1. Introduction

Monolithic mode-locked lasers (MLLs) are excellent candidates for generating short pulses for a range of applications, such as millimeter-wave signal generation and all-optical clock recovery. These applications require optical pulse trains with low phase noise and timing jitter [1]. Several factors degrade the timing jitter of MLLs, such as self phase modulation (SPM), which is a major factor that not only affect the timing jitter, but, in extreme cases, leads to severe degradation of the optical spectrum [2,3]. On the other hand, recent work on fiber lasers has demonstrated that in order to reduce timing jitter, it is desirable to operate as close to the zero dispersion point as possible [4]. However, operating at the zero dispersion point implies a high optical intensity (for the same pulse energy) and hence an increased SPM.

Furthermore, it is suggested in Henry’s linewidth formula for semiconductor lasers that increasing the round trip time can improve the timing jitter [5], although MLLs with repetition frequencies below 100 GHz are relatively long devices (e.g. ~4 mm for a 10 GHz laser). Lasers with long all-active cavities may increase the level of SPM, which is known to lead to significant deteriorations in both the optical and mode-locked spectra [3]. Also according to Henry’s theory, it is shown that these effects can be suppressed by reducing the cavity losses and increasing the saturation energy (E_sat) which in turn can be achieved by reducing number of QWs. Recently, this has resulted in a timing jitter as low as 570 fs (4-80 MHz) for a 10 GHz passive MLL on an all-active quantum well (QW) structure [6] and a −3 dB radio-frequency (RF) linewidth of 30 kHz for a 21 GHz MLL [7], which are currently the best results reported in the literature.

MLLs with narrow far-field patterns (FFPs) are highly desirable for simple, highly-yield optical alignment, as low divergence angles improve the coupling efficiency and impose less stringent tolerances in the alignment between the MLL and single-mode fiber (SMF). Recently we have demonstrated 40 GHz AlGaInAs/InP λ ~1.55 μm all-active QW MLLs with a small RF linewidth (25kHz) and low divergence angle based on a novel epitaxial structure which consists of a three-QW active layer incorporating a passive far field reduction layer (FRL) [8]. The FRL’s purpose is to pull the guided mode slightly into the lower cladding, which results in an increased mode size d (d: transverse spot size which is defined as the distance from the beam axis to the position where the amplitude of the optical field is 1/e times the amplitude at the beam axis) with a reduced overlap with the QWs (Γ_QW), leading to less SPM and a reduction in waveguide dispersion. This also has the additional benefit of reducing the internal loss α_in by pulling the mode away from the upper p-cladding layer and reducing the far-field divergence of the output beam. As the free-carrier absorption in the p-cladding layer is the main contributor to the internal optical losses in strain-compensated multiple quantum-well (SC-MQW) lasers [9]. In addition, the use of the FRL eliminates the need for overgrowth, which is applicable to AlGaInAs/InP-based lasers, and the stringent fabrication tolerance as required for that of slab-coupled optical waveguide lasers (SCOWL) [10], so lasers can be fabricated as readily as conventional ridge waveguide devices.

In this work, we present a detailed discussion on the design and optimization of the FRL and calculate the associated internal loss which is in excellent agreement with the measured result. Furthermore, we extend the FRL concept from 40 to 10 GHz AlGaInAs/InP λ~1.55 μm passively MLLs, which in comparison has a longer cavity length that subsequently provides a lower threshold current density and lower associated spontaneous emission noise. In addition, the longer laser cavity results in a decrease of the spectral linewidth of each longitudinal mode [11], and also enhances the four wave mixing process and associated phase correlation between modes through a reduced optical mode spacing [12]. All these effects should lead to a further reduction of the RF linewidth during mode-locking operation of the 10 GHz MLL [13]. Using a MLL with a 10 GHz repetition frequency, we achieve a RF linewidth reduction of as little as 2 kHz and a corresponding timing jitter of 194 fs (4-80 MHz), which is to the best of our knowledge, the best results to date for passive QW MLLs.

