1. Introduction

Femtosecond pulse lasers with a gigahertz repetition rate are attractive for a variety of applications, including the analysis of nanomechanical and optomechanical systems [1], as a multiphoton tool for nanomedicine and nanobiotechnology [2, 3], for high-speed asynchronous optical sampling [4], and as a carrier-envelope-offset (CEO)-locked frequency comb with a wide mode spacing [5, 6]. When we measure soft materials, such as biological tissue, using nonlinear microscopy, the signal intensity is limited by the photodamage threshold of the sample when we employ commercial femtosecond pulse lasers at a typical repetition rate of around 100 MHz. The advantage of increasing the repetition rate of femtosecond pulse lasers up to 1 GHz is that we can reduce the peak intensity applied to samples to avoid photodamage and also reduce dye bleaching while maintaining the detected signal level. In addition, higher average powers can be applied to the sample, resulting in an improved signal-to-noise ratio (SNR). Recently, a new method was developed for characterizing the resonant properties of nanomechanical systems by using a femtosecond pulse laser at a 1-GHz repetition rate [1]. Tuning the repetition rate of the femtosecond pulse laser to a subharmonic of a mechanical resonance of a thin membrane makes it possible to determine its quality factor and lifetime accurately. A wider tuning range is required for the repetition rate for further applications of this method to various measurements. In addition, a femtosecond pulse laser operating at a repetition rate in the GHz regime is useful for achieving a CEO-locked frequency comb with a wide mode spacing [6], and so it could be applied to future photonic networks, astronomical spectroscopy [7, 8], and line-by-line optical pulse shaping [9].

Conventional methods for generating femtosecond optical pulses are based on a mode-locking technique. Mode-locked lasers have long played an important role in the measurement of ultrafast phenomena. Mode-locked semiconductor lasers and Er-doped fibre lasers have been developed in the 1.5-μm band. However, since the cavity length must correspond to the repetition rate, it is difficult to obtain femtosecond pulses with a high repetition rate exceeding 1GHz. Moreover, the repetition rate and wavelength have limited tunability.

One promising way to overcome this problem is to use an external optical modulator instead of a mode-locking technique [10, 11]. This approach does not need a resonant cavity. The phase and intensity of the light from a continuous-wave (CW) laser diode (LD) are modulated with an optical modulator driven by a radio frequency (RF) synthesizer. Then, the modulated light is converted into short pulses by compensating for the frequency chirp with a dispersive medium. The repetition rate is changed by the RF synthesizer. The centre wavelength is also changed by adjusting the wavelength of the LD. Previously, Hanna et al. successfully achieved 3.2-ps pulse duration with a soliton-assisted compression method [12]. Recently, 168-fs laser pulses at a 10-GHz repetition rate were generated by using a Mach-Zehnder modulator based flat comb generator and a dispersion-flattened dispersion-decreasing fibre [13]. However, soliton-assisted compression would create multiple pulses when the average input power of optical pulses is increased [12]. It would therefore be difficult to obtain sub-100-fs pulses with this method by simply increasing the input power. Utilizing only SPM instead of soliton-based broadening is a known technique for preventing multiple pulse generation [14, 15]. The technique has been used to generate 100-fs pulses with a comb-like dispersion profiled fibre (CPF) consisting of highly nonlinear fibres. However, it is very complicated. In addition, 115-m- [14] and 1.8-km-long [15] CPF were used, which means it would be difficult to achieve a CEO-locked frequency comb [6] using this approach since the feedback-loop length becomes longer. To solve these problems, we devised a method that utilizes a different physical mechanism: progressive expansion of the spectrum in an erbium-doped fibre amplifier (EDFA) through the self-phase modulation (SPM) process. Our method is a simple and compact configuration consisting of commercially available devices. The high power amplifier itself acts as the nonlinear compressor.

In this paper, we describe a 100-fs-class pulse generation method with a tunable repetition rate and wavelength based on a simple configuration consisting of a laser diode and an optical modulator, and report a 1-W, 120-fs pulse train with a gigahertz repetition rate by using a progressive expansion of the spectrum in the SPM process in the EDFA.

