1. Introduction

Since the first observation of mode-locking in ruby laser by Gurs and Muller 50 years ago [1], there has been tremendous progress in ultrafast lasers and the understanding of mode-locking methods [2,3]. In the intervening five decades, the generation of ultrashort pulses has paved the way for a manifold applications in various scientific and technological fields including nonlinear optics, high-intensity physics, frequency metrology, time-domain spectroscopy, optical microscopy, medicine, and material processing [4,5]. From active to passive, many mode-locking techniques have been exploited for short pulse generation. Laser gain media with broad fluorescence bandwidths, such as Ti:sapphire [6], offer the greatest potential for ultrashort pulse generation, in addition to the wavelength tuning capability. Many ultrafast sources, such as the traditional dye laser, various chromium-doped crystalline media, as well as Yb, Er, and Tm fibers have been developed using different mode-locking methods. Among these, the Kerr-lens-mode-locked (KLM) Ti:sapphire laser [7] has been established as the workhorse of ultrafast science and technology over the past two decades, addressing numerous applications [4]. However, the tuning range of the KLM Ti:sapphire laser and other existing mode-locked solid-state sources is still confined to limited spectral bands in the near-infrared.

Nonlinear frequency conversion techniques offer a highly attractive approach to extend the spectral coverage of lasers to new wavelength regions [8,9]. In particular, synchronously-pumped optical parametric oscillators (OPOs) are now established as viable sources of picosecond and femtosecond pulses, expanding the wavelength range of mode-locked ultrafast lasers to new limits in the ultraviolet, visible and mid-infrared [10]. At the same time, the indispensible requirement for cavity length synchronization and the need for a mode-locked laser pump source inevitably lead to relatively complex system architecture, large size and high cost for such ultrafast OPOs. As such, it would be desirable to devise alternative new strategies for tunable ultrashort pulse generation using OPOs, which could overcome the need for mode-locked ultrafast laser sources and synchronous pumping. One such promising approach could be the direct application of mode-locking methods, as used in conventional lasers, to OPOs under continuous-wave (cw) pumping.

The gain mechanism in an OPO is different from the laser. In a typical mode-locked laser, there is gain storage and the generated pulse extracts energy over several cavity round-trips. However, in an OPO, to realize efficient parametric generation, the spatial overlap of the interacting waves is of critical importance, given the instantaneous nature of gain. The small, but finite, temporal synchronism between the pump, signal and idler, due to mode-locking could generate pulses, albeit with reduced efficiency. In earlier work, a simplified theoretical model has been developed in which an analogy is derived between an actively mode-locked laser and this type of OPO under negligible pump-depletion [11]. In a separate report, a theoretical model on passive mode-locking of a pump-swept OPO was developed [12].

Previously, there have been some attempts at active mode-locking of OPOs under quasi-cw and cw pumping. Using an acousto-optic modulator (AOM) as the mode-locking element in an OPO based on MgO-doped periodically-poled LiNbO₃ (MgO:PPLN), stable nanosecond pulses were obtained in doubly- and singly-resonant configurations [11,13]. It is well-known, in the context of lasers, that active mode-locking can be achieved using amplitude or frequency modulation techniques [14–21]. It is also recognized that the use of an AOM results in mode-locking through amplitude modulation, whereas an electro-optic modulator (EOM) can be used to achieve both amplitude- and frequency-modulation mode-locking of lasers [22]. However, an EOM offers important advantages over AOM for mode-locking, including reduced sensitivity to thermal drift and easily variable operating frequency, as has been discussed in earlier reports [17,18]. In addition, the use of an EOM as the mode-locking element has resulted in shorter optical pulses [17]. In order to achieve mode-locking in lasers, EOMs with different modulation frequencies have been deployed [14–18,20,21]. In the context of lasers [20], it has been shown that the shortening of the pulses can be achieved using an EOM with high modulation frequency. However, such modulators require large radio frequency (RF) power to attain reasonable modulation depth for mode-locking. This can cause heating of the EOM, which could result in cavity instabilities due to the thermal loading and refractive index changes in the modulator crystal. On the other hand, a low-frequency EOM can achieve the same modulation depth, but at a low RF drive voltage, thus avoiding thermal loading and enhancing operational stability.

