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We demonstrate that a 2f-to-3f self-referencing interferometer (SRI) becomes a useful tool for stabilizing a carrier-envelope offset frequency of an Er-doped fiber laser. A dual-pitch periodically poled lithium niobate (PPLN) ridge waveguide, consisting of two monolithically integrated segments with different quasi-phase matching pitch sizes, allows us to generate third-harmonic light with high efficiency. By using this device, we obtain a 45-dB signal-to-noise ratio in 100-kHz bandwidth of a heterodyne beat signal and instability of the in-loop fCEO of 8 × 10−18 at 1 s of averaging time. This result is important for fCEO stabilization of a frequency comb, for which it is difficult to obtain a one-octave supercontinuum spectrum.
© 2014 Optical Society of America
1. Introduction
Stabilizing the carrier-envelope offset (CEO) frequency in an optical frequency comb has dramatically advanced the fields of precision spectroscopy [1, 2], femtosecond pulse shaping [3], and astronomical physics [4]. In these fields, a widely mode-spaced optical frequency comb is desired because each frequency mode can be spectrally resolved in a simple manner and become accessible for individual use. In the past few years, the repetition rate of 10 GHz has been achieved with a mode-locked Ti:sapphire laser [5]. Also, phase/intensity-modulated lasers are able to produce higher mode spacing (in our case 25 GHz) of a frequency comb, which is achieved by sinusoidally modulating the phase and intensity of a continuous-wave laser diode with electro-optic modulators [6–8]. In addition, microresonator-based optical frequency combs (micro-combs) increase frep drastically with miniaturized and chip-scale microphotonic devices [9–11].
Stabilizing a widely mode-spaced optical frequency comb with the commonly used f-to-2f self-referencing scheme might be difficult. This is because the pulse energy is inversely proportional to frep, and, as a result, it becomes difficult to obtain a one-octave supercontinuum (SC) spectrum. For this reason, we focused on a 2f-to-3f self-referencing interferometer (SRI), in which 2/3-octave bandwidth of the SC spectrum is used. Such a high-order self-referencing scheme was actually demonstrated with the first self-referencing frequency comb described by J. Reichert et al [12], in which even higher order self-referencing, namely, 7f-to-8f (or 3.5f-to-4f), was used. Although such a high-order self-referencing scheme has been replaced by an f-to-2f self-referencing scheme because of progress in SC spectrum broadening, a high-order scheme is still important for stabilization of a frequency comb, for which it is difficult to obtain a one-octave SC spectrum with a highly nonlinear fiber (HNLF). The fCEO stabilization with a 2f-to-3f SRI has already been achieved with a mode-locked Ti:Sappahire laser [13, 14]. In addition, the construction of a 2f-to-3f SRI and related work with a 2f-to-3f SRI using a fiber laser have been reported [15–18]. However, stability comparable to an f-to-2f SRI [19] has not been obtained with a high-order SRI because the signal-to-noise ratio (SNR) of the heterodyne beat with a high-order SRI is not sufficient compared with that obtained with an f-to-2f SRI.
In this work, we stabilized fCEO of an Er-doped fiber laser with a phase-locked loop (PLL) circuit by implementing a 2f-to-3f SRI with a single-pitch (SP-) and dual-pitch (DP-) periodically poled lithium niobate (PPLN) ridge waveguide, as described below. The SP- (DP-) PPLN ridge waveguides are used to generate SH (TH) light with high efficiency – on the order of a few mill watts (about one hundred microwatts). By using these devices, we obtain a 45-dB SNR in 100-kHz bandwidth of a heterodyne beat signal and instability of the in-loop fCEO of 8 × 10−18 at 1 s of averaging time. The SNR of the heterodyne beat in our work is much larger than those obtained in previous works with a high-order SRI, and is comparable to conventional f-to-2f scheme. This result indicates that our 2f-to-3f SRI relaxes the requirement for the SC generation and will be an important technique for mode-locked lasers with higher repetition rate in the near feature.
