Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser

Atsushi Ishizawa; Tadashi Nishikawa; Akira Mizutori; Hidehiko Takara; Atsushi Takada; Tetsuomi Sogawa; Masafumi Koga

doi:10.1364/OE.21.029186

1. Introduction

In the last decade, carrier-envelope offset (CEO)-locked optical frequency combs (OFCs) have revolutionized precise optical frequency measurements by making it possible to directly link between microwave and optical frequencies. Nowadays, the CEO-locked OFC has become an indispensable tool in a variety of applications, ranging from optical frequency metrology [1] and optical clocks [2] to attosecond science [3]. A CEO-locked OFC with wide mode spacing is of interest for applications such as calibration standards for astronomical spectrographs [4] and direct frequency-comb spectroscopy [5]. These applications all benefit from the feature of a stable OFC with wide mode spacing, which provides easy access to individual modes and high-power modes. A wide mode OFC would also be very attractive for future photonic networks because it can provide absolute frequency references in optical fiber communications and a standardized optical frequency grid with 12.5-GHz spacing or wider. Recent research and development of fiber transmission technology has shifted from intensity modulation, such as on-off keying, to phase/multilevel modulation, such as phase-shift keying and quadrature amplitude modulation, which requires an optical carrier light source with high coherency and high frequency stability. A CEO-locked OFC will not always be required in such optical communications applications. However, a frequency stabilized light reference will be required for optical communications in the future and the CEO-locked OFC will be beneficial for it. Thanks to the contribution of high-speed digital signal processing (DSP), coherent communications have revived, and dramatic increases in spectral efficiency (SE) and transmission capacity have been reported in the last decade. Recent records are 1 Peta bit/s per fiber and over 10 bit/s/Hz. DSP-based schemes can now realize rectangular Nyquist filters for achieving higher SE. The frequencies of light sources should be stabilized so that the wavelength-division multiplexing is dense enough to match the Nyquist filter. For this purpose, some OFC references will be beneficial and we have proposed the concept of “optical frequency synchronized networks” [6].

In optical communications, the optical carrier light sources are assigned to a frequency grid, which has been standardized in the ITU-grid as integer multiples of 12.5-, 25-, 50-, and 100-GHz at the anchor frequency of 193.1 THz. Therefore, we are trying to achieve a CEO-locked OFC with 25-GHz mode spacing [7]. The conventional method for achieving a CEO-locked OFC is based on a mode-locking technique. The mode spacing of the current CEO-locked OFC is still too narrow to be spectrally resolved in a simple manner and is thus not accessible for individual comb modes. At wavelength of 800 nm, a CEO-locked OFC with 10-GHz mode spacing has been achieved by using a mode-locked Ti:sapphire laser [8]. However, at present, the widest mode spacing of a CEO-locked OFC in the 1.5-μm band is 300 MHz [9]. The problem is that the laser pulse energy becomes lower as the repetition rate increases. Sources with more than 10-GHz repetition rates typically have relatively long pulse durations and reduced pulse energy, which makes it difficult to generate octave-spanning supercontinuum (SC) spectra as required for the detection of the CEO frequency.

To overcome the above problems with the mode-locked laser, we tried to reduce the required laser pulse energy for the CEO-locking [10] and then created short optical pulses at 25-GHz repetition rate with phase/intensity-modulated lasers instead of the mode-locking technique [11–15]. Using the short optical pulse, we demonstrated the generation of one-octave-wide SC spectra, which is needed for CEO locking in an f-to-2f self-referencing interferometer (SRI) [7]. Since the coherence of each comb with the phase/intensity-modulated laser is sensitive to the phase noise of an external RF synthesizer driving the optical modulators, the coherence of each comb mode in the shorter- and longer-wavelength regions of the SC light is assumed to deteriorate. The phase noise of the OFC and the SC light generated with the phase/intensity-modulated laser has not been experimentally investigated yet. Note that the phase-noise characteristics of the SC light hold extremely important clues to CEO frequency detection in an f-to-2f SRI or 2f-to-3f SRI.

