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We present a fiber femtosecond laser oscillator that incorporates a pair of chirped fiber Bragg gratings (CFBGs) to augment the cavity length elongation produced by a PZT actuator. With a magnification factor of 18.2, the CFBG pair offers a 4.44 mm cavity length extension, providing a 25.59 kHz tuning range of the repetition rate from a 41.56 MHz nominal value without loss of mode locking. The extended tuning range enhances the performance of comb stabilization in uncontrolled environments and pulse-to-pulse interferometry for step height measurements.
© 2017 Optical Society of America
1. Introduction
Stabilization of the frequency comb of a femtosecond pulse laser by locking to microwave or optical frequency references requires precision control of the repetition rate [1–3]. The repetition rate can be regulated by adjusting the optical cavity length of the oscillator by means of the pump power control, electro-optic modulation and piezoelectric length extension [4–7]. The latter method is preferably selected when the repetition rate has to be tuned over a wide range. Nonetheless, the maximum elongation of PZT actuators available today is usually limited to a few hundreds of micrometers at best. The limitation makes it difficult to maintain the comb stabilization in temperature-uncontrolled environments; particularly for a lengthy fiber oscillator running on a low repetition rate, since the thermal expansion of the cavity length often exceeds the maximum elongation range of the PZT actuator in use.
The limited elongation of the PZT actuator also restricts the performance of metrological applications such as Fourier-transform spectroscopy [8,9], surface profile metrology [10,11], distance measurement [12,13] and optical coherence tomography [14]. These applications commonly exploit a femtosecond laser as the light source to perform pulse-to-pulse interferometry by scanning one pulse over the other overlapped in auto-correlation or cross-correlation mode. The pulse-to-pulse scanning is made by passing one pulse through a delay line extended by a PZT actuator [15] or through a long unbalanced arm while sweeping the repetition rate by stretching the cavity length using a PZT actuator [9,11,16]. The performance of pulse-to-pulse interferometry consequently improves by extending the pulse-scanning span that is currently restrained by the PZT actuator, requiring an alternative solution to cope with the problem.
In this investigation, we include a pair of chirped fiber Bragg gratings (CFBGs) within a fiber oscillator to achieve a wide tuning range of the repetition rate. The CFBG pair is devised to augment the optical path elongation produced by a PZT actuator by a magnification factor of 18.2. Accordingly, this CFBG-incorporated oscillator permits a 4.44 mm cavity extension, offering a 25.59 kHz tuning range of the repetition rate from 41.56 MHz while maintaining the mode-locking stability of the original oscillator. The extended tuning capability is applied to two experiments; long-term comb stabilization in temperature-uncontrolled environment and 3-D surface metrology of largely stepped profiles by pulse-to-pulse interferometry.
2. CFBG-incorporated oscillator
Figure 1(a) shows the system diagram of the oscillator configured in this study to extend the tuning range of the repetition rate by incorporating a pair of CFBGs. The oscillator is a ring type and employs an erbium(Er)-doped gain fiber bi-directionally pumped by two laser diodes supplying 500 mW power at a 980 nm wavelength. The normal dispersion of the Er-doped gain fiber is compensated by adding a single-mode fiber of negative dispersion, so the net cavity dispersion is set at approximately −0.012 ps2 to maintain a stretched-pulse generation regime. Mode locking is attained by combining a nonlinear polarization rotation (NPR) unit with a saturable absorber (SA). The transmission-type SA (SA-1550-25-FC/PC, Batop) used here offers a 2 ps relaxation time with 300 µJ/cm2 saturation fluence. The NPR unit is comprised of two half-wave plates (HWPs) and two quarter-wave plates (QWPs). This hybrid mode-locking scheme permits the net output power to increase to ~150 mW, whereas the intra-cavity power is regulated not to induce excessive nonlinear effects within the Er-doped gain fiber [17]. Developed pulses exit the oscillator via a polarizing beam splitter (PBS) within the NPR unit.
