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Abstract
In this paper, we present a theoretical model based on the nonlinear Schrödinger equation to characterize GHz-range passively mode-locked fiber lasers. The modeled cavities of the lasers are configured by a highly doped and polarization-maintaining single fiber of a single type. For different pulse repetition rates, ranging from 1.0 to 10.0 GHz, gain parameters and pump threshold for a stable mode-locked laser emission are studied. Pulse time width, spectral width, and semiconductor saturable absorber mirror (SESAM) properties are defined to achieve stable emission. To experimentally validate our theoretical model, 1.0 and 2.2 GHz laser cavities have been built up and amplified. A stable and robust operation for both frequencies was obtained, and the experimental measurements have been found to match the theoretical predictions. Finally, enhanced environmental stability has been achieved using a cavity temperature control system and an antivibration enclosure.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Femtosecond and picosecond pulsed lasers with high repetition rates (tens of megahertz to tens of gigahertz) are commonly used in different applications. Some of them are photonic-assisted analog-to-digital conversion (PADC) [1,2], ultrafast spectroscopy [3], optical biomedicine [4–6], and ultrahigh-bit-rate communications such as wavelength-division multiplexing [7,8]. In reference to PADCs, it has been known since the 1970s [9–14] that short optical pulses (${\lt}100\;{\rm{ps}}$) can be used to enhance the speed of electronic sampling switches through an optoelectronic design. The optical pulse provides lower pulse-to-pulse jitter than electronics, as well asfaster rise times. Currently available lasers capable to deliver GHz-range pulse repetition rates are not quite robust and provide low-quality signals. This made impossible implementing a reliable PADC system, which is now an open possibility due to the kind of laser presented in this work. An interesting solution to obtain high-repetition rates in a mode-locked configuration is to use linear Fabry–Pérot cavities [10,15–18]. One of the most important parameters when referring to mode-locked laser (MLL) combs in PADC is their long-term stability. A 1 GHz single-fiber Fabry–Pérot oscillator has been achieved before [15]. However, the thermal damage threshold of the semiconductor saturable absorber mirror (SESAM) is reached producing progressive damage in the SESAM surface and eventually changing laser properties. At this point, the necessity of a theoretical model to study GHz-rate passively mode-locked fiber laser cavities emerges.
In this work, a theoretical model based in nonlinear Schrödinger equation (NLSE) has been developed. Different repetition rates have been studied changing the cavity total length (1.0, 2.2, 5.0, and 10.0 GHz). Some of the key parameters characterized for each of the frequencies studied are the pump power threshold and gain conditions for stable mode-locked emission, SESAM properties, pulse time width, and spectral width. The oscillator cavity has been modeled by using a single fiber specially selected to absorb the power of the continuous-wave optical signal and the laser light reaching the SESAM, allowing it to work below its thermal damage threshold, ${\lt}1\;{\rm{mJ}}/{\rm{cm}}^2$. To reach the required absorption values of hundreds of dB/m, a co-doped Erbium/Ytterbium fiber has been used, which also provides the dispersion properties needed to generate a solitonic solution of the NLSE, resulting in a stable mode-locked emission. Moreover, all the laser stages (pump and cavity) have a complete PM configuration that, correctly aligned, makes the laser work in a single-polarization regime, enhancing the stability due to the lack of mode competition compared to previous publications. 2 GHz all-fiber lasers [19] and cavities with frequencies ${\gt}{{10}}\;{\rm{GHz}}$ [20] have been previously achieved using complex architectures or specially designed optical fibers. However, in this work, the focus is on obtaining optimized, robust, compact, and repeatable GHz all-fiber lasers using commercial components. When integrating mode-locked fiber lasers in practical applications such as PADC, it is mandatory to guarantee the long-term and environmental stability of the laser source. To confirm experimentally the reliability of the model, robust, stable, and ultra-short pulsed-light sources have been achieved for 1.0 and 2.2 GHz. Finally, a mechanical design has been developed to enhance the environmental stability of the laser, introducing a cavity temperature control system and an antivibration enclosure.
2. THEORETICAL MODEL
Laser mode-locking is the best technique to achieve ultra-short pulses with a temporal width of a few ps or less. For this purpose, one must establish a rigid phase relation among the many longitudinal modes that can exist in a laser cavity of a certain length. When this length is short (${\lt}0.2\;{\rm m}$), gain conditions for laser emission, which imply high values for both pump absorption and emission cross section, are difficult to meet. Additionally, low and anomalous net dispersion values are required to achieve a solitonic regime, which is needed in this kind of lasers. There is no consolidated theoretical model to predict the necessary parameters for a stable mode-locking emission in ultra-high frequency cavities (1.0–10.0 GHz). The aim of this work is to provide a method to predict the requirements that a laser cavity must meet to achieve a stable passively mode-locked emission regime in all-fiber laser cavities of short cavity length (20.0–2.0 cm).
