Femtosecond-laser frequency combs revolutionized the field of precision metrology after their introduction in 1999. Today, they are commonly used in atomic clock calibration, low-noise frequency synthesis, astronomical spectrograph calibration and precision spectroscopy. Scientists are now pushing to extend frequency combs into the mid-infrared and extreme ultraviolet spectral region with Yb:fiber technology.
Artist’s impression of an extreme ultraviolet (XUV) frequency comb, which creates attosecond pulse bursts at XUV wavelengths. Each of the resulting harmonics has its own set of “teeth,” creating a frequency comb within each harmonic.
The Ye group and Brad Baxley, JILA
A frequency comb is a visual model of a mode-locked laser spectrum generated from a series of femtosecond (fs) pulses. A train of pulses from a mode-locked laser produces a spectrum with a series of sharp spectral lines, each at a specific frequency, that resemble the teeth of a comb. The combs typically operate in the near-infrared and visible spectrum. However, various spectroscopic applications rely on combs that cover the extreme ultraviolet (XUV) as well as the mid-infrared (MIR) spectral region, enabled by high-power sources to drive nonlinear conversion schemes.
A frequency comb—which contains thousands of individual modes—is determined by only two radio frequencies (RF): the repetition rate, frep, which defines the separation between adjacent modes, or comb teeth, and the offset frequency, f0, which determines the absolute position of the comb structure. One can measure the f0 by using a self-referencing technique: In an octave-spanning spectrum, the frequency-doubled modes from the long wavelength side are shifted by the f0 compared to corresponding modes from the original spectrum. The desired f0 is derived from the beat signal between the two. One can then determine the frequency of each optical mode νn by the equation: νn = n × frep + f0, with n being an integer representing the mode number. Conversely, stabilizing these two RF-frequencies via phase-locked loops fixes the overall comb structure down to the level of the frequency references used.
Fiber frequency comb technology
Frequency combs were originally based on Ti:sapphire laser technology. In 2005, researchers demonstrated Er:fiber frequency combs. These devices allowed ease-of-use; rugged, compact and low-cost setups; and reliable long-term operation. The introduction of Yb:fiber technology to frequency combs led to dramatic improvements in optical linewidth, phase-locking performance and average power approaching the 100 W-level. These improvements not only closed the gap to Ti:sapphire technology but opened the door to new possibilities, especially for frequency conversion schemes. Yb:fiber systems serve as the basis for frequency combs at almost any wavelength between the XUV and the MIR spectral regions. Due to their robust performance and the opportunities for tight phase-locking, these systems are the ideal tools for precision spectroscopy.
Passively mode-locked fiber oscillators, a key component for frequency combs, have been intensely studied over the past three decades. Breakthroughs in this area have resulted in significant improvements in laser performance, especially in terms of pulse energy. The first passively mode-locked fiber oscillators demonstrated in the early 1980s were based on optical soliton generation in the laser cavity. Their pulse stability relies on the balance between the phase contributions resulting from anomalous dispersion (β2 < 0) and self-phase modulation. This kind of fiber oscillator is limited to values of about 100 pJ due to the large nonlinear phase shifts from the tight confinement of the electric field in the fiber core and the long interaction lengths.
Tremendous progress has been made by operating passively mode-locked Yb:fiber oscillators at normal cavity dispersion. The pulses are not subject to a balancing effect, but rather they broaden in the spectral and temporal domain during pulse evolution at normal dispersion. Understanding the pulse dynamics in the normal dispersion regime and its manipulation allows for the scaling of the pulse energy towards µJ-levels when the laser is operated at high-cavity dispersion.
Frequency comb. A frequency comb consists of narrow equidistant optical modes with positions determined by the repetition rate frep and the offset frequency f0. The f0 is measured by self-referencing.
Amplified Yb:fiber frequency comb. SA: saturable absorber; SMF: single-mode fiber; YDF: Ytterbium-doped fiber; FBG: fiber Bragg-grating; WDM: wavelength division multiplexer; ISO: optical isolator; and DCF: depressed-cladding fiber.
Phase noise and linewidth
Increased phase noise is the price to pay for the improvements in pulse energy. Noise reduction can only occur up to a certain bandwidth set by the actuators used for phase control. Noise at frequencies higher than this locking bandwidth cannot be cancelled by feedback control. Feedback control is also limited by the travel range of the actuators. Pulse energy scaling helps to reduce direct timing jitter resulting from the coherent addition of amplified spontaneous emission to the pulse amplitude.