Fig. 1 Wide repetition rate tunable femtosecond laser with a pair of CFBGs. (a) System layout of the proposed laser oscillator. (b) Group delay profiles of CFBG1, CFBG2 and CFBG1 + CFBG2. (c) Magnification of cavity length’s tunable range by stretching a CFBG out of a pair of CFBGs. CFBG: chirped fiber Bragg grating, OC: optical circulator, PZT: piezo-electric transducer, LD: laser diode, WDM: wavelength division multiplexer, EDF: Er-doped fiber, I: isolator, SA: saturable absorber, NPR: nonlinear polarization rotation, H: half-wave plate, Q: quarter-wave plate, PBS: polarization beam splitter.
The CFBG pair installed inside the oscillator cavity consists of two identical fiber gratings, named CFBG1 and CFBG2. Each grating is a type of distributed Bragg reflector fabricated in a fused-silica single-mode fiber by creating a variation in the refractive index of the fiber core using ultraviolet light. The grating pitch undergoes a linear decrease to reflect optical wavelengths in the range of 1,525 – 1,585 nm. The two CFBGs are spliced together in opposite directions via a four-port circulator so that the intra-cavity light propagates through CFBG1 and CFBG2 in order inside the ring cavity. This configuration permits the group delay dispersion (GDD) of one grating to be canceled out by the other as depicted in Fig. 1(b). Consequently, the net GDD of the CFBG pair is measured ~0.00179 ps/nm, small enough not to give rise to significant pulse broadening or distortion after being attached to the oscillator [18,19]. In tuning the repetition rate, only CFBG1 is stretched using a PZT actuator to vary the cavity length of the oscillator by inducing the group delay (GD) of CFBG1 while the total GDD of the CFBG pair remains unchanged.
As illustrated in Fig. 1(c), the geometrical length increase δ produced in CFBG1 by the PZT actuator shifts the reflection point of the Bragg wavelength λB by an amount of
in terms of the optical path length ΔL [20]. In Eq. (1), n denotes the refractive index of the fiber grating before stretching, and its variation due to the length extension of the fiber material is considered by adopting the elasto-optic coefficient pe [21]. In addition, γ is referred to as the magnification factor that is proportional to the ratio of the initial Bragg wavelength λ0 to the wavelength bandwidth Δλ of the chirped fiber Bragg grating. The value of pe for fused silica is known to be ~0.22 and, with λ0 and Δλ being 1,525 nm and 60 nm, respectively, the amplification factor γ for CFBG1 is estimated to be 19.8. Lastly, the optical length shift ΔL induced in CFBG1 leads to a cavity length extension of 2ΔL within the oscillator, so the repetition rate fr undergoes a variation Δfr that can be approximated aswith L being the cavity length (~7.21 m) of the oscillator before stretching.3. Repetition rate tuning
Figure 2(a) depicts how CFBG1 was actually connected to the PZT actuator with a chirped grating portion of 70 mm fabricated in the middle part of a fused-silica single-mode fiber of a 210 mm total span. One end toward the oscillator was fixed stationary and the other end was clamped on an elastic flexure being driven by the PZT actuator. Figure 2(b) shows how the repetition rate of the CFBG-incorporated oscillator varies with increasing the input voltage to the PZT actuator. The maximum variation of Δfr is measured 25.59 kHz from a nominal value of 41.5569275 MHz, so the corresponding optical path change is estimated to be 4.44 mm from Eq. (2). When only the grating portion of CFBG1 is considered, its elongation δ is 78.62 μm and the resultant contribution to Δfr is 24.42 kHz with 2ΔL being 4.24 mm. The magnification factor γ is worked out to be 18.2, which is found to be slightly smaller than the theoretical value of 19.8. The discrepancy is reckoned attributable to the inaccuracy of ~10% error in estimating the refractive index n of CFBG1.