2. Devices and the experimental setup
For the TH generation, we used 38 mm of the DP-PPLN ridge waveguide, which consists of two monolithically integrated segments with different quasi-phase matching (QPM) pitch sizes (Λ1 and Λ2) [Fig. 1(a)] [20, 21]. Efficient TH generation is achieved by confining the frequency comb with a ridge waveguide structure. In addition, a monolithic design free from optical coupling loss provides high conversion efficiency. Further advantages are discussed in [20], K. Hitachi et al. The TH light is generated as follows: First, the longer-wavelength component at around 1800 nm (f1) of the frequency comb is frequency-doubled (2f1) in the first segment with the pitch size of Λ1 (23.55 μm). Then, the sum frequency (f3) is generated in the second segment with Λ2 (10.51 μm), using the SH component at around 900 nm (2f1) and f1’, which is close to f1. Even though f1 ≠ f1’, a carrier-envelope offset frequency of f3 at around 600 nm is 3fCEO. For the SH generation, we used a SP-PPLN ridge waveguide with the pitch size of 9.55 μm, in which the quasi-phase was matched for SH light at around 1200-nm fundamental wavelength.
Fig. 1 (a) Schematic illustration of a DP-PPLN ridge waveguide for generating TH light. (b) Experimental setup for detecting and stabilizing fCEO with a 2f-to-3f SRI.
Figure 1(b) shows the experimental setup for detecting fCEO. We used a passively mode-locked Er-doped fiber laser system, which delivers 100-fs, 1.2-nJ laser pulses at a repetition rate of 250 MHz with a center wavelength of 1560 nm. The light is launched into the HNLF, in which more than 2/3-octave bandwidth of the SC spectrum is generated. Then, a dichroic mirror spectrally separates the frequency comb at 1500 nm and guides the short- (long-) wavelength component of frequency comb into the SP- (DP-) PPLN devices to produce the SH (TH) light at the wavelength of 600 nm. Finally, the two beams are superimposed by a polarization beam splitter and focused on an Si photodetector. The fCEO is observed when we inject the output of the photodetector with an RF spectrum analyzer. To increase SNR of a heterodyne beat signal, we adjusted the powers of SH and TH light with a half-wave plate, which is placed between a polarization beam splitter and the photodetector. From the CEO signal, the heterodyne beat note between the interference components yields a frequency difference fCEO. This is phase-locked to fCEO = 20 MHz using a PLL circuit, which is detected by the phase difference between the CEO beat and a local oscillator based on the GPS reference signal. Note that frep of the fiber laser is also phase-locked with a PLL circuit.
3. The SC spectrum and the SH (TH) light from SP- (DP-) PPLN devices
Figure 2(a) shows the SC spectrum (average power: 288 mW) from the HNLF measured with a spectrometer. The power of the frequency comb at 1200 (1800) nm, which is a fundamental wavelength of (the first part of a) quasi-phase matched SP- (DP-) PPLN device, is −9 (−9) dB from the maximum, respectively, which is enough for generating SH (TH) light with high power. It should be mentioned that the SC spectrum from an HNLF can be easily altered by adjusting the input power of the fiber laser. We adjusted the input power so as to maximize SNR of fCEO.
Fig. 2 (a) SC spectrum generated from the HNLF. (b) SH light generated from the SP-PPLN ridge waveguide. The observed peak at 605 nm (labeled with a triangle) satisfies the QPM condition. (c) Spectrum from the DP-PPLN device after bandpass filtering (center wavelength at 607 nm). Only TH light (at around 605 nm, labeled with a traingle) is transmitted through the filter. (Inset to b and c) The input power dependence of SH and TH light.