To reach passive solitonic mode-locked stable emission, an option is to use a SESAM as the saturable element inside the cavity. The SESAM considered in our model and used to experimentally assemble the laser is consider a fast type, with a recovery time of 2 ps, a modulation depth of 37%, and a saturation fluence of $40\;{\rm \unicode{x00B5}s}/{{\rm cm}^2}$. For a detailed theoretical and analytical analysis of SESAM use in the development of MLL, see [21–24].
Considering the gain conditions that the laser cavity is expected to need, and since the required emission wavelength is located in the telecommunications band C, a fiber doped with Erbium and Ytterbium has been chosen for the theoretical model. This double doping is performed to achieve higher pump absorption (${\gt}300\;{\rm dB/m}$) through the Ytterbium [25], to improve the efficiency of the Erbium emission, located around 1550 nm.
Figure 1 shows the laser architecture used in the theoretical model and the experimental setup used to compare and validate the results of the theoretical model. It is a mode-locked, polarization maintaining (PM, as the model works with a single polarization), Fabry–Pérot threshold fiber cavity. The active fiber has been directly connectorized to minimize transitions and polarization changes inside the cavity.
Fig. 1. Oscillator internal structure. PWDM, polarizer wavelength division multiplexer; DM, dichromic mirror; SESAM, semiconductor saturable absorber mirror; PISO, polarizer isolator; PFC, polarizer fiber coupler.
A laser diode (LD, 915 nm/980 nm) was used as pump [915 nm pumping was used in long cavities (1.0 GHz and 2.0 GHz) because the absorption at 980 nm was too high, and the pump light was completely absorbed in the first third of the cavity, causing a signal re-absorption and a negative gain regime.]. The light from the LD was inserted into the laser cavity through a dichroic mirror (DM) coated on the FC/PC connector of the common port of a standard single-mode 915/1550 nm polarizer wavelength division multiplexer (PWDM), which couples the pump to the laser cavity. A second FC/PC connector attached directly to the active fiber of the cavity is coated with a DM that has a reflectance of 99% at 1550 nm, and a transmittance of more than 90% at 900–1000 nm. The DM is positioned between the two flat connectors. The active fiber is a highly Erbium and Ytterbium co-doped PM fiber (OFS YPC23401) of length $L$ with an anomalous dispersion of approximately 16 ps/nm/km at 1550 nm. The end of the active fiber is attached to another FC/PC connector. A Batop InGaAs SESAM with a modulation depth, saturation fluence, and recovery time of 37%, $30\;{\rm \unicode{x00B5} J}/{{\rm cm}^2}$, and 2 ps, respectively, was butt-coupled to the FC/PC connector.
The laser light (1550 nm) emitted from the cavity passes through the DM and is extracted from the 1550 nm port of the PWDM. A PM single-mode polarizer isolator (PISO) was fusion-spliced to the 1550 nm port of the WDM to protect the cavity from back-reflections and guarantee its long-term stability. Finally, a 90:10 standard single-mode PM polarizer fiber coupler (PFC) was fusion-spliced to the output port of the isolator, allowing multiple measurements to be carried on simultaneously. This experimental setup enables an easy modification of the cavity to go through a full study of different fiber lengths, thus different repetition rates (10 cm/10.0 GHz, 4.7 cm/2.2 GHz, and 1.0 cm/10.0 GHz) (The oscillator is built using a Fabry–Pèrot structure. This means that the length of the fiber and the length of the cavity are different concepts and are related to each other as ${{\rm Length}_{\rm{cavity}}} = 2{{\rm Length}_{\rm{Fiber}}}$).
Real and accessible elements have been used to build the theoretical model. As a result, the modeled cavities are easy to manufacture so that they can evolve into a commercial laser prototype as simple as possible.
