Ultra-high precision dual-comb spectroscopy traditionally requires two mode-locked, fully stabilized lasers with complex feedback electronics. We present a novel mode-locked operation regime in a thulium-holmium co-doped fiber laser, a frequency-halved state with orthogonally polarized interlaced pulses, for dual comb generation from a single source. In a linear fiber laser cavity, an ultrafast pulse train composed of co-generated, equal intensity and orthogonally polarized consecutive pulses at half of the fundamental repetition rate is demonstrated based on vector solitons. Upon optical interference of the orthogonally polarized pulse trains, two stable microwave RF beat combs are formed, effectively down-converting the optical properties into the microwave regime. These co-generated, dual polarization interlaced pulse trains, from one all-fiber laser configuration with common mode suppression, thus provide an attractive compact source for dual-comb spectroscopy, optical metrology and polarization entanglement measurements.
© 2017 Optical Society of America
Laser frequency comb spectroscopy with a recent focus on dual comb spectroscopy has emerged as a powerful, ultra-high precision and sensitivity technique for non-intrusive gas detection, sensing and biomedical diagnostics. Dual comb spectroscopy [1–5] commonly relies on two mode-locked laser sources with slightly different repetition rates that are stabilized with complex feedback electronics and overlapped in a temporal interferometer for a heterodyne measurement. The optical characteristics are thus down-converted in a photodetector into a RF signal at high sampling speeds without requiring any moving optical parts. However, the need for complex infrastructure consisting traditionally of two stabilized frequency combs with good phase-locking and thus high relative coherence properties can limit dual-comb spectroscopy to specific research applications. Thus, to achieve the full potential of this real-time analysis method, has stimulated a quest for innovative laser sources without requiring multiple oscillators nor complex stabilization configurations. In this paper, we present a robust fiber laser in the eye-safe thulium wavelength regime: A novel polarization vector soliton operation in a frequency-halved state with orthogonally polarized interlaced pulses is demonstrated that can be utilized as a compact source for dual-comb spectroscopy without requiring any free-space alignment. In this configuration, common noise is suppressed and good coherence can be obtained since the pulses are co-generated in the same cavity.
Passively mode-locked fiber lasers offer a compact, highly stable and straightforward operation for exploiting ultrafast and nonlinear phenomena . While various mechanisms have been studied to induce mode-locking, the combination of soliton mode-locking with a saturable absorber features a simple and flexible cavity construction [7–11]. In fiber lasers mode-locked with nonlinear polarization rotation (NPR)  or nonlinear loop mirrors (NOLMs) , the inserted polarization sensitive elements generally lead to linearly polarized pulse train generation . However, in saturable absorber mode-locking, usually the cavity does not incorporate any polarization discriminating elements: It is well known that in fiber lasers, the asymmetrical nature of the fiber core geometry, combined with strain and bending, induces birefringence in single mode fibers (SMF). Thus, two degenerate orthogonal polarization modes  can propagate in the fiber that interact with each other through nonlinear polarization coupling and cross phase modulation. Depending on the cavity parameters, including the fiber birefringence, the two polarization eigenmodes can be locked to emit stable, elliptically polarized solitons that propagate as a single entity with the same group velocity, resulting in polarization-locked vector solitons (PLVS) [16–22]. They can evolve with an overall rotating polarization ellipse at multiples of the round trip time, whose periodicity is described by a polarization evolution frequency (PEF).
Vector solitons with different polarization states can fuel new applications based on polarization sensitivity in the telecommunication field, e.g. polarization division multiplexing, quadrature phase shift keying or other polarization modulation schemes [21,23]. For effective optical trapping of atoms or manipulation of nanoparticles, strong control and switching of polarization are a key enabler. As coherent energy transfer between the orthogonally polarized constituents of vector solitons has been reported , these sources can be of interest for a polarization entangled photon source.
While vector soliton studies have predominantly been conducted in erbium or ytterbium fiber lasers with semiconductor based saturable absorbers [16,17,19,20], similar effects were observed in fiber lasers with graphene and carbon nano-tube saturable absorbers [22,24,25]. With the emergence of low-loss thulium (Tm) gain fiber, selective studies of vector solitons in Tm based fiber lasers [26,27], e.g. simultaneous switching between scalar and vector solitons with 3 ps duration and period-doubling behavior , have been demonstrated. The broad emission wavelength of Tm based laser sources in the eye-safe region, from 1.7 μm to 2.1 μm , makes them particularly attractive for applications such as remote ranging and sensing, atmospheric propagation, LIDAR, gas spectroscopy and biomedical diagnostics and treatment. The high achievable quantum efficiency  offers an advantage over erbium fiber lasers which is the other eye-safe fiber laser. Thus, a Tm laser source providing ultrafast pulse trains with controllable polarization dynamics can be a strong candidate for comparative measurements in optical metrology, Fourier-transform spectroscopy and dual comb spectroscopy.