Fig. 2 CFBG control for tuning the repetition rate. (a) CFBG1 attachment mechanism to a PZT actuator. (b) Optical cavity length (2ΔL) versus the tuning range (Δfr).
The mode-locking stability of the CFBG-incorporated oscillator was experimentally verified as in Fig. 3. For the test, the PZT actuator was given an input voltage signal of a sawtooth profile in the time domain, to which the repetition rate responded as observed in Fig. 3(a). The rise and fall of the repetition rate was deviated slightly from the straight-line command profile, which is explained by the hysteresis effect in the actual displacement of the PZT actuator generated in response to the voltage input. The PZT actuator in itself has a 300 Hz natural frequency and it tends to reduce when the external load increases while stretching CFBG1. Nonetheless, the mode-locking stability of the oscillator is confirmed by the optical spectrum as well as the pulse duration of the output pulses from the oscillator, both of which displayed no significant change during the repeated operations of the PZT actuator as monitored in Fig. 3(b) and 3(c), respectively. The optical spectrum is centered at a 1,568 nm wavelength with a 6.7 nm spectral bandwidth (FWHM). The measured spectral bandwidth is found narrower than that of the same oscillator before the CFBG pair is installed [17]. The main reason is attributed to the high order dispersion of CFBG1 arising during elongation, which is not perfectly cancelled out by CFGB2. Further, the longer wavelength side of the optical spectrum is seen slightly cut off since the operating range (1,525 – 1,585 nm) of the CFBG pair is offset towards the shorter wavelength side. The pulse duration was measured 455 fs using an autocorrelator, which is also confirmed to not be affected by the repetition rate control.
Fig. 3 Spectral and temporal characteristics of the mode-locked femtosecond pulses with a wide range tuning of the repetition rate. (a) Time trace of the repetition rate (solid) controlled with a sawtooth command signal (dotted). (b) Optical spectrum of the output pulses. (c) Pulse duration measured by interferometric autocorrelation.
In order to evaluate the comb structure of the mode-locked pulses produced from the CFBG-incorporated oscillator, the RF spectrum was observed at a repetition rate of 41.56 MHz as shown in Fig. 4(a). The RF spectrum monitored with a 300 kHz resolution bandwidth (RBW) reveals that RF harmonics up to 1 GHz are clearly distinguished with ~70 dB amplitudes above from the noise floor without notable parasite harmonics. The linewidth of the 24th harmonic near 1 GHz is estimated to be ~5 Hz as monitored in Fig. 4(b) with a 30 kHz RBW. The phase noise of the comb structure was assessed by beating a continuous-wave distributed feedback (DFB) laser having a 50 kHz linewidth about a 1,550 nm center wavelength, of which the beat signals turned out to be ~30 dB notes when the comb was operated in a free running state. All these RF data confirm that the CFBG-incorporated oscillator maintains a well-developed comb structure as a mode-locked laser.
Fig. 4 RF spectral characteristics. (a) Harmonic spectrum of the pulse repetition rate (RBW: 300 kHz). (b) Magnified view of the 24th RF harmonic for noise analysis with 30 kHz RBW. (c) RF beat notes with a cw distributed feedback (DFB) laser (RBW: 100 kHz).