To numerically model the emission properties of our fiber laser, pulse propagation in the laser cavity is computed by solving the NLSE [Eq. (1)] using a standard symmetrized split-step Fourier method algorithm [26]:
Equation (1) is a crucial equation in a fiber transmission system. It describes the propagation of the single-polarized slowly varying envelope$A(z,T)$ of the scalar electric field of an optical pulse normal to its propagation axis. $z$ is the spatial coordinate along the fiber length, and $T$ is a group velocity moving-frame time defined as $T = t - {\beta _1}z$, with $t$ being the absolute time and ${\beta _1}$ being the inverse of the group velocity. $\hat L$ is a linear operator that accounts for gain, losses, and dispersion of the optical fiber, and $\hat N$ is a nonlinear operator that governs the effect of fiber nonlinearities on pulse propagation. Regarding the $\hat L$ and $\hat N$ operators, $\alpha$ is the fiber loss coefficient, $g$ is the signal gain (dependent on pump power and wavelength), and ${\beta _n}$ are the n-order group velocity dispersion parameters. In Eq. (3), we have only considered self-phase modulation (SPM) through the nonlinear parameter $\gamma$ of the fiber. More complex nonlinear effects are neglected in the simulations. In [27], a complete mathematical process to correctly model a solitonic passive MLL was described.
The key point to characterize the conditions for a stable mode-locked emission is the gain equation. To apply it in a more realistic scenario, a dependence in the $z$ position has been considered. From [27], we can extract the following:
In Eq. (4), $\Gamma$ and ${N_t}$ are the estimated overlap factors between the mode field and Erbium dopant distribution and the total ion density, respectively. Parameters ${\sigma _{\rm{abs}}}(\lambda)$ and ${\sigma _{\rm{em}}}(\lambda)$ represent the wavelength-dependent absorption and emission cross sections of the active fiber. ${P_S}$ denotes the average pulse power, calculated as ${P_S} = {E_P}/{T_R}$, with ${E_P}$ being the energy of the pulse and ${T_R}$ being the cavity round-trip time. ${P_{\rm{sat}}}$, $P_P^{\rm{th}}$, and $P_{\rm{sat}}^*$ are the intrinsic saturation power of the active medium, the pump power threshold (the pump power for which the ground and upper populations are equal), and the effective saturation power of the fiber. The mathematical expression used to characterize ${P_{\rm{sat}}}$, $P_P^{\rm{th}}$, and $P_{\rm{sat}}^*$, and its usage to describe passive MLL emitting in a solitonic regime is elaborated in detail in [27]. Eq. (4) relies on a quasi two-level system valid to describe Erbium-doped systems. The Ytterbium co-doping leads to a significant increase in the conversion efficiency of the Erbium fibers, which is caused by a decrease in the Erbium ion clustering [28]. The theoretical model has been adapted using the Erbium/Ytterbium co-doped fiber-pump wavelength-absorption value given by the manufacturer and increasing accordingly the cross-section (absorption and emission) values of the fiber to match the high conversion efficiency given by Ytterbium.
Regarding the SESAM effect in the numerical calculation, it was evaluated as an insertion loss dependent on the pulse intensity, as done in [29]. The equation describing the temporal response of the intensity-dependent losses in the SESAM, $q(t)$ is the following:
In Eq. (5), $A(z,t)$ is the slow-varying component of the electromagnetic field of the signal, ${q_0}$ is the modulation depth, ${E_{\rm{SA}}}$ the saturation energy, and ${\tau _{\rm{SA}}}$ the recovery time.
Table 1. Simulation Parameters
Table 1 shows the values used in the simulations of this work to adapt the theoretical model to GHz-repetition-rate cavities.
The performance of the oscillator has been completely simulated and the results experimentally validated. As an example, Fig. 2 shows the calculated stable mode-locked pulse formation in our laser system corresponding to the laser architecture described in Fig. 1 for the 1.0 GHz cavity (top) and for the 2.2 GHz cavity (bottom). Evolution of both the spectra and the time full width at half maximum (FWHM) of the output pulses are depicted in the insets. Stability of both parameters is reached after few hundreds of round trips, when the initial random noise input is mode-locked into a stable pulse. Pulse width is 2.1 ps for the 1.0 GHz cavity and 1.1 ps in the 2.2 GHz case. As the length of the active fiber of the cavity changes, so does the net dispersion of the oscillator, which leads to different resulting pulses. According to the spectral width obtained, the Fourier transform of the 1.0 GHz cavity gives a minimum pulse of 1.3 ps and the 2.2 GHz cavity, a minimum pulse of 1.0 ps, obtained from a spectral FWHM of 2.0 nm and 2.5 nm, respectively. Accordingly, the obtained results are consistent with the expected case.
