1. Introduction

With numerous stable orthogonal frequency components in spectral domain, the femtosecond optical frequency comb exhibits some unique advantages in the fields of spectroscopy [1–3], microwave generation [4], distance metrology [5–7], and optical communication [8]. To apply the optical frequency combs as well as the relative techniques outside the lab, even in the space [9, 10], several kinds of techniques have been developed.

Soon after the first demonstration of Ti: Sapphire-based frequency combs [11, 12], frequency comb obtains vast attention and developed fast. Giga-hertz repetition frequency [13] and sub-radian stability of f_CEO (carrier envelop offset frequency) are already achieved [14]. Further, the environmentally robust frequency comb has been discussed and researched by several groups [15–17]. The fiber-based frequency comb, which is based on fiber-based femtosecond oscillator and amplifier, exhibits better mechanical stability and thus becomes the common choice. KAIST demonstrated that the femtosecond fiber laser can overcome radiation induced attenuation in satellite operation [9]. Menlo Systems has also built a fiber-based frequency combs which can operate in outer space [10]. The problem of polarization wander has also been solved by adopting the polarization-maintaining (PM) fiber-based structure, which is firstly proposed by the team of N. R. Newbury. For example, the forced-vibration induced instability is decreased via introducing PM fiber-based oscillator [18]. Moreover, polarization wander is solved completely by further incorporating the PM highly nonlinear fiber (HNLF) [19].

However, the additional phase noise induced by severe acoustic interruption is still an urgent matter. Technically, how to measure the resonant frequencies of the oscillator in order to facilitate the design of the isolation system has not been solved yet. In addition, as is well known, fiber-based frequency comb is vulnerable to ambient temperature fluctuation. Then, for engineering application purpose, the influence of temperature fluctuation has also to be minimized.

In this contribution, we would like to fill this gap. With an all PM fiber-based frequency comb, we have studied its environmental stabilities in more detailed. Firstly, the measurement of resonant frequencies of the system has been demonstrated. We find that the comb system is only vulnerable to the high frequency acoustic wave (>350 Hz). So we propose that acoustic-vibration induced phase noise should be eliminated by a low pass vibration-isolation structure. Secondly, we demonstrate the existence of the optimum working temperature (289.6 K). At this temperature, the noise performance and the thermal stability reach the best levels. In addition, through a 240-day-long record of the f_CEO, we prove that the all PM fiber-based frequency comb is stable under different humidity (18% ~80%).

2. Comb design

As shown in Fig. 1, the comb system includes a femtosecond PM-Erbium-fiber oscillator, a PM fiber-based amplifier, a direct digital synthesizer (DDS), an f_CEO detector, a high speed field-programmable gate array (FPGA), and a temperature controller.

 

Fig. 1 Comb design. (a) Comb structure: red line stands for PM fiber, and black line for electrical signal path. ISO: isolator, WDM: wavelength-division multiplexer, PD: photo detector, EDF: erbium doped fiber. The three insets are the spectrum of the super continuum generated by HNLF (I), the optical spectrum (II) and the autocorrelation trace (III) of the comb. The temperatures of the SESAM and the oscillator are controlled together with a single temperature controller. The blue dot besides the SESAM is the temperature detection point. (b) The spectrum (I) and the autocorrelation trace (II) of the mode-locked pulse. (c) The rf power spectrum of the free running f_CEO in loop.

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As shown in the blue circle of Fig. 1(a), the oscillator, mode locked by semiconductor saturable absorber mirror (SESAM), operates at the stretched pulse region. The SESAM (Batop GmbH), with a saturable loss of 34% and a modulation depth of 18%, is placed in a temperature controlled copper room. A piece of 1.55-m Erbium-doped PM fiber with normal dispersion (OFS EDF-PM, D = −27.99 ps/nm/km) acts as the gain media. The other fiber in the oscillator is standard PANDA fiber (Fujikura SM15-PS-U25A) with a total length of ~2.56 m. The total cavity dispersion is evaluated as about −0.01 ps². An intra-cavity delay line (General Photonics MDL-002-O-15-56-NC-PP, 0 ~500 ps) is applied to make the repetition frequency of the oscillator (f_r) tunable in the range of 49.5 ~50.5 MHz. The spectral width, pulse duration, single pulse energy, and average output energy of the output pulse respectively are 17 nm, 170 fs, 6.6 pJ, and 330 μW, as shown in Fig. 1(b). The final output pulse energy is amplified to 2.2 nJ (with a pulse duration of 300 fs and an average output power of 200 mW) via a two-stage amplifier (built with OFS, EDF-PM fiber).