4. Comb stabilization and pulse-to-pulse interferometry
The extended tuning range was exploited for comb stabilization when the CFBG-incorporated oscillator was exposed to a temperature change of 5.75 °C underneath a heating lamp. The repetition rate underwent a large drift of 1.29 kHz in free running as observed in Fig. 5(a). Then, the repetition rate was phase-locked to the Rb clock by stabilization control of the PZT actuator as shown in Fig. 5(b). The repetition rate under stabilization is assessed to maintain a frequency stability of 1.95 × 10−11 at 10 s in terms of the Allan deviation as depicted in Fig. 5(c). The Rb clock used as the RF reference for comb stabilization has a 6.92 × 10−12 stability at 10 s. Figure 5(d) shows a case of 12-hour long-term stabilization control, in which the temporal fluctuation level of the repetition rate is analyzed to have a 0.59 mHz standard deviation when the ambient temperature was subject to a ± 0.3 °C fluctuation with on-off air conditioning. All the test results demonstrate that the extended repetition rate range of the CFBG-incorporated oscillator is capable of stabilizing the comb structure even in the presence of a large amount of uncontrolled temperature change, which ordinary fiber oscillators of a limited tuning range can no longer afford [22]. No noticeable degradation in the performance of stabilization control was observed even after the continuous and repeated operation of the CFBG pair for a long period of 12 hours. In addition, the output power fluctuation was monitored within ~1%, indicating no significant variation in the overall performance of the CFBG-integrated oscillator.
Fig. 5 Comb stabilization test results. (a) Repetition rate drift with a temperature change of 5.75 °C. (b) Comb stabilization by phase-locking of the repetition rate to the Rb clock. (c) Frequency stability in terms of the Allan deviation. (d) Long-term stabilization control of the repetition rate during 12 hours.
Next, the CFBG-incorporated oscillator was applied as the light source to a pulse-to-pulse interferometer to measure a large step height of 1.3 mm prepared by combining gauge blocks. The pulse-to-pulse interferometer was configured in an unequal path Twyman-Green type as illustrated in Fig. 6(a). The unequal path is set to a single optical cavity length (7.21 m) so that the measurement pulse (nth pulse) is overlapped with the reference pulse (n + 1th pulse) during repetition rate tuning. The pulse-to-pulse interferogram was monitored using an infrared digital camera, of which the interference intensity for an arbitrary pixel is expressed as
where I0 is the background intensity, Γ is the envelope function, h is the step height, and k is the wavenumber of the fundamental wavelength of the light source. The interference intensity I becomes maximum when the measurement pulse and the reference pulse are exactly overlapped, i.e., ΔL = h. Thus, the top surface A (ΔL = hA) and the bottom plate B (ΔL = hB) can be located using the centroid and A-bucket algorithms as in authors’ previous pulse-to-pulse interferometric measurements of large-step microstructures [11]. Finally, the step height h is determined as h = hA- hB. Figure 6(b) illustrates the 3-D surface profile of the gauge block assembly, from which the step height is evaluated to be 1.305 mm by identifying Δfr (~15 kHz) as depicted in Fig. 6(c) and 6(d). Figure 6(e) shows a test result of repeatability taken over 15 consecutive measurements, which turns out 510 nm in standard deviation being mainly attributable to the overall system stability of the CFBG-incorporated oscillator.Fig. 6 Measurement of large step height. (a) Pulse-to-pulse interferometer configuration. (b) Reconstructed surface 3-D profile of a 1.3 mm gauge block assembly. (c) Acquired interferograms. (d) Sectional view of step height (along line a-a’ in (b)). (e) Measurement repeatability. Abbreviations are; fr: repetition rate, SMF: single-mode fiber, DCF: dispersion compensating fiber, C: coupler, L: lens, LP: linear polarizer, IL: imaging lens.
5. Conclusions
The Er-doped fiber oscillator developed in this study by incorporating a pair of chirped fiber Bragg gratings (CFBGs) provides a 25.59 kHz tunable range of the repetition rate by augmenting the cavity length elongation induced by a PZT actuator by a factor of 18.2. The CFBG-incorporated oscillator permits a mm-range extension of the cavity length without loss of mode-locking stability, allowing for comb stabilization under temperature-uncontrolled environment and pulse-to-pulse interferometry for large step-height surface measurements.
Funding
National Research Foundation of the Republic of Korea (NRF-2012R1A3A1050386); Singapore National Research Foundation under its NRF Fellowship (NRF-NRFF2015-02) and from the Singapore Ministry of Education under its Tier 1 Grant (RG85/15).
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