The presented vector soliton dynamics with their inherent two orthogonal polarization eigenstates lend themselves naturally to a design of a dual-comb laser source: By incorporating two quarter-wave plates into a solid-state Nd:YAG laser, two independent pulse trains with orthogonal polarization states  were demonstrated for the first time, however for pulse durations around 20 ps. Upon insertion of a birefringent crystal into an external cavity semiconductor based disc laser with pulse durations around 15 ps, the slight difference in the effective refractive indices for the fast and slow axis and the resulting difference in repetition rate was utilized to generate microwave beat combs [32,33]. A multi-pulse unidirectional Er fiber ring laser with simultaneous femto- and picosecond pulse durations was demonstrated  and dual wavelength operation . Exploring bi-directional propagation in a free-space Ti:sapphire solid-state ring laser  and in a free-running erbium fiber ring laser , it was recently shown that dual microwave beat combs could be generated due to the slight repetition rate difference of the optical pulse trains. Vector soliton generation in a double external cavity with vertical-cavity surface-emitting lasers has also been achieved  which can pave the way to achieve unique vector soliton states in semiconductor lasers.
While this selective work on dual-comb sources based on vector solitons paves a promising pathway towards compact single-sources for high precision spectroscopy, most configurations rely on special birefringent cavity elements in a free-space alignment laser. In this study, for the first time, we show an ultrafast vector soliton pulse train with femtosecond pulse duration, which is composed of co-generated, consecutive, equal intensity and orthogonally polarized pulses, without requiring any external birefringent materials. Instead, the fiber birefringence is adjusted with an inline polarization controller. This novel vector soliton state is achieved when the PEF is locked at exactly half of the repetition rate of the fiber laser. In this particular case, the vector soliton can be fully decomposed into two independent and orthogonally polarized interlaced pulse trains with similar pulse energy and pulse duration, which are co-generated in the fiber laser cavity. However, due to inherent fiber birefringence, a slight repetition rate difference between the orthogonally polarized counterparts is induced. In this paper, a successful generation of a wide-band dual microwave frequency comb by the interference of the orthogonally polarized constituents of the frequency-halved vector soliton state is shown. This marks the first demonstration of such a frequency half state in a fiber laser cavity without the need for any external birefringent components and without cross-coupling between pulses within the cavity. While the current implementation with a thulium-holmium co-doped gain fiber in the 2 μm wavelength regime is particularly relevant for sensing and spectroscopy applications, the general concept can be applied to any fiber laser design. Thus, this configuration can provide a practical and simple laser source for dual comb spectroscopy that does not require complex feedback schemes since both pulse trains originate in the same oscillator.
2. Frequency-halved state analysis
The linear laser cavity design is illustrated in Fig. 1(a): A 70 cm long thulium-holmium (Tm/Ho) co-doped silica based single-clad gain fiber (TH512, from Coractive) is spliced to a 5 cm long passive fiber piece (SMF-28e + ). The SMF fiber end of the cavity is directly butt-coupled to a semiconductor saturable Bragg reflector (SBR, SAM-2000-20, from Batop GmbH), for details compare . The SBR features a modulation depth of 10%, a saturation fluence of 65 µJ/cm2 and a relaxation time of 10 ps with a peak modulation around a wavelength of 1960 nm. The other end of the cavity is coupled to an output coupler (OC) with 10% transmission. A single-mode cw Ti:Sapphire laser is focused into the gain fiber to pump the fiber laser at a wavelength of 790 nm, corresponding to the peak absorption wavelength of the gain medium. The laser output signal is separated from light at the pump wavelength with an external dichroic mirror (DM). The cavity is optimized for single-mode operation in an anomalous dispersion regime (total group velocity dispersion of 0.11 ps2) so that ultrafast pulses are generated based on soliton mode-locking operation in a self-starting operation facilitated by the saturable absorber. An inline polarization controller (PC) is used to control the net birefringence of the cavity. An external linear polarizer (LP) in the output path decomposes the pulse train into its orthogonal polarization constituents, cf. Figure 1(b).
