Ultrafast Lasers and Frequency Combs

A. Femtosecond laser technology

Ultrashort pulse lasers are an enabling technology for a whole range of fundamental and applied research areas as well as industrial applications. To generate such short pulses typically multiple longitudinal modes in a laser resonator are excited and locked to each other, such that a pulse much shorter than the cavity round-trip time is created inside the laser resonator. In the frequency domain, the mode-locked pulse train emitted from the oscillator represents a frequency comb, i.e., a series of discrete, equally spaced laser lines. The shortest pulse that can build up is then limited by the gain bandwidth of the amplifying medium. Our group has made major contributions to both the understanding of the pulse generation mechanisms involved in the various types of lasers and the emerging technologies leading to shorter and shorter pulse durations. The progress of pulse shortening culminated in the generation of the shortest pulses directly from a laser oscillator approaching a single optical cycle at 800 nm from Kerr-lens mode-locked Ti:sapphire lasers, developed in our group [1,2,3,4,5]. Using double-chirped mirror pairs (DCMPs) and a phase-matched output coupler, the cold cavity dispersion can be well managed with an octave bandwidth (600-1200 nm) [6,7]. As a result, octave-spanning spectra can be obtained with various repetition rates up to >2GHz [8,9]. To further optimize the output spectrum, both the cold cavity dispersion and the round-trip nonlinear phase are taken into account to compensate for such that the spectrum wings are enhanced with an improved beam profile.

Fig. 1. (a) High reflectivity and precise dispersion compensation with double-chirped mirror pairs (DCMPs). (b) Experimental intracavity spectra with different OCs, a 5% PMOC (red) and a ZnSe/MgF2 1% OC (blue), and the residual cold cavity phase (black) of the laser with a 5% PMOC, which has an addition phase feature in the long wavelength regime to match the round-trip nonlinear phase around 1140nm. This phase feature greatly enhances the spectral density in the long wavelength wing especially around 1140 nm (~12dB) even when comparing with the spectrum achieved with the 1% OC.

Femtosecond mode-locked lasers exhibiting ultralow noise have opened new research possibilities. Measurement of phase noise in optical pulse trains by converting to a radio frequency signal is extremely difficult because RF measurement techniques are limited by thermal noise in terminating resistors as well as the signal level available for input to the phase noise measurement system. Recently we have demonstrated a direct optical technique—balanced optical cross correlation— with higher sensitivity by avoiding the photo-detection process [10]. We measured the timing error spectrum between phase locked optical pulse trains produced from two nearly identical 10-fs Ti:Sapphire lasers running at 82 MHz, and demonstrated a record low integrated timing error of less than 13 attoseconds (measured from DC to the Nyquist frequency of the pulse train) [11]. This corresponds to the lowest value of high frequency phase noise ever recorded of -203 dBc/Hz (assuming a 10 GHz carrier) for offset frequencies greater than 1 MHz. For many applications, high repetition-rate (>1 GHz) lasers with femtosecond pulse duration are required in addition to ultralow noise. For nonlinear bio-optical imaging in which photo-induced damage is caused by pulse energy rather than average power, increasing pulse repetition-rate will improve signal-to-noise ratio and reduce data acquisition time. Frequency combs — achieved by fully stabilizing both the repetition-rate and the carrier-envelope offset frequency of multi-GHz lasers — exhibit large line spacing that may permit access to and manipulation of each individual comb line. Such capabilities have opened numerous frequency-domain applications including optical arbitrary waveform generation, high-speed analog-to-digital conversion, and high-resolution spectroscopy.

Fig. 2. Spectrum of phase error between two mode-locked Ti:Sapphire laser pulse trains, scaled to a 10 GHz carrier. The result of the optical cross correlator measurement is plotted in red, and in black is the noise floor of the optical cross correlator measurement determined by measuring the output of the balanced detector when blocked. There are four noise spurs at 80 MHz, 60 MHz, 40 MHz, and 20 MHz, none of which are counted towards the integrated timing error of the pulse train. At 80 MHz is the pulse repetition rate of the lasers, fR; at 20 and 60 MHz is the difference frequency beat between the two laser optical spectrums due to their different carrier envelope offset frequencies(fb=fCEO1-fCEO2); at 40 MHz is a mixing product between the two fCEO signals and the fR signal in the photodiodes. In addition, when calculating the integrated timing error from the Nyquist frequency (41.3 MHz) to 100 Hz, the falling response of the detector beyond 20 MHz is corrected to give a white noise floor. The estimated quantum limited phase noise for the lasers measured here, plotted in green, assumes only that the laser cavities have zero dispersion. The corresponding quantum limited integrated timing error does not exceed one attosecond until approximately 200 Hz offset frequency.

