Fiber laser cavity with dynamically transformable topology for switchable bidirectional pulse generation

Let us now consider laser radiation propagation inside the active fiber loop. Voltage-controlled CW generation can be modeled by solving the following gain-loss balance equation in a stationary lasing regime:

$$\begin{equation}{P_\Sigma } = g{P_{{\text{cc}}}}({\alpha _{{\text{cc}}}}{T_{{\text{cc}}}} + {\alpha _{\text{c}}}{T_{\text{c}}})\end{equation} \tag{ 3 }$$

where ${\alpha _{\text{c}}}$ and ${\alpha _{{\text{cc}}}}$ are the intracavity loss coefficients for light propagating clockwise and counterclockwise inside the active loop, respectively. ${P_\Sigma }$ is the total lasing power, delivered at the SOA output in both clockwise and counterclockwise directions, ${P_{{\text{cc}}}}$ is the SOA output power in counterclockwise direction. The intracavity transmittance and reflectivity of the Sagnac fiber loop formed by the passive fiber loop and the WEOS were modelled assuming a negligibly small nonlinear phase shift as ${T_{{\text{cc}}}} = {\text{co}}{{\text{s}}^2}\left( \xi \right)$ and ${T_{\text{c}}} = {\text{si}}{{\text{n}}^2}\left( \xi \right)$, where $\xi = \pi {U_{{\text{con}}}}/{U_{{\text{max}}}}$ is a dimensionless parameter of the control voltage, ${U_{{\text{max}}}} \approx 13$ V.

The SOA saturable gain $g$ can be calculated from the gain-loss balance condition for light propagating counterclockwise around the active loop: $g = {({\alpha _{{\text{cc}}}}{T_{{\text{ cc}}}})^{ - 1}}$. Then the SOA output power ${P_\Sigma }$ can be derived from SOA specification for a known gain.

Finally, the dependence of the SOA output power delivered in counterclockwise direction on the dimensionless control voltage parameter $\xi$ can be found from equation (3) as:

$$\begin{equation}{P_{{\text{cc}}}} = \frac{{{P_\Sigma }}}{{g({\alpha _{{\text{cc}}}}{T_{{\text{cc}}}} + {\alpha _{\text{c}}}{T_{\text{c}}})}}.\end{equation} \tag{ 4 }$$

We can also retrieve powers for the clockwise and counter-clockwise laser radiation flows at all points of interest inside the laser cavity for a known $g{\text{ }}$ and ${P_{{\text{cc}}}}$.

We summarized the modeling results in figure 4 by plotting the following laser power characteristics as functions of the control voltage: (i) output laser power at the 1% output coupler (from the common radiation flow in the amplifying loop); (ii) output laser power at the port 1 of the 10% output coupler (from the clockwise radiation flow in the passive loop); (iii) output laser power at the port 2 of the 10% output coupler (from the counter-clockwise radiation flow in the passive loop).

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We have also performed experimental measurements of the corresponding CW laser power characteristics by using our test-bed laser setup (figure 3) and a high-precision optical power meter. To this end, we slowly varied (with a step of 0.1 V) the control voltage applied to the WEOS from 0 to 13 V and then backward from 13 to 0 V. The laser radiation power was measured for each voltage step at the 1% output coupler in the amplifying loop and at the both ports of the 10% output coupler in the passive loop of the laser cavity. The measurement cycles were repeated several times. The measurement results are summarized in figure 5. They are in a good agreement with the modelling results and additionally confirm reversibility and reproducibility of the voltage-controlled directional switching of CW generation in the proposed transformable laser cavity. The measured characteristics feature a non-zero power in the middle of the control voltage range mainly because of the amplified spontaneous emission (ASE) being delivered from the SOA when the laser generation is absent. In practice, it does not matter since there is no reason to keep control voltage in the middle of the range. Closer to the boundaries of the control voltage range, the laser ensures high spectral purity of generation, as evidenced by the measured spectra shown in figure 6.

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The demonstrated mechanism of voltage-controlled direction switchable CW generation can be further developed to produce two counterpropagating complementary pulse trains in the passive loop. To this effect, one has to modulate the WEOS control voltage by a periodic signal providing pulse-to-pulse directional switching of the intracavity laser power flow.

It is worth noting also that by increasing significantly the lasing power (for instance, by incorporating another intracavity OA) one can achieve a significant nonlinear phase shift of the order of π in the Sagnac fiber loop. The loop will act as a nonlinear optical loop mirror (NOLM [18]) in that case. It can be also modified to a nonlinear amplifying loop mirror (NALM [19]). The WEOS-based designs of NOLMs and NALMs hold promise for implementing a range of electronically switchable and tunable mode-locking regimes which will be subject of our upcoming studies. In this paper, however, we restrict ourselves to the consideration of the linear mode of operation of the Sagnac fiber loop whose transmittance and reflectivity are governed by the variable WEOS-based coupler and, consequently, by modulation of the WEOS control voltage.

The suggested approach for generating bidirectional pulses can be broadly termed as active Q-switching. Q-switching can effectively occur for the two opposing unidirectional laser cavity configurations (as shown in figure 2) which dynamically alternate with each other. In certain cases, the proposed method can also be utilized for active mode-locking. In order to achieve this, the repetition rate (F_rep) of the aforementioned switching needs to be inversely proportional to the intracavity round trip time (T_RT) of the laser radiation.