Once the mode-locking threshold at 90 mW of coupled pump power is surpassed, mode-locking (ML) operation is achieved in a self-starting, reproducible and turn-key fashion. As shown in Fig. 2(a), a single pulsing ML state is achieved for a coupled power of 100 mW, producing an average output power of 6 mW at intracavity pulse energies of 0.44 nJ. For the characterized state, the PC is adjusted such that the output signal features linearly polarized scalar soliton pulses.
The optical spectrum (measured with an optical spectrum analyzer, Yokogawa AQ6375) is centered at a wavelength of 1975 nm with a 3 dB full-width at half-maximum bandwidth (FWHM) of 9.8 nm, yielding a transform-limited pulse duration of 400 fs, assuming a sech shaped soliton, cf. Figure 2(a). Characteristic Kelly sidebands of soliton operation are observed. In Fig. 2(b), the fundamental laser repetition rate at 135.2 MHz is depicted, which matches the overall length of the laser cavity (measured with a RF spectrum analyzer from Rohde & Schwarz, FSUP50 and a 12.5 GHz photodetector Eotech ET5000). This high resolution bandwidth (RBW at 5 kHz) RF spectral trace shows a signal-to-background ratio greater than 70 dB, without any polarization induced side peaks. A wider RF spectrum trace (RBW of 50 kHz) is shown in Fig. 2(c) up to 30th RF harmonic, underlining a good stability of the pulse train.
The temporal trace of the ML state is measured with a sampling oscilloscope (HP 53480A), cf. Figure 2 (d): The pulse spacing is periodic at 7.4 ns, which corresponds directly to the repetition rate of 135.2 MHz. Stable ML operation for longer than 24 hours was observed combined with good reproducibility of the same ML state when operating the laser under the same conditions.
For a small range of polarization controller settings, scalar soliton states are achieved, as previously shown [39, 40]. However, since the fibers in the cavity feature a natural birefringence, the majority of ML states for different PC orientation settings feature elliptically polarized vector soliton trains. The level of the ellipticity, i.e. the distribution ratio of the orthogonally polarized eigenstates in each pulse, is characterized by the PEF . The PEF is resolved after decomposing the orthogonally polarized components with the external LP, which translates into the RF spectrum as an additional RF side-peak, as seen in the second column of Fig. 3. The evolution of the optical and RF spectrum of the vector solitons states with respect to the PC orientation and setting is shown in Fig. 3. Here, the impact of the PC rotation setting is captured in the following by the angle θ, which represents the twist imposed on the fiber with respect to the natural position of the fiber. An almost linear mapping between the PEF and the fiber twist θ can be deduced based on the RF measurements. The novel state we report here is that the PC setting can be modified so that the PEF is locked at the half of the fundamental repetition rate of the cavity, corresponding to a maximum polarization rotation at every other pulse. What is unique in this particular state is that both orthogonally polarized eigenstates feature the same amplitude, different from elliptically polarized states.
Since the PEF is locked exactly at the half of the repetition rate, corresponding to 67.6 MHz, the orthogonal polarization eigenstates can be fully attributed to consecutive pulses. Changing the angle of the LP confirms that each pulse solely is composed of only one orthogonal eigenstate and the same polarization eigenstate repeats itself for every second pulse, as illustrated in Fig. 1(b). The angle α of the external linear polarizer represents one of the polarization eigenstates of this pulse train. In this case, an absolute value of α = 54° is found which describes the amount of rotation of the LP in clock-wise direction along the propagation direction of the pulses from an initial state where the lines of the LP are vertical with respect to the optical table.
Thus, for an LP angle of α + 90° the same RF trace is recorded. Since two equal intensity pulse trains are generated at half of the repetition rate whose polarization switches between the two orthogonal eigenstates from pulse to pulse, we refer to this novel pulse train as a frequency-halved state in the following.
