Open Access
Add to BibSonomyAbstract
A modelocked fiber laser, operating in the soliton regime without any explicit intracavity polarizers, is observed to spontaneously lock its output polarization for certain values of the intracavity birefringence. For other settings of the intracavity birefringence the output polarization undergoes pulse-to-pulse evolution. The dependence of the output polarization evolution on intracavity birefringence outside of the locking regions can be understood with a simple model. The locking behavior exhibits several surprising aspects and is not completely understood.
©1997 Optical Society of America
1. Introduction
Modelocked fiber lasers have recently attracted significant attention primarily due to their potential as compact sources of ultrashort (< 1 ps) pulses.[1] There are several applications for compact ultrafast sources; for fiber lasers the most promising is telecommunications.[2] However modelocked fiber lasers can also display interesting and complex dynamics, particularly when they are operated with net anomalous dispersion in the cavity so that the pulse exhibits soliton-like behavior. In this regime, the group-velocity-dispersion (GVD) is canceled by the self-phase-modulation (SPM), yielding a stable, circulating pulse in the cavity.[3]
Numerous techniques have been developed to modelock fiber lasers. These include additive-pulse-modelocking, using either a nonlinear fiber loop mirror [4] or nonlinear polarization rotation, [5,6] and using an intracavity saturable absorber (typically semiconductor). [7–9] Modelocking based on nonlinear polarization rotation has been performed in both the soliton [5] and nonsoliton (stretched pulse) [6] regimes.
Here we examine the evolution of the output polarization from a fiber laser [8,9] that is modelocked using a semiconductor saturable absorber and operating in the soliton regime. This laser is different from most others in that it does not contain any explicit polarizing elements or polarization maintaining fiber. The polarization is then free to evolve under the combined influences of any weak, strain-induced fiber birefringence and nonlinear polarization rotation. When the laser is modelocked, we observe that for certain values of net cavity birefringence that the output polarization stops evolving, i.e., the output polarization is “locked”. This behavior is attributed to the interplay between linear birefringence and nonlinear polarization rotation, although the detailed stability mechanisms remain unclear.
Fig. 2 RF spectra without (a) and with (b) the external linear polarizer. Δ denotes the polarization evolution frequency (PEF). (c) shows how the pulse-to-pulse evolution of the polarization ellipse is mapped into amplitude modulation , t is the cavity round-trip time.
2. Laser Cavity and Measurement
The laser is a simple linear cavity consisting of three pieces of fiber fusion-spliced together (see Fig. 1). The central piece is Er/Yb co-doped gain fiber, approximately 15 cm in length. A 30 cm piece of standard single mode fiber (SMF) is spliced to one end of the gain fiber. The other end of this piece of SMF is connectorized and a dielectric output coupler is deposited directly on the face of the ferrule (~1% transmission at 1550 nm). In addition, the pump light from a 980 nm telecom grade laser diode is coupled into the cavity through this mirror, which has high transmission at 980 nm. The other side of the gain fiber is spliced to a ~155 cm piece of SMF that is butt-coupled to a Saturable Bragg Reflector (SBR). [8–10] The SBR consists of an AlAs/GaAs Bragg high reflector with a pair of InGaAs/InP quantum wells grown in the top layer. The quantum wells provide saturable absorption that modelocks the laser. The 155 cm piece of SMF is wrapped around 2 paddles (5.6 cm radius, 3 wraps each) of a standard fiber polarization controller. [11] Fiber lasers of this design have been used as the source in a wavelength-division multiplexed transmitter. [12]
To measure the evolution of the polarization of the output pulses, we monitor the RF spectrum after passing the pulses through a linear polarizer. RF spectra with and without the linear polarizer are shown in Fig. 2. Without the polarizer the RF spectrum consists simply of the comb of harmonics corresponding to the repetition rate (Fig. 2a). With the linear polarizer in place, strong sidebands appear in the spectrum (Fig. 2b). These sidebands can readily be understood as arising from the evolution of the pulse polarization during each round trip. The cavity birefringence transforms the polarization state of the pulse during a round trip. The linear polarizer selects a given axis of the polarization ellipse, mapping the polarization evolution into amplitude modulation (see Fig. 2c). The amplitude modulation results in the observed sidebands in the RF spectrum, with spacing denoted by Δ in Fig. 2. The spacing of the sidebands from cavity harmonics is a measure of the rate at which the polarization evolves, hence we denote it as the polarization evolution frequency (PEF). The PEF is inversely proportional to the birefringence beat length Lb, i.e., Lb = Lc/(Δτ), where Lc is the length of a cavity round-trip and τ is cavity round trip time. Note that the measured PEF is the real REF modulo the half of the cavity repetition rate since we only sample the polarization once per round-trip (at the output coupler). If the polarization evolution undergoes greater than one complete cycle per cavity round-trip it is aliased to a lower frequency in our measurement. If aliasing does occur, the relationship between PEF and beat length no longer holds.