Recently, using an EOM with a resonant frequency of 80 MHz, in combination with an antiresonant ring (ARR) interferometer, we achieved hybrid mode-locking of a cw OPO in doubly-resonant oscillator (DRO) configuration [23]. In this scheme, mode-locking was achieved by the combined effect of amplitude modulation assisted phase modulation, with the ARR providing phase-to-amplitude conversion in the cavity. Subsequently, we demonstrated the generation of picosecond pulses by direct mode-locking of a cw OPO in singly-resonant oscillator (SRO) configuration, only by deploying intracavity phase-modulation, without the use of an ARR interferometer for phase-to-amplitude conversion [24]. In phase-modulation-mode-locked OPO, the cavity is designed to ensure resonance with the EOM. The resonant EOM generates sidebands at a frequency equal to the axial mode spacing. These additional sidebands of the resonant parametric wave with a fixed phase relationship overlap with the longitudinal modes in the cavity, thus producing short pulses. After studying the SRO, where the resonant wave bandwidth are much narrower (~600 GHz), one would obviously be interested in studying the effect in a DRO, where the bandwidth supported by parametric gain can be significantly broader, spanning few THz.

In this report, we explore direct frequency-modulation mode-locking of a cw OPO in the DRO configuration using an EOM as a single mode-locking element. Although cw DROs are typically characterized by non-monotonous tuning, they offer substantially lower pump power threshold than SROs. Moreover, while DROs have been traditionally regarded as undesirable device formats due to poor output power and frequency stability, recent results on DROs under type I phase-matching have shown that at exact degeneracy such oscillators can operate with excellent power and frequency stability in passive conditions, with the DRO operating stably over many hours without active stabilization [25–27]. Stable operation of degenerate cw DROs has also been reported in the presence of thermal loading [28]. This passive stability property in DROs arises from self-phase-locking of the signal and idler waves which, under type I phase-matching, become indistinguishable and phase-coherent at exact degeneracy. With active stabilization and the use of phase-stable pump sources, such DROs can be further made to provide an output constituting optical frequency combs and used as precision tools for high-resolution spectroscopy. In the spectral domain, such DROs have been shown to exhibit broad bandwidths in degenerate operation, under cw and synchronous pumping [25–27], offering the promise for frequency comb generation. In the time domain, therefore, operation of DROs in the degenerate regime could offer the possibility of generating short optical pulses, given the potentially broad bandwidths and a phase-locked spectrum. As such, the DRO is a promising configuration for the study of mode-locking in cw OPOs.

In this work, we report on the studies of direct active mode-locking of a cw DRO based on MgO:sPPLT pumped at 532 nm by a cw laser and operating near degeneracy at 1064 nm. Given the advantages of frequency- over amplitude-modulation, we deploy an intracavity EOM as the single mode-locking element, resulting in the generation of 533 ps pulses at 80 MHz repetition rate. To our knowledge, this is the first report of an actively mode-locked cw DRO based on MgO:sPPLT using low resonant frequency EOM as a single mode-locker.

