A difference frequency generation scheme that is potentially applicable to self-stabilization of the carrier-envelope-offset phase is demonstrated for the first time with a fiber-laser-based system. By taking advantage of the unique dispersion of the photonic-crystal-fibers, short pulses at 615 nm can be efficiently and selectively generated with low noise via Cherenkov-radiation in a 23-mm-PCF with a mode-locked Yb-fiber laser. Difference frequency generation between the 615-nm pulses and the 1030-nm output pulses from the Yb-fiber amplifier produces pulses at ~1530 nm, which can be readily amplified by Er-doped-fiber amplifiers. This scheme may provide a new route to a fiber-laser-based CEO-phase-stabilized source.
© 2005 Optical Society of America
Since the first demonstration of the carrier-envelope-offset (CEO) phase locking in a Ti:sapphire laser system in 2000 , several groups have attempted to transfer this technique into fiber-based systems [2–4]. The scheme generally requires an octave-spanning spectrum, an f-2f interferometer to detect the CEO-frequency fCEO and the phase-tracking electronics with servo-loop feedback to lock the carrier-envelope phase.
Alternatively, without using electronic feedback systems, difference-frequency-generation (DFG) between components within the spectrum of a broad-spectrum pulse provides an all-optical way to generate self-CEO-phase-stabilized pulses . This was demonstrated and verified, first with optical parametric amplifiers [6, 7] at kHz repetition rate, and later with a Ti:sapphire oscillator at MHz repetition rate , however incorporating this technique into a fiber-based laser system could lead to a potentially more practical system.
Both schemes require two well-separated spectral components generated with a single input pulse via Kerr nonlinearity in order to preserve the CEO-phase of the pulse. This relies on the spectral broadening when an ultrashort pulse propagates in nonlinear media such as CaF2, Sapphire or photonic-crystal-fibers (PCFs) [1, 6–8]. In the conventional f-2f self-referencing technique, CEO-frequency can be detected with as low as tens of nano-Watts of optical power . In contrast, since the self-CEO-phase-stabilized pulses are produced via DFG, the system has to produce high-peak-power components at two specific well-separated wavelengths to achieve high DFG efficiency at a usable wavelength. Due to the complexity of the supercontinuum generation in PCF, there has been no effective way to achieve this. Previously, only 2 µW of average power at the difference frequency (DF) were generated when using 350-mW of 9-fs pulses from a Ti:sapphire oscillator . This becomes the major limiting factor, when replacing the Ti:sapphire laser with a fiber laser as the light source, because fiber lasers generally produce substantially longer pulses.
In supercontinuum generation with PCF, the dramatic spectral broadening is attributed to the fission of higher-order solitons into redshifted fundamental solitons and blueshifted Cherenkov radiation (CR) . The formation of fundamental solitons and subsequently the Raman soliton self-frequency shift pushes towards longer wavelength, while the blueshifted CRs contribute the shorter wavelength part of the spectrum; spectrum with over an octave-spanning is thus generated. Both of these processes usually have to be used to generate spectrum that is broad enough for the experiments [1, 2, 8].
As the result of the significant dispersion change of the PCFs over the spectral bandwidth of the soliton, phase matching between the linear dispersive wave and the soliton can be obtained. This results in energy leakage from the soliton to dispersive wave, producing CR. Depending on the slope of the dispersion, CR can occur in the blue-shifted  or red-shifted  sides of the soliton. Recently, it has been found that the process can be very efficient. A prominent visible component with up to 25% of the total input power can be generated via CR in a very short piece of PCF . A wide-range of tunability of this component can be achieved by either varying the input wavelength of the seeding pulses  or changing the core size of the PCF, thus the zero-dispersion-wavelength (ZDWL) of the fiber . The CR occurs in a very early stage of the propagation of the pulse [9, 11]. This enables one to achieve large-spanning spectrum in a very short PCF before excessive noise accumulates in the supercontinuum generation process [2, 13, 14]. Furthermore, the tunability of this process allows us to efficiently direct energy into a spectral component at a desired wavelength. Low-noise pulses with less than 100 fs, at wavelengths across the visible spectrum can be generated by using a PCF with appropriate core diameter. Furthermore, we have recently shown that by longitudinal dispersion micro-management, the bandwidth and conversion efficiency can be controlled .
