A precise way of optical frequency generation is demonstrated with direct use of the frequency comb of a mode-locked femtosecond laser. Only a single mode is extracted at a time on demand from the frequency comb through a composite filtering scheme and then amplified by means of optical injection locking with extremely low background noise. Generated output signals are found to preserve not only the narrow linewidths of the selected individual modes but also the absolute frequency positions of the original comb over a wide spectral range. These outstanding performances of optical frequency generation could find applications in high precision spectroscopy, frequency calibration, and length metrology.
©2008 Optical Society of America
Stabilizing control of the frequency comb of a mode-locked femtosecond laser has permitted the advance of the precision frequency measurement in the optical range [1, 2]. The stabilized frequency comb provides about a million number of evenly-spaced optical modes that can be stabilized simultaneously to a precision level of one part in 1015 . This unique advantage has led to the development of next-generation optical clocks , the extension of the range of clockwork to the x-ray regime , and the advancement of precision spectroscopy  and length metrology . The generation of optical signals from the frequency comb is also an important issue  that finds diverse applications in high precision spectroscopy, frequency calibration, and length metrology.
A genuine optical frequency generator based on the frequency comb should be able to perform two functions in sequence; the first is to extract any wanted modes, one at a time, out of the frequency comb, and the second is to amplify the extracted mode to a desirable power level with extremely low background noise. The consequence should be the pure power enhancement of only a single mode, which maintains the original frequency stability of the frequency comb, particularly in terms of the linewidth and absolute frequency position. The external phase locking of a high power laser diode to the frequency comb was the first version of the optical frequency generator , followed by the use of an external cavity laser diode . This approach of external locking offers an extensive range of frequency tuning, but tends to suffer degradation in both the linewidth and absolute frequency position due to the limited frequency stability of the diode laser in comparison with the original frequency comb. The replacement of the diode laser with either a distributed-feedback laser  or an optical parametric oscillator  could improve the achievable frequency stability but at the sacrifice of the tunable range and speed.
On the other hand, it has long been known that the optical phenomenon of injection locking allows a weak-power seed signal to be amplified with low background noise. The feasibility of adopting the optical injection locking to the optical frequency generation from the frequency comb was tested in several investigations of high precision spectroscopy [11–13], proving its validity within a narrow tunable range. Nonetheless, constructing a practical form of optical frequency generator using the same principle requires an effective means of expanding the tunable range wide enough to cover the whole spectral range of the frequency comb. Our investigation aims to fulfill the task by devising a special filtering technique that enables the extraction of a single optical mode out of the broadband frequency comb under an automated systematic supervisory control scheme.
2. Optical frequency generator
The optical frequency generator (hereafter abbreviated as OFGenerator) constructed in this investigation is comprised of three sub-assembly hardware blocks as illustrated in Fig. 1; a frequency-stabilized femtosecond laser, a spectral filter of single mode extraction, and a power amplification unit. The femtosecond laser (Del Mar Photonics, Trestles-50) housing a crystal of titanium-doped sapphire produces pulses of ~35 fs width at an 81 MHz repetition rate with 400 mW average power [Fig. 1(a)]. The resulting frequency comb is centered at 800 nm in wavelength with a 50 nm bandwidth. The frequency stabilizing unit adopts an Rb clock (SRS, FS725), to which the repetition rate is phase-locked using the PLL technique . For this stabilization, the output-coupling mirror of the resonance cavity of the femtosecond laser is micro-controlled longitudinally using a piezoelectric actuator. The spectral range of the frequency comb is broadened using a photonic crystal fiber (Crystal Fibre, FemtoWhite 800), and thereby the carrier-offset frequency is stabilized to the same Rb clock through the self-referencing technique based on f-2f interferometry . For this latter part of stabilization, a periodically poled lithium niobate (PPLN) crystal is used for frequency doubling, and the tilt angle of the end mirror of the resonance cavity is micro-controlled.