2. Experimental setup

The schematic of the cw mode-locked DRO is shown in Fig. 1. The fundamental pump source is a frequency-doubled diode-pumped cw Nd:YVO₄ laser (Coherent, Verdi-10) delivering up to 10 W of output power at 532 nm in a single-frequency, linearly-polarized beam with M² factor <1.1. To maintain stable output characteristics, we operate the laser at maximum power and use a combination of a half-wave plate (HWP) and a polarizing beam-splitter cube to attenuate the power. A second HWP is used to adjust the pump polarizationfor phase-matching in the nonlinear crystal, a 30-mm-long, 2.14-mm-wide and 1-mm-thick, 1% bulk MgO:sPPLT with single grating period of Λ = 7.97 μm [29]. The crystal is housed in an oven with a stability of ± 0.1°C and adjustable from room temperature to 200°C. The end-faces of the crystal are antireflection (AR) coated (R<1%) for 800-1100 nm, with >98% transmission at 532 nm. The coating has a reflectivity of 1%-15% over idler wavelength range 1100-1400 nm. Using a lens, L, of focal length, f = 150 mm, the pump beam is focused to a waist radius of w_p = 31 μm inside the crystal, corresponding to a confocal focusing parameter of ξ~1.2. The cw DRO is configured in a standing-wave cavity comprising two concave mirrors, M₁ and M₂ (r = 100 mm), one plane mirror, M₃, one concave mirror, M₄ (r = 1000 mm), and one output coupler (OC), M₅, through which the OPO output is extracted. Here, we use a standing-wave X-cavity configuration, however, travelling-wave cavity designs can also be explored. The DRO cavity design provides a signal (idler) beam waist radius of w_s = 46 μm at the center of the crystal, resulting in optimum mode-matching with the pump (b_p~b_s,i). Mirrors M₁ and M₂ are highly reflecting (R>99%) for signal and idler wavelengths over 1000-1090 nm and transmitting (T>93%) at 532 nm, while M₃ and M₄ are highly reflecting (R>99.9%) over 1000-1233 nm and 1000-1165 nm, respectively. The OC has a reflectivity of R~96.5% at 1064 nm. Thus, the reflectivity of the mirrors ensures DRO operation near degeneracy. For mode-locking, an EOM (New Focus, Model 4003) with a resonant frequency of ν = 80 MHz and tunability of ± 5MHz, is introduced inside the cavity close to the OC. The distance between the EOM end-face and the OC is z₀ = 1 cm. The EOM is based on a 40-mm-long MgO:LiNbO₃ crystal as the electro-optic medium, and has a 2 mm clear aperture, through which the beam diameter can be adjusted using mirror M₄. Mirror M₃ is mounted on a translation stage, so as to adjust the OPO cavity length for synchronization with the modulator resonant frequency. The total optical length of the DRO cavity, when synchronized with resonant frequency of phase modulator, is L = 2L_linear = 3.72 m.

 

Fig. 1 Schematic of the experimental setup. λ/2: Half-wave plate, PBS: Polarizing beam-splitter cube, L: Lens, M: Mirrors, OC: Output coupler; EOM: Electro-optic phase modulator.

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3. Results and discussion

In order to study the performance of the mode-locking element used, we initially characterized the EOM separately, external to the OPO cavity. This is important in calibrating the values of modulation depth when the EOM is subsequently used internal to the OPO cavity for mode-locking. An ytterbium-doped fiber laser (IPG Photonics, YLR-30-1064-LP-SF) providing 30 W of single-frequency radiation at 1064 nm with a nominal linewidth of 89 kHz was used as the input laser source to the EOM. With 1 W of input power, we observed the single-pass output from the EOM in frequency domain and also in time domain at different modulation depths and modulation frequencies. Figure 2(a) and 2(b) show the transmission spectra of the single-pass output through the EOM, measured using a confocal Fabry-Perot interferometer (FSR = 1 GHz, finesse = 400), for different modulation depths and frequencies, by keeping either parameter fixed, respectively. As seen in Fig. 2(a), 2(i), at theresonant frequency of ν = 80 MHz, with minimum modulation depth, μ₁, a single-frequency spectrum is observed, with a measured instantaneous linewidth of 4.6 MHz. With the increase in modulation depth to μ₂ in (ii), keeping ν constant, the amplitude of the central frequency begins to fall and sidebands appear on both sides of the central frequency. The amplitude of the sidebands increases with the increase in modulation depth to μ₃ in (iii). With further increase in modulation depth to μ₄ in (iv), the central frequency starts to disappear, and vanishes at the maximum available modulation depth of μ₅ in (v). The modulator produces two sidebands on either side of the central frequency, each separated by ~80 MHz. The sideband spacing is also observed to remain fixed at ~80 MHz, independent of the modulation depth. Figure 2(b) shows the effect of increase in modulation frequency, with the modulation depth kept fixed at μ₃. It is observed that at minimum modulation frequency of ν₁ = 75.2 MHz in (i), the spectrum remains single-frequency with a measured instantaneous linewidth of 4.7 MHz. However, as the modulation frequency is increased, prominent sidebands with highest amplitude appear at ν = 80 MHz in (iii), with weaker sidebands at other frequencies (ν₂ = 78.4 MHz, ν₃ = 81.8 MHz and ν₄ = 84.7 MHz). Hence, it is evident that the EOM shows better performance at moderate modulation depth of μ₃ and resonant frequency of ν~80 ΜΗz. We did not observe any change in output power from the EOM under different conditions of modulation depth and frequency.