The DDS, working as a frequency reference, consists of an ultra-low noise oven controlled crystal oscillator (OCXO, MITECH, 10060HP-5V) and two voltage controlled oscillators (VCO’s, HITTITE, HMC830). The OCXO is cheaper, smaller and more stable (in short term) than atom clock. After synchronized to the global navigation satellite system (GNSS), its long term stability is the same to the atom clock. The two VCO’s are both referenced to the OCXO. One VCO outputs 800-MHz sinusoidal signal, and is compared with the 16th harmonic of the f_r (which is detected by a 2.5-GHz photo detector). The other one works at 8 MHz and is adopted as the reference of the f_CEO.

The FPGA includes two controllers (1 and 2) for stabilizing f_r and f_CEO, respectively. As to Controller-1, when the signal (16th harmonic of the f_r) arrives, a fast piezoelectric ceramic transducer (PZT, Thorlabs, AE0203D08F, with a maximum displacement of 9.1 μm) and a slow PZT (Pantpiezo, PTJ2001414401, with a maximum displacement of 89.6 μm) are driven to compensate the cavity length variation. When the driving voltage of the slow PZT is moving out the range of 0~150 V, the optical delay line will be driven with an accuracy of 18 μm/step to compensate the cavity length. Under the governing of Controller-1, phase locking could be achieved, and the standard deviation of the f_r is smaller than 100 μHz. A nanometer-level cavity control precision is thus obtained.

To detect the f_CEO signal, as shown in Fig. 1(a), the feedback pulse duration is firstly compressed to 100 fs by a piece of single mode PANDA fiber (Fujikura SM15-PS-U25A). Then, the compressed pulse is injected into a 65-cm-long PM HNLF (OFS, PM-HNLF) to generate super continuum (SC, with a wavelength spans from 1000 to 2100 nm). Next, the f_CEO signal with a signal-to-noise ratio (SNR) of 33.5 dB, which is measured with a resolution bandwidth of 100 kHz and an average time of 5, is obtained by an f-to-2f interferometer [20, 21]. Meanwhile, the f_CEO signal exhibits a Lorentzian shape with a free-running linewidth of 150 kHz (Fig. 1(c)). Finally, the phase noise of the f_CEO is reduced by Controller-2 through modulating the pump power of the oscillator.

As for the f-to-2f interferometer, it includes a detachable pigtailed fiber collimator, a periodically-poled lithium niobate crystal (PPLN, HCP-custom) [22, 23], and a 10-nm bandpass filter (@1030 nm). When the SC signal is focused into the PPLN by the collimator, the 2060-nm spectral component is frequency doubled through the second harmonic generation process. As a result, a new light component around 1030 nm is generated. After the bandpass filter, two spectral components (the 1030 nm component of the SC and the newly generated component around 1030 nm) are kept. Finally, the beat signal named f_CEO is detected by a 2.5-GHz PIN photodetector. Moreover, to make the comb system more compact, the f-to-2f interferometer has been housed in an aluminum box with a fiber pigtail.

In addition, the SNR of the f_CEO signal is very sensitive to the amplified pulse energy, so, in order to prevent the pump power drifting away from its set point after long term operation, automatic gain control (AGC) circuits have been integrated into the 980-nm-LD drives to regulate the pump power.

