Abstract:
A modelocked fiber laser is designed to have strong pulse-shaping based on spectral filtering of a highly-chirped pulse in the laser cavity. The laser generates femtosecond pulses without a dispersive delay line or anomalous dispersion in the cavity.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit, under 35 U.S.C. 119(e), of U.S. Provisional Application No. 60/845,252, filed Sep. 18, 2006, which is hereby incorporated by reference in its entirety. 
    
    
     GOVERNMENT SPONSORSHIP STATEMENT 
     The work on this invention was supported by the National Science Foundation under Grant No. ECS-0500956 and by the National Institutes of Health under Grant No. EB002019. The Government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates in general to a femtosecond fiber laser that employs only normal dispersion elements through use of a unique pulse shaping technique. A spectral filter and other non-anomalous dispersion elements are employed in the technique. 
     2. Description of the Background Art 
     The need to compensate group-velocity dispersion (GVD) is ubiquitous in femtosecond pulse generation and propagation. Prisms, diffraction gratings and chirped mirrors have all been used to compensate or control GVD. Reliable femtosecond lasers had to await the development of a low-loss means of introducing controllable GVD. Pulse formation in modern femtosecond lasers is dominated by the interplay between nonlinearity and dispersion. In all cases of practical interest, a positive (self-focusing) nonlinearity is balanced by anomalous GVD. The need to compensate normal GVD in the laser, along with the balance of nonlinearity in soliton-like pulse shaping, underlies the presence of anomalous GVD in femtosecond lasers. 
     Most femtosecond lasers have segments of normal and anomalous GVD, so the cavity consists of a dispersion map, and the net or path-averaged cavity dispersion can be normal or anomalous. With large anomalous GVD, soliton-like pulse shaping produces short pulses with little chirp. Some amplitude modulation is required to stabilize the pulse against the periodic perturbations of the laser resonator. Pulse formation and pulse evolution become more complex as the cavity GVD approaches zero, and then becomes normal. The master-equation treatment of solid-state lasers, based on the assumption of small changes of the pulse as it traverses cavity elements, shows that stable pulses can be formed with net normal GVD. Nonlinear phase accumulation, coupled with normal GVD, chirps the pulse. The resulting spectral broadening is balanced by gain-narrowing. By cutting off the wings of the spectrum, gain dispersion shapes the temporal profile of the chirped pulse. Proctor et al showed that the resulting pulses are long and highly-chirped, as predicted by the analytic theory (B. Proctor, E. Westwig, and F. Wise, “Operation of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18, 1654-1656 (1993)). Stable pulse trains can even be produced without dispersion compensation, but the output pulses are picoseconds in duration and deviate substantially from the Fourier-transform limited duration, even after dechirping with anomalous GVD external to the cavity. 
     Fiber lasers can be constructed entirely of fiber with anomalous GVD, to generate solitons as short as ˜200 fs in duration. However, the pulse energy is restricted by the soliton area theorem and spectral sidebands to ˜0.1 nJ. Much higher energies are obtained when the laser has segments of normal and anomalous GVD. In general, the pulse breathes (i.e., the pulse duration varies periodically) as it traverses the cavity. Dispersion-managed solitons are observed as the net GVD varies from small and anomalous to small and normal, and selfsimilar and wave-breaking-free pulses are observed with larger normal GVD. The large changes in the pulse as it traverses the laser preclude an accurate analytical treatment, so numerical simulations are employed to study these modes. Among fiber lasers, Yb-based lasers have produced the highest femtosecond-pulse energies, recently reaching 15-20 nJ as reported in Buckley et al. (J. R. Buckley, F. W. Wise, F. O. Ilday, and T. Sosnowski, “Femtosecond fiber lasers with pulse energies above 10 nJ,” Opt. Lett. 30, 1888-1890 (2005)). The normal GVD of single-mode fiber (SMF) around 1 μm wavelength has been compensated by diffraction gratings, which detract from the benefits of the waveguide medium. 
     With the goal of building integrated fiber lasers, microstructure fibers and fiber Bragg gratings have been implemented to compensate dispersion at 1 μm. However, performance is sacrificed compared to lasers that employ diffraction gratings. Although from a practical point of view it would be highly desirable to design femtosecond-pulse fiber lasers without elements that provide anomalous GVD in the cavity, until now, no known fiber laser can generate ˜100-fs pulses without using anomalous GVD elements. 
     SUMMARY OF THE INVENTION 
     It is normally assumed that anomalous GVD is required in short-pulse lasers, for one of two reasons: 1) to compensate for components with normal GVD or 2) to form a pulse by the soliton mechanism of nonlinearity balancing anomalous GVD. The inventors have discovered that the aforementioned anomalous dispersion elements can in fact be eliminated from a fiber laser capable of generating femtosecond duration pulses (i.e. pulses with durations of hundreds of femtoseconds or less), thereby resulting in a femtosecond fiber laser that is formed with a cavity whose dispersion elements consist only of elements with normal GVD. The basis of the invention is a new pulse-shaping process: by increasing the nonlinear phase shift accumulated by a pulse circulating in the cavity and using a spectral filter to pass a narrow slice of the spectrum, self-amplitude modulation via spectral filtering is enhanced. This self-amplitude modulation dominates other pulse-shaping process, and the result is a highly-chirped pulse that circulates inside the laser cavity. 
