**3.4. Dynamics of the green ECDL system**

When external-cavity feedback is applied to a diode laser, complex temporal dynamics may take place [20, 21]. Thus, it is important for us to investigate the dynamics of the developed visible ECDL systems based on the GaN devices. In this subsection, we study the dynamic behaviors of the green ECDL system operated in *p*-polarized mode [22].

The complex dynamic behaviors have been studied intensively for both narrow-stripe diode lasers [23–26] and BALs [27–36] with external feedback. The dynamics of BALs have been investigated with short-cavity feedback [27–29], long-cavity feedback [30–32], tilt mirror feedback [33, 34] and lateral-mode-selected feedback [35, 36]. The feedback elements include ordinary mirrors [29–34], phase-conjugate mirrors [30] and spatially filtered mirrors [27, 28, 35, 36]. Different dynamic behaviors, such as low-frequency fluctuations (LFFs) [30, 31], selfpulsation [35], periodic oscillations [33, 36], pulse package oscillation (PPO) [28, 29, 36] and chaos [32], have been observed in the BALs with different external feedback. External grating feedback is widely used to achieve tunable high-power BAL systems [13–16]. However, the dynamics of such systems have only been studied in a very few cases [37].

**Figure 11** shows the time series of the output beam of the green ECDL system with operating currents of 211 and 213 mA. We can observe the periodic LFO for both injected currents. The corresponding oscillation frequencies are around 20 and 29 MHz with 211 and 213 mA injected currents, respectively. For both injected currents, we can observe the pulse packages consisted of pulses occurring at the external-cavity delay interval, this means the regular PPO takes place for both injected currents. The oscillation frequency of the regular PPO, νLFO, observed in **Figures 10** and **11** show its increase with the current injected to the laser device. This phenomenon was also observed in an integrated semiconductor laser with short-cavity feedback [38]. The intensity noise spectra with these two injected currents are also measured; the results are similar to the

**Figure 10.** (a) Time series and (b) intensity noise spectrum of the output beam from the green ECDL system with an

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operating current of 206.9 mA. The inset in (a) shows a close-up of the peak of one of the pulse packages.

results shown in **Figure 10(b)** and consistent with the time series shown in **Figure 11**.

The operating current is increased until to 420 mA, that is, more than twice the threshold of the ECDL system. The measured time series and intensity noise spectra at injected currents of

**Figure 11.** Time series of the output beam from the green ECDL system with an injected current of (a) 211 mA and (b) 213 mA.

As shown in **Figure 1**, the beam splitter, BS1, inserted in the external cavity reflects part of the beam to a silicon PIN photodiode, PD1, after a high-frequency amplifier; the amplified electronic signal is sent to an electrical spectrum analyzer to measure the intensity noise spectrum. The second beam splitter, BS2, reflects part of the output beam to the second photodiode, PD2, and a digital oscilloscope is used to measure the time series of the generated electronic signal. Since the green ECDL system is operated in *p*-polarized mode, the first-order diffraction efficiency is around 29%. Assuming a coupling efficiency of the feedback beam into the laser cavity is 50%, the feedback strength is around 14.5%, a moderate feedback strength for BALs [29, 35]. The physical length of the external cavity is around 33 cm.

The threshold current of the BAL is decreased from 250 to 205.5 mA by the external grating feedback. The wavelength is around 511.9 nm. We keep the feedback grating untouched during the experiment, meaning both the length of the external cavity and the wavelength of the green ECDL system are unchanged.