Figure 2(b) shows the visible spectral component generated inside the SP-PPLN ridge waveguide device with 9.55-μm-period QPM gratings. We observed SH light as the main peak at the wavelength of 605 nm (labeled with a triangle), which satisfies the QPM condition. We also observed several sub peaks at around 605 nm, which are irrelevant to the QPM condition. This structure appears when the input pulse energy is large, which is consistent with previous reports [16, 17]. Figure 2(c) shows the spectrum after the bandpass filter (center wavelength of 607 nm with 36-nm bandwidth) from the DP-PPLN ridge waveguide device with Λ1 = 23.55 and Λ2 = 10.51 μm-period QPM gratings. The spectrum of TH light at the wavelength of 605 nm (labeled with a triangle) is also observed from a DP-PPLN device. To confirm that the light from the SP- (DP-) PPLN device is really SH (TH) light generated from an original frequency comb, we investigated the power dependence of the visible light. As shown in the inset to Figs. 2(b) and (c), the light from the SP- (DP-) PPLN device has different slope with 2 (3) for P0 < 13 (75) mW. Note that the slope of SH and TH light is suppressed for higher input power of frequency comb, which is commonly observed for SH and TH generation.
For setting up a 2f-to-3f SRI, the SH and TH light should be spectrally overlapped. We can see that this condition is satisfied by comparing Figs. 2(b) and 2(c). The linewidth of the SH and TH light estimated with a high-resolution spectrometer is about 0.3 nm. In our experiment, we actually investigated the converted wavelength of the SH and TH light for several PPLN ridge waveguides with different QPM pitch sizes [20], and selected a pair of SP- and DP-PPLN devices so that both SH and TH light are spectrally well overlapped. To obtain the further spectral overlap, we also investigated the temperature dependence of the wavelength of the SH and TH light, and optimized the temperature of both devices. We found that the wavelength increases 1 nm as the temperature increases 20 deg. The temperature controller is also important for stabilizing the spectrum from the SH and TH light, because, without it, the heat from the input frequency comb would significantly increase the temperature of both devices. Here, we adjusted the temperature of the SP- (DP-) PPLN device to be 30 (33) deg.
The most important point for utilizing the SP- (DP-) PPLN device is the ability to generate high average power of SH (TH) light. When the input power is 288 mW [Fig. 2(a)], the output power of SH (TH) light is 4.6 mW (115 μW), which is large enough to observe fCEO with a 2f-to-3f SRI. Note that in our previous report, in which we employed a 10-m-long-HNLF fiber for generating a SC spectrum, the output power of SH (TH) light was only 9.1 (4.8) μW [20]. Such a difference can be explained by the input peak power of the frequency comb: The longer the HNLF, the longer the pulse duration becomes due to the increment in the group delay of the frequency comb after the light is transmitted from the HNLF.
4. Stabilization of CEO signal
Now, we turn our attention to the heterodyne beat note and the stability of the CEO signal fed by the PLL circuit. For detecting fCEO, the two beams should be spectrally, spatially, and temporally overlapped. The spectral overlap is obtained by selecting an appropriate pair of SP- and DP-PPLN ridge waveguides and optimizing their temperature as discussed above, while the spatial overlap is attained by carefully tilting the angle of the mirrors so that the two beams are collinearly aligned before the light is injected into the photodetector. For the temporal overlap, we utilized the delay line in the Mach-Zehnder interferometer [Fig. 1(b)]. It is also important to decrease the broadband noise irrelevant to the detection of fCEO by utilizing a bandpass filter at the wavelength of 607 nm with 36-nm bandwidth, which is placed after DP-PPLN ridge waveguides [Fig. 1(b)]. This filter blocks the SH light at around 900 nm (not shown) from the DP-PPLN device. Note that it is not necessary to remove the original frequency comb from the SP- and DP-PPLN device, because an Si photodetector has almost no sensitivity above the wavelength of 1000 nm, and the contribution of broadband noise is weak.