2. Phase-modulated lasers with 25-GHz repetition rate

Figure 1(a) shows our laser system for generating a 25-GHz pulse train. The phase and intensity of the light from a CW LD with a centre wavelength of 1552.52 nm and a linewidth of 2.3 kHz are modulated with three conventional phase modulators (PMs) driven by a sinusoidal-RF signal from an external RF synthesizer at a modulation frequency f_mod of 25 GHz. The external synthesizer is synchronized with a reference signal from a global positioning system. The applied modulation index obtained with the PMs is 20 π. This process causes repetitive up- and down-chirping at 25 GHz. The linear part of the down-chirping is selectively gated with an intensity modulator (IM) [6], resulting in a flat optical frequency comb with a 24-nm bandwidth (Fig. 1(b)). The timing of the RF signal that drives the PM and IM is adjusted with RF phase shifters. The average power after a standard single-mode fibre (SMF) is 100 mW. The pulse compression is achieved by passing the chirped pulse through the SMF with chirp compensation. Figure 1(c) shows an autocorrelation trace of an optical pulse at 25-GHz repetition rate. To determine the pulse width, we calculated a deconvolution factor of the autocorrelation trace by using the waveform derived from the simulation code (see section 4). Since the derived waveform depends on the amount of dispersion of the chirp compensation medium, we chose the waveform so as to reproduce the measured autocorrelation trace well. After measuring the full-width at half maximum of the autocorrelation trace, we found the pulse width to be 230 fs. However, the spectral bandwidth obtained with PMs is not sufficiently broad to generate 100-fs-class optical pulses.

 

Fig. 1 (a) Experimental set-up for generating a 25-GHz pulse train and experimental results for (b) the spectrum and (c) the autocorrelation trace of an optical pulse at a 25-GHz repetition rate.

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3. 120-fs pulse generation at 1-GHz repetition rate

To generate 100-fs-class optical pulses, we use a progressive expansion of the spectrum in the SPM process in the EDFA to expand the spectral bandwidth. Since the average output power of the EDFA is limited, we employed an optical gate (OG) to increase the peak intensity of the amplified pulse. Figure 2 shows the experimental set-up of the OG, which we installed after the IM described in the previous section. By applying RF impulse signals, which are generated by using a comb generator driven by a sinusoidal-RF signal from an RF synthesizer, the IM operates as the OG. This RF synthesizer is synchronized precisely with the other RF synthesizer to generate a 25-GHz pulse train (see previous section). At first, we operate the OGs at a 1-GHz repetition rate. The OG plays an important role in selectively picking up one optical pulse from the 25-GHz pulse train and suppressing the amplified spontaneous emission (ASE) component. After the OG, which reduces the repetition rate from 25 GHz to 1 GHz, the optical pulse train is amplified to an average power of 1 W in the EDFA. Since the peak intensity is estimated to be several kilowatts in the EDFA, spectral broadening should occur as a result of the SPM process. Then, the chirped pulse is compressed by a 1-m-long glass block. The beam diameter of the optical pulse in the glass block is expanded to avoid the nonlinear process that causes pulse shape deformation.

 

Fig. 2 Experimental set-up of the optical gate (blue dotted frame) installed after the intensity modulator.

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Figure 3(a) and (b) show spectra obtained before the glass block and autocorrelation traces obtained after the glass block, respectively, without the OG (red) and with the OG (blue). The output spectrum obtained with our scheme is stable over time. The spectrum without the OG, which spans 1536 to 1568 nm at the −30-dB level, is similar to the spectrum before the EDFA, and the pulse width of 260 fs is slightly broadened. This suggests that the peak intensity of the amplified pulse with a 25-GHz repetition rate is too low to expand the spectral bandwidth via SPM in the EDFA. Therefore, we employ the OG. The OG expands the spectrum from 1524 to 1583 nm at the −30-dB level, resulting in compression as narrow as 120 fs. This result indicates that the peak intensity with the OG is higher than that without the OG in an EDFA. The comb lines of the spectrum with the OG (blue) in Fig. 3(a) show that the OG does not isolate a single optical pulse completely from the 25-GHz pulse train, which is because the gate duration of the OG was 50 ps. Therefore, small satellite pulses corresponding to the 25-GHz pulse train 40 ps from the 1-GHz pulse are observed in the autocorrelation trace. By using the OG with the gate duration less than 40 ps, these satellite pulses could be eliminated.