Figure 4 shows the detailed optical, RF and temporal spectrum of the frequency-halved state for different external LP setting so that different projections of the orthogonally polarized eigenstates are captured. The optical and RF spectrum without any decomposition into eigenstates is shown in Fig. 4(a), yielding a 9.8 nm FWHM at a repetition rate of 135.2 MHz. The sampling oscilloscope trace confirms the 7.4 ns periodicity between pulses. With the introduction of the external linear polarizer, the optical spectrum parameters of center wavelength, FWHM and Kelly sideband positions all remain the same. When introducing the LP at the angle of α, as shown in Fig. 4(b), the resulting pulse train is a linearly polarized pulse train with a repetition rate of 67.6 MHz. The uniform RF trace verifies stability of the decomposed pulse train both in amplitude and time. Similarly, for an LP angle of α + 90°, the measured signal is the orthogonal counterpart of the other pulse train at a LP angle of α, shown in Fig. 4(c). In Fig. 4(d), the special case is shown where the LP angle is adjusted to α + 45°. This results in a pulse train that contains an equal decomposition of both orthogonal polarization eigenstates. The pulse train features comparable RF and temporal properties as in the original state without LP, cf. Figure 4(a), except that the eigenstates are decoupled. As discussed in previous studies , since the polarization eigenstates are coupled to each other at the rate of the PEF, introduction of a polarization sensitive element can lead to an inhibition of any possible coherent energy transfer between the eigenstates of the pulses. This phenomenon is confirmed by the sharp dip at the polarization induced side peak in the optical spectrum around a wavelength of 1989 nm. This spectral dip is maximized for an LP angle at α + 45° where the orthogonal polarization components have equal magnitudes, as shown in Fig. 4(d). The coherent energy transfer is less significant for LP angles at α and α + 90° since under those conditions, mostly single polarization eigenstates are recorded. The measured optical FWHM are almost identical for the projected polarization eigenstates, changing only from 9.75 nm to 9.85 nm, which corresponds to a change in the transform-limited pulse duration of 10 fs. The spectral locations of the polarization and Kelly sidebands between Figs. 4(b) and 4(c) are in a good agreement with each other, showing that the difference in the effective refractive indices for the fast and slow axes is very slight. All the pulse trains reveal a signal-to-background ratio greater than 70 dB, verifying the stability of each pulse train.
3. Stability and noise performance
Further stability analysis of the frequency-halved state is performed with relative intensity and phase noise measurements, shown in Fig. 5. The relative intensity noise (RIN) measurements are conducted with a photodetector (Thorlabs PDA10D from DC to 15 MHz), at an attenuated optical power of 300 µW to avoid any possible saturation and nonlinear effects, corresponding to an output voltage of 0.45 V for a 50 Ohm termination. The RIN curves for each eigenstate combination are measured along with the detector and RF analyzer floor. As the shot noise level for the given optical power level is −155 dB, the noise measurements are not limited by the instrument noise floor. The rms intensity fluctuations are calculated based on the RIN curves over a frequency interval of 10 Hz to 2 MHz, as shown in Fig. 5(a). The scalar pulse train from Fig. 2 is characterized by a root-mean-square (rms) intensity fluctuation of 0.14% (for a frequency interval from 10 Hz to 2 MHz). An upper limit for the pulse-to-pulse timing jitter is found as 20 fs (for a frequency interval from 10 Hz to 1 MHz, measured at the fundamental repetition rate, but limited by contributions from the instrument noise floor). The frequency-halved state features an rms relative intensity noise (RIN) of 0.2%, which is slightly higher than for the scalar soliton state. However, the decoupled eigenstate combinations show lower rms intensity fluctuation values between 0.1% and 0.15%. This result shows that the relative intensity fluctuations in the pulse train are higher when there is a coherent energy coupling between the polarization eigenstates. This offers new insights and a potential pathway how to obtain ML pulse trains with better intensity stability.
For phase noise (PN) measurements, an attenuated optical power of 0.5 mW is focused on the photodetector (ET5000) and the electrical signal is amplified to +10 dBm value. The single sideband (SSB) PN analysis is performed for the fundamental repetition rates of each pulse train. The timing jitter is integrated over the frequency interval of 10 Hz to 2 MHz, where the measurements are normalized with the corresponding repetition rate values, see Fig. 5(d). The frequency-halved state features an upper limit for timing jitter of 25 fs for the given frequency interval. The timing jitter measurements also confirm the trend noticeable in the RIN measurements that the decoupled pulse trains have slightly better PN stability.