     In the preferred embodiment of the invention, the laser cavity includes two key pulse shaping elements. A pulse chirping element broadens a multiple frequency pulse and spreads its frequency components apart over time. A spectral filter is then employed to pass a narrow slice of the chirped pulse containing only frequency components centered about a selected center frequency. Preferably, the cavity also includes other conventional elements for additional self-amplitude modulation of the pulse that are mainly provided to insure start up and stable operation of the laser. In the preferred embodiment, these include nonlinear polarization evolution (NPE) inducing elements, such as a polarization beam splitter, wave plates, etc. Being a fiber laser, the laser of course also includes a fiber gain element, which may be made from doped Yb or a similar material. 
     In experiments conducted on a laser constructed in accordance with the preferred embodiment, the resulting pulse before it exits the cavity is still chirped but is stable and of a picosecond magnitude. The pulse is then output from the cavity and preferably passed through a final dechirping element, such as a dispersive delay line, to form the femtosecond pulses. In the experiments, the picoseconds pulses in the cavity were dechirped to 170 fs outside the laser cavity. These results are remarkable considering that the cavity consisted of ˜10 characteristic dispersion lengths of fiber with respect to the dechirped pulse, yet no dispersion control was provided. The pulse energy was 1-3 nJ, and the laser is stable and self-starting. The laser thus employs a new approach to modelocking which offers significant practical advantages over previous fiber lasers through the freedom from anomalous dispersion. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The features and advantages of the present invention will become apparent from the following detailed description of a preferred embodiment thereof, taken in conjunction with the accompanying drawings which are briefly described a follows. 
         FIG. 1  is a schematic diagram of a laser cavity depicting the elements employed to simulate a fiber laser using dispersion elements with only normal dispersion in accordance with the operating theory of the present invention. A graph is also provided that shows the duration of a pulse as it travels through the various elements in the cavity based on simulations. 
         FIG. 2  is a schematic diagram of an all-normal-dispersion fiber laser that is configured in accordance with a preferred embodiment of the present invention and was actually constructed to verify the operational theory of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The design of a femtosecond fiber laser without dispersion control in the cavity in accordance with the operational theory of the present invention will now be presented in greater detail. The master-equation analysis does not apply quantitatively to fiber lasers, but one is guided qualitatively and intuitively by its predictions.  FIG. 1  shows the elements of a fiber laser cavity  10  that were employed in a simulation to test the theory of the present invention. These elements include a first, fairly long segment of single-mode fiber (SMF)  12 , a short segment of doped gain fiber  14 , a second segment of SMF  16  after the gain fiber  12 , a saturable absorber (SA)  18 ; and a spectral filter (SF)  20 . A ring cavity is assumed (though the invention is not limited to use with a ring cavity), so the pulse enters the first segment of SMF  12  after the SF  20 . As illustrated by the graph of  FIG. 1 , a pulse traveling through the cavity  10  experiences broadening in the sections of SMF  12  and  16 , followed by a corresponding narrowing in the SA  18  and especially in the SF  20 . 
     Numerical simulations show that stable solutions do exist in such a laser for a reasonable range of parameters. The gain bandwidth has a major influence on the pulse evolution. With large gain bandwidth (&gt;˜30 nm), approximately parabolic pulses evolve as in a self-similar laser. As the bandwidth is reduced to ˜10 nm, the spectrum develops sharp peaks on its edges, and for narrower bandwidths the solutions do not converge. The simulations show that spectral filtering of a strongly phase-modulated pulse can produce substantial amplitude modulation under realistic conditions. With additional amplitude modulation from NPE, stable solutions exist. The pulse is highly-chirped inside the cavity, but the phase is roughly parabolic near the peak of the pulse, so the pulse can be dechirped outside the laser. 
     With reference to  FIG. 2 , a preferred embodiment of a fiber laser  30  is illustrated that was actually constructed to verify the operational theory of the present invention. The phrase “fiber laser” means that optical fiber is used at least for the gain medium of the fiber but typically for many of the lasers other components as well. The laser  30  includes a closed ring cavity  32  that includes dispersion elements having only normal GVD. More particularly, a fiber section  34  is provided which preferably consists of ˜3 m of SMF  36  and 20 cm of highly-doped Yb gain fiber  38 , followed by another ˜1 m of SMF  40 . It should be understood, however, that other types of fibers, such as multimode fibers, could be employed in place of SMF if desired. In addition, the two segments of SMF  36  and  40  could be replaced by a single section if desired. Further, there are many other active materials that could be used to make the gain fiber  38 . The core diameter of the gain fiber  38  was chosen to be 4-μm core diameter (which is smaller than the 6-μm core diameter selected for the SMF segments  36  and  40 ) to increase self-phase modulation (SPM) in the gain fiber  38 . A 980-nm laser diode  42  delivers ˜350 mW into the core of the gain fiber  38  via a wavelength-division multiplexer (WDM)  44  as is conventional in a ring fiber laser. 