Fig. 3 Polarization evolution frequency as function of the angles of the two polarization controller paddles for CW operation of the laser.
3. Linear Operation
To obtain an understanding of the polarization evolution in the laser cavity without the complication of nonlinear polarization rotation due to Kerr nonlinearities, we first replace the SBR with a dielectric high reflector. In this case the laser runs CW. Although the sidebands are not nearly as well defined as for modelocked operation, it is still possible to determine the PEF. In Fig. 3 we show a map of the PEF as a function of the angles of the two polarization controller paddles (Θ1 & Θ2 in Fig. 1). The polarization controller paddles essentially act as waveplates, where the birefringence is due to bending induced strain. [11] There is a small correction for the twist between paddles, but it only amounts to a few degrees.
4. Simulation
To understand how the PEF depends on the angles of the two polarization controller paddles, we constructed a simple simulation based on the Jones matrix formalism. [13] We model the cavity as a series of three bulk waveplates, with adjustable retardance and angle. For each round trip through the cavity each waveplate is transited twice, in the correct sequence. The cavity is unfolded, so that the flip in handedness upon reflection is canceled by transiting the waveplate in the opposite direction. Two of the three waveplates model the two polarization controller paddles, the third represents the residual birefringence elsewhere in the cavity.
To obtain the PEF, a transfer matrix for a single round-trip through the cavity is calculated for a given setting of the waveplates. An arbitrary initial polarization state is chosen. The transfer matrix is then applied 512 times, and the intensity along one linear polarization state is recorded after each application. These 512 intensities are taken as a time series, the average values subtracted out (to remove the DC term), and a Fourier transform performed to obtain the RF spectrum. The PEF is then defined as the strongest channel in the spectrum. The PEF does not depend on the arbitrary initial polarization state, but the amplitude of the resulting modulation does.
Fig. 4 Simulated PEF(Θ1,Θ2). ϕ12 is the retardance of the two polarization controllers, ϕR is the residual retardance.
As a starting point we first simulate the case where the two paddles of the polarization controller are quarter-wave-plates and there is no residual birefringence in the cavity. An estimate of the retardance based on Ref. 11 shows that a quarter wave of retardance should be a good estimate for the geometry of our controller. However these parameters yield a PEF(Θ1,Θ2) map that consists of diagonal stripes (Fig. 4a), i.e. not reproducing the experiment. Since there is no absolute angle reference, it can easily be understood that only the relative angle between the two paddles is relevant.
The need for an absolute angle reference suggests the inclusion of a weak waveplate with fixed angle to model the residual birefringence (a retardance of ϕR) elsewhere in the cavity. However this alone does not provide qualitative reproduction of the experiment (Fig. 4b). Only upon adjustment of the magnitude of the retardance for the polarization controller paddles (ϕ12, they are always taken to be identical) do we obtain satisfactory agreement with the experiment (Fig. 4d). To demonstrate that both ingredients are necessary to reproduce the experiment, the result for only adjusting the value of ϕ12 is shown in Fig. 4c. We find that ϕ12 = 1.2 radians and ϕR = 0.5 radians provides good agreement.