4. Dual RF comb generation
The frequency stability of each polarization eigenstate in the frequency-halved state is further analyzed with a frequency counter. Over a time span of 100 s with the step size of 10 ms, the peak repetition rates are recorded with a frequency counter resolution of 100 mHz for each pulse train. As illustrated in Fig. 6(a), the histograms show frequency drifts of 110 Hz and 120 Hz for the peak repetition rates of 67,622,100 Hz and 67,622,610 Hz for the orthogonally polarized pulse trains, respectively. These drifts can be explained by thermal and mechanical fluctuations in the free-running laser cavity. From the histograms, the repetition rate difference is determined as 510 Hz for the given frequency-halved state. The difference in the repetition rates is caused by the fiber birefringence, i.e. the slight difference in the refractive indices for the slow- and fast- axis of the single mode silica fiber. These frequency drifts are also confirmed by the Allan deviation (2·10−7 for a gating time of 100 ms) derived from the timing jitter values given in Fig. 5(d) for the short and long time spans, respectively.
To generate an optical interferogram, the frequency-halved state is decomposed by a polarizing beamsplitter, oriented at the angle of α, into its two orthogonally interlaced polarized pulse trains with equal power. Since the pulse trains feature orthogonal polarizations and are offset by one round trip time of the cavity, one pulse train is delayed by the cavity round trip time of 7.4 ns to optimize the overlap for optical interference. As shown in Fig. 6(b), for the delayed pulse train, the polarization is rotated by 90° with a half-wave plate (HWP) so that both pulse trains feature the same polarization orientation. The pulse trains are combined in a fiber coupler and simultaneously focused on the photodetector (Thorlabs PDA10D).
The two resulting microwave beat RF combs in comparison to the fundamental repetition rate signal are shown in Fig. 6(c) where the microwave background signal (denoted as baseline) is due to the RF amplifier. This microwave beat signal is only generated when the beams have the same polarization for a strong optical interference. Thus, in this case, the optical frequency comb is directly down-converted so that the individual beat notes can be measured in the microwave domain. With a 40 MHz low pass filter and DC block, the signal contribution from the fundamental repetition rate and its harmonics is reduced and the microwave comb signal is amplified with a +40 dBm RF amplifier. A high resolution bandwidth RF trace (RBW = 10 Hz) of the beat combs is plotted in Fig. 6(d): The microwave beat combs are centered around 31.2 MHz and 36.4 MHz, corresponding to the respective difference between the carrier-envelope offset frequencies of the two pulse trains. The individual line structure is shown for a narrow frequency interval of 3 kHz centered at 31.254 MHz as an inset in Fig. 6(d). Here, the fine spectral lines with a separation of around 510 Hz are resolved. As the individual frequency drifts are much smaller than the repetition rate difference of the interfered pulse trains, a continuous and stable microwave beat comb is generated. The long term stability of the beat combs is confirmed for a period over than 24 hours.
In conclusion, we demonstrated a novel mode-locked operation regime, a frequency-halved state, which is composed of co-generated, equal intensity and orthogonally polarized interlaced pulses. In a compact, fiber-based linear cavity with an inline polarization controller, we demonstrate that for a special polarization locked vector soliton state an ultrafast pulse train is generated that is fully decomposable into its two orthogonal polarization eigenstates. This frequency-halved state is induced without requiring any active modulation, any additional birefringent materials nor any specific stabilization schemes. As both pulse trains are co-generated in the same laser cavity, good coherence properties are obtained and common noise is reduced. As the two pulse trains at twice the round trip time are interlaced with one round trip offset, no pulse crossing occurs within the cavity that could otherwise induce nonlinearities and cross-coupling. Due to slight differences in the encountered refractive index for both orthogonal polarizations, the two decomposed orthogonally pulse trains are characterized by slightly differing repetition rates. This leads to a stable microwave RF beat comb generation when optically interfering the two pulse trains. Since the frequency drift of the orthogonal pulse trains is smaller than the repetition rate difference, continuous and stable generation of wide bandwidth RF beat combs has been achieved. The fine and dense RF lines of the combs, as well as the compact and single source configuration, can make the proposed frequency-halved state a strong candidate for comparative measurements in optical metrology and spectroscopic applications. While most dual-comb spectroscopy set-ups rely on two individually generated pulse trains, which need to be stabilized in complex feedback schemes, the demonstrated interlaced pulse trains are generated directly from the same cavity, exposing both pulse trains to the same drift and environmental fluctuations. Thus, this can provide an enabling technology for dual-comb spectroscopy from a compact, fiber laser source without requiring any intracavity free-space components.
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