A more severe effect occurs at high cavity dispersion. The large difference between the free-running longitudinal mode positions given by the cavity dispersion and the equidistant position caused by the mode-locking mechanism results in a large timing jitter and increased phase noise. Researchers have shown that there is a direct relationship between the cavity dispersion and the comb linewidth, often represented by the bandwidth of the f0 beat signal.
A recently published study shows that the free-running f0 linewidth was reduced by two orders of magnitude from 6 MHz to 65 kHz by changing the cavity dispersion from 0.011 ps2 to zero. Therefore, one should aim to achieve high pulse energy at zero cavity dispersion when designing a suitable mode-locked oscillator for a frequency comb. These are the main contributions to passive stability. Technical noise resulting from the pump laser also must be avoided.
These considerations are accounted for in the laser design shown in the amplified Yb:fiber frequency comb figure on the right. The 150 MHz Yb:fiber oscillator is based on a Fabry-Perot cavity design and passively mode-locked by a sub-picosecond (ps) lifetime saturable absorber mirror. Using a real saturable absorber, for example, based on InGaAs quantum wells, not only increases the oscillator’s self-starting capability, but also ensures a more stable setup.
Artificial saturable absorbers for fiber oscillators, such as nonlinear polarization evolution, rely on a defined evolution of nonlinear phase shifts altered by various effects like environmental changes in birefringence. This can gradually destabilize or even prevent mode-locking. However, in the oscillator design, the dispersion is compensated to a slightly positive value by a fiber Bragg-grating, which also serves as the output coupler.
Due to the availability of highly doped ytterbium gain fibers, the repetition rate can now be scaled up to 1.1 GHz with this design. High repetition rates are not only beneficial for spectroscopy—as this means a higher power per comb mode—but also for other applications such as calibrating astronomical spectrographs and low phase-noise RF generation. These applications still require passive filter cavities to scale the repetition rate to tens of gigahertz. However, the usage of high-repetition-rate oscillators significantly relaxes the requirements for the external filter cavities.
Phase-locking Yb:fiber frequency comb. This frequency comb has high bandwidth transducers. (a, b) The beat signal (100 kHz RBW) and phase noise power spectral density with the integrated phase error for the f0-lock using an AOM. (c, d) The beat signal (100 kHz RBW) and phase noise power spectral density with the integrated phase error for the frep-lock to a cw laser at 698 nm using an intra-cavity EOM.
For most practical applications, the pulse train from Yb:fiber oscillators must be amplified to reach pulse energies of a few nanojoules. Self-phase modulation is considered to be detrimental when amplifying frequency combs because it results in amplitude-to-phase-noise conversion. One can realize linear chirped pulse amplification by stretching the pulses in depressed-cladding as well as standard fibers and amplifying them in a cladding-pumped fiber amplifier. A fully integrated setup, including compensation up to third-order dispersion, can be developed by using a fiber coupler for pump light delivery. After recompression in a grating compressor, 80-fs pulses at Watt-level average powers are possible.
The passive stability of this laser design is reflected by a free-running f0 linewidth of less than 15 kHz. The noise performance is not quantum-limited, but it is still subject to technical noise, mainly from the pump laser. Reducing the relative intensity noise of the oscillator via a feedback mechanism was shown to result in a further decrease in phase noise. This is highlighted by the reduction of the f0 and beat signals with continuous wave (cw) lasers. The strong correlation between the pump laser’s intensity noise spectrum and the comb’s frequency noise spectrum indicates that amplitude-to-frequency-noise conversion in the oscillator is the dominant source of noise. Amplitude noise is caused by the pump laser as well as by quantum-noise contributions dominating at higher sideband frequencies.
In order to apply feedback for phase control to a mode-locked oscillator, one must implement actuators for dynamic control of frep and f0. Typically, piezoelectric transducers are used to change the cavity length, and hence, frep. This allows for phase noise compensation up to sideband frequencies of 180 kHz, limited by acoustic resonances. Together with f0-servomechanisms (servos) based on pump power modulation, this gives a good set of control parameters. In rare-earth doped fibers, the upper state lifetime of the laser transition is on the order of a few milliseconds, preventing f0-servos at high frequencies.