 

Fig. 2 Single-pass EOM output spectrum (a) at ν = 80 MHz for different modulation depths (μ₁<μ₂<μ₃<μ₄<μ₅) of (i) μ₁ (ii) μ₂ (iii) μ₃ (iv) μ₄ (v) μ₅, and (b) for fixed modulation depth of μ₃ at different modulation frequencies (ν₁<ν₂<ν<ν₃<ν₄) of (i) ν₁ (ii) ν₂ (iii) ν (iv) ν₃ (v) ν₄.

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We then calculated the different values of modulation depth, which is the optical phase shift induced by the EOM used. The amplitude of the central carrier frequency is given by [J₀(μ)]², where J₀ is the Bessel function of zero order and the argument, μ, is the optical phase shift or the modulation depth [14]. The sidebands seen in Fig. 2(a) for different modulation depths show the Bessel function amplitudes, as shown in Fig. 3. Comparing the amplitude of the central carrier frequency obtained from the transmission spectrum at different modulation depths of EOM in Fig. 2(a), with the amplitude of [J₀(μ)]² from the theoretical Bessel plot in Fig. 3, the modulation depths of μ₁, μ₂, μ₃, μ₄ and μ₅ have been calculated to be 0, 1.63, 1.83, 1.99 and 2.4 radians, respectively.

 

Fig. 3 Bessel function amplitude of order 0, 1, 2 and 3 representing the amplitudes of carrier frequency, 1st, 2nd, and 3rd sidebands, respectively, with modulation depth, μ, as argument.

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We also monitored the output from the EOM in the time domain using an InGaAs photodetector (20 GHz, 18.5 ps) and a fast oscilloscope (3.5 GHz, 40 GS/s). It is to be noted that the modulation signal applied to the EOM using a RF driver is sinusoidal. At a modulation frequency of ν = 80 MHz and increasing the modulation depth from 0 to 1.99 rad, we did not observe any modulation in the output. However, keeping the modulation frequency fixed at ν~80 ΜΗz and increasing the modulation depth further to the maximum, a slight modulation at a repetition rate of 160 MHz with a temporal width of 3 ns was observed.

