damage threshold of 1 W shown in the red dashed line limits accessible power with fiber couplers with connectors.

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From the SHG parameters derived in the analysis of the experiment we can estimate the 729-nm powers to be generated in the extended CBC stages by using the formula (5). The scaling of the SHG is known to be limited by thermal distortion of the PPLN waveguides with large input powers, which becomes more serious at shorter wavelengths [31,32,34]. Although the input power threshold for causing the thermal effect depends on actual manufacture of PPLN waveguides, we assume that a rough estimation of the tolerable input power level could be derived in comparison with previous reports on similar devices. An example is found with a PPLN device at 1180 nm [35], which allows an input of 1.2 W without the thermal effect. This suggests that a 1 W input at 1458 nm generated by the four-stage CBC (16 SOAs) with reduced SOA drive currents would be available to the SHG without the thermal effect. We estimate generation of as much as 358 mW at 729 nm with the setup.

5. Conclusion

We present a scalable design of a multi-stage CBC using off-the-shelf optical components at 1458 nm. Experimental issues of combining efficiency, of stable operation and of actual construction have been addressed by building and evaluating a three-stage CBC setup consisting of eight SOAs and seven active phase-lock feedback loops. An output of 723 mW at 1458 nm was generated from eight 120-mW SOAs with a combining efficiency of 75.3%. Continuous generation of the output without degradation nor interrupts for 3 days (72 hours) has been demonstrated, together with re-lock functionality to recover the operation after interrupts. As an application the combined beam at 1458 nm was used for SHG in a PPLN waveguide to generate a 239 mW coherent radiation at 729 nm. The obtained 729 nm power is comparable with those generated directly by Ti:S lasers and amplified ECDLs. An averaged single-stage combining efficiency of 89.5% was derived from the measurement and was used to estimate scaling up to five-stage CBC containing 32 SOAs. We note that our multi-scale design is applicable in wavelength ranges where standard SOAs and fiber couplers are available.