3. Stability performance and optimization

3.1 Stabilization of the comb

Figure 2 shows a 10,000-second-long stabilization record of f_r (a-I) and f_CEO (b), the standard deviations of the f_r and f_CEO signals are measured after the optical amplifier and CEO detector respectively. The standard deviations with 1s gate time are 91.7 μHz and 2.5 mHz respectively, corresponding to a static uncertainty of about 350 Hz in the optical frequency domain (((91.5 × 10⁻⁶ × 3.85 × 10⁶)² + (2.5 × 10⁻³)²)^1/2 ≈350 Hz). The values of integrated phase noise (IPN, from out-of-loop errors) are 36.1 μrad and 3.14 rad respectively (The integrated window is shown in Fig. 3(b) and 3(c)). As Fig. 2(a-II) shows, a glitch occurs at 9243s when the slow PZT has arrived at its maximum range and the delay line is triggered to compensate the cavity length variation. In Fig. 2(a-II), it can be clearly seen that, after a one-second-long relaxation, the f_r signal can still return to the phase-locked state, while the f_CEO stability is almost not affected during this relaxation process, as shown in Fig. 2(b).

 

Fig. 2 Deviation of counted phase-locked f_r (σ_r) and f_CEO (σ_CEO) for a total lasting time of 10,000 second. (a-I) Counted f_r. (a-II): Relaxation process of the f_r when the optical delay line moves. (b) Counted f_CEO.

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Fig. 3 Acoustic impulse response test. (a) Waveform (I) and spectrogram (II) of the acoustic impulses. (b) Phase spectral density and IPN of f_r for the static (red and orange) and vibrated states (blue and violet). (S_φr(f_φ) stands for phase spectral density, when the density is small, S_φr(f_φ) [dBrad²/Hz] ≈(L_r(f) + 3) [dBc/Hz]. L_r(f) is the single sideband spectrum. The L_r(f) is measured by R&S FSUP 26 Signal Source Analyzer.) (c) Phase spectral density and IPN of f_CEO for the static (red and orange) and vibrated states (blue and violet). The phase deviation is measured by HF2LI Lock-in Amplifier - Zurich Instruments, and then converted to phase spectral density by Fourier transform.

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3.2 Acoustic resonant frequencies of the system I: Impulse response test

The optical delay line as well as other fiber components inevitably suffers from the acousticnoiseof environment. To quantify its impulse response to the acoustic vibration, we measure the phase spectral density of the f_r and f_CEO when the oscillator of the comb is vibrated.

At first, the oscillator has been sealed in an aluminum box with every component fixed. Then the oscillator is shaken by periodically acoustic impulse train and the corresponding temporal waveform is shown in Fig. 3(a-I). The repetition frequency is 5 Hz and the peak acceleration is 1.45 g (gravity acceleration). Correspondingly, this periodical signal possesses a comb-shaped spectrum spanning from 5 Hz ~1.2 kHz with spacing of 5 Hz. The spectrogram is shown in Fig. 3(a-II).

The acoustic impulse is originally synthesized by software. It is then converted into a voltage signal by a digital analog converter to drive PZT’s and generate theacoustic impulse. Finally, the impulse is conducted into the oscillator cavity by the aluminum box. (No cushion material has been used.)

Figure 3(b) shows the acoustic impulse response of the f_r at phase-locked state. When the oscillator keeps static, the phase spectra density (S_φr) curve (red curve) drops nearly proportional to 1/f ² as the offset frequency increases. The IPN is 36.1 μrad (orange curve). On the contrary, the phase noise around 1 kHz swoops up to −105 dBc (as the blue curve shows) and the IPN increases to 75.7 μrad (as the violate curve shows) under acoustic impulse. Obviously, the phase of the f_r signal is modulated by multiple frequencies resulted from the modulation of the cavity length. Explicitly, when the acoustic impulse arrives at the oscillator, optical components inevitably vibrate with the resonant frequencies of themselves and thus the cavity length is modulated. Therefore, the modulation frequencies are in accordance with the resonant frequencies of the components.