To actively mode-lock the OPO, we introduced the EOM inside the DRO cavity very close to the OC, as shown in Fig. 1. Without the EOM and with the crystal temperature (T) kept at 51.5 °C, the DRO provides an output power of 526 mW for 9.7 W of pump power and has an oscillation threshold of 1.1 W. However, with the insertion of the EOM into the cavity, the oscillation threshold increases to 1.9 W and the cw DRO provides 484 mW of output power for a pump power of 9.7 W. The increase in threshold power is attributed to the EOM insertion loss. It is to be noted that the oscillation threshold for the DRO in standing-wave X-configuration with a shorter cavity length, comprising of three high-reflecting mirrors and one OC was 700 mW. The increase in threshold pump power from 700 mW to 1.1 W is attributed to the additional cavity mirror, M₄. Further, the threshold of 1.9 W of cw DRO with the EOM inside the cavity is more than 3 times lower as compared to that of the cw SRO in [24]. At T = 51.5 °C, the generated signal and idler wavelengths are λ_signal = 1049 nm and λ_idler = 1079 nm, respectively. At these wavelengths, the parametric gain curve of the nonlinear crystal is calculated to have a full-width-half-maximum bandwidth of 3 THz. When the EOM is switched ON, with modulation depth of μ₃ = 1.83 rad and frequency, ν, exactly synchronized with the cavity length, some perturbation is seen in the output in time domain, but no mode-locked pulses are observed. However, when the modulation frequency is slightly detuned by Δν, on either side of ν, pulses with duration of 471 ps at 160 MHz repetition rate are observed. Figure 4(a) shows the temporal output from the DRO, depicting the effect of change in modulation depth at modulation frequency of ν ± Δν. As evident, in (i) at minimum modulation depth, some perturbation is observed, but with the increase in modulation depth to 1.63 rad in (ii), 871 ps pulses at 160 MHz are observed, which then shorten to 471 ps at 1.83 rad of modulation depth in (iii). With further increase in modulation depth to 1.99 rad in (iv), alternatively equal amplitude pulses at 160 MHz are observed with high-intensity pulses of 473 ps duration and low-intensity pulses of 437 ps duration. In (v), with the modulation frequency kept fixed at ν ± Δν, further increase in the modulation depth to the maximum of 2.4 rad results in the generation of 533 ps pulses at 80 MHz. We observed that the phase-locked pulses at maximum modulation depth of 2.4 rad in (v) are gradually extinguished over time. We believe this could be due to the dissipation of energy from the carrier frequency to the sidebands. Another possible reason for extinction of these pulses could be due to various drifts originating from double resonance in the cavity. However, the extinction of pulses with increased modulation depth was also observed in a SRO [24], despite the higher intrinsic stability compared to DRO. In Fig. 4(b), we also show the generated pulse train when the modulation depth is kept fixed at μ₃ = 1.83 rad and modulation frequency is detuned by Δν´ on either side of ν, where Δν´>Δν. In this case, pulses at 80 MHz with duration of 533 ps are also observed. The values for Δν´ and Δν are of the order of kHz, and correspond to a very narrow zone of variation in the cavity length. Any change in the modulation frequency not corresponding to Δν or Δν´ leads either to the switching off of the OPO or no pulse formation. Hence, to obtain stable short pulses at 80 MHz, a careful adjustment of the modulation frequency or precise change in cavity length over a narrow zone, at a moderate value of modulation depth is required. The use of a piezoelectric transducer (PZT)-driven self-tuning mirror as one of the cavity mirrors could be very helpful, not only for fine adjustmentof the cavity length to achieve the required repetition rate, but also to actively stabilize the cavity length, thus reducing the possibility of any arbitrary switching of the repetition rate between 80 MHz and 160 MHz, if that may occur. The inset of Fig. 4(b) shows the zoomed version of stable pulses with 533 ps duration at 80 MHz repetition rate obtained at modulation depth of 1.83 rad and modulation frequency of ν ± Δν´. Unlike an earlier report on mode-locked cw OPO [13], we have not observed any cw background in the output pulse intensity.

 

Fig. 4 (a) Pulse train obtained at modulation frequency ν ± Δν for modulation depths of (i) μ₁ (ii) μ₂ (iii) μ₃ (iv) μ₄ and (v) μ₅. (b) Pulse train obtained at modulation frequency ν ± Δν´ for modulation depth of μ₃. Inset: Zoomed 533 ps pulses at 80 MHz.