The single-mode extraction filter [Fig. 1(b)] is a composite type, consisting of a diffraction grating, a single-mode optical fiber, and a scanning Fabry-Perot interferometer (SFPI). A beam of 250 mW average power is branched from the stabilized femtosecond laser and then made incident onto the diffraction grating, which is ruled with a grating pitch of 1200 lines/mm to produce 1.35 mrad/nm resolving power. The polarization of the incident beam is adjusted using a half-wave plate so that the power distribution between the 0th- and 1st-order diffracted beams becomes 20: 80. The 0th-order diffracted beam is reserved as the reference to be used to detect the frequency shift generated using an acousto-optic modulator in the next stage of Fig. 1(c). The 1st-order diffracted beam of 200 mW average power is focused on the optical fiber for coarse filtering. To provide band-pass filtering capability, a thermal diffusion expansion process is applied to the inlet endface of the optical fiber , thus enlarging the effective core diameter to 10 µm to yield a ~100 GHz spatial window of Gaussian shape. The enlarged core also improves the coupling efficiency of the focused beam into the fiber with less difficulty of beam alignment. Next, for fine filtering, the output beam from the optical fiber is transmitted through the SFPI (Thorlabs, SA210) of a ~10 GHz free spectral range (FSR). The transmission linewidth of the SFPI is measured as 67 MHz, which is narrow enough to permit only one mode to pass through [Fig. 1(d)]. The encircled numbers indicate the locations of corresponding signals within the overall optical layout. Both APD1 and APD2 are connected to a Rb clock for the stabilization of the frequency comb by activating PZT1 and PZT2, respectively. And APD3 and APD4 are connected to a rf-spectrum analyzer of high resolution bandwidth. The spectral range of filtering is coarsely adjusted by rotating M7 through PZT3 at first, and the wanted mode is after all selected by activating the SFPI using PZT4 with simultaneous monitoring the signal from APD3. The final output frequency is verified using a wavelength meter and also an optical spectrum analyzer of SFPI type (Thorlabs, SA200). The beam quality regarding the linewidth and absolute frequency position is confirmed using the signal obtained from APD4. Several parasite modes, appearing modulo the FSR of the SFPI, may be leaked in this process of fine filtering, but they are all suppressed in the subsequent process of injection locking. The active range of injection locking varies with the cavity length and reflectance of the laser diode in use and also the power level of the input light [15, 16]. It can appropriately be narrowed to a ~300 MHz width so that only the selected mode is amplified with subsequent suppression of spurious modes.
The overall performance of the single-mode extraction filter is evaluated by assessing the final output beam using an optical spectrum analyzer together with a rf-spectrum analyzer of high resolution bandwidth [Fig. 2(a)]. If more than a single mode survives the filtering process, beat frequencies of multiples of the mode spacing of the frequency comb (81 MHz) are clearly observed. No appearance of any beat frequencies confirms the successful extraction of a single mode. The output beam immediately after the process of single-mode filtering yields an extremely small optical power of ~150 nW. This beam is then fed as the seed for injection locking to a laser diode (Blue Sky Research, VPSL-0808-100-9-B) to amplify the optical power with high suppression of background noise [Fig. 1(c)]. The diode is of anti-reflection coated Fabry-Perot type and has a tunable range of 800 – 810 nm in wavelength. To avoid undesirable optical feedback to the laser diode during the process of injection locking, the input beam is polarization-controlled using a half-wave plate along with an optical isolator (Linos, DLI1). The optical power after the injection locking is measured to reach a level of a few tens mW with an amplification gain of 50 to 60 dB. For verification of the beam quality after injection locking, the output beam is frequency-shifted using an acousto-optic modulator (AOM) with subsequent monitoring of its beat frequency with the 0th-order diffracted beam from the grating [Fig. 2(b)]. The effect of the injection locking on the linewidth of the output beam is precisely quantified from the frequency spectrum of the beat signal observed using a high-resolution rf-spectrum analyzer (Agilent, E4440A), and is measured to be less than 1 Hz [Fig. 2(c)]. At the same time, the frequency instability of the beat signal is evaluated by monitoring the same frequency spectrum over a long period of time, and is measured as 3.0 parts in 1015 over 10 s averaging time [Fig. 2(d)]. This experimental result confirms that the injection locking realized in the OFGenerator is capable of maintaining the original frequency stability of the frequency comb, more specifically in terms of both the linewidth and the absolute frequency position. Note that the frequency comb in use is subject to a fractional instability of 1.3 part in 1012, and the frequency instability induced by injection locking is three orders of magnitude smaller, causing no significant degradation [Fig. 2(d)].
