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High bandwidth carrier phase and repetition rate control are critical for the construction of low phase noise optical frequency combs. Here we demonstrate the use of a graphene modulator for the former and a bulk electro-optic modulator for the latter enabling record low phase noise operation of an Er fiber frequency comb. For applications that do not require carrier phase control, we show that the form factor of a fiber comb can be reduced by adapting a graphene modulator for rapid repetition rate control. Moreover, the whole system demonstration is performed with all-polarization maintaining Er fiber frequency combs, highly suitable for applications in the field.
© 2015 Optical Society of America
1. Introduction
Optical frequency combs, which consist of hundreds of thousands of longitudinal modes of order n, characterized by a frequency spectrum fn = fceo + nfrep with a carrier envelope offset frequency (fceo) and a frequency spacing set by the laser repetition frequency (frep), have been applied to many technology areas comprising for examples; optical atomic clocks, ultra-precise metrology, microwave generation, communication, spectroscopy, imaging and astronomical calibration [1, 2]. Indeed, optical frequency combs have evolved into an indispensable tool for many research laboratories. More recently, driven by emerging real world applications, the demand for fieldable optical frequency combs, has been growing. To fully exploit the capabilities of frequency combs, robust, portable, low phase noise optical frequency references are required, which have also greatly improved during the last ten years [3, 4]. Fieldable optical frequency combs with low phase noise are bound to further revolutionize measurement technology and to make it possible to exploit these advances outside of research laboratories. Oftentimes comb applications not only require low phase noise, but also low amplitude noise in order to be competitive with alternative technologies. Radar and navigation applications further rely on precision frequency division from the optical to the microwave domain [5–7].
Optical frequency combs based on Ti;sapphire solid-state lasers have so far generated the lowest fceo phase noise noise at about 0.045 rad [8]. However, Ti;sapphire optical frequency combs are difficult to operate under the influence of demanding environments because of their limited potential for integration. Diode-pumped solid state lasers have also achieved impressive phase noise performance [9, 10] but may have limited application potential for some demanding applications such as communications or space missions, because they are relatively bulky and very sensitive to environment. Fiber-based optical frequency combs based on nonlinear polarization rotation (NPR) [11] or saturable absorber (SA)-assisted NPR mode-locking mechanisms have proven to be viable alternatives and have also been operable at low values of phase noise, i.e. the lowest fceo phase noise values achieved for fiber combs to date are 0.15 rad for Tm frequency combs [12], 0.32 rad for Yb frequency combs [13], which is estimated from the coherent carrier power fiof the phase locked fceo as shown in [13], and about 0.4 rad for Er frequency combs [14], 0.4 rad for Er frequency combs [14], which is estimated from the PSD of the phase locked fceo as shown in Fig. 3(b) of [14]. However, all these results have been obtained in non-polarization maintaining fiber cavities, which are subject to environmentally induced fluctuations of performance. Consequently, polarization-maintaining (PM) fiber-based optical frequency combs have been long sought for comb applications in the real world [15]. Although there are a few reports about all-PM frequency combs, so far the fceo phase noise has been > 1 rad, limiting their application potential in high precision applications [16, 17].
Two fast modulators are crucial for optical frequency combs with ultra-low phase noise because of their two degrees of freedom; fceo and frep. Typically, pump current modulation is used for stabilization of fceo and an electro-optic modulator (EOM) is used to stabilize frep [14, 18–20]. However, the feedback bandwidth for pump current modulation is limited by the response time of the gain medium [21]. For example, the feedback bandwidth for pump current modulation for Er fiber lasers is around 100 kHz, which hampers ultra-low phase noise operation. Alternatively, as shown in [8], an extra-cavity acousto-optic modulator (AOM) can be used for fceo control, though the limited diffraction efficiency and induced spatial dispersion can be an issue, causing the modulation-frequency dependent loss. This would generate additional intensity noise and modulation-frequency dependent changes of the signal-to-noise ratio for the fceo. More importantly, the response time of an extra-cavity AOM is limited by the propagation delay of the acoustic waves in the crystal, resulting in around 250 kHz feedback bandwidth [22].