We investigate the dynamic behaviors of the green ECDL system by increasing the injected current from just above the threshold to more than two times threshold. **Figure 10(a)** shows the time series of the output beam with an operating current of 206.9 mA; a low-frequency periodic oscillation with a period around 220 ns is observed. The inset of **Figure 10(a)** shows the details of the time series in short time scale, an oscillation with a period around 2.4 ns is observed, the period of this oscillation is equal to the external-cavity delay time. This highfrequency oscillation is named as external-cavity oscillation with single-round-trip externalcavity frequency *ν*EC [28, 35]. **Figure 10(b)** shows the intensity noise spectrum of the output beam. Besides the peak at *ν*EC, a peak round 4.5 MHz and its harmonics for the low-frequency oscillation (LFO) shown in **Figure 10(a)**, *ν*LFO, are observed. Additionally, some peaks around *ν*EC with the frequency difference of *ν*LFO are also visible. **Figure 10** shows that the output of the green ECDL manifests a typical dynamic state named regular PPO, which mainly takes place in short cavity feedback condition [28, 29], where the external-cavity loop oscillation is modulated by a periodic LFO.

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**3.4. Dynamics of the green ECDL system**

14 Laser Technology and its Applications

When external-cavity feedback is applied to a diode laser, complex temporal dynamics may take place [20, 21]. Thus, it is important for us to investigate the dynamics of the developed visible ECDL systems based on the GaN devices. In this subsection, we study the dynamic

The complex dynamic behaviors have been studied intensively for both narrow-stripe diode lasers [23–26] and BALs [27–36] with external feedback. The dynamics of BALs have been investigated with short-cavity feedback [27–29], long-cavity feedback [30–32], tilt mirror feedback [33, 34] and lateral-mode-selected feedback [35, 36]. The feedback elements include ordinary mirrors [29–34], phase-conjugate mirrors [30] and spatially filtered mirrors [27, 28, 35, 36]. Different dynamic behaviors, such as low-frequency fluctuations (LFFs) [30, 31], selfpulsation [35], periodic oscillations [33, 36], pulse package oscillation (PPO) [28, 29, 36] and chaos [32], have been observed in the BALs with different external feedback. External grating feedback is widely used to achieve tunable high-power BAL systems [13–16]. However, the

As shown in **Figure 1**, the beam splitter, BS1, inserted in the external cavity reflects part of the beam to a silicon PIN photodiode, PD1, after a high-frequency amplifier; the amplified electronic signal is sent to an electrical spectrum analyzer to measure the intensity noise spectrum. The second beam splitter, BS2, reflects part of the output beam to the second photodiode, PD2, and a digital oscilloscope is used to measure the time series of the generated electronic signal. Since the green ECDL system is operated in *p*-polarized mode, the first-order diffraction efficiency is around 29%. Assuming a coupling efficiency of the feedback beam into the laser cavity is 50%, the feedback strength is around 14.5%, a moderate feedback strength for BALs

The threshold current of the BAL is decreased from 250 to 205.5 mA by the external grating feedback. The wavelength is around 511.9 nm. We keep the feedback grating untouched during the experiment, meaning both the length of the external cavity and the wavelength of the

We investigate the dynamic behaviors of the green ECDL system by increasing the injected current from just above the threshold to more than two times threshold. **Figure 10(a)** shows the time series of the output beam with an operating current of 206.9 mA; a low-frequency periodic oscillation with a period around 220 ns is observed. The inset of **Figure 10(a)** shows the details of the time series in short time scale, an oscillation with a period around 2.4 ns is observed, the period of this oscillation is equal to the external-cavity delay time. This highfrequency oscillation is named as external-cavity oscillation with single-round-trip externalcavity frequency *ν*EC [28, 35]. **Figure 10(b)** shows the intensity noise spectrum of the output beam. Besides the peak at *ν*EC, a peak round 4.5 MHz and its harmonics for the low-frequency oscillation (LFO) shown in **Figure 10(a)**, *ν*LFO, are observed. Additionally, some peaks around *ν*EC with the frequency difference of *ν*LFO are also visible. **Figure 10** shows that the output of the green ECDL manifests a typical dynamic state named regular PPO, which mainly takes place in short cavity feedback condition [28, 29], where the external-cavity loop oscillation is

behaviors of the green ECDL system operated in *p*-polarized mode [22].

dynamics of such systems have only been studied in a very few cases [37].