Different from the situation of f_r, the f_CEO signal is found almost immune to the vibration, and the degradation of the measured phase noise is not apparent to unaided eye, as Fig. 3(c) shows. When f_CEO signal is locked, both at static (red) and vibrated (blue) state, the two phase spectral density increase slightly and smoothly with offset frequency to around 75 kHz, and then drop with a manner similar to that of 1/f ² noise. The IPN’s are 3.14 (orange) and 3.24 (violet) rad, respectively. Benefiting from the all PM-fiber-based comb structure and a relatively large bandwidth of the PLL (75 kHz), polarization wander problem and additional attenuation caused by the components vibration are avoided and compensated completely.

3.3 Acoustic resonant frequencies of the system II: Swept-sine test

The resonant frequencies of the oscillator have also been measured by a standard swept-sine technique. To measure the resonant frequencies, the oscillator isforced vibrated by sine waves with different frequencies and amplitudes. The IPN of f_r is recorded during the whole procedure. If any part of the oscillator as well as its package resonates with the driving force, an obvious degradation (increment) of the IPN will be observed. The major frequency of the acoustic noise in reality, especially those generated from vehicle, distributes in the range of 10 Hz ~1 kHz [24]. Therefore, the frequency of the applied force is set in the range of 5 Hz ~1.1 kHz with the maximum amplitude of 3 μm.

As Fig. 4(a) illustrates, the IPN degrades on the order of magnitude, when the forced frequency (the frequency of applied force) is 400~475 Hz, 800 Hz, and 1 kHz. Obviously, acoustic resonance happens at these frequencies. The strongest resonanceoccurs at around 400~475 Hz (red area in the picture), where the IPN of f_r increases by more than 15dB. The acoustic waves at 800Hz and 1 kHz also boost the IPN by 10.5 dB and 14.6 dB, respectively. It is noteworthy that the system is insensitive to the vibration frequency below 375 Hz indicating the resonant frequencies of the optical components are all above 375 Hz. For analysis convenience, the test result of the impulse response f_r is given in Fig. 4(b) (the same data as the blue curve in Fig. 3(b), but the offset frequency along the vertical axis is presented in linear scale).

 

Fig. 4 Vibration characteristic analysis. (a) Resonant frequencies measurement. The degradation (increment) of the IPN under particular vibration amplitude at particular frequency is represented by the color of each point in the image. (b) Phase spectral density of the f_r under the vibration of acoustic impulse. The offset frequency is shown as the vertical axis and in linear scale.

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The resonant frequencies of the optical components inside the oscillator can be identified from Fig. 4. They are distributed around 400~475 Hz, 800 Hz, and 1 kHz. The plastic-sealed optic delay line has multiple resonant modes and relative low resonant frequencies because of its relative complex structure and big volume. Therefore, the noise around 400~475 Hz is from the delay line.The resonant at around 800 and 1000 Hz are from the other optical components. In real life, many kinds of acoustic noises distribute in the range of 400 Hz ~1 kHz. Therefore, the influence from the ambient acoustic noise can be greatly improved by using a passive low-pass filter.

In addition, the resonant frequency of the package has also been optimized carefully by adjusting the shape and volume. As Fig. 4(a) shows, when the forced frequency is swept to 600-Hz, an increment of ~7 dB in IPN is found, while no obvious spectral density increment at around 600 Hz is observed during the previous impulse response test, as shownin Fig. 4(b). Obviously, the resonant frequency of the packageused for protecting the oscillator is 600 Hz. When the forced frequency equals to the resonant frequency of the package, the package will shake the optical components with much greater amplitude. So the spectral density increment occurs at 600 Hz corresponding to the slender area in Fig. 4(a).

3.4 Measurement of optimum working temperature

In this section, the working temperature of the oscillator (the oscillator is presented in the blue circle in Fig. 1(a)) is changed to observe its influence on the system. Figure 5 shows the attenuation of a SESAM (blue curve), the degradation of IPN for f_r (blank curve), and the tuning sensitivity of f_CEO (red curve) versus temperature. At point A (289.28 K, 10.75 dB), the attenuation of the SESAM is the minimum. At point B1 (289.6 K, 0), the IPN of f_r reaches the optimum level. At point B2 (289.6 K, 306.7 ± 5.2 kHz/mW, the uncertainty may be caused by temperature fluctuation of the SESAM), the tuning sensitivity of f_CEO reaches the maximum level, and correspondingly, its slope is 0 kHz/(mW∙K). For a temperature fluctuation of ± 0.25 K, the range of slope variation is ± 22 kHz/(mW∙K), which can be estimated from the fitted curve. Obviously, 289.6 K is the optimum temperature point for the optical frequency comb.