Significantly higher servo bandwidths can be realized with electro- and acousto-optical modulators (EOM and AOM). We used 1-mm long LiTaO3 crystal as an EOM in the free-space section of the laser cavity. It acts as a frequency transducer with a servo bandwidth of 390 kHz, directly controlling the cavity length through its index change. A 200 MHz AOM with a servo bandwidth of 250 kHz was implemented to serve as an f0-actuator outside the cavity. The phase-locking performance of this scheme is displayed in the figure below, which shows the in-loop phase noise power spectral density together with the integrated timing jitter, as well as the in-loop beat signal.
Excellent locking performance was also achieved with another stabilization scheme: phase-locking two comb teeth to two different optical references. This is an alternative to the use of self-referencing. These two methods of complete phase stabilization demonstrate that optical coherence can be established anywhere within the spectral coverage, which is significantly extended by supercontinuum generation.
Nonlinear spectral broadening in highly nonlinear fibers is another building block for fiber frequency combs because octave-spanning optical spectra required for self-referencing are not directly available from fiber oscillators. Supercontinuum generation is also essential for all applications reliant on wavelengths outside the laser gain bandwidth. The key issue for supercontinuum generation is the preservation of coherence and comb structure.
Spectral output after supercontinuum generation. The superconinuum was created in a suspended-core fiber. (a) The pump wavelength and the zero dispersion wavelength of the fiber are shown, along with a schematic of the coherence measurement using two narrow-linewidth cw lasers. (b) Out-of-loop beat signal between the Yb:fiber frequency comb and a cw laser at 1.54 µm exhibiting 1.5 Hz linewidth. (c) Tuning characteristic of the longest wavelength Raman soliton.
When ultrashort pulses pump a nonlinear fiber in the anomalous dispersion regime, the spectral broadening process is an interplay among many nonlinear processes, such as self-phase modulation, soliton fission, four-wave mixing and intrapulse Raman scattering. For the supercontinuum shown in the figure, we launched the pulse train at an energy of 1.2 nJ into a 24-cm long suspended-core fiber, and did numerical simulations on the basis of a generalized nonlinear Schrödinger equation. They showed a remarkable agreement with the experiment. Several spectral features of the supercontinuum generation can be clearly distinguished, including the Raman-shifted solitons at long wavelengths and the corresponding dispersive waves in the visible spectrum connected by four-wave mixing.
Optimization of both the pump pulse and the nonlinear fiber enables preserving the phase coherence during spectral broadening. It can be optimized to transfer coherence over the entire spectral width of the supercontinuum. The heterodyne beat between the phase-locked Yb:fiber frequency comb and a Hz-level cw laser pictured to the right exhibits a linewidth of 1.5 Hz. This corresponds to a coherence time of 200 ms or 3 × 107 pulses from the 154 MHz pulse train.
Detailed numerical simulations revealed no changes in the phase standard deviation of the supercontinuum comb lines, indicating that the supercontinuum is not the limiting factor in this measurement. This is supported by the fact that the measured heterodyne beat signal corresponds to the estimated optical linewidth of the 1.54 µm laser. Yb:fiber frequency combs can coherently bridge the large spectral gap between the visible wavelengths (where optical clocks operate) and the c-band of optical telecommunication used for long-distance frequency dissemination via fiber links in a simple and robust scheme.
An 80-Watt Yb:fiber frequency comb. Pulse characteristics are measured by frequency resolved optical grating.
Raman solitons—spectral features of supercontinuum generation—are stable and temporally isolated pulses that exhibit an interesting feature. Their tunability allows for pulse generation between 1.1 and 1.6 µm, phase-locked to the driving pulse as shown in the figure on the left. The original pulse train at 1.05 µm still exhibits Watt-level average powers. Such a coherent two-color source constitutes an ideal basis for difference frequency generation. As both fields were generated with the same source, the resulting idler output is offset-free, requiring only frep to be phase-locked. This nonlinear mixing scheme enables a tunable frequency comb source in the MIR spectrum. It is highly desirable for spectroscopy in the molecular fingerprint region, such as trace gas detection. Based on difference frequency generation in a gallium selenide crystal, we recently demonstrated a MIR source continuously tunable from 3 to 10 µm at mW-power level.
Average power scaling
The true strength of Yb:fiber technology is its ability to scale the average power of ultrafast laser systems to almost the kilowatt level. This feature is particularly interesting for frequency conversion schemes, pushing frequency comb technology into wavelength regions not accessible by lasers but desired for spectroscopic measurements. The most demanding of these schemes is high harmonic generation enabling coherent radiation in the XUV spectral region. The reduction of the repetition rate to kHz-level is usually applied to reach the required peak intensities of 1013 to 1014 W/cm2, but this can’t be used with frequency combs.