Fig. 5 Modelocked PEF(Θ1,Θ2). a) full map, b) higher resolution scan of polarization locking regions.
5. Modelocked Operation
With the SBR in the cavity, modelocked (ML) operation is obtained with an output pulse width of approximately 400 fs. The laser shows all of the hallmarks of soliton operation: the optical spectrum is well fit by a sech2, it displays spectral sidebands due to periodic perturbation of the soliton by the cavity [14] and the spectral width is limited by the sidebands. The number of pulses circulating in the cavity increases with increasing pump power. [15] For all of the results presented here, a single pulse is circulating in the cavity. The soliton length [3] is on order of the cavity length.
The PEF(Θ1,Θ2) for ML operation is shown in Fig. 5a. These results show a dramatic new feature that is not present for CW operation, namely the regions where the polarization “locks”, i.e. it does not evolve. These regions are shown as black in Fig. 5. It is important to note that in these regions the amplitude of the sidebands vanishes (it drops below the noise floor of the measurement, which is 25–30 dB down). All of these data were taken with careful control to maintai n the same optical spectrum.
Fig. 7 Optical (left) and corresponding RF (right) spectra for 3 different settings of Q1 and Q2. For the top two panels the polarization is not locked, for the bottom panel it is locked. In the optical spectra, CSB denotes sidebands that are due to the period perturbation by the cavity, while PSB denotes sidebands due to the period evolution of the polarization over several cavity round trips. The peak marked by C in the RF spectra is the fundamental repetition rate, while those marked by P are due to polarization evolution. The small peaks in the polarization locked case is due to mode beating in the pump laser, not polarization evolution.
A higher resolution map of the PEF(Θ1,Θ2) in the vicinity of locking reveals that there are actually several distinct locking regions (Fig. 5b). One of these regions occurs near where the PEF naturally goes to zero (as estimated from the nearby non-locking behavior, or from the CW operation, it is near the center of the elliptically shaped region). In this region one might argue that a small polarization-dependent loss could overcome the small polarization ellipse rotation that occurs due to the birefringence experienced during each round trip. However there are several other areas that also display locking, although the “natural” PEF is clearly non-zero.
Several aspects of the locking regions can be seen more clearly in a high resolution, one dimensional scan. In Fig. 6, the results are shown for scanning Θ2 while holding Θ1 fixed at 110°. In this figure we plot PEF = 0 in the locked regions. The three locking regions are clearly evident. It also clear that the transition between locked and unlocked regions is very abrupt, it occurs for a 1 degree change in angle, which is essentially the resolution of the setup. The PEF for CW and ML operation track very well, except for the regions where polarization locking occurs.
Examination of the ML data near Θ2 = 40° shows that a locking behavior occurs here as well. This is manifest as a several degree region for which the PEF stays constant at exactly half the laser repetition rate, i.e. this corresponds to a period doubling behavior. Period tripling can be observed near Θ2 = 30°, although over a narrow range (only 1–2°). It is interesting to note that the period doubling and tripling locking only occur at the values of Θ2 mentioned, and do not occur at the other values of Θ2 for which the PEF goes through these frequencies.