 

Fig. 5 Influence of the SESAM temperature on the comb stability. (a) IPN of f_r (blank curve) and attenuation of SESAM (blue curve) versus temperature. (b) Tuning sensitivity of the f_CEO (red curve) and attenuation of SESAM (blue) versus temperature. (c) Phase noise comparison of f_r under different temperatures.

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As illustrated in Fig. 5(a), at 289.6 K, the phase noise reaches the lowest level and it increases (degrades) with the attenuation of the SESAM. Physically speaking, the quantum noise is determined by the cavity loss, which cannot be eliminated by automatic control methods [25]. As a result, optimization of the SESAM working temperature equals to the decrease of quantum noise in the oscillator. In addition, as shown in Fig. 5(c), a lot of spurs appear on the phase spectral density curve when temperature is set at 292.5 K leading to the increment of IPN.

From the results shown above, it can be seen that the temperature induced additional noise is due to the temperature sensitivity of the SESAM attenuation, which is determined by the material property of the SESAM. To minimize the attenuation induced noise, the oscillator, especially the SESAM, have to be operated under the optimum temperature. Technically, a thermoelectric cooler (TEC) pad should be placed under the SESAM to precisely control the temperature.

As is well known, one can tune the frequency of the f_CEO signal continuously by changing the pump power of the oscillator. In our system, as the pump power is around 12 mW, under different temperatures, the tuning sensitivity of f_CEO can vary in the range of 100 ~300 kHz/mW (corresponding to a proportional gain of 314 ~942 krad/(s∙mW)). As shown by the black ellipse in Fig. 5(b), the maximum slop of the tuning sensitivity curve reaches 160 kHz/(mW∙K). This means when the temperature of the SESAM is badly selected, such as 288 K, the open-loop gain of the control system will change at most by 16% with a 0.1 K temperature drift. Fortunately, there is a 0.5-K-wide temperature area around 289.6 K, at which the f_CEO can be stabilized with the smallest sensitivity drift (≤ ± 22 × 0.25 = 5.5 kHz/mW) due to the minimum slop and maximum closed-loop gain.

The tuning sensitivity of f_CEO is in proportion to the strength of the nonlinear effects in the fiber, especially the Raman self-frequency shift effect, and thus is directly related to the pulse peak power [26]. Therefore, the f_CEO tuning sensitivity can be greatly affected by the temperature of SESAM through the variation of cavity loss.

The optimization of cavity structure may not be able to totally eliminate the affection of temperature. Explicitly, as the temperature of the SESAM changes, the attenuation will change correspondingly. No matter which kind of mode locking regime (stretched or soliton pulse) the laser operates, the variation of the cavity attenuation is only determined by the SESAM temperature property. So the CEO sensitivity is always affected by the temperature fluctuation. To our knowledge, temperature control may be the direct and effective method to solve the problem.

3.5 Humidity-Dependent Comb Stability

Humidity-dependent comb stability is also verified through a period of 240 days. During this time, the comb has been transported to another city and experienced a humid summer (80% humidity) and a dry (18% humidity) winter. The power (blue curve) and SNR (blank curve) stability of the detected f_CEO is shown in Fig. 6. During this 240-day-long period, the variation of the power and SNR, measured with a resolution bandwidth of 100 kHz and an average time of 5 by a spectrum analyzer, are all less than 1.5 dB. This means that the parameters of the comb, such as the polarization, pulse energy, pulse chirp, efficiency of the PPLN crystal, and so on, vary little in hundreds of days, since tiny variation of these parameters can affect the SNR of f_CEO. Furthermore, the short period variations of the SNR and power have also been illustrated by the error bars in Fig. 6. Every error bar is obtained by measuring the SNR for six times with random time interval. The SNR varies no more than 2 dB during every measurement.