For many applications, such as THz or difference frequency generation (DFG), as well as Raman spectroscopy, only frep control is required, since the generated frequencies are independent of fceo. For these purposes, a fast modulator, which has low loss and is easy to install in oscillators, is sought rather than a relatively unwieldy waveguide or bulk EOM. Note that an extra-cavity AOM cannot be used for repetition rate control.
In this work, we demonstrate that a graphene based EOM can work as a high bandwidth modulator not only for fceo, but also for frep in an all PM Er fiber optical frequency comb, including an oscillator, an amplifier, and highly nonlinear fiber (HNLF). This may initially seem counterintuitive, since a graphene modulator induces frequency shifts of fceo and nfrep via rapid cavity loss modulation [12, 23] that cancel near the optical carrier frequency, resulting in no overall shift of these comb teeth. However, we can stabilize frep by locking to a beat frequency (fbeat') made by subtracting the measured fceo from an optical beat (fbeat) between one of the comb teeth and a CW reference laser by a double balanced mixer. This locks nfrep to the CW reference, while allowing fceo to change freely, as discussed in section 4.2. This means that the fast response of a graphene modulator (GM) can be applied to frep, bypassing the limit of the gain dynamics of the laser medium. This enables single servo loop control of frequency combs at higher modulation bandwidths than methods relying on pump current modulation [24] or even bulk EOMs, particularly for comb systems operating at high repetition rates. As pointed out in section 3, GMs are compatible with any laser operating from the visible to the mid IR; therefore this scheme can also be adapted to ultra-compact, high repetition rate, solid-state combs.
Moreover, for applications that require stabilization of both fceo and frep, a GM and an EOM can be used to simultaneously stabilize fceo and frep, respectively, with little cross talk and very high modulation bandwidths. Because of the availability of two fast modulators, record low integrated phase noise of both fceo (0.25 rad from 10 Hz to 3 MHz) and fbeat (0.11 rad from 10 Hz to 3 MHz) are obtained.
2. Laser configuration
For an all PM configuration, a Fig. 8 laser based on a nonlinear loop mirror [16] for passive amplitude shaping or a laser mode locked with a semiconductor SA [17] are suitable. Since operation at high repetition frequencies (e.g. > 200 MHz) and incorporation of a GM are difficult for a Fig. 8 laser, we opted for a linear cavity with SA. The schematic of the oscillator is shown in the dotted green line in Fig. 1(a). The cavity is comprised of a length of non-doped PM fiber and Er-doped PM fiber with a net overall cavity dispersion of about −12000 fs2, ignoring the dispersion of the SA and GM. The oscillator was pumped from 100 mW with a laser diode operating at 976 nm. To minimize phase noise by reducing the cavity loss, a 5% fiber output coupler was employed. The polarization beam splitter prevents oscillation along the fast axis of the PM fiber. The use of a SA with sub ps carrier lifetime was critical to enable stable laser oscillation at small dispersion values [15]. Extended life-time testing of the SA revealed no noticeable SA degradation over months of operation.
Fig. 1 (a) Schematic of laser system. LD, laser diode; WDM, wavelength divison multiplexer; EDF, erbium-doped fiber; PZT, piezoelectric transducer; HWP, half waveplate; PBS, polarization beam splitter; EOM, electro-optic modulator; SA, saturable absorber; BPF, bandpass filter; PD, photo detector; HNLF, highly nonlinear fiber; PPLN, periodically-poled LiNbO3. (b) Optical spectrum from the oscillator. (c) RF spectrum of free-running fceo with 100 kHz RBW.
The output power from the oscillator is about 1 mW. The repetition frequency is about 80 MHz. As shown in [25], a repetition rate of around 80 MHz is a good compromise in terms of laser stability and achievable phase noise in microwave applications. The maximum spectral bandwidth obtained from the oscillator is about 20 nm [Fig. 1(b)], which corresponds to about 130 fs of Fourier transform-limited pulse duration, assuming a sech2 pulse shape.
An intracavity EOM based on lithium niobate was used for high bandwidth repetition frequency control and a GM for carrier phase control. A piezo-electric transducer (PZT) was further implemented for slow frep control on the side of the fiber. The graphene modulator was designed with a modulation range of 2.5% for an insertion loss of 10% and is further described in the next section. The output from the oscillator is divided into two parts. The first part is used as a monitor for phase locking of the frequency fbeat between the comb and a single-longitudinal mode CW laser with specified 3 kHz linewidth. The second part is amplified to 100 mW by a PM positive dispersion Er fiber amplifier. The Er amplifier is pumped from both directions with forward and backward pump powers of 200 mW and 600 mW, respectively.