References

1. O. D. Mücke, L. Matos, and F. X. Kärtner, “Solid-State Laser Technology for Optical Frequency Metrology”, in Solid-State Lasers and Applications, edited by A. Sennaroglu, 389 (CRC Press, 2006, ISBN 0849335892).
2. R. Ell, U. Morgner, F. X. Kärtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Generation of 5fs pulses and octave-spanning spectra directly from a Ti:sapphire laser,” Opt. Lett. 26, 373, (2001).
3. L. Matos, O. Kuzucu, T. R. Schibli, J. Kim, E. P. Ippen, D. Kleppner and F. X. Kärtner, “Direct frequency comb generation from an octave-spanning, prism-less Ti:sapphire laser,” Opt. Lett. 29, 1683 (2004).
4. O. D. Mücke, R. Ell, A. Winter, J.-W. Kim, J. R. Birge, L. Matos, and F. X. Kärtner, “Self-Referenced 200 MHz Octave-Spanning Ti:Sapphire Laser With 50 Attosecond Carrier-Envelope Phase Jitter,” Opt. Express 13, 5163 (2005).
5. H. M. Crespo, J. R. Birge, E. L. Falcão-Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire Laser,” Opt. Lett. 33, 833 (2008).
6. L.-J. Chen, M. Y. Sander, F. X. Kärtner, “Kerr-lens Mode‐locking with Minimum Nonlinearity Using Gain‐Matching Output Couplers,” Opt. Lett. 35, 2916 (2010).
7. M. Y. Sander, E. P. Ippen, and F. X. Kärtner, “Carrier-Envelope Phase Dynamics of Octave-Spanning Dispersion-Managed Ti: Sapphire Lasers,” Opt. Express 18, 4948 (2010).
8. L.-J. Chen, A. J. Benedick, J. R. Birge, M. Y. Sander, and F. Kärtner, “Octave-spanning, dual-output 2.166 GHz Ti:sapphire laser,” Opt. Express 16, 20699 (2008).
9. M. Y. Sander, J. Birge, A. Benedick, H. M. Crespo, and F. X. Kärtner, “Dynamics of dispersion managed octave-spanning titanium:sapphire lasers,” JOSA B 26, 743 (2009).
10. J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser & Photonics Reviews 4, 432 (2010).
11. A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photon. 6, 97 (2012).

B. Femtosecond sources based on Yb-fiber laser technology

High repetition-rate (>1 GHz) lasers with femtosecond pulse duration are required in many applications. For nonlinear bio-optical imaging (e.g., two-photon fluorescence excitation microscopy) in which photoinduced damage is caused by pulse energy rather than average power, increasing pulse repetition-rate will improve signal-to-noise ratio and reduce data acquisition time. Frequency combs — achieved by fully stabilizing both the repetition rate and the carrier-envelope offset frequency of multi-GHz lasers — exhibit large line spacing (equal to the laser’s repetition rate) that may permit access to and manipulation of each individual comb lines. Such capabilities have opened numerous frequency-domain applications including optical arbitrary waveform generation, high-speed analog-to-digital conversion, and high-resolution spectroscopy.
Many applications require GHz femtosecond pulses at the wavelength range that cannot be directly generated from mode-locked fiber lasers. For example, most live biological specimens exhibit a minimum light attenuation in the range of 1.2-1.35 μm. Using GHz femtosecond pulses of this wavelength range for nonlinear bio-optical imaging allows deeper penetration through turbid specimens and meanwhile avoids photo-induced damage caused by pulse energy. Recently we have demonstrated a 3-GHz Yb-fiber laser system with >10-W average power, constituting a powerful laser platform to access other wavelength range via nonlinear wavelength conversion [1]. Using fiber-optic Cherenkov radiation [2,3], we have demonstrated a 3-GHz, 14-fs source overlapping with the Ti:sapphire laser wavelength region (700-900 nm); with >300-mW average power, it constitutes a potential substitute of multi-GHz Ti:sapphire lasers [4]. Using stimulated Raman scattering inside photonic crystal fibers, we have implemented a 3-GHz femtosecond Raman soliton source tunable between 1.06-1.35 μm; at 1.35 μm, the source produces average power of 900 mW [5].