Fig. 2. Calculated stable mode-locked pulse formation regime corresponding to the setup described in Fig. 1. (top) 20.8 cm cavity, 1.0 GHz rep. rate; (bottom) 9.6 cm cavity, 2.2 GHz rep. rate.
A 10.0 GHz cavity (of 1.0 cm fiber length) was tested under the same pumping conditions, modeling also the co-doped Erbium/Ytterbium fiber. The algorithm did not converge because the short active length of the cavity did not provide a proper positive gain regime. From this point onwards, some modifications were required to reach the proper emission regime. The first one was to model a 980 nm pump to exploit the fact that the absorption of the active media is higher for this wavelength (355 dB/m at 915 nm versus 600 dB/m at 980 nm). With a cavity absorbing more pump power, the required gain conditions should be easier to reach. The convergence test that contemplates these conditions can be seen in Fig. 3 (top). As the image shows, a 980 nm pump was not enough to achieve a convergence in the algorithm. To reach a theoretical convergence, the gain of the cavity must be improved either by increasing the pump power or by increasing the emission cross section of the active media.
Fig. 3. Calculated mode-locked pulse formation regime for a 1.0 cm cavity. (top) 980 nm pump wavelength, gain conditions and pump power same as those for 1.0 GHz and 2.2 GHz simulations (${\sigma _{\rm{em}}} = 51\;{{\rm pm}^2}$); (bottom) 980 nm pump wavelength, emission cross-section three times higher than in the 1.0 and 2.2 GHz simulations (${\sigma _{\rm{em}}} = 150\;{{\rm pm}^2}$).
In Fig. 3 (top), a pulse evolution for 10.0 GHz can be observed. Despite the simulation converging, the values of pump power (${\gt}1\;{\rm W}$) are out of the experimental possibilities as the SESAM cannot hold such a high pump power, and there is no commercial fiber matching the emission cross-section requirements. However, these simulations show that a 10.0 GHz cavity is buildable if the architecture adapts to its necessities.
The following is a full analysis for different frequencies, to study and predict the ideal conditions for mode-locked emission and transfer them to real prototypes. Fixing the laser architecture (same SESAM, same active fiber, same dichroic mirror), convergence at different lengths of the cavity has been studied, those being 20.8 (1.0), 9.6 (2.2), 4.0 (5.0), and 2.0 cm (10 GHz). For each of these frequencies, a complete sweep has been performed by varying the pumping power and recording key parameters: spectral width, temporal width, and average power.
Figure 4 shows the spectral width as a function of the pump power at convergence of the simulations. When the convergence gives a near-to-zero spectral bandwidth, there is no stable mode-locking emission. Stable emission starts when the width curve becomes monotonous and shows a smooth evolution. To estimate the pump power threshold for stable mode-locked emission for each of the frequencies, the pump power where the slope of the derivative is 45º has been used, being $112\;{\rm mW}@1.0\;{\rm GHz}$, $142\;{\rm mW}@2.2\;{\rm GHz}$, $257\;{\rm mW}@5.0\;{\rm GHz}$, and $693\;{\rm mW}@10.0\;{\rm GHz}$.
Fig. 4. Spectral bandwidth after the convergence of the algorithm for different frequencies of the cavity. The threshold power for stable mode-locking emission is represented by a vertical dotted line.
Figure 5 shows temporal width (top) and average output power (bottom) as a function of the pump power after the convergence of the simulation for different frequencies of the cavity. For all frequencies, the pulse time width at convergence is similar, about 2 ps. This can be easily explained by considering the key factors that determine the duration of the output pulses in mode-locked cavities, which are both the net dispersion and three SESAM parameters: relaxation time (${\tau _{\rm{SA}}}$), fluence, and modulation depth ($\Delta R$). However, they do not affect the pulse width as the SESAM is the same for all cases. On the other hand, to calculate the net dispersion of the cavity, the group velocity dispersion of the fiber ($D$) can be estimated as $D = - 16\;{\rm ps/nm/km}$. Despite the difference in relative value between the lengths of the cavities, from 20.8 to 2.0 cm, the net value of the dispersion barely changes (3.4 fs/nm for 20 cm and 0.32 fs/nm for 2.0 cm), resulting in pulses of similar temporal width.
Fig. 5. Temporal width (top) and average output power (bottom) as a function of the pump power after the convergence of the algorithm for different frequencies of the cavity.
Looking at the average output power, it is observed that for the higher frequency cavities (5.0 and 10.0 GHz), the net gain is lower, so the efficiency is smaller. This can also be seen in Fig. 4, in which the emission threshold for high-frequency cavities is also higher, 110 mW for 1.0 GHz and more than 600 mW for 10.0 GHz.