The spectrum is broadened in the amplifier; the combination of two lengths of standard negative dispersion communications fiber before the Er-doped fiber (EDF) and after the EDF is optimized to obtain the shortest pulse duration before the HNLF. A pulse duration of below 40 fs, measured by an autocorrelator, is obtained. An octave spanning spectrum is obtained after propagation through 50 cm of HNLF. The fceo was detected with a standard f-2f interferometer; two filters with 2 and 10 nm bandwidth were inserted to filter out the second harmonic signal at 1100 nm. A short piece of undoped PM fiber after the HNLF is used to adjust the group delay between 1100 nm and 2200 nm downstream from the frequency doubling crystal (periodically poled LiNbO3). The carrier envelope offset frequency was detected with more than 35 dB SNR at 100 kHz resolution bandwidth [Fig. 1(c)], though we have also observed >40 dB SNR for slightly longer oscillator pulses. The linewidth of the free-running fceo is about 40 kHz, which is the narrowest of any Er mode-locked laser with a SA [26, 27] to date and comparable to Er fiber lasers based on nonlinear polarization rotation [14, 19].
3. Graphene modulator
The graphene modulator [12, 23] used in this experiment, as shown in Fig. 2, was fabricated using graphene grown on copper foil by chemical vapor deposition. The growth started with evacuating a growth chamber made from a quartz tube to ~10−6 Torr while the chamber was heated to 1000°C. Then hydrogen and methane were flowed into the tube while the temperature was maintained at 1000°C for 5 minutes, after which the chamber was cooled down passively at room temperature with only hydrogen flowing. Next, the copper foil with graphene was spin-coated with polymethyl methacrylate (PMMA) on one side before the copper was etched by ferric chloride solution. The etchant solution was repeatedly diluted by deionized water, and then with the PMMA/graphene layer floating in the water, the substrate was brought into contact with it, completing the transfer process. The substrate consists of a silicon wafer with an oxidized layer, a 100 nm gold layer as the bottom contact (applied via thermal evaporation), and ~120 nm of tantalum pentoxide as a high-k gate dielectric layer (applied via reactive sputtering with a pure tantalum target). After the graphene is transferred onto the substrate, PMMA was removed by acetone and a metallic top contact layer was deposited by thermal evaporation (20 nm of Ti and 100 nm of Au), which was patterned by a liftoff process.
Fig. 2 Sliced structure of the graphene modulator. The bottom contact, a thin layer of metal with high reflectance (silver or gold for near IR light), serves both as an electrical contact and a highly reflective mirror. The thickness of the high-k dielectric determines the intensity of light experienced by graphene, thus providing design freedom in the insertion loss and modulation depth of the device, despite the universal broadband 2.3% absorption of graphene.
Although the absorption of monolayer graphene is only 2.3%, one can tailor the total modulation depth and insertion loss of the modulator by changing the thickness of the tantalum pentoxide gate dielectric. Since the thickness of graphene is only one atomic layer, its modulation effect on the change of optical path length is to the first order negligible, whereas the absorption change can be higher than 50% of the total absorption. For this particular fiber oscillator, we chose the thickness of tantalum pentoxide to be 120 nm, yielding ~10% total insertion loss (5% from the bottom metallic contact; 5% from graphene) and ~2.5% modulation depth. An increase in modulation depth generally increases the fceo tuning range with minimal effect on modulation bandwidth. In the present system the diameter of the aperture for the GM was chosen as 700 µm, which, with the contact resistance of metal on graphene, and coupled with the capacitance due to the large aperture, gave an RC-limited 3dB modulation bandwidth of around 2.5 MHz. We fabricated several such modulators and have not observed any degradation of performance even after 1 year of operation under ambient conditions.