Fig. 3. Schematic setup of the 3-GHz master-oscillator-power-amplifier system and optical spectra at the output of the 3-GHz oscillator (blue line), pre-amplifier (red line), and power amplifier (green line), respectively.

Fig. 4. (a) Filtered spectra of broadband fiber-optical Cherenkov radiation at three different fiber length: 28 mm (red line), 37 mm (black line), and 48 mm (blue line). These three spectra are generated at different input pulse energies: 1430 pJ (28-mm PCF), 780 pJ (37-mm PCF), and 440 pJ (48-mm PCF). The spectra are all normalized to their spectral peak at 940 nm. (b) Black line: measured autocorrelation trace of the compressed FOCR pulse using DCMs to compensate for the phase from the FOCR spectrum (i.e., black curve in (a)) generated from the 37-mm PCF with 780-pJ input pulse energy. Red dashed line: calculated autocorrelation trace of the transform-limited pulse given by the FOCR spectrum. (c) Raman induced soliton red-shift at the different input power at 87 cm PCF (NL-3.2-945) length. Inset: autocorrelation trace of the Raman soliton at 1.3 µm. The spectra are normalized to the first order Raman soliton peak.

References

1. H.-W. Chen, G. Q. Chang, S. H. Xu, Z. M. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37, 3522, (2012).
2. G. Q. Chang, L.-J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express 19, 6635 (2011).
3. G. Q. Chang, L.-J. Chen, and F. X. Kärtner, “Highly efficient Cherenkov radiation in photonic crystal fibers for broadband visible wavelength generation,” Opt. Lett. 35, 2361 (2010).
4. H.-W. Chen, H. Zia, J. K. Lim, S. H. Xu, Z. M. Yang, F. X. Kärtner, and G. Q. Chang, “3 GHz, Yb-fiber laser based, few-cycle ultrafast source at the Ti:sapphire laser wavelength,” Opt. Lett. in press (2013).
5. J. K. Lim, H.-W. Chen, S. H. Xu, Z. M. Yang, G. Q. Chang, and F. X. Kärtner, “3 GHz, Watt-level femtosecond Raman soliton source,” Opt. Lett. (to be submitted).

C. Femtosecond-laser frequency combs and their applications

Femtosecond-laser frequency combs have revolutionized the field of optical frequency metrology [Nobel Prize in physics 2005 for John L. Hall and Theodor W. Hänsch (together with Roy J. Glauber)] and facilitated the construction of optical clocks. Our group developed a carrier-envelope frequency independent optical clockwork for the HeNe/CH4 optical molecular clock. Our clockwork is based on sum/difference-frequency generation between different portions of a Ti:sapphire frequency comb in a PPLN crystal [1,2]. The HeNe/CH4 optical clock was realized in collaboration with Jun Ye’s group at JILA in Boulder, CO (U.S.A.) and Mikhail A. Gubin and coworkers from the Lebedev Physical Institute in Moscow (Russia) [2,3]. The photo below shows the HeNe/CH4 optical clock in operation at MIT. Such ultrastable frequency combs can also be used for extremely precise large-scale timing distribution in accelerators and next-generation X-ray FELs [4].

Fig. 5. HeNe/CH4 optical clock in operation at MIT.

Recently we have also applied frequency-comb technology to precision calibration of astronomical spectrographs (“astro-comb”) [5-14]. Highly precise and highly accurate calibration of astronomical spectrographs is necessary to enable astronomers to use the radial velocity method to search for planets outside our solar system and to unravel other cosmological mysteries. In this method, astronomers monitor the light emitted from stars to observe a slight periodic shift in the emitted spectrum caused by the motion of the star induced by an orbiting planet. In this application, both the accuracy and precision of the frequency comb will be utilized to enable searches for earth like planets and solar systems. We have developed three astro-combs to calibrate the absolute frequency of a high-resolution astrophysical spectrograph over a 100 nm band in the deep red [12, 14], over 15 nm in the blue [9, 11], and over 100 nm in the green [5, 6]. Astro-combs at the short wavelength end of the emission spectrum of Sun-like stars (400-600 nm) are highly desired. In addition to providing the largest photon flux, this wavelength region is rich with spectral features of high quality most suitable for use with precision-radial-velocity measurements. Our green astro-comb with wavelength coverage of 500 – 620 nm provides >7000 astro-comb lines equally spaced by 16 GHz with powers varying by less than 8 dB. The frequency of each astro-comb line is accurate to 1 cm/s level over years because it is referenced to the Global Positioning System (GPS). We have deployed this green wavelength astro-comb at the Telescopio Nazionale Galileo (TNG) on La Palma in the Canary Islands as a calibration source for the HARPS-N spectrograph [5,6], which is performing precision-radial-velocity observations of bright stars to detect and characterize long-period, Earth-like exoplanets.