In this paper, we report the first demonstration of the measurement of phase-noise characteristics of both the 25-GHz-spaced frequency comb and SC light with a phase/intensity-modulated laser. As the frequency separation from the frequency of the continuous wave (CW) laser diode (LD) for the seed light source increases, the integrated phase noise of each comb mode of both the phase/intensity-modulated laser and the SC light generated by it increase with the same slope as a function of the mode number. The dependence of the integrated phase noise on mode number with the mode-locked fiber laser of the CEO locking is much smaller than with the phase/intensity-modulated laser. However, we found the integrated phase noise of the latter is extremely lower than that of the former in the frequency region around the CW LD. Therefore, the integrated phase noise of the phase/intensity-modulated laser could be estimated and was found to be comparable to that of the mode-locked fiber laser with the CEO locking even at the wavelengths required in the f-to-2f SRI and smaller than it at the wavelengths required in the 2f-to-3f SRI. Our experimental results show the possibility of achieving an offset-frequency-locked frequency comb with the phase/intensity-modulated laser.

2. Phase-noise characteristics of 25-GHz-spaced optical frequency combs with a phase-and intensity-modulated laser

The phase/intensity-modulated laser generates short optical pulses with sinusoidal electro-optic phase/intensity modulation as well as linear chirp compensation in a dispersive medium [see Fig. 1(a)]. When a CW LD is phase/intensity-modulated by a sinusoidal signal of frequency f_m, the k^th optical field of the OFC is expressed as [16]

E_{k} (t) = E_{0} \sum_{n = - \infty}^{\infty} [J_{n} (m_{I M}) J_{k - n} (m_{P M}) \times \exp {- i (2 π f_{s} t + k (2 π f_{m} t - Ψ (t)) - ϕ_{k})}],

where E₀ and f_s are the optical field amplitude and the frequency of the mode number of the 25-GHz-spaced OFC, respectively, J_n is a Bessel function of the first kind, and m_IM and m_PM are modulation indexes in intensity and phase modulation, respectively. The mode number k (k = 0, ± 1, ± 2,‥‥) is defined as the number of comb modes from the center frequency (mode number 0) of 193.1 THz (1552.52 nm). The plus and minus signs indicate higher and lower frequency, respectively. The phase ϕ_k is the initial phase of the light source. The summation of n represents the convolution of intensity-modulator components for all sidebands created by a phase modulator (PM); n is an integer. An RF synthesizer for f_m generally has phase noise denoted as Ψ. Therefore, the instantaneous phase θ_k and the instantaneous frequency f_k of the k^th optical field of the OFC are respectively expressed as

θ_{k} = 2 π f_{s} t + k (2 π f_{m} t - Ψ (t)) - ϕ_{k}

and

f_{k} = \frac{1}{2 π} \frac{d θ_{k}}{d t} = f_{s} + k (f_{m} - \frac{1}{2 π} \frac{d Ψ (t)}{d t}) .

The linewidth difference Δf_k between the zeroth mode and the k_th mode is expressed as

Fig. 1 (a) Experimental setup for measuring the phase-noise characteristics of an optical frequency comb with 25-GHz mode spacing. LD: laser diode. SMF: single-mode fiber. OC: optical coupler. PD: photodetector. (b) Experimental and (c) calculated optical spectrum of an optical frequency comb with 25-GHz mode spacing. (d) Phase-noise characteristic of eternal RF synthesizer C.

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Δ f_{k} = | f_{k} - (f_{s} + k \cdot f_{m}) | = \frac{1}{2 π} | \frac{d Ψ (t)}{d t} | \cdot k .

Equation (4) indicates that the phase noise of the phase/intensity-modulated laser shows a linear increase with the mode number and that the slope corresponds to the amount of the phase noise in the external RF synthesizer.