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Depending upon the temporal characteristics, operation of the DRO can be divided into two distinct regions. The two regions can be shown to represent a series of pulses, with one having a repetition rate equal to the modulation frequency and the other at twice the modulation frequency. As also observed earlier in the context of lasers [30], here when the train of pulses at 160 MHz is compared with the sinusoidal modulation signal, the pulses appear at the peak and minima of the modulation signal. This implies two pulses travelling back and forth inside the cavity, with one pulse delayed in time by L_linear/c with respect to the other. Hence, there exist two oscillating states of mode-locked pulses. For the 80 MHz pulse train obtained, the pulses pass through the modulator either at the peak or the minima of the modulation signal. The two mode-locked states are clearly visible at modulation frequency of ν ± Δν and depth of μ₃ = 1.99 rad in panel (iv) of Fig. 4(a), where alternatively equal pulses are observed with one state having higher intensity than the other. The two oscillating states with unequal amplitude are also observed when the modulation depth and frequency are kept fixed at 1.83 rad and ν ± Δν, respectively, while slightly detuning the cavity length.

The output power from the DRO has been monitored for different conditions of modulation frequency and depth. The average output power drops to 30 mW and 8 mW for 160 MHz and 80 MHz pulses, respectively, as compared to 484 mW of average power in cw condition. The drop in the average output power from cw to mode-locked operation can be understood by considering the time-domain picture of pulse formation in the OPO. Under cw operation, the output efficiency is 5%, whereas in the mode-locked condition the output efficiency for 160 MHz and 80 MHz repetition rate is 0.32% and 0.1%, respectively. Under these conditions, we recorded pulse duration of 471 ps and 533 ps at 160 MHz and 80 MHz, respectively. It is to be noted that the free spectral range of the cavity is the same for all these cases. Hence, considering the interaction time of signal and idler with pump, the efficiency reduction is calculated to be 13.2 times for 160 MHz pulses and 23.4 times for 80 MHz pulses.

We recorded the average passive power stability in mode-locked operation for 160 MHz repetition rate pulses at maximum pump power, for a modulation depth at 1.83 rad and frequency at ν ± Δν. As evident from Fig. 5(a), an average passive power stability better than 3.5% rms over 15 minutes was measured. The fluctuation in the average power is attributed to the mechanical vibrations, air currents, and temperature variations, as the measurements were obtained in open laboratory environment and under free-running conditions for the DRO. The corresponding pulse train recorded in the microsecond time-scale, depicting the intensity noise on the output pulses, is shown in the inset (i) of Fig. 5(a). We have analyzed different sections of pulse train, and found that the pulse duration only varies by 1.7%, showing uniform steady-state pulse durations over microsecond time-scale. Further, we have analyzed the pulse peak-to-peak fluctuation, as shown in inset (ii) of Fig. 5(a), where we have obtained a stability better than 4.3% rms.

 

Fig. 5 (a) Time trace of the mode-locked output at 160 MHz over 15 minutes. Inset: (i) Mode-locked output pulse train, and (ii) pulse peak stability at 160 MHz over 20 μs. (b) Pulse train at 160 MHz for z₀ = 6 cm. Inset: Zoomed 953 ps and 471 ps pulses for z₀ = 6 cm and 1 cm, respectively.

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In order to study the dependence of pulse duration on the position of the EOM inside the OPO cavity, we increased the separation between the EOM and the OC to z₀ = 6 cm (see Fig. 1), and observed the output from DRO in time domain for different modulation conditions. The behavior of the DRO output is similar to that when EOM is placed very close to OC (z₀ = 1 cm), except for the difference in the pulse width. Figure 5(b) shows the pulses obtained at modulation depth of 1.83 rad and modulation frequency at ν ± Δν for z₀ = 6 cm, and the inset shows zoomed versions of the pulse trains obtained with (i) z₀ = 6 cm, and (ii) z₀ = 1 cm. As can be seen, the pulse duration for z₀ = 6 cm is 953 ps, which is more than two times longer than the 471 ps pulse duration obtained for z₀ = 1 cm. It can be shown [31] that when a modulator is placed in a standing-wave cavity, the modulation index or the phase retardation of the modulator is directly proportional to the cosine function of the distance between the modulator and end mirror of the cavity. The closer the modulator is placed to the end mirror, the larger is the modulation index, which results in more efficient mode-locking. When placed inside the OPO cavity, the modulator generates sidebands that are locked to the axial modes, when the cavity is synchronized with the resonant frequency of the modulator. The mode-locking is thus more efficient when the modulator is placed close to the end mirror. Our results are consistent with the early predictions for lasers, where it has been suggested that the modulation coupling strength has a direct dependence on the location of the modulation element inside the cavity [30]. When the EOM is very close to the cavity mirror, z₀~0, the coefficient in the coupled equation is maximized, resulting in an increase in locking of the modes, and thus shorter pulse durations [30].