 

Fig. 3 (a) Spectrum before the glass block without (red) and with (blue) the optical gate. (b) Autocorrelation trace after the glass block without (red) and with (blue) the optical gate.

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4. Short pulse generation at 250-MHz repetition rate

We investigated a further reduction in the pulse width by spanning the spectral width in the EDFA. For this purpose, we increased the peak intensity obtained in the EDFA by reducing the repetition rate of the OG to 250 MHz. We then amplified the optical pulse at a 250-MHz repetition rate to 1 W by using a 1-W EDFA. Figure 4 shows (a) a spectrum obtained before the glass block and (b) an autocorrelation trace obtained after the glass block with the OG operated at a modulation frequency of 250 MHz. We demonstrated that the spectral bandwidth expanded further and the pulse width was successfully compressed to 80 fs. There are wings on the autocorrelation trace in Fig. 4(b). They come from the nonlinear chirp components created with the PMs, which could not be eliminated by the following IM. These wings can be supressed by passing the optical spectrum through a bandpass filter to remove the nonlinear chirp components [11]. In our scheme, the limitation of the variable range of the repetition rate comes from the bandwidth of an RF amplifier for 25 GHz. For example, the bandwidth from 17 to 27 GHz is available with a Microwave Power Inc.’s RF amplifier. By using this RF amplifier, the repetition-rate tunable range of 0.68-1.08 GHz and 170-270 MHz can be achieved by the configuration with the OGs of 1/25- and 1/100-frequency dividing, respectively.

 

Fig. 4 Experimental results for (a) spectrum and (b) autocorrelation trace obtained using the configuration with the optical gates at 250 MHz.

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To confirm the validity of our experimental results, we calculated the optical spectrum and the waveform of the optical pulse obtained with our scheme with 250-MHz gated optical pulses by using a VPI transmission Maker^TM simulation code. In this simulation code, a split-step Fourier method is used to solve a nonlinear Schrödinger equation describing the propagation of linearly polarized optical waves in optical fibres. This code takes account of SPM, stimulated Raman scattering, cross-phase modulation, and a high-order nonlinear effect. Figure 5(a) shows the calculated spectra obtained after the intensity modulator in Fig. 1(a). Figure 5(b) and (c), respectively, show the calculated spectra and the waveform obtained after the glass block. The calculation showed that the spectral broadening is caused by the SPM process in the EDFA, and the pulse width can be compressed to 66 fs when the glass block length is optimised. These calculated results are consistent with our experimental results.

 

Fig. 5 Calculated results for (a) the spectrum after the IM in Fig. 1(a), (b) the spectrum and (c) the waveform (blue) and phase (red) after the glass block.

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In our generation method using SPM, the key to short pulse generation is to increase the peak intensity in the EDFA rather than to decrease the repetition rate. Since the output power of the EDFA in our experiment was limited, there was a trade-off between the obtained pulse width and the repetition rate. Because the achieved peak intensity in the EDFA decreases as the input optical pulse repetition rate increases, the amount of spectral broadening caused by the SPM process is suppressed and thus the obtained pulse width becomes wider. Our calculation suggests that if we use a 4-W EDFA, the pulse widths could be 66 and 34 fs for 1-GHz and 250-MHz repetition rate input pulses, respectively.

5. Conclusion

A 1-W, 120-fs optical pulse train at 1 GHz and a 1-W, 80-fs optical pulse train at 250 MHz has been demonstrated by using a simple and compact configuration consisting of commercially available devices. As far as we know, the 80-fs pulses are the shortest pulses ever achieved using a CW LD as a seed light source. Our method utilizes the SPM process in the EDFA to span the spectral bandwidth. Our scheme could provide a sub-100-fs laser with widely tunable repetition rate and wavelength by changing the modulation frequency of the RF synthesizer and the wavelength of a tunable laser diode. Regarding widely tunable wavelength, however, an optical fibre amplifier with wide gain bandwidth would be required. These features mean that our proposed laser system has the potential to become a powerful tool for a variety of applications.