Fig. 6. (top) Blue: temporal width for different frequencies when the cavity average power output is 500 µW. Green: measured temporal width after the amplification stage. (bottom) Spectral width for different frequencies when the cavity average power output is 500 µW.
Fig. 7. Autocorrelation traces measured using a Femtochrome FR-103XL autocorrelator. (top) For the 1.0 GHz cavity when its average power output is 500 µW. (bottom) For the 2.2 GHz cavity when its average power output is 500 µW.
The target applications of this work need an average output power greater than that obtained for the cavities (50–1000 µW). To achieve the correct power specification (${\gt}{{100}}\;{\rm{mW}}$) by amplification, while maintaining a correct signal-to-noise ratio (SNR) (${\gt}{{27}}\;{\rm{dB}}$), the seed average power to the amplifier must be in the order of magnitude of hundreds of µW. Figure 6 illustrates a comparison between the simulated temporal and spectral width of each cavity for those conditions in which they emit 500 µW of output average power and the measured temporal and spectral width using an autocorrelator and a spectrum analyzer, respectively. The sensitivity of the autocorrelator was not high enough to measure signals with an average power of ${\lt}{{1}}\;{\rm{mW}}$ at high frequencies. To obtain the autocorrelation traces, the pulses were measured after the amplification stage. Corresponding autocorrelation traces are shown in Fig. 7. The value of temporal width at FWHM for 1.0 and 2.2 GHz cavities are 2.8 and 2.0 ps, respectively. To obtain the values of temporal width, a deconvolution factor of 0.648 has been applied, assuming a ${{\rm sech}^2}$ pulse shape.
There are two main reasons why the simulated values may differ from the measured ones. On one hand, due to the dispersion introduced through the fiber of the amplifier, the temporal pulse width increases from the oscillator to the amplification stage. On the other hand, dispersion resulted from Gires–Tournois interferometers (intrinsic to the SESAM functioning) has not been taken into account in the calculations. In long cavities, with a maximum frequency of several hundreds of megahertz, the dispersive effect of the SESAM is neglected. Once the cavity length is sufficiently short, its value must be considered. The SESAM used to build the cavities in this work has a dispersion value that is strongly dependent on the wavelength from 2.74 fs/nm at 1525 nm to ${-}2.74\;{\rm fs/nm}$ at 1560 nm, being 0.73 fs/nm at 1535 nm.
3. EXPERIMENTAL RESULTS
To verify the validity of the theoretical study and achieve the implementation of a prototype of stable emission at GHz-range frequency, cavities of 1.0, 2.2, and 10.0 GHz have been built. Furthermore, to perform measurements with a wider dynamic range and to meet the power needs of the target application, the output from the laser cavities has been amplified with a fiber amplifier (see Fig. 8).
A. Oscillator
Figure 9 (top) shows the measured optical spectrum (blue line) corresponding to a cavity with a repetition rate of 1 GHz and 140 mW of pump power, where the red line shows the theoretical predicted spectrum. In the legend box, spectral FWHM (both measured and simulated) is shown. Figure 9 (bottom) shows the measured optical spectrum (blue line) corresponding to a cavity with a repetition rate of 2.2 GHz and 180 mW of pump power. Again, the red line shows the theoretical predicted spectrum. The high stability of this laser optical spectrum during long-term stability measurements (${\lt}0.3\;{\rm dB/nm}$ in a 4-h-long MAX HOLD vs MIN HOLD measurement) relies on the all-PM-fiber cavity.
Same tests have been performed using the same laser architecture for 5.0 and 10.0 GHz cavities. As predicted by our simulations, the required gain conditions were not reached. To have the conditions for an adequate gain regime, the pumping power should be increased to levels higher than the SESAM damage threshold, or a greater gain in the fiber should be achieved by making a non-commercial fiber design. High fundamental frequency fiber MLL (10–20 GHz) have been previously demonstrated using carbon nanotubes as a saturable absorbent [16]. However, in this work, the focus is getting optimized, robust, compact, and repeatable GHz all-fiber lasers using commercial components.
B. Amplifier
After the oscillator stage, a co-doped Erbium/Ytterbium double-cladding PM fiber amplifier has been included. Figure 8 shows the amplification stage. A 976 nm laser diode (PD) delivering a maximum output power of 8 W was used as a pump. Light delivered from the PD was introduced into the first clad of the active fiber through the pump input of the power combiner (PC). This stage is shared for all cavities of different repetition rates.