     The fiber section  34  is interfaced at each end by first and second collimators  46  and  48  to various non-fiber elements. NPE, which serves the same function as the saturable absorber  18  in  FIG. 1 , is implemented with quarter-waveplates (QWP)  50  and  52 , a half-waveplate (HWP)  54 , and a polarizing beamsplitter (PBS)  56 . An output  58  of the laser cavity  32  is taken directly from an NPE ejection port  60  of the PBS  56 . 
     For the spectral filter, an interference filter  62  centered at 1030 nm, with 10 nm bandwidth, is employed. An isolator  64  is also provided in the cavity  32  to insure one directional flow of the laser pulses as is conventional. 
     The optimum location for the filter  62  initially was not clear. Placing it after the gain fiber  38  or second SMF segment  40  would maximize the amplitude modulation from spectral filtering. However, the desire also is to output the broadest spectrum and the largest pulse energy, to achieve the shortest and most intense pulse. Considering these factors, the filter  62  preferably should be placed after the beam splitter  56 . This location also allows as much of the laser to be spliced together as possible. The total dispersion is ˜0.1 ps 2  for this arrangement. It should be understood, however, that the laser  30  can operate with the elements in the cavity  32  being rearranged in numerous different configurations. 
     In experiments on the laser  30  of  FIG. 2 , the threshold pump power for modelocking was ˜300 mW. Self-starting modelocked operation was achieved by adjustment of the waveplates. The laser  30  produced a stable pulse train with 45 MHz repetition rate. Although the continuous-wave output power can be as high as ˜200 mW, in modelocked operation the power was limited to 120 mW, which corresponds to a pulse energy of ˜3 nJ. Stable single-pulsing was verified with a fast detector down to 500 ps, and by monitoring the interferometric autocorrelation out to delays of ˜100 ps. Also, the spectrum was carefully monitored for any modulation that would be consistent with multiple pulses in the cavity. Remarkably, there was no evidence of multi-pulsing at any available pump power. However, with a single pump diode the pump power only exceeded the modelocking threshold by ˜20%. 
     Typical results for the output of the laser  30  established that the laser&#39;s spectrum is consistent with significant SPM within the cavity. The laser generated ˜1.4-ps chirped pulses at the output  58  of the cavity, but these pulses were dechirped with an optional pair of diffraction gratings, dispersive delay line or other suitable dechirping elements  66  disposed outside the laser cavity  32 . The pulse output  68  from the dechirping element  66  was narrowed to 170 fs. The dechirped pulse duration was within ˜16% of the Fourier-transform limit. The interferometric autocorrelation shows noticeable side-lobes, which arise from the steep sides and structure of the spectrum. Nevertheless, these amount to only ˜10% of the pulse energy. The output pulse energy was ˜2.7 nJ, and after dechirping with the lossy gratings  54 , the pulse energy was ˜1 nJ. Pulse energies of 2 nJ could be obtained by dechirping with high-efficiency gratings or photonic-bandgap fiber. The experiments established that the laser is stable and self-starting. In addition to verifying as carefully as possible that the laser is not multi-pulsing, the pulse peak power was compared to that of a fully-characterized femtosecond laser available in the lab. Within the experimental uncertainties, the two-photon photocurrent induced by the all-normal-dispersion laser scales correctly with the nominal peak power, which is ˜5 kW. 
     Detailed understanding of pulse formation and evolution in the subject laser will require more experimental work and theoretical analysis. Because the simulated laser is not identical to the experimental version, it is not appropriate to compare the calculated and measured performance in detail. However, qualitative and even semi-quantitative observations of the laser properties are consistent with the intended pulse-shaping through spectral filtering. The behavior of the laser  30  depends critically on the spectral filter  62 : without it, stable pulse trains are not generated. By rotating the spectral filter  62  to vary the center wavelength, either of the sharp spectral features can be suppressed, which may slightly improve the pulse quality. When the spectrum changes, the magnitude of the chirp on the output pulse can change substantially: the pulse duration varies from approximately 1 to 2 ps. 
     With standard femtosecond Yb-doped fiber lasers, mechanical perturbation of the fiber extinguishes modelocking. In the laser of the subject invention, it is possible to touch and move the fiber without disrupting modelocking, which indicates that NPE plays a reduced role in pulse-shaping. Simulations show that the role of NPE is reduced compared to a laser with a dispersion map, but it is still crucial to the generation of stable pulses. 
     Although the invention has been disclosed in terms of a preferred embodiment and variations thereon, it will be understood that numerous additional variations and modifications could be made thereto without departing from the scope of the invention as defined by the following claims.