Figure 1(a) shows our experimental setup. Our laser system generates a 25-GHz pulse train. The phase and intensity of the light from a CW LD with a center wavelength of 1552.52 nm and a linewidth of 800 Hz are modulated with three conventional PMs driven by a sinusoidal-RF signal from an external RF synthesizer at a modulation frequency fmod of 25 GHz. Since the drift of the CW LD obscures the phase-noise measurement, the center frequency of the CW LD is stabilized by using a CEO-locked OFC based on an Er-doped fiber laser with repetition-rate locking as an optical frequency standard. The external synthesizer is synchronized with a reference signal from a global positioning system (GPS) receiver whose stability is 5 × 10⁻¹³ in 1 s (model K + K GPS6 by Menlo Systems GmbH). The applied modulation index obtained with the PMs is 17 π. The Vpi of the PMs at 25 GHz is 2.5-4.6 V. The RF power of 32-35 dBm is applied to each PM. 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) [11, 12], resulting in a flat OFC with a 20-nm bandwidth [Fig. 1(b)]. Our experimental setup yields 100 light carriers with 25-GHz mode spacing. The IM is placed in front of the PMs because the bandwidth of the IM is limited. Figures 1(b) and 1(c) show experimental and calculated results for the optical spectrum of the 25-GHz-spaced OFC, respectively. To confirm the validity of our experimental results, we calculated the optical spectrum of the 25-GHz pulse train obtained with our scheme using a VPI transmission Maker^TM simulation code. The calculation result in Fig. 1(c) is consistent with the experimental result in Fig. 1(b). In these experiments, we compared the phase-noise characteristics of the OFC using three kinds of external RF synthesizers (A, B, C). Each synthesizer has different phase-noise characteristics. The phase-noise characteristics of external RF synthesizer C is shown in Fig. 1(d). For the measurement of the phase-noise characteristics of each comb mode, we need a tunable laser with a narrow linewidth and high stability. We carefully performed the phase-noise characterization using the interference signal between each comb mode in the 25-GHz spaced OFC and a tunable laser with a 16-kHz linewidth. The photodiode mixes the optical fields of the two lasers to produce an electrical RF tone at the frequency difference between the two optical frequencies. The measurement of the phase-noise characteristics was performed with a signal source analyzer with a low noise floor and a cross-correlation method (E5052B, Agilent).

Figures 2(a) and 2(b) show the beat note in the third mode and 38th mode of spectral lines generated by the CW LD, respectively, obtained by the 25-GHz-spaced OFC and the tunable laser when we used external RF synthesizer A. The linewidth of the beat note provides the phase-noise characteristics with the phase/intensity-modulated laser. The optical frequency of the tunable laser is not stabilized at the setup frequency and drifts slowly. Therefore, the optical linewidth of the beat note is overestimated. The linewidth of the beat note in the 38th mode of the spectral lines becomes wider than in the third mode. This linewidth difference indicates that the phase-noise characteristics are different for each mode of the 25-GHz spaced OFC.

Fig. 2 (a) The beat note obtained by third mode of the spectral lines generated from the CW LD and a tunable laser. (b) The beat note obtained by the 38th mode of the spectral lines and the tunable laser.

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Figure 3(a) shows the phase-noise characteristics of the interference signal in the zeroth, 2nd, 9th, 29th, and 41st mode obtained by the 25-GHz-spaced OFC and a tunable laser. Here, the phase-noise characteristics were measured with external RF synthesizer B. In our experimental setup, it is impossible to distinguish between the intensity and phase contribution, but the phase noise is probably the dominant contribution. This result means that the interference signal between the CW LD and the tunable laser already has such phase-noise characteristics since the phase noise in the zeroth mode of the 25-GHz-spaced OFCs is the same as that of interference signal between the CW LD and the tunable laser. Notice the inset, which shows that the amplitude of the phase noise increases with increasing mode number at the offset frequency of more than 1 MHz. Since the optical frequency of the tunable laser is not stabilized and drifts slowly, the phase noise cannot be measured at the offset frequency of less than 1 MHz. These results suggest the phase noise in the OFC is multiplied by factor k as shown in Eqs. (1)–(4). We evaluate the integrated phase noise at the offset frequency of more than 1 MHz as follows:

Integrated phase noise = \frac{1}{2 π f_{c}} \sqrt{2 \int_{t_{1} = 1 M H z}^{t_{2} = 40 M H z} 10^{\frac{L (f)}{10}} d f,}

where f_c is the center frequency and L(f) is the phase-noise spectrum. Figure 3(b) shows the dependence of the integrated phase noise on the mode number, measured by using the three external RF synthesizers. The integrated phase noise shows a linear increase with mode number. We investigated the dependence of the phase-noise characteristics of the 25-GHz-spaced OFC on the mode number and the external RF synthesizer. The phase noise is largest for external RF synthesizer A, followed by B and C. The slope corresponds to the amount of phase noise Ψ(t) of the external RF synthesizer in Eq. (1). The integrated phase noise of the RF output signal at 25 GHz measured using external RF synthesizers A and C are 4.5 and 2.5 fs, respectively, at the offset frequencies from 1 to 40 MHz. The integerated noise of the y-intercept in Fig. 3(b) indicates a fluctuation of the tunable laser for the probe laser beam. These results indicate that the amplitude of the phase noise of the external RF synthesizer influences the phase-noise characteristics of the 25-GHz-spaced OFC.

Fig. 3 (a) Phase-noise characteristics when using external RF synthesizer B. The inset shows the phase-noise characteristics at the offset frequency of more than 1 MHz. (b) Dependence of integrated phase noise on the external RF synthesizer.

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3. Phase-noise characteristics of SC light generated by the phase- and intensity-modulated laser

Figure 4(a) shows our experimental setup for measuring the phase-noise characteristics of SC light generated by the phase/intensity-modulated laser. We used external RF synthesizer C. To generate SC light, we need higher pulse energy in our laser system. Since the average output power of the erbium-doped fiber amplifier (EDFA) is limited, we employed an optical gate to increase the peak intensity of the amplified pulse. The gate frequency is set to 12.5 GHz in order to detect higher signal-to-noise ratio of the interference signal between each comb mode and the tunable laser. The optical gate plays an important role in selectively picking up one optical pulse from the 25-GHz pulse train and suppressing the amplified spontaneous emission component. The IM with the extinction ratio of 35 dB operates as the optical gate by applying RF impulse signals, which are generated by using a comb generator driven by a sinusoidal-RF signal from the RF external synthesizer. After the optical gate, which reduces the repetition rate from 25 to 12.5 GHz, the optical pulse train is amplified to an average power of 1 W by the EDFA. 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. The pulse width before the SC generation is successfully compressed to 211 fs (assuming a Lorentzian pulse shape), while the transform limit of the pulse is 187 fs. We use 1-m-long highly nonlinear fiber (HNLF) for generating SC light. Finally, the amplified pulse is launched into HNLF and the SC light is generated in the range from 1350 to 1700 nm [Fig. 4(b)]. The zero dispersion wavelength of the HNLF is 1458 nm. The mode field diameter of the HNLF at 1550 nm is 3.8 μm. The dispersion slope at 1550 nm is 0.03 ps/nm²/km. Figure 5(a) shows the phase-noise characteristics of frequency combs before and after the SC generation. It is found that the slopes of the integrated phase noise before and after the SC light are the same in the region of low mode number. The values of the slope before and after the SC generation are 0.59 ± 0.06- and 0.62 ± 0.07 ps, respectively, when we fit a linear function. The errors in these slopes are standard deviations. Figure 5(b) shows the phase-noise characteristics in the zeroth mode of the OFCs before and after the SC generation. The zero-dispersion wavelength of the HNLF is 1485 nm. It is considered that the difference in the y-intercept before and after the SC generation indicates the Gordon-Mollenaour effect due to self-phase modulation [17] and phase-noise generation in the HNLF due to the SC generation in the anomalous dispersion region. If the SC light had generated in the normal dispersion region, the amount of the phase noise would have been lower. As a result, the difference of the y-intercept before and after the SC generation in Fig. 5(a) would become smaller. The degradation of the phase noise for the high-frequency component becomes larger as the mode number increases. It is found from the result in Fig. 5(a) that the phase-noise characteristics of the SC light take over those of the phase/intensity-modulated laser and the influence of the external RF synthesizer on the phase noise of the SC light is the same as on that of the phase/ intensity-modulated laser.

Fig. 4 (a) Experimental setup for measuring the phase-noise characteristics of supercontinuum (SC) light generated by the 25-GHz-spaced OFC. LD: laser diode. SMF: single-mode fiber. EDFA: erbium-doped fiber amplifier. HNLF: highly nonlinear fiber. OC: optical coupler. PD: photodetector. (b) Spectrum before (red) and after (blue) the SC generation.