Fig. 6. System layout for the broadband green astro-comb. SM fiber: single-mode fiber, PZT: piezo electric transducer, DCM: dispersion compensation mirror, PCF: photonic crystal fiber.

Fig 7. (a) Blue curve: octave-spanning spectrum of the Ti:sapphire source comb; green curve: spectrum after the short-wavelength pass filter before the DCMs; red curve: spectrum after the tapered PCF. (b) Dimensions of the tapered fiber used to generate the green comb. Vertical and horizontal sizes not to scale. (c) Close-up of (a). Purple curve: spectrum after the filtering cavities.

References

1. O. D. Mücke, O. Kuzucu, F. N. C. Wong, E. P. Ippen, F. X. Kärtner, S. M. Foreman, D. J. Jones, L.-S. Ma, J. L. Hall, and J. Ye, “Experimental implementation of optical clockwork without carrier-envelope phase control,” Opt. Lett. 29, 2806 (2004).
2. S. M. Foreman, A. Marian, J. Ye, E. A. Petrukhin, M. A. Gubin, O. D. Mücke, F. N. C. Wong, E. P. Ippen, and F. X. Kärtner, “Demonstration of a HeNe/CH4-based optical molecular clock,” Opt. Lett. 30, 570 (2005).
3. A. Benedick, D. Tyurikov, M. Gubin, R. Shewmon, I. Chuang, and F. X. Kärtner, “Compact, Ti:sapphire based methane-stabilized optical molecular frequency comb and clock,” Opt. Lett. 34, 2168 (2009).
4. A. Winter, F. Ö. Ilday, O. D. Mücke, R. Ell, H. Schlarb, P. Schmüser, and F. X. Kärtner, “Towards high-performance optical master oscillators for energy recovery linacs,” Nucl. Instr. and Meth. A 557, 299 (2006).
5. G. Q. Chang, C.-H Li, A. G. Glenday, G. Furesz, N. Langellier, L.-J. Chen, J. K. Lim, H.-W. Chen, D. F. Phillips, D. Sasselov, A. Szentgyorgy, R. Walsworth, and F. X. Kärtner, “Femtosecond laser frequency combs for astrophysical spectrograph calibration,” paper ATh1A.4, Conference on Advanced Solid-State Lasers, Paris (2013)
6. C.-H. Li, A. G. Glenday, N. Langellier, A. Zibrov, G. Q. Chang, L.-J. Chen, G. Furesz, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgy, R. Walsworth, “A broadband green astro-comb for sub-10 cm/s calibration on astrophysical spectrographs,” paper CTu1I.2, CLEO/QELS, San Jose (2013).
7. G. Q. Chang, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, R. L. Walsworth, and F. X. Kärtner, “Optimization of filtering schemes for broadband astro-combs,” Opt. Express 20, 24987 (2012).
8. C.-H. Li, G. Q. Chang, A. Glenday, D. F. Phillips, F. X. Kärtner, and R. L. Walsworth, “Conjugate Fabry-Perot cavity pair for astro-combs,” Opt. Lett. 37, 3090 (2012).
9. D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Q. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb” Opt. Express 20, 13711 (2012).
10. L.-J. Chen, G. Q. Chang, C.-H. Li, A. J. Benedick, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Broadband dispersion-free optical cavities based on zero group delay dispersion mirror sets,” Opt. Express 18, 23204 (2010).
11. A. J. Benedick, G. Q. Chang, J. R. Birge, L.-J. Chen, A. G. Glenday, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175 (2010).
12. C.-H. Li, A. Glenday, A. Benedick, G. Q. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibration lines to better than 10 cm/s,” Opt. Express 18, 13239 (2010).
13. G. Q. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: Effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18, 12736 (2010).
14. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610 (2008).