1. Introduction

Optical frequency combs and pulse trains from self-referenced laser oscillators are versatile tools for stable and accurate measurements in frequency metrology, time resolved and frequency-domain spectroscopy [1], optical arbitrary waveform generation (OAWG) [2] and calibration of astronomical spectrographs [3]. To enable more compact and more powerful frequency comb systems, ultra-broadband laser oscillators operating at high repetition rates are highly desirable. For frequency metrology and spectroscopy higher repetition rates correspond to larger mode spacing and higher power per mode, enabling higher signal-to-noise ratio, and for OAWGs or in spectrograph calibration it enables the use of lower resolution spectral dispersers or the calibration of lower resolution spectrographs, respectively. However, the construction of frequency combs needs two successive nonlinear processes which degrade with increasing repetition rate, as the pulse energy is reduced at a given average power from the laser. These processes are either intracavity or extracavity spectral broadening for obtaining 1f and 2f components and the self-referencing involving second-harmonic- generation for producing a carrier-envelope (CE) beat note. Over the past few years, several Ti:sapphire lasers [4–9], with gigahertz-repetition rates up to 10 GHz achieved most recently [10], have been demonstrated. However, octave spanning operation was only obtained up to 1.35 GHz by Fortier et al. and at the high end the CE beat note was already reduced from 31 to 25 dB measured with a 300kHz resolution bandwidth (RBW) when increasing the repetition rate from 550MHz to 1.1GHz [6], making a transfer oscillator necessary. Although these authors have shown that the continuum generation resulting from an enhanced self-amplitude modulation by introducing a convex mirror can be used to assist octave-spanning operation even when the dispersion is only controlled across the center portion of the Ti:sapphire gain bandwidth, we demonstrate here that broadband dispersion compensation helps to maintain an octave spanning spectrum for even 2GHz repetition rate In this work, a self-referenced octave-spanning Ti:sapphire laser with a repetition rate of >2 GHz is demonstrated while maintaining a CE beat note of >50 dB measured with a 100kHz RBW, which shows to our knowledge the highest repetition rate and ~20dB improvement (using 100kHz RBW) of CE beat note for a gigahertz-repetition-rate phase-stabilized laser oscillator. This is possible, because the laser uses specially designed double-chirped mirror pairs [11] with excellent dispersion characteristics over the full Ti:sapphire gain bandwidth. In addition, one of the mirrors is designed to transmit the 1f and 2f spectral components used for CE-phase stabilization as a second output, separately from the main output from the output coupler, in a non-intrusive manner [12]. This design allows the laser to deliver a phases-tabilized, octave-spanning laser beam directly from main output ready for future applications.

2. Laser cavity design and alignment

The laser setup is shown in Fig. 1. We use a 4-mirror Kerr-lens-mode-locked (KLM) ring cavity consisting of two dispersion-matched pairs of broadband double-chirped mirrors (DCM), (M1,M2) and (M3,M4), which is a modified design based on our recently proposed configuration for maximum carrier-envelope (CE) beat signal generation [12]. A 2.2 mm long Brewster-cut Ti:sapphire crystal (α=4.5 cm^-1) is located between two concave DCMs with a radius of curvature (ROC) of 2.5cm. The laser is pumped by a multimode diode-pumped solid-state laser (Millennia Xs) through a lens with a focal length of 4 cm. The folding angle at the curved mirrors is set to 21 degree for astigmatism compensation. To increase the stability of the laser when mode-locked at high repetition rate, we replace M4 with a slightly convex mirror (ROC=50 cm), instead of using two flat mirrors for the second DCM pair. It was pointed out earlier by Bartels et al. [5] that this configuration leads to a stronger self-amplitude modulation coefficient or KLM strength δ inside the cavity.

 

Fig. 1. Setup of CE phase stabilized octave-spanning Ti:sapphire (Ti:S) laser and phase-locking electronics. The four-mirror cavity is formed by two pairs of DCM, (M1,M2) and (M3,M4). M1 and M2 are concave mirrors (ROC=2.5cm). M4 is a convex mirror (ROC=50 cm). AOM, acousto-optic modulator; L1, pump lens (f=4 cm); FS OC, wedged fused silica output coupler; SM1-3, silver mirrors; DM, dichroic mirror; L2–L3, lens (f=20mm); IF, interference filter centered at 580nm; PBS, polarization beamsplitter; APD, avalanche photodetector; DPD, digital phase detector; S, power splitter; LO, local oscillator; LPF, low-pass filter; VSA, vector signal analyzer; RF-SA, RF spectrum analyzer.