Figure 3(a) shows the beat signal detected with a RF spectrum analyzer. We observed fCEO at 20 MHz with 45-dB SNR at 100-kHz bandwidth, which is enough for stabilizing fCEO as described below. The 10-kHz bandwidth of fCEO is shown in Fig. 3(b). The full width half maximum linewidth of the beat signal is about 100 kHz, which is comparable to our developed frequency stabilized f-to-2f SRI [22]. The beat signal is then phase locked, as shown in Fig. 1(b), by feedback to a photo-excited current fed from the pump laser diode. We estimated the instability of the locked fCEO with a frequency counter (Agilent 53230A), in which fCEO at n-th point, fCEOn is defined as follows:
where τ is the averaging time in the frequency counter. This counter provides overlapped Allan deviation. We used the “RCON” mode in this counter, which gives continuous gap-free measurements by means of a reciprocal counting method. In this mode, the counter functions are π type. Figure 4(a) shows the counted fCEO as a function of time with τ = 1 s. Indeed, during the period of more than 1 h, there is no significant jump of fCEO in the frequency domain. The standard deviation of fCEO is 1 mHz.Fig. 3 (a) RF signal from a heterodyne beat note observed with a spectrum analyzer at a 100-kHz bandwidth. The SNR of fCEO at 20 MHz is 45-dB at 100 kHz bandwidth. (b) Detailed observation of the beat signal with a 10-kHz bandwidth at around fCEO equal to 20 MHz.
Fig. 4 (a) Real-time observation of an output from a frequency counter at a 1-s gate time for a fCEO. (b) The measured Allan deviation for various gate time τ.
The instability of a CEO frequency is estimated in terms of the Allan deviation σ(τ), for each value of τ, which was measured with the frequency counter. To calculate the Allan deviation, we assumed the telecommunications wavelength. The result is shown in Fig. 4(b). For example, the Allan deviation at τ = 1 s is as low as σ = 8 × 10−18, which is comparable to the instability obtained with a conventional f-to-2f SRI. Compared with the result in previous 2f-to-3f SRIs [14, 18], in which Ti:sapphire laser and a fiber laser were stabilized, respectively, the Allan deviation in our device is more than three orders of magnitude smaller. These results indicate that fiber-laser-based fCEO stabilization becomes possible with our 2f-to-3f SRI. This is an important technique for fCEO stabilization of a frequency comb, for which it is difficult to obtain a one-octave SC spectrum with an HNLF, i.e., a high-repetition rate frequency comb.
We attribute such a stability of fCEO with a 2f-to-3f SRI to the SNR of the heterodyne signal. The SNR of a heterodyne signal (45 dB) is much higher than in previous reports: 20-dB SNR for a Ti:sapphire laser [14] and 25-dB SNR for a fiber laser [18]. Furthermore, the SNR of fCEO in our data is comparable to that obtained with an f-to-2f SRI [19]. The reason for such a SNR of fCEO is the high power of TH light, as described before. Note that in [17], C. Langrock et al, the SNR of fCEO is more than 30 dB with a 2f-to-3f SRI, which is possible for stabilizing fCEO. However, the SNR of our beat signal is higher due to the optimization of the QPM pitch conditions for generating SH and TH lights.
5. Conclusion
In conclusion, we have demonstrated fCEO stabilization with a 2f-to-3f SRI using SP- and DP-PPLN ridge waveguides. The monolithic design of the DP-PPLN ridge waveguide allows us to generate TH light with high power. By using the SP- and DP-PPLN ridge waveguides, we generated a SNR of the heterodyne beat (45 dB) and stabilized fCEO (the in-loop fCEO is σ = 8 × 10−18 at 1 s of averaging time). This approach is important for fCEO stabilization of a frequency comb for which it is difficult to obtain a one-octave SC spectrum with an HNLF.
Acknowledgment
We thank H. Gotoh and H. Mashiko for helpful discussions. This work was supported by JSPS KAKENHI Grant Number 24360143.
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