We estimate that GMs can be used for intra-cavity loss modulation in the whole near IR spectral range from 0.7 to 2.5 µm. At the short wavelength extreme, GMs can be limited in their modulation depth due to the large mismatch between their Fermi level (typically 0.2 eV below the Dirac point) and the energy of the states that absorb light (at half the photon energy below the Dirac point, which is ~0.9 eV for 0.7 µm light). At the long wavelength extreme, absorption saturation at high illuminating intensity may potentially be a limitation, but in the present system we operated with an intensity on the GM of around 3.5 MW/cm2, which is only around 1 - 2% of its saturation intensity of Isat = 90-400 MW/cm2 at 1550 nm, as has been measured by several research groups [28–30] and as predicted by rate equation calculation [31]. According to the same theory [31] and a summary of measured saturation intensity at different wavelengths [32], the saturation intensity decreases with increasing wavelength, which may make the saturable absorption observable in GMs for wavelengths longer than 2.5 µm. However, this can in principle be overcome by increasing the beam size on the GM, or by choosing an optimum thickness of the high-k dielectric such that the field amplitude in the graphene layer is low, with the compromise of lower modulation depth.
4. Phase locking
4.1 fceo and fbeat
The carrier envelope offset frequency was detected as shown in Fig. 1(c). For stabilizing frep, an optical beat between one of the comb teeth and a single longitudinal mode CW laser is obtained by interfering the two lasers through a 50:50 coupler. A 40 dB SNR at 100 kHz resolution bandwidth is obtained.
Ideally, cross talk between the two modulators should be small to tightly stabilize both fceo and fbeat. A GM modulates fceo and nfrep by almost the same amount, but with opposite signs, i.e. its fixed point [33] is very close to the optical carrier frequency, shown schematically in Fig. 3, which is experimentally confirmed by adding the sinusoidal modulation to the GM while observing signals; fceo, fbeat, and nfrep. Here, n is an integer and, in our case, about 2.4 × 106, with nfrep being the optical carrier frequency (~190 THz). On the other hand, the modulation of fceo by an EOM is 100 times smaller than the modulation of nfrep [34], which indicates that the fixed point of the EOM is close to fceo. This means that the combination of a GM and an EOM for highly desirable orthogonal control and phase locking of both fceo and fbeat at high modulation bandwidths is possible.
Fig. 3 Schematic for locking of fceo and fbeat. fceo is observed by the self-referencing scheme, and locked by a GM. fbeat is the beat between one of the comb teeth and a single longitudinal mode CW laser and locked by an EOM. The fixed point of a GM is near the optical carrier frequency. The fixed point of an EOM is near fceo.
Since the modulation depth of a GM is not sufficient to capture the appropriate beat for fceo control, we also employ pump current modulation as a slow modulator for fceo. To stabilize fbeat, it is possible to use only the EOM, at least in principle, but the halfwave voltage for a bulk-EOM is very high (typically a few 100 V), which limits the feedback bandwidth. Thus, a PZT, with a large modulation depth, is used as a slow cavity length modulator, and the EOM is used as a fast modulator.
To show the advantage of a GM compared with pump current modulation for fceo control, the amplitude and phase response for optical power modulation by the GM and pump current modulation are measured [Figs. 4(a) and 4(b)]. The response of the optical power should be very similar to the response of fceo as shown in [35], because any optical power change by cavity loss modulation influences nonlinear effects in the cavity, such as SPM or self-steepening, resulting in a change of fceo. Amplitude modulation at high frequencies is mostly unaffected by pump current modulation because of the lifetime of Er, which works as a low pass filter. The amplitude response of a GM is significantly larger at high frequencies. Furthermore, phase rotation for pump current modulation is larger than for a GM, which makes it difficult to design a loop filter for feedback.
Fig. 4 Transfer function of graphene modulator (GM) (red) and pump current modulation (blue) for optical power, in (a) amplitude and (b) phase. (c) RF spectrum of locked fceo by GM with 3 kHz RBW. The inset is the RF spectrum of locked fceo by pump current modulation with 3 kHz RBW. (d) RF spectrum of locked fbeat by an EOM with 3 kHz RBW. (e) PSD of locked fceo. (f) PSD of locked fbeat. (b, c, d, and e) are in-loop measurements.