The final feature observed in Fig. 6 is the presence of a small region for which there is no data for ML operation (near 100°, at the edge of the polarization locking region). In this region the laser does not produce stable modelocking. We speculate that the intracavity birefringence is such that it generates close to a linear polarization state in the gain medium, resulting in polarization hole burning which destabilizes the modelocking. In general, we discount polarization hole burning as a mechanism for the polarization locking because it should be present in CW operation as well, and we never observe CW polarization locking. Ultrafast hole burning could play a role in the observed behavior, and may be present as spectral holes with a homogeneous width of approximately 10 nm have been observed in erbium amplifiers. [16]
In Fig. 7, the optical and RF spectra are shown for 3 settings of the polarization controller paddles. In (a) and (b), the polarization is not locked, while in (c), it is locked. The sidebands due to the periodic perturbation of the soliton by the cavity is observable in all three optical spectra (marked by CSB in the figure). In (a) and (b), where the polarization is not locked, additional sidebands are present. These sidebands correspond to a periodic perturbation with a period of several cavity round trips, i.e., the time it takes for the polarization to undergo a complete cycle. We therefore designate these as polarization sidebands (PSB) in Fig. 7. The position of these sidebands does depend on the settings of the polarization controller paddles (compare (a) and (b)) as expected. The PSB spacing decreases with decreasing PEF because a smaller PEF corresponds to a perturbation with a longer period. Additionally, (c) shows that they disappear when the polarization locks. Note that, in the RF spectrum (c), the remaining peaks are not due to polarization evolution (they are not properly spaced), but rather due to mode beating in the 980 nm pump laser.
Feedback into a laser cavity can dramatically effect both modelocking and polarization dynamics. We have observed these effects for several different configurations of the components external to the cavity, including launching the laser output into a fiber amplifier with an optical isolator. We therefore conclude that feedback does not play a role in the observed polarization locking.
6. Output Polarization
We have measured the output polarization state in the locked regions. The measurements were performed using a Hewlett-Packard 8509B Polarization Analyzer. A fiber polarization controller between the laser output coupler and polarization analyzer was used to null out the birefringence of the intervening fiber pigtails. We confirmed the proper setting of the polarization controller by free space coupling linearly polarized light in place of the laser output.
We observe that, in the locking regions that correspond to a “natural” zero of the PEF, the laser output is elliptically polarized. In the other regions, where the PEF is “naturally” non-zero, the output is nearly linearly polarized. (The small residual ellipticity is within that expected due to imperfect nulling of the pigtail birefringence.) In the latter regions, the axis of linear polarization systematically rotates from one side of the region to the other. The output polarization returns to the same state after cycling the pump power. Additionally the polarization state does not depend on the details of the pulse spectrum (as long as the polarization remains locked).
7. Discussion
The polarization locking is clearly a nonlinear process as it only occurs when the laser is modelocked. The locking regions are sensitive to the spectral width, which is probably due to the concomitant change in the soliton pulse width. All of the data shown above were taken with careful control to maintain the same spectral width throughout. A simple extension of the simulation described in section 4 to include Kerr nonlinearities as a lumped element (nonlinear polarization rotation) does not give locking behavior. This is not surprising as it is well known that nonlinearity and birefringence must be handled simultaneously. [17]
A more complete analysis requires the solution of coupled nonlinear Schrödinger equations to describe the propagation of the solitons under the combined influences of birefringence and nonlinearity. Analytical and numerical studies of soliton propagation in birefringent fiber have concluded that the Kerr nonlinearity can cancel the effect of birefringence, locking the orthogonal states together. [18–20] There has been experimental confirmation of this. [19,21] These results are related to the idea of a vector soliton, i.e. a soliton that maintains not only its intensity profile but also its polarization state, even if it is not propagating along one of the principal axes of the fiber. [3]
8. Conclusion
We have presented experimental results that demonstrate the spontaneous locking of the output polarization state from an isotropic, modelocked fiber laser operating in the soliton regime. A simple simulation provides good reproduction of the polarization evolution when the laser is running CW. The polarization locking only occurs in the modelocked regime and is clearly due to fiber nonlinearity. A detailed understanding of the locking mechanisms requires a more extensive and sophisticated model and/or analysis.
Acknowledgments
The authors thank J.E. Cunningham and W.Y Jan for providing the SBR, D.J. DiGiovanni for providing the Er/Yb fiber, G.T. Harvey for the loan of the polarization analyzer, E.P. Ippen for helpful discussions and L.E. Nelson for a critical reading of the manuscript.