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Fig. 5 (a) Dependence of the integrated phase noise on mode number with the SC light generated by the phase/intensity-modulated laser. (b) Phase-noise characteristics in the zeroth mode before and after the SC generation and in the 114th and 139th mode after the SC generation. (c) Dependence of the integrated noise on mode number with the carrier-envelope-offset (CEO)-locked fiber laser. (d) Speculated the integrated noise with the phase/intensity-modulated laser and the CEO-locked fiber laser at the wavelength (mode number: 3277 and 2269) for measuring the CEO frequency signal in the f-to-2f self-referencing interferometer (SRI) and the 2f-to-3f SRI.

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Next, we investigated the phase-noise characteristics of the fiber laser in order to compare them with those of the phase/intensity-modulated laser. We used a passively mode-locked Er-fiber laser amplifier system. The amplifier laser delivers a 100-fs, 1-nJ laser pulse with a center wavelength of 1560 nm in the spectral range from 1450 to 1600 nm. The repetition frequency of the fiber laser system was controlled to be 250 MHz by using the GPS reference signal. The CEO frequency was measured with the f-to-2f SRI and locked by a feedback circuit. Figure 5(c) shows that the increase of the integrated phase noise with the fiber laser is smaller than with the phase/intensity-modulated laser. The y-intercept of the integrated phase noise with the CEO-locked fiber laser in Fig. 5(c) is higher than with the phase/intensity-modulated laser at wavelengths around the center frequency of the CW LD. As shown in Fig. 5(a), the integrated phase noise of the phase/intensity-modulated laser increases lineally with mode number. The CEO frequency will be obtained at the wavelength of 1090 nm in the f-to-2f SRI and of 1200 nm in the 2f-to-3f SRI. From these results in Figs. 5(a) and 5(c), we should be able to roughly estimate the value of the integrated phase noise at 1090 and 1200 nm. The wavelengths of 1090 and 1200 nm correspond to the 3277th and 2269th modes, respectively. Since the CEO frequency of this fiber laser can be locked by using an f-to-2f SRI, this integrated phase noise value of around 1.6 ns does not interrupt the CEO locking although the spectral broadening process may introduce additional phase noise through nonlinear optical mechanisms. The integrated phase noise at the wavelengths of 1090 and 1200 nm with the phase/intensity-modulated laser is estimated to be around 2 and 1.5 ns, respectively [Fig. 5(d)]. We observe the CEO frequency signal with about a 30-dB signal-to-noise ratio with an RF spectrum analyzer set to 100-kHz resolution bandwidth by using the mode-locked fiber laser. From the above results, we conclude that the measurement of the CEO frequency could be possible by using the phase/intensity-modulated laser.

4. Conclusion

We have experimentally demonstrated the measurement of the phase-noise characteristics in each comb mode of a 25-GHz-spaced OFC based on a phase/intensity-modulated laser. The integrated phase noise was found to linearly increase as the mode number increases. We could understand that the integrated phase noise of the external RF synthesizer, which operates the phase modulator, influences the integrated phase noise of the 25-GHz-spaced OFC. We also found that the phase noise of the SC light generated by the phase/intensity-modulated laser is mostly influenced by the external RF synthesizer used to drive the phase/intensity-modulator. On the other hand, the increase of the integrated phase noise with the fiber laser is small. The integrated phase noise of the phase/intensity-modulated laser at near the wavelength of the seed light source is extremely lower than that of the fiber laser. Therefore, even if the integrated phase noise of the SC light generated by the phase/intensity-modulated laser increases with mode number, the integrated phase noise of the phase/intensity-modulated laser at the wavelength required for the CEO locking is estimated to be the same order as that of the mode-locked fiber laser. Considering these results, we expect to be able to obtain the CEO-frequency using the phase/intensity-modulated laser.

Acknowledgments

We thank H. Gotoh for helpful discussions. This work was supported by JSPS KAKENHI Grant Numbers 23360173 and 24360143.

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Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser

Abstract

1. Introduction

2. Phase-noise characteristics of 25-GHz-spaced optical frequency combs with a phase-and intensity-modulated laser

3. Phase-noise characteristics of SC light generated by the phase- and intensity-modulated laser

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (5)

Optics Express