Figure 3 (c) shows the RF spectra of the locked fceo. The servo bump induced by pump current modulation is at 150 kHz. On the other hand, the servo bump due to loss modulation via the GM exceeds 1 MHz, which improves the coherent peak from 30 dB to 45 dB at 3 kHz RBW. The integrated in-loop phase noise of the locked fceo by loss modulation is about 0.25 rad from 10 Hz to 3 MHz [Fig. 3(e)]. For fbeat, the RF spectrum and power spectral density (PSD) are shown in Fig. 3(d) and 3(f). Some spikes caused by mechanical resonances of the EOM appear at 300 kHz and 1 MHz. The obtained integrated in-loop phase noise from 10 Hz to 3 MHz is as small as 0.11 rad. The obtained phase noise of fbeat is smaller than that of fceo, because the intrinsic phase noise of fbeat is smaller than that of fceo. Note that we did not observe any difference of the fceo RF spectrum with and without phase locking of fbeat, and vice versa, and the shown RF spectra and PSDs are taken when both fceo and fbeat are phase locked simultaneously.
4.2 nfrep
Since many application require only precise stabilization of frep, a compact alternative to conventional EOMs for fast repetition frequency modulation is highly sought. Here, we show that a GM can also work to stabilize frep. To access frep in the optical domain, the fceo is electronically subtracted from fbeat [7, 24];
This scheme is particularly useful for single servo loop control of frequency combs. fbeat' does not depend on fceo, and nfrep is phase-locked to fcw by stabilizing fbeat’. Experimentally, this is realized by mixing fbeat and fceo in the RF domain by a double balanced mixer. Although the actual locking results depend on the setting of the loop filter and the applied voltage to the EOM, fbeat' locking by a GM is better than by an EOM with respect to the obtainable coherent peak signal to noise ratio. The coherent peaks of locked fbeat' by graphene and EOM are 40 dB and 35 dB at 3 kHz RBW, respectively, as shown in Fig. 5(a) and 5(b). From Fig. 5(a), the carrier power of locked fbeat' with the GM is estimated to be 90%, resulting in 0.32 rad integrated in-loop phase noise from DC to 2 MHz. Since fceo is completely free-running, and a fixed RF filter is used to extract fceo, phase locking could not be preserved long enough to measure the PSD of the phase locked signal. This will be readily solved by loosely locking fceo. Since a 1 Hz of feedback bandwidth is large enough, a software-based loop filter can be used to keep fceo within an RF filter bandwidth.
Fig. 5 (a) In-loop RF spectrum of locked fbeat' by GM with 3 kHz RBW. (b) In-loop RF spectrum of locked fbeat' by EOM with 3 kHz RBW.
We trace back the slightly worse performance of a GM when applied to frep rather than fceo locking to the difference between the free-running linewidths for fceo and fbeat', although, ideally, the free-running linewidths of fceo and fbeat' should be almost the same because the fixed point of the oscillator is around the laser frequency [33]. Also since the modulation bandwidth of loss modulation depends linearly on frep [12], we expect even better performance of a GM for frep locking for a 200 or 400 MHz mode-locked laser. Note that a GM can be incorporated into a cavity with a much smaller form factor compared to an EOM. Indeed, we have completely packaged a GM and its electronic driver as an end mirror of the above laser, in an 8 mm long button with a diameter of 15 mm.
4. Conclusion
In conclusion, we demonstrated phase locking of both carrier phase and repetition rate in a mode locked laser for the first time. The implementation of cavity loss modulation compared to pump modulation increases the carrier phase response bandwidth by around an order of magnitude; the use of a graphene modulator in conjunction with an EOM allows for high bandwidth control of both carrier phase and repetition frequency. The adaptation of a graphene modulator to the important telecom wavelength range of 1.55 µm enables the construction of compact Er fiber lasers with record low phase noise for both carrier phase and repetition frequency locking. Moreover, for applications where carrier phase control is not required, a graphene modulator can be used for repetition frequency control as an alternative to conventional electro-optic modulators while also allowing for a smaller form factor and lower phase noise. Finally, the implementation of a dispersion compensated all polarization maintaining fiber oscillator ensures a robust system design compatible with even the most challenging environments. We believe that ultra low phase noise frequency combs as demonstrated here will greatly expand the application potential of frequency comb technology.
Acknowledgements
We acknowledge stimulating discussions with Frank Quinlan and Scott Diddams. This work was supported in parts by the DARPA PULSE program with a grant from AMRDEC, by the DAPRA Young Faculty Award (N66001-11-1-4156), and by the NSF Early Career Award (1253044).
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