2. Epilayer structure

Figure 1(a) shows the simulated effective index (n_eff) as a function of the FRL thickness for different spacer thicknesses (from 1.0 μm to 0.25 μm with a step of −0.25 μm) with their cut-off thickness for the second order mode, i.e., m = 2 at 0.11, 0.17, 0.29, and 0.52 μm correspondingly. For all the spacer cases, it was shown that as the FRL thickness increased, the Γ_QW at m = 0 is dramatically decreased and the corresponding Γ_QW at m = 1 is increased (Fig. 1(b)). For the first 3 cases, the fundamental and first order guided modes are shown in Fig. 2 . It can be seen that as the FRL is widened and moved closer to the QW layer, the fundamental mode is widened and pulled into the lower cladding layer, thus reducing the overlap with the p-cladding layer. This reduces the losses resulting from free carrier absorption, because the absorption due to holes is higher than that due to electrons. If the FRL is too thin, the fundamental transverse mode size is increased by very little (Fig. 2(a)). However, if the FRL structure is made too thick, an unfavourable amount of the fundamental mode moves into the FRL, which considerably reduces the Γ_QW value of the fundamental mode. Also, the first order mode is affected by the FRL in some structures leading to a significant overlap of the first order mode with the QWs (Fig. 2(c)) and results in a multi-mode output. Table 1 also lists the calculated optical confinement factors for the QWs, the p- and n- cladding layers (Γ_QW, Γ_p, and Γ_n respectively). For calculating the internal losses, we use: α_in = Γ_QW·k_MQW + Γ_p·k_p + k_n·k_n, where k_QW, k_p, and k_n are the absorption coefficients at λ = 1.55 μm in QWs, and in the p- and n-cladding layers, respectively [9]. These values are: k_QW = 35 cm⁻¹ [14], k_P = 22 cm⁻¹ for p-InP with doping level p = 8.6 × 10¹⁷ cm⁻³, k_n = 1 cm⁻¹ in n-InP with doping level n = 10¹⁸ cm⁻³ [15]. This data also shows that p-cladding absorption is the main contributor to the internal losses. Taking into consideration both the maximization of the d/Γ_QW value for the fundamental transverse mode and maintaining a single mode waveguide, the FRL consisted of 0.16 μm with a bandgap wavelength of 1.1 μm (In_0.85Ga_0.15As_0.33P) placed 0.75 μm below the active region as shown in Fig. 2(b). The calculated internal loss for this structure is 8.4 cm⁻¹ (Table 1). Moreover, the expansion of the cross-sectional area of the fundamental transverse mode leads to a reduction in the corresponding far-field, throughFourier transformation. A schematic of the complete epitaxial structure together with the corresponding conduction band diagram can be found in [8].

 

Fig. 1 (a) simulated effective index (n_eff) and (b) the overlap with the QWs as a function of FRL thickness for the different transverse mode.

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Fig. 2 The optical intensity through the epilayer structure for various FRL configurations: (a) 0.11 μm FRL, 1.0 μm spacer, (b) 0.16 μm FRL, 0.75 μm spacer, and (c) 0.29 μm FRL, 0.50 μm spacer.

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Table 1. Calculated Parameters of the Structures Simulated in Fig. 1

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3. Device structure and fabrication

The fabricated devices have a total length of 4,320 μm and consist of a gain section (4,230 μm) and an 80 μm long saturable absorber (SA). The isolation gap between the sections is 10 μm wide and provides electrical isolation in excess of 1.5 kΩ. The ridge waveguide is 2.5 μm wide and 1.65 μm high, i.e. the dry etching process stopped 200 nm above the 20 nm thick wet-etch stop layer, which not only protects the MQW active layer but also acts as a compromise between reducing the horizontal direction divergence angle and decreasing the threshold current. The laser fabrication process was described in [8]. As a final step, the sample was cleaved into individual laser bars with both the SA facets and the gain facets left uncoated. The devices were mounted epilayer-up on a temperature controlled copper heat sink set at 20°C and tested under CW conditions.

4. Device characteristics

The threshold current with an unbiased SA section was 94 mA (Fig. 3(a) ). The internal loss for the novel epitaxial wafer design was estimated to be ~8/cm using the Hakki Paoli method [8], which is in excellent agreement with that predicted by the modelling. The differential modal gain value was ~2.7 × 10⁻¹⁷ cm² [8]. The divergence angles for the horizontal andvertical direction were 14.7° and 27.3°, respectively (Fig. 3(b)). The measured butt coupling efficiency with a SMF was about 20% - double that of a conventional five-QW MLL (~10%). The −1dB alignment tolerances in horizontal, vertical and optical-axis have been significantly relaxed [8]. When the ridge waveguide height was increased from 1.65 to 1.85 μm the horizontal divergence angle increased and the vertical angle was slightly decreased, thus the symmetry of the FFP was as round as 23.7° × 25.1° (Fig. 3(c)), which is highly desirable when coupling with an optical lens system, but the butt coupling efficiency with a SMF was slightly decreased.