As a proof of concept, we successfully initiated both of the previously mentioned pulsed lasing regimes in our experimental laser setup. The optimal timing for Q-switching is typically determined by the optical gain recovery time, ensuring the maximum accumulation of pump energy. A typical SOA exhibits a significantly shorter (sub-nanosecond) gain recovery time in comparison to most solid-state active media including rare-earth-doped fibers. Consequently, the permissible timing for Q-switching in an SOA-based fiber laser is mainly determined by the number of the intracavity round trips required to achieve complete pulse build-up. Typically, tens to hundreds of intracavity round trips are necessary to that effect. Since the round-trip time (T_RT) in our laser setup was about 66 ns, we assumed that switching periods longer than 10 µs would be sufficient for proper Q-switched lasing. It is important to note that SOAs cannot store as much pump energy as active media with larger interaction volumes and longer lifetimes of the excited state, such as rare-earth-doped fibers. However, SOAs allow for a broader range of permissible pulse repetition rates in the actively Q-switched and cavity-dumped laser configurations with fiber resonators [16, 17]. The faster gain dynamics of SOAs helps to avoid relaxation oscillations and other instabilities commonly encountered in the aforenamed laser configurations utilizing rare-earth-doped fibers [20, 21].

Thus, we conducted experimental trials to generate bidirectional pulse trains by implementing the suggested topology-conditioned active Q-switching. Initially, we operated at a low arbitrary repetition rate and then adjusted it to satisfy the condition F_rep = 1/T_RT, which facilitated active mode-locking.

Figure 7 displays the recorded time traces of the counterpropagating laser pulse trains. The control voltage was varied from ∼0.5 to 12.5 V as the pulse-periodic signal at a repetition rate of 1 kHz with the duty cycle first set at 50% (figure 7(a)) and then at 25% (figure 7(b)). The difference in the duty cycles leads to the corresponding difference in the durations of the two switchable topological states of the laser and, consequently, leads to the same difference in the durations of the counterpropagating pulses.

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Next, we increased the repetition rate of the cavity topology switching to a much higher value, specifically F_rep = ∼15.2 MHz. This repetition rate is inversely proportional to the intracavity round trip time, T_RT. We assumed, that such timing of switching could potentially result in actively mode-locked bidirectional operation of the laser. In figure 8, we present the output laser characteristics measured during this mode of operation. The generated bidirectional pulse trains were accessed via the opposite ports of the 10% output coupler. Figure 8(a) shows the synchronously measured time traces of the counterpropagating laser pulse trains. The WEOS control voltage was swept within the range ∼0.5–12.5 V as a biased sine wave. Analysis of the measured oscillograms allowed us to determine that the duration of the bidirectional pulses was approximately 30 ns at half maximum. By finely adjusting the repetition rate, DC bias, and amplitude of the control signal, we were able to shorten pulses down to 27 ns.

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Figure 8(b) illustrates the overlay of the optical spectra measured for the counterpropagating pulses. The spectra exhibit similar wavelengths and widths of their peaks with no noticeable differences. The optical signal-to-noise ratio exceeds 30 dB. The measured spectral characteristics in overall testify to insignificance of ASE from SOA in such a lasing regime.

We also measured the RF spectra of the counterpropagating pulse trains (figures 8(c) and (d)). These measurements enabled us to evaluate the stability and regularity of the bidirectional pulse trains using criteria similar to those employed for mode-locked lasers. The recorded RF spectra exhibit the characteristic comb-like structure with a relatively high signal-to-noise ratio, reaching nearly 50 dB in the vicinity of the pulse repetition frequency.

It is well-known that actively mode-locked lasers can be made to operate in harmonically mode-locked regimes by multiplying the modulation frequency (i.e. the frequency driving an intracavity modulator) [22]. To achieve similar regimes in the proposed laser configuration, one must trigger the cavity topology switching at a multiple of the fundamental repetition rate. As a proof of concept, we successfully generated bidirectional pulse trains at the 3rd-order harmonic of the fundamental repetition rate (i.e. at a frequency of about 45.6 MHz). Figure 9(a) shows the synchronously measured time traces of the counterpropagating laser pulse trains which were generated in this regime. They exhibit significantly shorter pulse duration (down to approximately 9 ns) compared to the fundamental regime. Figures 9(b) and (c) demonstrate the RF spectra (centered at the achieved pulse repetition frequency) which were measured for the both pulse trains. These spectra demonstrate relatively high signal-to-noise ratios (up to 50 dB), similar to those observed in the fundamental regime.

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We anticipate that use of much faster equipment in the laser setup will allow for much higher pulse repetition rates, potentially surpassing 1 GHz. This can be accomplished by employing an ultra-high-speed WEOS with a sub-nanosecond switching time, which is commercially available from the same EOSPACE company. Such technical upgrade will enable the bidirectional generation of much shorter (even sub-nanosecond) pulses, similarly to the previously demonstrated unidirectional pulse generation in an SOA-fiber ring laser with the high-order harmonic mode-locking driven by a fast electro-optic modulator [22].

Additionally, we expect that also the energy capabilities of the proposed transformable lasers can be significantly improved as compared to the proof-of-concept setup, which provided relatively modest average output powers (up to 0.5 mW for each direction) in pulsed regimes. To demonstrate this, we plan to use a higher-gain intracavity amplifier utilizing an Er-doped fiber in the follow-up study. It is worth noting that a higher intracavity power will make the nonlinear phase incursion considerable. Consequently, the overall transmittance of the passive fiber loop and the WEOS will become considerably nonlinear (power-dependent), similar to an effective NOLM. We expect that it will enable the shaping of ultra-short pulses in a hybrid mode-locked regime driven by both the switching of cavity topology and the effective 'saturable absorption' in the NOLM.