Fig. 9. Experimental and simulated output optical spectrum of the mode-locked fiber oscillator in logarithmic scale for the 1.0 GHz cavity (top) and 2.2 GHz cavity (bottom).
The seed signal coming from the oscillator is introduced in the core of the active media through the main input of the PC. The PC is spliced to 1.5 m of double-clad co-doped Erbium/Ytterbium PM fiber (Nufern PM-EYDF-6/125-HE). A PM single-mode isolator was fusion-spliced to the output of the active fiber to protect the cavity from back-reflections and guarantee its long-term stability.
The performance of the setup to amplify the oscillator output signal has been analyzed. Figure 10 shows average power of the laser signal at the output of the amplifier vs. current driving the pump laser diode. As it can be seen in Fig. 10, the amplifier performance in terms of power is similar for 1.0 and 2.2 GHz frequency inputs.
Fig. 10. Amplifier output power vs pump diode current. 200 mW of output average power are reached at the 4 A current of the pump diode (at 4 A, the pump diode gives 5 W of continuous wavelength signal at 976 nm). In black, amplified average output power for 1.0 GHz seed. In red, amplified average output power for 2.2 GHz seed.
It is possible to evaluate the gain factor in terms of power of the amplifier, using equation Eq. (6). The final product will have 100 mW of output power, which is the value used for ${P_{\rm{out}}}$ in both cases. For the 1.0 GHz seed, ${P_{\rm{in}}} = 185\;{\rm \unicode{x00B5} W}$; and for 2.2 GHz, ${P_{\rm{in}}} = 355\;{\rm \unicode{x00B5} W}$. The pulse energy is 18.5 and 16.1 pJ, respectively, for 1.0 and 2.2 GHz cavities.
The long-term stability of the laser working in a ${\gt}100\;{\rm mW}$ average power output regime has been studied. Figure 11 shows a record of the average laser output power on the left ordinate axis and a record of the calorimeter measuring head temperature on the right axis, both measurements taken at 5-second intervals. The observable temperature variations are caused by uncontrolled environmental changes around the measuring head, specifically, the variation after 45 h happens because there was an increase in laboratory activity due to the end of the test. A standard deviation on the output average power of ${\lt}0.25\%$ is obtained. The high long-term stability indicates that there is no SESAM degradation over time due to the high-absorption fiber chosen in the cavity that prevents undesired $Q$-switch laser modes and thermal damage caused by the pumping power in the SESAM. In short cavities, uncontrolled $Q$-switching instabilities can also cause permanent thermal damage in the SESAM, leading to an unstable behavior [30]. For this reason, during the experiments, the damage threshold of the SESAM ($1\;{\rm mJ}/{{\rm cm}^2}$) was neither overcome by the pumping power nor by the power of the laser signal.
The all-PM design of both oscillator and amplifier forces the laser to work in a single-polarization regime that enhances the overall power stability. Similar curves have been obtained for both, the 1.0 and 2.2 GHz cavities. The one shown in Fig. 11 corresponds to 2.2 GHz rep. rate.
The amplifier structure has been numerically simulated for the 1.0 GHz seed using the pulse propagation engine described in Section 3, but changing the clad pump absorption from 355 to 10 dB/m, the core signal absorption from 30 to 37 dB/m, and the lengths of active and passive fibers. All the characterizing parameters (temporal width, average output power, and spectral width) have been obtained theoretically and measured in the laboratory. The comparison between them can be seen in Table 2.
Table 2. Simulation Comparison
The very small differences between measured and simulated values indicate that the theoretical values of fiber length (1.5 m) and net dispersion (0.024 ps/nm) used in the simulation are an accurate approximation to the real values of these parameters. The oscillator output pulse from the previous simulation was employed as the initial seed in the amplifier stage. For the sake of completeness, a simulation of the output oscillator pulse through the amplifier stage in comparison with the oscillator output pulse is shown in Fig. 12. The temporal width stretching of the pulse after the amplification stage is due to the dispersion introduced by the amplifying fiber, and it was estimated by experimental results, obtaining a value interval of 12–16 ps/nm/km.
Fig. 12. The blue line represents the oscillator output pulse; the red line represents the amplified oscillator output pulse.