 

Fig. 6 240-day-long performance of the detected f_CEO signal under different Humidity.

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4. Summary

We have demonstrated an all PM fiber-based optical frequency comb and provided the detailed stability analysis results. The resonant frequencies of the system have been measured. We find that the comb system is only vulnerable to the high frequency acoustic wave (> 350 Hz).So we propose that acoustic-vibration induced phase noise could be eliminated by a low pass vibration-isolation structure. Meanwhile, we have demonstrated the existence of the optimum SESAM working temperature, 289.6 K for the proposed comb system. At this temperature point, the IPN of the f_r signal has the minimum value (reaches the minimum, 36.1 μrad) and the tuning sensitivity of the f_CEO arrives at the highest level (300 kHz/mW) and its thermal sensitivity descents to ~0 kHz/(mW∙K). In addition, we prove that the present PM fiber-based frequency comb is stable under different humidity (18% ~80%) by recording the 240-day-long performance.

Appendix measurement of the acoustic resonant frequencies

Figure 7 shows the detailed design of the test platform of acoustic resonant-frequencies. The oscillator and the optical amplifier have been sealed in two aluminum box with every component fixed respectively. Then the oscillator is shaken by periodically acoustic impulse train. The acoustic signal is synthesized by software with 16 bit accuracy and 48000 Hz sampling rate, and converted to voltage signal by a digital analog converter (Linear, LTC1650, with voltage output). The voltage signal drives PZT’s to generate the acoustic impulse. Finally, the impulse is then conducted to the laser cavity by the aluminum box.

 

Fig. 7 Test platform of acoustic resonant-frequencies. (a) Mechanical design of the platform. PZT: a fast piezoelectric ceramic transducer (with a max displacement of 4.6 μm ± 10%, and a max drive voltage of 150 V). CS: copper spike. All parts are connected directly by hard contact. (b) Waveform (I) and spectrogram (II) of the acoustic impulses.

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The repetition frequency of the acoustic impulse is 5 Hz, and the rise time of the impulse is 0.27 ms, as Fig. 7(b-I) shows. Correspondingly, this periodical signal possess a comb-shaped spectrum spanning from 5 Hz ~ 1.2 kHz, and the comb spacing is 5 Hz. The amplitude of each frequency component is set the same. The spectrogram is shown in Fig. 7(b-II).

The acoustic impulse is synthesized by the formula:

$$P\left(t\right)={\displaystyle \sum }_{k=1}^{240}A\times \sin \left(2\pi \times 5k\times t\right),$$

where A is the effective amplitude of every frequency component. Then the acceleration is:

$$\alpha \left(t\right)=-4{\pi }^{2}A{\displaystyle \sum }_{k=1}^{240}{\left(5k\right)}^2\sin \left(2\pi \times 5k\times t\right).$$

So the peak (maximum) acceleration is:

$$\left|{\alpha }_{peak}\left(t\right)\right|=4{\pi }^{2}A{\displaystyle \sum }_{k=1}^{240}{\left(5k\right)}^2.$$

The PZT has a maximum displacement of 4.6 μm ± 10% (≥ 4.2 um), and a maximum drive voltage of 150 V. In the experiment, the synthesized P(t) is finally amplified to ± 37.5 V to drive the PZT’s, so A can be estimated as:

$$A\ge \frac{4.2}{150}\times 37.5\times \frac{1}{\sqrt{2}}\times \frac{1}{240}=0.0031\text{μm}$$

As a result, the peak acceleration is:

$$\left|{\alpha }_{peak}\right|=\text{4}{\pi }^{\text{2}}\times \text{3}.\text{1}\times \text{1}{0}^{-\text{9}}\times \text{115}.\text{921}\times \text{1}{0}^{\text{6}}=\text{1}.\text{45}g$$

Acknowledgments

This work was supported by National Major Scientific Instrumentation Development Program of China (2011YQ120022), Natural Science Foundation of China (61275164), and CAS/SAFEA International Partnership Program for Creative Research Teams.

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