We demonstrate a carrier-envelope-offset (CEO)- locked frequency comb with 230-pJ fiber coupling pulse energy by using a passively mode-locked Er-fiber amplifier laser. For the generation of an octave-bandwidth spectrum in a highly nonlinear fiber and the second harmonic in a self-referenced interferometer with the lower pulse energy, we use a tellurite photonic crystal fiber and a direct-bonded quasi-phase-matched LiNbO3 ridge waveguide, respectively. Our method is feasible for locking the CEO with a lower pulse energy to obtain a low-noise and high-accuracy optical frequency comb at telecommunications wavelengths.
©2008 Optical Society of America
A carrier-envelope-offset (CEO)-locked frequency comb at telecommunications wavelengths with a downsized, low-noise, narrow-linewidth, and high-repetition-rate laser system could provide an optical frequency “ruler” in a robust, power-efficient full fiber-optics package that would be suitable for a variety of applications. Such combs should prove useful in high-precision spectroscopy , phase-coherent optical transfer , coherent lidar , and frequency metrology . As applications are being proposed, the need for a low-noise CEO-locked frequency comb operating unattended over long periods of time with low pulse energy is evident. The total phase noise power spectral density (PSD) from multiple, uncorrelated noise sources is calculated by simply adding up the phase noise PSDs from the intracavity noise and the extracavity noise . The intracavity noise is described by length fluctuations, loss fluctuations, pump noise, and ASE quantum noise. The extracavity noise is described by excess noise during supercontinuum generation, shot noise, and length fluctuations. The phase noise PSD generated in a photonic crystal fiber (PCF) with around 1-nJ pulse energy influences the CEO beat frequency . In addition, it contributes to the linewidth of the frequency comb . In general, the lower the pulse energy of the laser is, the lower the phase noise PSD becomes. A frequency comb with lower phase noise PSD and narrower linewidth would be very advantageous for applications.
In telecommunications application, there is the need for a CEO-locked frequency comb with a more than 10-GHz repetition rate because the modes of the frequency comb are resolved with an arrayed-waveguide grating . However, CEO locking of a fiber laser at the telecommunications wavelengths has been achieved only below 1-GHz repetition-rate at present. In order to achieve the CEO locking at higher repetition rates with low noise, developments from the two sides are necessary. On one side, the output power of a high-repetition-rate fiber laser should be increased. On the other side, the pulse energy required for CEO locking should be reduced. Recently, Hartl et al. succeeded in locking the CEO with 600 pJ . For the generation of an octave-bandwidth spectrum and the second harmonic with an f-to-2f self-referencing interferometer, they used a highly nonlinear fiber and a butt-coupled periodically poled lithium niobate (LN) waveguide, respectively. However, the use of the high-nonlinear fiber makes it difficult to reduce the pulse energy to less than 600 pJ.
In this paper, we propose a method to lock the CEO by using a tellurite PCF and a direct-bonded quai-phase matching (QPM)-LN ridge waveguide. Using our method, we demonstrate a CEO-locked frequency comb at telecommunications wavelengths with 230-pJ fiber-coupling pulse energy. Our method is feasible for achieving a CEO-locked frequency comb with lower phase noise at telecommunications wavelengths.
For the generation of an octave-bandwidth spectrum in a nonlinear fiber with lower pulse energy, we use a tellurite PCF we developed . Figure 1(a) shows scanning electron microscope (SEM) images of the tellurite PCF. The core size, outer hole diameter, and outer fiber diameter are 2.6, 25, and 110 µm, respectively. The core area is optically isolated from the outer glass region by four thick supporting bridges. The predicted effective mode area Aeff for a core size of 2.6 µm is 3.54 µm2. Tellurite-based glass has a nonlinear refractive index of 5.9×10-19-m2/W. Therefore, we calculate a highly nonlinear coefficient γ to be 675-W-1km-1, which is 30 times as large as that of a conventional highly nonlinear fiber . The propagation loss of the tellurite PCF is 0.4-dBm-1 around 1560 nm. Figure 1(b) shows the chromatic dispersion curve of the tellurite PCF and tellurite glass material. We have successfully shifted the zero-dispersion wavelength toward 1573-nm.
For the generation of the second harmonic in a self-referenced interferometer  with the lower pulse energy, we use our fabricated direct-bonded QPM-LN ridge waveguides . The waveguide length is 38 mm. A periodically poled structure with periods of 26.95-µm was formed on the LN wafer. Since no ion-exchange/diffusion process is employed in the fabrication, the ridge waveguide exhibits strong resistance to photorefractive damage and no degradation of the nonlinear coefficient even at room temperature. In addition, direct-bonding provides strong light confinement owing to the step index profile. Consequently, high conversion efficiency can be obtained by using ridge-waveguide structures in QPM waveguide devices. Therefore, there is possibility of locking the CEO for long periods of time with this direct-bonded QPM-LN ridge waveguide.