Passive enhancement cavities provide a solution to this problem, as they are capable of increasing the average power of the driving frequency comb by a factor of several hundred. In the intracavity focus, the peak intensities are high enough to generate high harmonics in noble gases. This approach relies on high-power frequency combs that are fully compatible with low-noise phase control.
Chirped pulse amplification in large-mode-area fibers allows for easy power scaling of high-repetition-rate fiber laser systems. However, low noise optical phase control in frequency combs also requires pedestal-free ultra-short pulses. This specification is difficult to fulfill because not only the mismatch in group-delay between stretcher and compressor need to be compensated but material dispersion introduces significant contributions in fiber laser systems.
Fortunately, tailored dispersion properties are available from many fibers, such as high-order mode fibers or depressed cladding fibers. A combination of these can be used to compensate almost arbitrary dispersion profiles and provide an integrated and alignment-free platform unique for high-power chirped pulse amplification.
An 80-W fiber frequency comb based on the oscillator design we described here was recently demonstrated. It highlighted the unique power scaling capability of Yb:fiber frequency combs. By carefully adjusting the length of the stretcher fibers, the researchers optimized the pulse compression until they achieved 120-fs pulses. The pulse characteristic shown on the right was measured by frequency-resolved optical gating and revealed that only 14 percent of the pulse energy remains in the pedestal. The deviations from the ideal phase—especially at the blue side of the optical spectrum—are attributed to the residual fourth-order dispersion, which, according to theoretical estimations, is only compensated by 90 percent.
Due to the strictly linear amplification, the B-integral (representing the integrated nonlinear phase shift) is as low as 0.2. The pulse characteristic is independent of the output power, highlighting the amplification at negligible nonlinear phase shifts. Such linear cladding-pumped fiber amplifier schemes are fully compatible with low-noise phase control. This was confirmed in long-term measurements where the frequency comb was phase-locked to an Rb-microwave clock for more than eight hours. Both in-loop signals were simultaneously counted with 1-s gate time and exhibited an instability of 0.88 mHz RMS for f0 and 0.35 mHz for frep.
The laser system described here was used to demonstrate the first full repetition rate XUV frequency comb covering wavelengths down to 40 nm, pushing the boundaries of frequency comb technology to unprecedented wavelength ranges. By isolating single harmonics, it was possible to resolve high-energy transitions of argon at 82 nm and neon at 63 nm revealing an upper boundary for the width of individual comb teeth of less than 10 MHz. The performance of this XUV comb is currently limited by the enhancement cavity, rather than by the fiber frequency comb operated only at 30 Watts—40 percent of its maximum power.
Fiber laser technology provides a unique technological platform for integrated and alignment-free laser setups. Frequency combs based on ultrafast fiber lasers became an indispensable tool for many emerging applications in fundamental and applied science, including optical metrology, atomic clock calibration, low-noise frequency synthesis and especially high-precision spectroscopy. Due to the huge potential for power scaling, Yb:fiber frequency combs are ideally suited for frequency conversion schemes extending the wavelength coverage of frequency combs beyond spectral regions accessible by laser gain materials.
The contributions of I. Hartl and M.E. Fermann at IMRA America Inc., U.S.A.; A. Gambetta and M. Marangoni at Politecnico di Milano, Italy; K.S.E. Eikema at VU University, Amsterdam, the Netherlands; and M.J. Martin, C. Benko, D.C. Yost, A. Cingöz and J. Ye at JILA, University of Colorado and NIST, U.S.A., are acknowledged and greatly appreciated.
Axel Ruehl is a postdoc in the department of physics and astronomy at VU University Amsterdam, the Netherlands.
References and Resources
>> A. Ruehl et al. Opt. Lett. 35, 3015 (2010).
>> A. Cingöz et al. Opt. Lett. 36, 743 (2011).
>> L. Nugent-Glandorf et al. Opt. Lett. 36, 1578 (2011).
>> A. Ruehl et al. Phys. Rev. A 84, 011806 (2011).
>> C. Benko et al. arXiv:1202.5199v1 (2012).
>> A. Cingöz et al. Nature 482, 68 (2012).
>> A. Ruehl et al. arXiv: 1203.2441 (2012).