 

Fig. 3 (a) Typical L-I_gain characteristics for different V_SA, from 0 to −3 V with a step of −0.5 V, and (b) measured FFP of the device with a 1.65 μm high ridge, and (c) measured FFP of the device with a 1.85 μm high ridge.

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Passive mode-locking (ML) of the device was achieved by forward biasing the gain section (I_gain) and reverse biasing the SA section (V_SA). The purest 10 GHz ML with 100% modulation was obtained over a large bias range: V_SA from −1.6 V to −3.2 V, and for I_gain from 120 mA to 300 mA and above, which is shown in Fig. 4(a) . The mesh region in Fig. 4(a) indicates second harmonic (20 GHz) ML regimes which can be explained by the model in [16]. Figure 4(b) presents the evolution of the full width at half maximum (FWHM) of the autocorrelation (AC) trace as a function of both V_SA and I_gain, which was measured by second-harmonic-generation (SHG) autocorrelation. We note typical trends, i.e. pulses broaden with increasing I_gain and shorten with increasing |V_SA|. The shortest pulse width was observed at V_SA = −2.8 V, which we attribute to a short SA recovery time, and for I_gain = 142 mA, where the impact of SPM is weak. The period of the measured emitted pulse train was 99.3 ps (Fig. 5(a) ), corresponding to the peak observed in the RF spectrum at 10.074 GHz. The autocorrelation width of an isolated pulse was 1.64 ps, which deconvolves to a 1.06 ps pulse duration assuming a sech² pulse shape (Fig. 5(b)), and is much shorter than that reported in [6] (8.4ps). A Lorentzian fitting of the RF spectrum gives a −3 dB linewidth of 2 kHz (with a 1 kHz resolution bandwidth (RBW)) (Fig. 5(c)). It should be stressed here that, to the best of our knowledge, such a narrow linewidth has never been obtained with a conventional QW MLL and is comparable to that obtained from a 17 GHz passive quantum-dot MLLs at a nominal wavelength of 1.55 μm [12], and in comparison to the −3 dB RF linewidth of 25 kHz obtained in [8], the results presented here confirm that increasing the cavity length leads to a reduction in the threshold current density (from 1.12 to 0.83 kA/cm²), which lowers the spontaneous emission noise and thus decreases the RF linewidth [11]. The optical spectrum was centered at 1555.5 nm with a −3 dB bandwidth of 5.65 nm (Fig. 5(d)). The time-bandwidth product (TBP) of the pulse is equal to 0.74, which is larger than the transform-limited value (≈0.315). This is likely to be due to SPM in the gain section [2]. The phase noise trace hits the thermal noise floor at the offset frequency of 9 MHz [17] (Fig. 5(e)). Using the expression for the integrated rms timing jitter in [18] or extrapolating the trace in Fig. 5(e) from 9 MHz at the standard roll-off of −20 dBc/Hz per decade results in a timing jitter value of 194 fs (4-80 MHz), the lowest reported to date of any 10 GHz passive QW MLL.

 

Fig. 4 (a) Measured map of ML regime of laser operation vs the I_gain and V_SA, and (b) FWHM of the autocorrelation trace vs the I_gain for different V_SA.

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Fig. 5 (a) Measured autocorrelation pulse trains, (b) an isolated pulse fitting by a sech² shape, (c) RF spectrum, (d) optical spectrum, and (e) SSB noise for I_gain = 142 mA, V_SA = −2.8 V.

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5. Conclusion

In conclusion, a novel epitaxial laser wafer structure with a three-QW active layer incorporated with a passive FRL for the fabrication of 10 GHz passive AlGaInAs/InP MLLs has been designed with a significantly improved FFP, RF linewidth, and timing jitter. The far-field was as small as 14.7° × 27.3°, which doubled the coupling efficiency to a flat cleaved SMF. Sech² pulses of 1.06 ps duration were generated at a repetition rate of ~10.0 GHz with a state-of-the-art timing jitter of 194 fs (4-80 MHz) and a RF linewidth of 2 kHz.