3. Control for optical frequency generation
The overall tunable range of the injection locking to a particular laser diode is restrained by the gain curve of its own lasing medium typically to a finite width of 5 to 10 THz about a certain center frequency. Therefore, multiple diodes of different tunable ranges need to be employed in a proper combination in order to cover the whole spectral range of the frequency comb in use [Fig. 3(a)]. Further, spectral broadening using photonic crystal fibers  along with prior amplification by adopting a tapered diode amplifier  may be considered. This would allow the frequency comb to be extended over the entire visible and near infrared spectral region.
The generation procedure of the optical output of demanded frequency is basically comprised of five steps being conducted in sequence under the supervision of a personal computer [Fig. 3(b)]. The first step is to vary the repetition rate of the optical comb so that one particular mode of the frequency comb is brought near the targeted output. The second step is for coarse tuning of the one-mode extraction filter, which involves rotating the mirror M7 [Fig. 1(b)] according to a lookup table prepared through prior calibration. The third step is to tune the injection-locking range of the laser diode to the targeted output by controlling the input current and temperature simultaneously. The fourth step is for fine tuning of the SFPI by monitoring the transmitted light intensity so as to allow only the selected mode to pass. The fifth and final step is to confirm the output beam using an optical spectrum analyzer along with a rf-spectrum analyzer. The whole procedure is controlled automatically with the aid of LABView software.
The standard output from the OFGenerator is a single isolated beam generated one at a time as commanded, where the frequency of the beam corresponds to the mode selected from the frequency comb [Fig. 4(a)]. The time required to change from one mode to another varies with the spectral separation of the two modes, being affected by the mechanical time needed to set the one-mode extraction filter to a new mode. Within the tunable injection locking range of a single laser diode, the mechanical time constant of the filter system for the mode change is usually in the order of ~10 ms. Thus, like the radio-frequency counterpart, the output frequency can be modulated in synchronization with time to meet versatile demands [Fig. 4(b)]. Furthermore, short-range frequency shifting of a selected mode within a repetition rate of 81 MHz can be made in a continuous manner using an acousto-optic modulator, of which the modulation frequency can also be referenced precisely to the same Rb clock used for stabilizing the frequency comb.
To conclude, the proposed OFGenerator is a practical form of optical frequency generator that is constructed with direct use of the frequency comb as an ideal active means, capable of providing any optical signal on demand in the same way as its counterpart in the radio frequency range operates. Only one mode is extracted at a time out of the broadband frequency comb through a composite filtering scheme consisting of an optical fiber, a diffraction grating, and a scanning Fabry-Perot interferometer. The selected mode having a very low power of 10 – 100 nW is amplified by 50 to 60 dB to the mW level by means of injection locking to a laser diode, permitting pure power enhancement with extremely low background noise. Experimental verifications reveal that the original linewidth undergoes a negligible degradation of less than 1 hertz, and the absolute frequency position is also subject to a small disturbance of less than 3 parts in 1015 over 10 s averaging. Covering the full spectral range of the frequency comb, the outstanding performance of optical frequency generation could find applications particularly in precision spectroscopy, frequency calibration, and length metrology.
This work was supported financially by the Ministry of Science and Technology of the Republic of Korea as the Creative Research Initiatives Program for Billionth Uncertainty Precision Engineering.
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