[29, 35]. The physical length of the external cavity is around 33 cm.

green ECDL system are unchanged.

modulated by a periodic LFO.

**Figure 10.** (a) Time series and (b) intensity noise spectrum of the output beam from the green ECDL system with an operating current of 206.9 mA. The inset in (a) shows a close-up of the peak of one of the pulse packages.

**Figure 11** shows the time series of the output beam of the green ECDL system with operating currents of 211 and 213 mA. We can observe the periodic LFO for both injected currents. The corresponding oscillation frequencies are around 20 and 29 MHz with 211 and 213 mA injected currents, respectively. For both injected currents, we can observe the pulse packages consisted of pulses occurring at the external-cavity delay interval, this means the regular PPO takes place for both injected currents. The oscillation frequency of the regular PPO, νLFO, observed in **Figures 10** and **11** show its increase with the current injected to the laser device. This phenomenon was also observed in an integrated semiconductor laser with short-cavity feedback [38]. The intensity noise spectra with these two injected currents are also measured; the results are similar to the results shown in **Figure 10(b)** and consistent with the time series shown in **Figure 11**.

The operating current is increased until to 420 mA, that is, more than twice the threshold of the ECDL system. The measured time series and intensity noise spectra at injected currents of

**Figure 11.** Time series of the output beam from the green ECDL system with an injected current of (a) 211 mA and (b) 213 mA.

occurring at the external-cavity delay interval are almost invisible, as shown in **Figure 12(c)**. Finally, the time series shows a chaotic behavior with an injected current of 420 mA. The corresponding intensity noise spectra for the injected currents of 340 and 420 mA are shown in **Figure 12(g**, **h)**. The peak for LFO is not observed, and the broad intensity noise spectra from

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The external-cavity feedback is classified into two regimes: short- and long-cavity regimes. When the relaxation oscillation frequency of the solitary diode laser, *ν*RO, is lower than νEC, the feedback is in short-cavity regime; otherwise, it is in long-cavity regime [26, 38, 39]. Regular PPO was first observed in 2001 by Heil et al. in short-cavity feedback narrow-strip diode laser systems [26]. With moderate feedback strength, the previous study shows that the PPO mainly takes place in the diode laser with short-cavity feedback, while LFF and chaos take place in the long-cavity regime [29, 38]. Recently, we observed regular PPO in a BAL with a lateral-mode-selected long-cavity feedback [36]. Here, regular PPO is observed in a BAL with grating external-cavity feedback. Different routes to chaos in different ECDL systems have been found [23, 40], here, we observe the transition from regular PPO to chaos in the green

Normally, an external-cavity length of a few centimeters is classified into short-cavity regime, thus in this point, the 33 cm external-cavity length in our case is in the long-cavity regime. The *ν*RO of the solitary diode laser is proportional to the square root of the difference between the injected current and the solitary laser threshold current [38, 39]. This means the definition of *ν*RO is valid only when the injected current is higher than the threshold current of the solitary laser, and the classification of short- and long-cavity regime is meaningful only on such condition. In our experiment, the PPO mainly takes place with the operating current lower than the

threshold of the solitary laser. In this point, this is a new regime for the ECDL system.

dynamic behaviors from regular PPO, irregular PPO, to chaos are observed.

In summary, the dynamics of the green high-power ECDL system with grating feedback operated in *p*-polarized mode is investigated. As the increase of the injected current, different

Both blue and green high-power, tunable, narrow-bandwidth ECDL systems based on GaN broad-area diode lasers and external grating feedback are demonstrated. For the blue ECDL, two gratings are applied. The holographic grating is for obtaining high power, a 530 mW output power with a tunable range of 1.4 nm is obtained with this grating; the ruled grating is for achieving broad tunable range, an output power of 80 mW with a tunable range of 6.0 nm is achieved with the ruled grating. For the green ECDL, the laser system can be operated in two modes, for *p*-polarized mode operation, an output power of 50 mW with a tunable range of 9.2 nm is obtained; for *s*-polarized mode operation, an output power of 480 mW with a

The tuning range and the output power optimization of an external-cavity diode laser system with grating feedback is investigated based on the experimental results on the blue and green

low to high frequency indicate typical chaotic dynamics of the output beam.