References and Links
1 . I.N. Duling III and M.L. Dennis , Compact Sources of Ultrashort Pulses ( Cambridge Univ. Press, Cambridge , 1995 ).
2 . see M.C. Nuss , W.H. Knox , and U. Koren , “ Scaleable 32 channel chirped-pulse WDM source ”, Electron. Lett. 32 , 1311 – 1312 ( 1996 ). [CrossRef]
3 . G.P. Agrawal , Nonlinear Fiber Optics ( Academic Press, San Diego , 1995 ).
4 . I.N. Duling III , “ Subpicosecond all-fiber erbium laser ”, Electron. Lett. 27 , 544 – 545 ( 1991 ); D.J. Richardson , R.I. Laming , D.N. Payne , M.W. Phillips , and V.J. Matsas , “ 320 fs soliton generation wit h passively mode-locked erbium fiber laser ”, Electron. Lett. 27 , 730 – 732 ( 1991 ). [CrossRef]
5 . M. Hofer , M.E. Fermann , F. Haberl , M.H. Ober , and A.J. Schmidt , “ Modelocking with cross-phase and self-phase modulation ”, Opt. Lett. 16 , 502 – 504 ( 1991 ); C.J. Chen , P.K.A. Wai , and C.R. Menyuk , “ Soliton fiber ring laser ”, Opt. Lett. 17 , 417 – 419 ( 1992 ); V.J. Matsas , T.P. Newson , D.J. Richardson , and D.J. Payne , “ Selfstarting Passively Mode-Locked Fiber Ring Soliton Laser Exploiting Nonlinear Polarization Rotation ”, Electron. Lett. 28 , 1391 – 1393 ( 1992 ); K. Tamura , H.A. Haus , and E.P. Ippen , “ Self-starting additive pulse mode-locked erbium fiber ring laser ”, Electron. Lett. 28 , 2226 – 2228 ( 1992 ). [CrossRef] [PubMed]
6 . K. Tamura , E.P. Ippen , H.A. Haus , and L.E. Nelson , “ 77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser ”, Opt. Lett. 18 , 1080 – 1082 ( 1993 ); K. Tamura , L.E. Nelson , H.A. Haus , and E.P. Ippen , “ Soliton versus nonsoliton operation of fiber ring lasers ”, Appl. Phys. Lett. 64 , 149 – 151 ( 1994 ); H.A. Haus , K. Tamura , L.E. Nelson , and E.P. Ippen , “ Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Lasers: Theory and Experiment ”, IEEE J. Quant. Electron. 31 , 591 – 598 ( 1995 ). [CrossRef] [PubMed]
7 . E.A. De Souza , C.E. Soccolich , W. Pleibel , R.H. Stolen , J.R Simpson , and D.J. DiGiovanni , “ Saturable Absorber Modelocked Polarization Maintaining Erbium-Doped Fiber Laser ”, Electron. Lett. 29 , 447 – 449 ( 1993 ); B.C. Barnett , L. Rahman , M.N. Islam , Y.C. Chen , P. Bhattacharya , W. Riha , K.V. Reddy , A.T. Howe , K.A. Stair , H. Iwamura , S.R. Friberg , and T. Mukai , “ High-power erbium-doped fiber laser mode locked by a semiconductor saturable absorber ”, Opt. Lett. 20 , 471 – 473 ( 1995 ). [CrossRef]
8 . S. Tsuda , W.H. Knox , J.L. Zyskind , J.E. Cunningham , W.Y. Jan , and R. Pathak , “ Broadband compact mode-locked Er/Yb fiber Laser ”, Conf. Laser Electro-Optics ’ 96 , OSA Tech. Digest Series 9, ( OSA, Washington DC , 1996 ) 494 .