We also investigated the duration of the DRO output pulses for different input pump powers, keeping z₀ = 6 cm. The pulse duration has been observed to be affected by the variation in pumping level, although not significantly. For example, we measured a decrease in pulse duration from 953 ps to 848 ps at 160 MHz for a decrease in pump power from 9.7 W to 6.8 W, accompanied with the decrease in the pulse amplitude. With further decrease in pump power to 3.4 W, the OPO ceases operation. Given the fact that the EOM is placed at 6 cm from OC, and phase retardation is maximum at z₀ = 0 cm, only weak dependence is observed here with pumping level.

In addition, we studied the spectral characteristics of the DRO under cw and mode-locked condition using a spectrometer (Ocean Optics HR4000). Figure 6(a) shows the output spectrum in cw operation, with the signal and idler wavelengths well away from degeneracy. Under this condition, where the modes are not phase-locked and oscillate independently, we observe spectra extending over 11 nm and 10 nm for the signal and idler, respectively. However, when the modulation depth is increased to 1.83 rad and frequency tuned to ν ± Δν, a spectrum with almost the same bandwidth is observed for signal and idler, but with an envelope, as seen in Fig. 6(b). The lower intensity of idler in both cases is due to the low reflectivity value of DRO cavity concave mirrors at the idler wavelength.

 

Fig. 6 Spectrum of the output extracted from the DRO at T = 51.5 °C under (a) cw operation, and (b) mode-locked operation at a modulation frequency of ν ± Δν and depth of μ₃ = 1.83 rad.

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If we decrease the crystal temperature to T = 50 °C, keeping modulation frequency at ν ± Δν and depth at μ = 1.83 rad, the signal and idler branches merge at degeneracy, resulting in a spectrum spanning over 31 nm, as seen in Fig. 7(a). When the modulation frequency is detuned to ν, the spectrum broadens to its maximum width, and we observe an increase in the average DRO output power to 176 mW. The result is shown in Fig. 7(b), where a spectrum spanning over 52 nm is measured at T = 50 °C. The corresponding measurement in time domain showed only some perturbation with no mode-locking, however at modulation frequency of ν ± Δν, pulses are observed with the same duration as at T = 51.5 °C. The spectral behavior in our DRO is broadly consistent with earlier observations in a monolithic cw DRO based on MgO:PPLN with intracavity phase modulation [25]. Thus, at degeneracy, where the signal and idler merge, resulting in a large bandwidth, most efficient phase-locking could be expected for best mode-locked operation.

 

Fig. 7 Spectrum of the output extracted from the DRO at T = 50°C for modulation depth of μ₃ = 1.83 rad and at modulation frequency of (a) ν ± Δν and (b) ν = 80 MHz.