Finally, the optical spectra at the output of the amplifier for different values of the pump current are shown in Fig. 13, for 1.0 (top) and 2.2 GHz (bottom) signal seeds, respectively. As it is shown, the curve shape remains unchanged. This means that the peak power of the amplified pulses remains below the threshold of nonlinear effects. The SNR is higher for higher frequencies (27 dB for 1.0 GHz and ${\gt}40\;{\rm dB}$ for 2.2 GHz). The energy of the pulses at the input of the amplifier is similar (18.5 pJ for 1.0 GHz and 16.1 pJ for 2.2 GHz). Taking this into account, the SNR improvement must be caused by the increase in the frequency. The higher repetition rate implies less time of the active media being pumped with no signal going through, which translates into less amplified spontaneous emission energy, which can be observed in Fig. 13 (top) at ${\sim}1543\;{\rm nm}$.
Fig. 13. Spectra at the output of the amplifier for different values of the current applied to the LD. 2.2 A corresponds with the 100 mW average output power.
From the point of view of the spectral domain, MLL are, indeed, optical frequency combs. Frequency tones of the comb are not seen in the spectra represented in Fig. 13 because the spectrum analyzer resolution of 50 pm is insufficient to resolve tones of an FSR of 8 pm (1.0 GHz) or 18 pm (2.2 GHz).
To visualize the optical spectrum of the comb with detail, a Brillouin optical spectrum analyzer (BOSA) has been used. BOSAs are equipment that reach resolutions up to 0.08 pm, far better than regular optical spectrum analyzers [31]. Figure 14 (top) shows a 0.1 nm span, 0.08 pm resolution measurement of the optical spectrum at the output of the amplifier for the 2.2 GHz laser architecture. The 18 pm free spectral range between harmonics corresponds with the 2.2 GHz repetition rate, measuring ${\gt}50\;{\rm dB}$ SNR of spurious free spectrum between two consecutive tones. Figure 14 (bottom) shows the same measurement with a 2.0 nm span.
Fig. 14. Optical spectrum of the 2.2 GHz amplified signal measured with a Brillouin optical spectrum analyzer. (top) Span of 0.1 nm and resolution of 0.08 pm. (bottom) Span of 2 nm and resolution of 0.08 pm.
C. Amplifier: Radio Frequency Domain
Radio frequency (RF) measurements of the photo-detected oscillator output were carried out for both 1.0 and 2.2 GHz frequencies. Figure 15(A) shows the RF spectrum of the photo-detected fundamental harmonic of the mode-locked laser (MLL) oscillator output corresponding to a setup with a FSR of 0.999 GHz, with a SNR of 65 dB at 500 kHz offset from the fundamental frequency.
Fig. 15. A,B: RF spectra of the photo-detected fundamental harmonic of the mode-locked oscillator output corresponding to setups of 1.0 and 2.2 GHz pulse repetition rates. A: fundamental harmonic, bandwidth of a 1 MHz and 2 Hz resolution. B: fundamental harmonic, bandwidth of a 10 MHz and 2 Hz resolution. C,D: corresponding RF spectra with a 25 GHz span and 6.2 MHz resolution.
Figure 15(B) shows the RF spectrum of the photodetected fundamental harmonic of the MLL oscillator output corresponding to a setup with a FSR of 2.231 GHz and a SNR of 76 dB at the 500 kHz offset from the fundamental frequency. Figure 15(C), 15(D) shows a 25-GHz-spanned RF spectrum of both photo-detected oscillator signals.
These measurements have been reproduced after the amplifier stage. As it can be observed in Fig. 16(A,B), the RF spectra has an SNR of ${\gt}110\;{\rm dB}$ at the 500 kHz offset from the fundamental frequency. Figure 16(C),16(D) shows the corresponding RF spectra with a 25 GHz span. Figure 16 shows that this laser (at both repetition rates) has a very low phase noise, and it is free of spurious frequencies within the FSR between harmonics of the fundamental frequency. The signal–noise relation in the RF measures is better than the oscillator one, because the higher power output allows to take advantage of the entire dynamic range provided by the measurement system consisting of a photo detector plus spectrum analyzer.
Fig. 16. A,B: RF spectra of the photo-detected fundamental harmonic of the mode-locked amplified laser with a 100 mW of average power output corresponding to setups of 1.0 and 2.2 GHz pulse repetition rates. A: bandwidth of a 500 kHz and 2 Hz resolution. B: bandwidth of a 500 kHz and 2 Hz resolution. C,D: corresponding RF spectra with a 25 GHz span and 6.2 MHz resolution.
These measurements were carried out with an Agilent electric spectrum analyzer (N9020A-526-EA3-B25-P26-PFR-N9075A-2FP-N9068A-2FP).