9 . B.C. Collings , K. Bergman , S.T. Cundiff , S. Tsuda , J.N. Kutz , J.E. Cunningham , W.Y. Jan , M. Koch , and W.H. Knox , “ Short Cavity Erbium/Ytterbium Fiber Lasers Modelocked with a Saturable Bragg Reflector ”, submitted for publication.
10 . S. Tsuda , W.H. Knox , E.A. de Souza , W.Y. Jan , and J.E. Cunningham , “ Low-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femtosecond modelocking in solid-state lasers ”, Opt. Lett. 20 , 1406 – 1408 ( 1995 ); S. Tsuda , W.H. Knox , S.T. Cundiff , W.Y. Jan , and J.E. Cunningham , “ Mode-Locking Ultrafast Solid-State Lasers with Saturable Bragg Reflectors ”, IEEE J. Sel. Topics Quant. Electron. 2 , 454 – 464 ( 1996 ). [CrossRef] [PubMed]
11 . H.C. Lefevre , “ Single-mode fiber fractional wave devices and polarization controllers ”, Electron. Lett. 16 , 778 – 780 ( 1980 ). [CrossRef]
12 . S.T. Cundiff , W.H. Knox , and M.C. Nuss , “ Active feed-forward channel equalization for chirped pulse wavelength division multiplexing ”, Electron. Lett. 33 , 10 – 11 ( 1997 ). [CrossRef]
13 . See E. Collett , Polarized Light ( Marcel Dekker, New York , 1993 ).
14 . N. Pandit , D.U. Noske , S.M.J. Kelly , and J.R. Taylor , “ Characteristic instability of fiber loop soliton lasers ”, Electron. Lett. 28 , 455 – 457 ( 1992 ); S.M.J. Kelly , “ Characteristic sideband instability of periodically amplified average soliton ”, Electron. Lett. 28 , 806 – 807 ( 1992 ). [CrossRef]
15 . B.C. Collings , K. Bergman , S. Tsuda , and W.H. Knox , “ Femtosecond short cavity 2.5 GHz fiber laser harmonically modelocked by a saturable Bragg reflector with low temporal jitter ”, presented at CLEO ’97, 1997 OSA Technical Digest Series 11 ( Optical Society of America, Washington DC , 1997 ) p. 343 – 344 .
16 . A.K. Srivastava , J.L. Zyskind , J.W. Sulhoff , J.D. Evankow jr. , and M.A. Mills , “ Room temperature spectral hole burning in erbium-doped fiber amplifiers ”, OFC ’96, OSA Technical Digest Series 2 ( Optical Society of America, Washington DC , 1996 ) 33 – 34 .
17 . H.G. Winful , “ Self-induced polarization changes in birefringent optical fiber ”, Appl. Phys. Lett. 47 , 213 – 215 ( 1985 ); H.G. Winful , “ Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices ”, Opt. Lett. 11 , 33 – 35 ( 1986 ). [CrossRef]
18 . C.G. Menyuk , “ Nonlinear pulse propagation in birefringent optical fibers ”, IEEE J. Quant. Electron. 23 , 174 – 176 ( 1987 ); C.G. Menyuk , “ Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes ”, Opt. Lett. 12 , 614 – 616 ( 1987 ). [CrossRef]
19 . S.G. Evangelides jr. , L.F. Mollenauer , J.P. Gordon , and N.S. Bergano , “ Polarization multiplexing with solitons ”, J. Lightwave Tech. 10 , 28 – 35 ( 1992 ). [CrossRef]
20 . N.N. Akhmediev , A.V. Buryak , J.M. Soto-Crespo , and D.R. Andersen , “ Phase-locked stationary soliton states in birefringent nonlinear optical fibers ”, J. Opt. Soc. Am. B 12 , 434 – 439 ( 1995 ). [CrossRef]
21 . Y. Barad and Y. Silberberg , “ Polarization Evolution and Polarization Instability of Solitons in a Birefringent Optical Fiber ”, Phys. Rev. Lett. 78 , 3290 – 3293 ( 1997 ). [CrossRef]