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The DCMs used here are identical to those in Ref. [12] and are designed to have a smooth average group delay and negative group delay dispersion (GDD) from 650 to 1100 nm to compensate for the positive dispersion of all other intracavity elements in this spectral range of interest. The coating on M3, same as M1, is designed to transmit 50% of the intracavity power around f and 2f components [12], which allows the main output to be completely separated from the 1f-2f output (coupled out from M3) so that the main pulses are not affected by any extracavity manipulations needed for CE-phase stabilization. A 1.5 mm-thick BaF2 plate and a 1 inch long fused-silica (FS) wedge with a central thickness of 1.7 mm are placed at Brewster angle. The corresponding path length of BaF2 and FS is 1.83 mm and 2.12 mm, respectively. Although there are some remaining fluctuations in the GDD of the DCMs for discussion of the dispersion compensation the average GDD curve is used. As shown in Fig. 2, considering the dispersion of all intra cavity components as well as the air path results in a vanishing net average GDD within a few fs² over the entire bandwidth of the Ti:sapphire crystal, which is the key to the generation of octave-spanning spectra [13]. Due to the physical limits of our cavity, the FS-wedge, which is used for fine-tuning of the intra cavity dispersion and the carrier-envelope offset frequency, is vertically mounted (perpendicular to the table) to maximize the range of adjustment. A 2% broadband output-coupler (OC) coating carried by the wedge is designed to enhance the spectral wings of the output pulses by increasing the reflectivity to >50% below 650 nm and above 1050 nm.

The cavity was initially aligned for best continuous-wave operation, which was judged by having a maximized output power and a clear transverse-mode transition from fundamental TEM₀₀ to circular symmetric higher-order modes when translating mirror M2 towards M1 at the inner edge of the stability region. Both criteria are very important for achieving optimum KLM because the former ensures that the laser gain is maximized, while the latter helps to verify that there is no transverse displacement or angular tilt between the optical axes of the cavity and the pump beam [14]. When above criteria are met, bidirectional mode locking is easily initiated by pushing M2 inward to the position where the first or second higher-order mode was supposed to appear. Unidirectional mode-locking is finally achieved by further translation of M2 by a few tens of microns.

 

Fig. 2. Calculated total intra cavity GDD (red solid curve) and individual GDD for each component including 2.2mm Ti:Sa (black dashed curve), 1.83mm BaF2 (purple short dotted curve), 2.12mm FS (blue short dashed curve), 15cm air (green dotted curve), and 2 DCM pairs (gray dash dotted curve).

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3. Laser performance

Figure 3 shows the radio-frequency (RF) spectra of the directly detected pulse stream when the laser is in unidirectional operation. The clean RF-spectrum indicates stable fundamental mode locking with a repetition rate of ~2.166 GHz which is slightly higher than our previous result [15]. At 10.5 W of pump power the laser generates a total output power of 812 mW including a main output of 750 mW and a 1f-2f output of 62 mW.

For comparison, the calibrated spectra displaying power spectral density for both outputs are shown in the same plot (see Fig. 4). The spectral components of the 1f-2f output below 600 nm and above 1120 nm, although containing only a few percent of the total power, are stronger than the main output. The result matches perfectly with our DCM design [16] and also shows that we can generate the necessary 1f–2f components in a very simple and efficient way without affecting the main output of the laser. Moreover, the main output covers a spectral range of more than 700 nm (extending from 570 nm to 1300 nm, when considering a 30 dB dynamic range from the maximum at 800 nm). The power per mode in the center of the spectrum is 18 µW with more than 100 nW per mode available from 250 THz to 500 THz. The power leaving the 1f–2f output port within a 10 nm bandwidth located at 580nm and 1160nm, the wavelengths used for the CE-lock, are 0.884 mW and 4.49 mW, respectively, which is more than enough power for subsequent self-referencing.

 

Fig. 3. RF spectrum of pulse train detected with a 10 GHz photo detector: With high resolution at the fundamental repetition rate of 2.166 GHz; inset shows full spectrum up to 16 GHz.

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Fig. 4. Output spectra of (a) 1f–2f output beam (black curve) and (b) main output beam (red curve) from the laser. The filled area between two curves visualizes that the spectral components of 1f–2f output below 600 nm and above 1120 nm are stronger than in the main output.

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4. Carrier-envelope phase stabilization of the laser

The CE-phase is detected with a 1f–2f interferometer at the output of M3 (see Fig. 1) in which a dichroic mirror is used to separate the 1f and 2f components for proper group delay adjustment to maximize the CE-beat signal. The f-to-2f beat note is generated and collected through a pair of uncoated lenses with a focal length of 2 cm. The first lens was used to focus the laser beam into a 1 mm-BBO crystal for second-harmonic generation (SHG), while the other is used to collect and re-collimate the fundamental and generated SHG beams, which are then filtered by a 10-nm-bandwidth interference filter centered at 580 nm, and directed to a fast avalanche photodiode (MenloSystems APD210). The delay line based on a dichroic beam splitter, rather than DCMs, is used for generating the CE-beat note since the overall achievable CE-phase error was dominated by the noise from the multimode pump laser used [12,18]. This simple and inexpensive scheme still generates a free-running CE beat note with a SNR of 50 dB measured in a 100 kHz resolution bandwidth (see Fig. 5(a)) and a similar result for the integrated residual phase jitter when compared with our previous lasers using the same type of pump laser [17, 18].