4. PROTOTYPE
Once the laser is working properly, the next step is to implement an optimal commercial mechanical design. The mechanical structure is organized by levels, one for the optical elements and the other for the system electronic control. A global sight of this structure is illustrated in Fig. 17.
Fig. 17. Left: fiber optic laser structure situated in a compact layout. Right: closed structure. Output elements are situated in the back of the laser.
As the target applications are focused on PADC and photonic radars, the laser must be stable, regardless of the environmental conditions. A chest (Fig. 18) has been implemented to introduce the laser cavity and control its temperature with an accuracy of 0.1°C using a Peltier cell. The chest is mounted on a platform with low-frequency anti-vibration components (2–20 Hz), to further improve the resistance and stability of the equipment, since it is possible that as a photonic radar the laser is implemented inside transport means (Normative: MIL-STD-810 Rev. G-CHG-1).
Fig. 18. Temperature control and antivibration mechanical design to enhance the stability (average power and frequency drift) of the laser cavity.
Fig. 19. MAX HOLD measure of the amplified signal during 2 h of continuous emission. In the $X$-axis, the frequency drift from 2.2311 GHz is represented.
The temperature control allows to optimize the stability of the output power and the temporal jitter, obtaining a drift in a frequency lower than 15 kHz, as Fig. 19 shows. To analyze the frequency drift, a MAX HOLD measurement has been done. This measurement keeps always the maximum intensity value for each frequency. The width of the RF spectrum corresponds to the frequency drift of the laser signal. The cavity is controlled in temperature (0.1°C accuracy), minimizing the length changes due to thermal expansion (${\lt}0.05\;{\rm \unicode{x00B5}{ m}}$). The control over the thermal expansion implies a controlled frequency drift (${\lt}15\;{\rm kHz}$).
The temperature control system allows to set the temperature of the cavity, controlling the laser emission frequency in a range of fundamental freq. ${\pm}300\;{\rm kHz}$ selection. A central frequency emission curve for different stabilization temperatures is shown in Fig. 20 with measured drifts ${\lt}20\;{\rm kHz}$ for the range 23–30°C.
5. CONCLUSIONS
From the need for a high-frequency fiber laser that could be used as a source in applications of PADC and photonic radar, and with the aim of making an optimal design of the laser cavity, a theoretical model based on the solution of the NLSE has been crafted. Using this theoretical model, a complete study has been made for cavities of 1.0, 2.2, 5.0, and 10.0 GHz, based on an architecture manufactured with accessible components. By recording values of interest (temporal width, average power, and spectral width), the convergence conditions for stable laser emission solutions have been obtained.
The 1.0 and 2.2 GHz cavities have been implemented using a fully reliable ready-for-industrialization laser architecture. To reach the necessary specifications in PADC and photonic radar, and to achieve measurements with a better dynamic range, an amplifying stage was added, increasing the power up to 100 mW. The system has been completely characterized: optical spectra, RF spectra, pulse width, spectral stability, and power output–power pump curves for each one of the frequencies. The spectra and pulse width obtained were consistent with the values obtained from the theory.
The higher frequency cavities (5.0 and 10.0 GHz) could not be built because the convergence occurred for pumping powers that were above the damage threshold of the SESAM. However, the consistency of the results for short cavities indicates that higher frequencies are feasible if adequate conditions are achieved. Some options would be using a pumping wavelength that is better absorbed in the active fiber of the cavity (980 nm instead of 915 nm), or using fibers with more absorption capacity and therefore more gain or a combination of both. The model offers the adequate parameters to build a correct laser architecture for 5.0 and 10.0 GHz.
Compared to previous works on GHz-rate fiber frequency combs, we have achieved a stable cavity with enhanced spectral and power stability and durability for 1.0 and 2.2 GHz. This feature relies on the singularities of our cavity: all-PM configuration and single-type fiber cavity have been specially selected to not reach the thermal damage threshold of the SESAM, as well as to engineer control on temperature and vibration.
Finally, a mechanical layout has been built to correct the instabilities caused by environmental changes: immunity to vibrations and temperature variations. For this, a copper chest has been built based on a thermoelectric cooler (TEC) system. Both parts, the TEC system and the chest, are located on an anti-vibration platform. This, together with the all-fiber configuration make the laser a robust system suitable for PADC and photonic radar applications.
Funding
Centre for Industrial Technological Development (LASER COMB, IDI-2014063); Ministerio de Economía y Competitividad (DI-15-07461).
Disclosures
The authors declare no conflicts of interest.
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