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Assuming Gaussian pulse shape and a time-bandwidth product of 0.44, the transform limited pulse duration for 31 nm bandwidth spectrum has been calculated to be ~50 fs. Also, considering the internal phase modulation that results in a linear frequency shift, as discussed in earlier reports [22], leading to a time-bandwidth product of 0.626, the pulse duration has been calculated to be ~75 fs. The pulse generation with calculated duration is the ideal condition when all cavity modes are locked in phase. The pulse duration obtained in the present experiment indicates that the contributing bandwidth is narrow, and the locking depends on the mode-locking efficiency. In addition, significant dispersion effects are in play in the present experiment, due to the long lengths of MgO:sPPLT and LiNbO₃ crystals in the cavity, as well as the dispersion in mirror and crystal coatings, which are currently unknown. As such, we believe that the use of shorter crystal lengths and a systematic control of intracavity dispersion, including mirror and crystal coatings, will enable the generation of shorter output pulses. Both these strategies will be possible in practice, given the relatively low threshold associated with the DRO. With the low sensitivity of the DRO to loss, as compared to the SRO, the use of a shorter nonlinear crystals and deployment of intracavity dispersion compensation in the DRO would be practical steps in achieving shorter pulse durations without substantial increase in oscillation threshold. In addition, shorter pulse durations could be expected by using high-frequency modulation with proper thermal management in the EOM, which could result in the increase in mode-locking efficiency.

We observed pulses of 533 ps duration at 80 MHz in the DRO as compared to our earlier report on a SRO [24], where we obtained 230 ps pulses at 80 MHz. We believe the difference in the pulse duration could be due to the phase modulator used in the experiment, which are specified for narrowband or single-frequency operation. As we have seen that the pulse duration changes with the pumping level, and also there are earlier reports on such observations [11], the difference in the pulse duration could also be due to the higher pumping level (5 times above threshold) in the DRO as compared to that in the SRO.

In order to confirm true mode-locked operation, namely, the real achievement of energy concentration in mode-locked pulses rather than power modulation, we performed external single-pass second-harmonic-generation (SHG) of the DRO output under different operating conditions in a 10-mm-long β-BaB₂O₄ (BBO) cut at θ = 26°, ϕ = 0°. Using a lens of focal length, f = 75 mm, the output for cw, 160 MHz, and 80 MHz pulses was focused consecutively at the centre of the crystal, and the SHG power was measured using a GaAsP photo-detector. We observed 4 times enhancement of the SHG power in mode-locked operation, both for 80 and 160 MHz pulses, as compared to that in the cw operation, for a fixed average fundamental power in both conditions. The SHG enhancement factor of 4 times is lower than that of the theoretically calculated value of 23 times, for 533 ps pulses at 80 MHz. As we have not observed any cw background with the mode-locked pulses, we believe that the cw background has negligible effect on the measured SHG enhancement factor. However, the low SHG enhancement could be attributed to various factors including narrow SHG acceptance bandwidth of the BBO crystal, as also reported earlier [23].

4. Conclusions

In conclusion, we have demonstrated the generation of picosecond pulses from a cw DRO based on MgO:sPPLT by direct active mode-locking using an electro-optic phase modulator as the single mode-locking element. Mode-locked pulses at 80 MHz and 160 MHz with 533 ps and 471 ps pulse duration at modulation depth of 1.83 rad and modulation frequency at ν ± Δν´ and ν ± Δν, respectively, have been generated. Mode-locked pulses for different operating regimes of the DRO, obtained with the change in modulation depth and frequency detuning have been explored. It has also been observed that as in lasers, in the OPO cavity the position of the modulator is an important factor in obtaining shorter pulses. The average passive power stability of the DRO output in mode-locked operation at 160 MHz has been measured to be better than 3.5% rms over 15 minutes. Under moderate modulation depth and at exact resonant frequency modulation, a spectrum spanning over 52 nm has been observed at degeneracy. Mode-locked operation has been further confirmed by obtaining a 4 times enhancement in SHG power under mode-locked condition, as compared to cw operation. With enhanced mode-locking efficiency using higher modulation frequencies, shorter crystal length, and deployment of intracavity dispersion control, reduced pulse durations could be supported. To further improve the stability of the DRO, active stabilization could also be implemented [32]. The combination of the technique with passive-mode-locking methods may also lead to the generation of shorter optical pulses. Further, the mode-locked output power can be optimized by incorporating an ARR interferometer as an output-coupler in the DRO cavity [33].