The CE-offset frequency (f_ceo) is locked to a local oscillator (LO) set at 20MHz through a phase-locked loop (PLL) (see Fig. 1) that feeds the phase difference between the CE-beat signal and the LO to an acousto-optic modulator regulating the pump power, thus shifting the CE-frequency. The PLL uses a digital phase detector to increase the capture range (-32π ~+32π) beyond a traditional analog mixer (-π/2 ~+π/2). Figure 5(b) shows the measured RF spectra of the CE beat note signal in both linear and log scale when the laser is locked. As demonstrated by the plot, a delta-function-like CE beat note with a linewidth of <10 Hz (the resolution limit of our RF spectrum analyzer) is achieved. The central peak within four times the 10Hz RWB contains 91% of the overall power that takes the entire pedestal caused by the amplitude and phase noise into account. In order to precisely estimate the residual CE phase error when the laser is locked, the following measurement is done. The residual phase noise of our system was obtained by splitting the CE-beat note signal and mixing one part of it directly with the local oscillator signal using a broadband analog mixer because it is difficult to measure the small residual phase fluctuations from the digital phase detector. The output from the mixer was filtered by a 10 MHz low-pass filter and fed into a vector signal analyzer (VSA) for measuring the one-sided power spectral density (PSD) of the residual CE fluctuations S_ϕ, (see red curve in Fig. 5(c)). The dashed curve in the same plot shows the integrated CE root-mean- square phase error calculated from

in general it is true that the range of integration should be up to Nyquist frequency [19], i.e., 1 GHz, it is difficult to measure S_φ at high frequencies as it is lower than the noise floors set by the photodetector. This has to be expected, since the major source of carrier envelope noise are intracavity intensity fluctuations, which rapidly decay beyond the relaxation frequency of Ti:sapphire lasers, which is typically a few hundred kHz. Therefore, the upper limit of integration in our case is set to be 1 MHz to exclude the high-frequency noise contributed by the noise floor rather than the laser phase noise itself. The accumulated phase error integrated from 0.1 Hz to 1 MHz is 0.187 rad. This is equivalent to a timing jitter of 79 as at the center wavelength of 800nm, which is slightly better than earlier constructed Ti:sapphire combs pumped by a multimode laser. Multimode pump lasers are known to have significantly higher relative intensity noise than a single-mode pump lasers at high frequencies, where the feedback loop of the PLL has already low gain for stability reasons or it is already outside the loop bandwidth at all [17, 18]. Thus the CE-phase noise can be further suppressed by switching to a single-frequency pump source such as Coherent Verdi-10.

Although in general it is true that the range of integration should be up to Nyquist frequency [19], i.e., 1 GHz, it is difficult to measure S_ϕ at high frequencies as it is lower than the noise floors set by the photodetector. This has to be expected, since the major source of carrier envelope noise are intracavity intensity fluctuations, which rapidly decay beyond the relaxation frequency of Ti:sapphire lasers, which is typically a few hundred kHz. Therefore, the upper limit of integration in our case is set to be 1 MHz to exclude the high-frequency noise contributed by the noise floor rather than the laser phase noise itself. The accumulated phase error integrated from 0.1 Hz to 1 MHz is 0.187 rad. This is equivalent to a timing jitter of 79 as at the center wavelength of 800nm, which is slightly better than earlier constructed Ti:sapphire combs pumped by a multimode laser. Multimode pump lasers are known to have significantly higher relative intensity noise than a single-mode pump lasers at high frequencies, where the feedback loop of the PLL has already low gain for stability reasons or it is already outside the loop bandwidth at all [17, 18]. Thus the CE-phase noise can be further suppressed by switching to a single-frequency pump source such as Coherent Verdi-10.

 

Fig. 5. (a). RF spectrum of the free-running CE-beat (RWB=100 kHz) showing a SNR of ~50 dB. (b). RF spectrum of the locked CE-beat signal in log scale (red dotted curve) and linear scale (black solid curve) showing a resolution-limited linewidth of 10 Hz. (c). Power spectral density (PSD) of the residual carrier-envelope phase fluctuations (black curve) and integrated carrier-envelope phase error (red curve). The accumulated phase error integrated from 0.1 Hz to 1 MHz is 0.187 rad.

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5. Conclusion

In conclusion, we demonstrated a self-referenced octave-spanning Ti:sapphire laser operating with the so far highest repetition rate of >2GHz while maintaining a strong (>50dB) CE-beat note in a 100kHz resolution bandwidth. The laser cavity uses novel double-chirped mirror pairs that provide both the main octave-spanning output carrying more than 90% of the total output power and a separate output port for the 1f-2f frequency components used for non-intrusive carrier-envelope phase-stabilization.