GaN BAL with grating external-cavity feedback.

**4. Conclusion**

tunable range of 2.1 nm is achieved.

**Figure 12.** Time series and intensity noise spectra of the output beam from the green ECDL with the injected current of (a, e) 230 mA, (b, f) 250 mA, (c, g) 340 mA and (d, h) 420 mA.

230, 250, 340 and 420 mA are shown in **Figure 12**. The pulse packages first oscillate irregularly, as shown in **Figure 12(a**, **e)** with an injected current of 230 mA. The time series in **Figure 12(a)** shows the pulse packages consisting of the pulse train with the period of external-cavity delay time oscillate irregular. The intensity noise spectrum in **Figure 12(e)** shows the peak for LFO and peaks for external-cavity oscillation at multiples of *ν*EC. However, the peaks at *ν*EC ± *ν*LFO originating from the mixing of external-cavity frequency *ν*EC and LFO frequency *ν*LFO, which is the indication of regular PPO are not observed. The broad peaks for *ν*EC and *ν*LFO mean that the intensity noise is increased strongly, and the dynamics of the laser system is more complex. When the operating current is increased to 250 mA, the time series in **Figure 12(b)** shows irregular PPO, and the high-frequency external-cavity oscillation is not as clear as in the condition of low injected current. The average duration of the pulse package is less than 20 ns. The broad peaks for *ν*EC and *ν*LFO mean the dynamic behavior of the laser system is more complex. The pulse package is not clear with the operated current of 340 mA, and the pulses occurring at the external-cavity delay interval are almost invisible, as shown in **Figure 12(c)**. Finally, the time series shows a chaotic behavior with an injected current of 420 mA. The corresponding intensity noise spectra for the injected currents of 340 and 420 mA are shown in **Figure 12(g**, **h)**. The peak for LFO is not observed, and the broad intensity noise spectra from low to high frequency indicate typical chaotic dynamics of the output beam.

The external-cavity feedback is classified into two regimes: short- and long-cavity regimes. When the relaxation oscillation frequency of the solitary diode laser, *ν*RO, is lower than νEC, the feedback is in short-cavity regime; otherwise, it is in long-cavity regime [26, 38, 39]. Regular PPO was first observed in 2001 by Heil et al. in short-cavity feedback narrow-strip diode laser systems [26]. With moderate feedback strength, the previous study shows that the PPO mainly takes place in the diode laser with short-cavity feedback, while LFF and chaos take place in the long-cavity regime [29, 38]. Recently, we observed regular PPO in a BAL with a lateral-mode-selected long-cavity feedback [36]. Here, regular PPO is observed in a BAL with grating external-cavity feedback. Different routes to chaos in different ECDL systems have been found [23, 40], here, we observe the transition from regular PPO to chaos in the green GaN BAL with grating external-cavity feedback.

Normally, an external-cavity length of a few centimeters is classified into short-cavity regime, thus in this point, the 33 cm external-cavity length in our case is in the long-cavity regime. The *ν*RO of the solitary diode laser is proportional to the square root of the difference between the injected current and the solitary laser threshold current [38, 39]. This means the definition of *ν*RO is valid only when the injected current is higher than the threshold current of the solitary laser, and the classification of short- and long-cavity regime is meaningful only on such condition. In our experiment, the PPO mainly takes place with the operating current lower than the threshold of the solitary laser. In this point, this is a new regime for the ECDL system.

In summary, the dynamics of the green high-power ECDL system with grating feedback operated in *p*-polarized mode is investigated. As the increase of the injected current, different dynamic behaviors from regular PPO, irregular PPO, to chaos are observed.