2. Experimental setup
The experimental setup is shown in Fig. 1. A recently developed passively mode-locked Yb:fiber oscillator is used as the light source . It is operated in stretched-pulse mode, producing 80-mW of average power with a repetition rate of 38 MHz. After a single-stage Yb:fiber amplifier and a grating compressor, pulses as short as 90 fs with up to 180 mW of average power are obtained. Figure 2(a) shows the optical spectrum with ~30 nm FWHM and the autocorrelation trace of the pulses. After the compressor, a half-wave plate (HWP) and a polarizing beam splitter (PBS) are used to split the beam into two beams. The power ratio is adjustable by rotating the HWP. The smaller portion of the power (40 mW) is directed into one arm providing 1030-nm component for the DFG. The rest of the power (140 mW) is coupled into a 3.3-µm-core, 23-mm-long PCF (NL-3.3-880, Crystal-Fibre) to generate up to 3-mW of CR at 615 nm providing the other component for DFG. DFG between the 615-nm CR pulses and the 1030-nm output pulses from the Yb-fiber amplifier produces pulses around 1530 nm, which can be readily amplified by Er-doped-fiber amplifiers. We believe that this is the first demonstration of a fiber-laser-based all-optical scheme for CEO phase stabilization.
3. Experimental result
The phase matching condition between the soliton and the CR wave is given by :
where ω0 is the center frequency of the soliton; βS(ω) and βC(ω) are the propagation constants of the soliton and CR wave respectively; βk is the k-th order derivative of β(ω), therefore βC(ω) at ω0; vS=1/β 1 is the group velocity at ω0; γ is the nonlinear coefficient of the PCF; and P0 is the soliton peak power.
We launch the 90-fs pulses at 1030 nm into 23-mm of different PCFs with various ZDWLs. Figure 2(b) shows that the CR wavelength strongly depends on the ZDWL of the PCF. It moves to shorter wavelength as the ZDWL decreases. This can be explained by the phase matching condition given by Eq. (1). When β 3 > 0 (β2<0 for soliton), the phase matching between CR and soliton occurs at shorter-wavelength-side of the soliton (ω<ω 0). The absolute value of β 2 at ω 0 (1030 nm) increases significantly faster than β3, as the ZDWL of the PCF moves to shorter wavelength , thus pushing the phase matching to higher frequency (shorter wavelength). For more precise analysis, higher order dispersions have to be included. As shown in Eq. (1), the contribution of nonlinearity to the phase-matching condition also pushes the CR to a shorter wavelength as the peak power of the seeding pulse increases. This wide-range of tunability for CR component allows us to select one PCF that is ideal for our experiment. When using the fiber NL-3.3-880, the CR pulse is located at 615 nm, which enables us to generate pulses at ~1530 nm by DFG between the CR pulses and the direct output pulses from the amplifier (615 nm-1030 nm→1526 nm). The CR spectrum has ~20 nm bandwidth (FWHM), as shown in Fig. 2(c). Measurement has shown that the pulse width of this type of CR pulse can be as short as 70 fs . This ensures a higher peak power in the DFG for higher efficiency.
As shown in Fig. 1, two components are combined with a short-pass dichroic mirror (cutoff wavelength at 1000 nm). The beam is focused onto a 1-mm-thick type II BBO crystal (θ=22.30). Phase-matching is obtained for DFG (615 nm (e)-1030 nm (o)→1526 nm (o), θ=20.80). The DF at ~1530 nm is coupled back into a single-mode-fiber (SMF) and the spectrum is analyzed by an optical spectrum analyzer. As shown in Fig. 2(d), as a result of the chirp in the pulses, the center wavelength of the DF spectrum depends on the delay between the 1030-nm and 615-nm components. It can be tuned across the gain bandwidth of Er-doped amplifiers (1520 nm~1560 nm) by varying the delay. The DF vanishes when the delay is larger than 100 fs, indicating that the CR pulses are shorter than 200 fs. The DF power coupled into the SMF is estimated to be 2 µW, with less than 20% coupling efficiency. This poor coupling efficiency is likely caused by the elliptical beam profile of the ~1530-nm beam as the result of the spatial walk-off in the BBO crystal. Since KTP has higher nonlinear coefficient and lower spatial walk-off than BBO, by changing the BBO-crystal into an optimized KTP crystal, the generated DF power is expected to increase by a factor of 4 with a more circular beam profile. Using an LBO crystal would give an even higher DFG efficiency, while its temperature dependence may add complexity into the setup. Another advantage of this scheme is that the 1030-nm component for DFG can be easily amplified up to watt-level by using an Yb:fiber amplifier, thus leading to higher DF power. Furthermore, after being amplified and frequency-doubled into 770 nm, it could serve as a seeding of Ti:Sapphire amplifiers for a high power CEO-phase-stabilized source for various applications. By using CR from PCFs with different core diameters, the DF component can be generated in the range 900 nm~1600 nm.
In conclusion, by taking advantage of controllable CR generation in PCFs, we have demonstrated the first fiber-laser-based all-optical scheme for CEO-phase stabilization. This scheme may provide a route to a fiber-laser-based CEO-phase-stabilized source. The noise and stability properties of this source are under further investigation and will be reported elsewhere.
References and links
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