2. Experimental setup
The experimental setup is shown in Fig. 2. We used a passively mode-locked Er-fiber laser amplifier system (Menlo Systems GmbH). The amplifier laser delivers a 100-fs, 1-nJ laser pulse with a center wavelength of 1560 nm. The repetition frequency of the fiber laser system was controlled to 250 MHz by using a global positioning system (GPS) reference signal. The reference signal stability from our GPS receiver is 5×10-13 in 1 s (model K+K GPS6 by Menlo Systems GmbH). Output power from the amplifier laser is collimated in free space by using a collimate lens and then launched into the tellurite PCF (core size: 2.6 µm) with typical efficiency of 29% by using an objective lens (NA=0.8). This typical coupling efficiency includes the 59% transmittance of the objective lens. The optical output spectrum after the tellurite PCF spans more than an octave. The CEO frequency fCEO is measured with an f-to-2f self-referencing interferometer. A long-pass filter transmits infrared components at 1930 nm. These components are then frequency-doubled into the direct-bonded QPM-LN ridge waveguide at room temperature and recombined with a 965-nm beam propagating through an arm of the f-to-2f self-referencing interferometer at a polarization beam splitter. The interference components are chosen with a grating. The beam is coupled onto an InGaAs avalanche photodiode detector. From the signal, the heterodyne beat between the interference components yields a frequency difference fCEO. The CEO signal is phase-locked to fCEO=20 MHz using a feedback circuit.
3. Results and discussion
We investigated the dependence of the supercontinuum (SC)-spectrum bandwidth on the direction of the linear polarization of the input laser by rotating a half-wave plate. The spectral structure reproduces itself approximately every 90°, in agreement with the symmetry of the PCF structure. We confirmed that the widest SC-spectrum is generated when we rotate the linear polarization by ±45° to the thick supporting bridge [see Fig. 1(a)].
Figure 3 shows the dependence of the SC spectrum on the length of the tellurite PCF and the fiber coupling pulse energy. The longer the length of the tellurite PCF is, the more complicated the spectrum becomes. The SC shape for different pulse durations, pulse energies, fiber structures, and fiber lengths has been calculated numerically [13–15]. The SC light is generated mainly by self-phase modulation. Apolonski et al. showed that some different nonlinear processes take place during propagation along the fiber . Our results are in good agreement with theirs. Our results indicate that the 30-cm long tellurite PCF can generate the SC light with low pulse energy. We found that a SC spanning more than an octave (950–2100 nm) at the -30-dB level can be generated with 80-pJ fiber-coupling pulse energy using 280-pJ output power from the amplified laser and a 30-cm long tellurite PCF. Hundertmark et al. observed a SC spanning more than an octave with pulse energies of about 200 pJ in an extruded SF6 fiber at 1560 nm . To the best of our knowledge, our 80 pJ is the lowest fiber coupling pulse energy at which a spectrum spanning more than an octave has been obtained by using a fiber without a complicated tapered structure in the telecommunications wavelength region.
We measured the CEO frequency fCEO with an f-to-2f self-referencing interferometer. We could not observe the beat signal with the 80-pJ fiber-coupling pulse energy [see Fig. 3(b)], probably because of the low output power from the tellurite PCF. Therefore, we increased the fiber coupling pulse energy in order to observe the beat signal. We used 800-pJ output power from the amplified laser and launched a 230-pJ pulse energy into the tellurite PCF. Figure 4(a) shows the spectrum between the fundamental light and the second harmonic generated by propagating in the direct-bonded QPM-LN ridge waveguide. From the SC-shape with the 230-pJ fiber coupling pulse energy [see Fig. 3(b)], we found that the largest beat signal could be obtained in the 965-nm region. Figure 4(b) shows that the beat signal between the frequency-doubled light at 1930 nm and the fundamental light at 965 nm is detected with an InGaAs avalanche photodiode. We observed the beat signal with about a 30-dB signal-to-noise ratio at a RF spectrum analyzer set to 100-kHz resolution bandwidth. The full width at half maximum linewidth of the beat signal is about 180 kHz. The beat signal was locked at 20-MHz reference frequency by controlling the 980-nm pump laser power using the feedback circuit. The inset in Fig. 4(b) shows that the difference signal between the beat signal and the local oscillator becomes smaller with the CEO lock. The local oscillator uses the GPS-based 10-MHz signal. We also locked the repetition frequency at 250 MHz by using this GPS signal.
Figure 5 shows the PSD of the phase noise measured with the demodulation technique using a vector signal analyzer (Agilent 89441A) [18, 19]. The CEO locked spectra (13 mHz-6 kHz) were compiled from six different spectra of decreasing span and increasing resolution to obtain higher resolution close to the carrier (displayed here as zero frequency). Without the CEO lock, it was difficult to measure the PSD signal at less than 1 Hz using our vector signal analyzer because of carrier frequency fluctuation. This means that the feedback loop with the CEO lock suppresses phase noise at frequencies less than about 1 kHz. We confirmed that the CEO could be locked in our system.
Since the coupling efficiency from the output of the laser to the PCF is low at present, an amplifier laser is needed. When angled V-groove splicing is used between the tellurite PCF and the silica fiber of the fiber laser output port, the loss of the splicing should be about 1.0-dB . Therefore, our method allows us to lock the CEO using only 290 pJ as the output pulse energy from the laser. This indicates that it would be possible to lock the CEO by using a fiber laser oscillator with low pulse energy .
We have demonstrated a CEO-locked frequency comb at the telecommunications wavelengths with 230 pJ, which, to the best of our knowledge, is the lowest fiber coupling pulse energy. We proposed the use of a tellurite PCF and a direct-bonded QPM-LN ridge waveguide for the generation of an octave-bandwidth spectrum and the second harmonic with an f-to-2f self-referencing interferometer, respectively. Our method might pave the way for the development of frequency combs with low-phase-noise PSD. The CEO-locked frequency comb at the telecommunications wavelengths with lower pulse energy will have great advantages for precise spectroscopy, telecommunications, coherent lidar, and frequency metrology.
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