Peak Power Optimization of Optical Pulses Using ... - OSA Publishing

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 13, JULY 1, 2013

Peak Power Optimization of Optical Pulses Using Low-Doped Gain-Medium in Femtosecond Fiber Laser Hussein E. Kotb, Student Member, IEEE, Mohamed A. Abdelalim, Katherine J. Bock, and Hanan Anis

Abstract—We have investigated both theoretically and experimentally a method to increase the peak power in femto-second fiber laser by using a low-doped long-length gain medium. The accumulated nonlinear phase shift as well as its threshold value for single pulse operation was studied and used to explain the robustness of such cavity against multipulsing and optical wave breaking. Index Terms—Fiber lasers, laser mode locking, optical pulses, optical solitons, ring lasers.

I. INTRODUCTION

U

LTRAFAST optics is a growing field with applications that span many disciplines from life sciences, medicine, and chemistry to industrial applications and optical communications. Femtosecond fiber lasers are attractive sources for generating pulsed light as they can be designed to be compact, all-fiber devices which require no alignment or complicated maintenance. They are particularly advantageous in that it allows for portable use for field-work or bed-side medical applications compared to more common-place, bulky, solid-state lasers typically used in research (i.e., titanium-sapphire lasers). Femtosecond fiber lasers using ytterbium-doped gain fibers lase at 1030 nm, are particularly suitable for biomedical applications due to low absorption of light in biological tissues near this wavelength. The main challenge in the fiber laser is to overcome the effect of the accumulated nonlinearity on the generated pulse which limits its power and energy. A lot of research has been done to avoid the optical wave breaking caused by the excessive accumulated nonlinearity and to generate high power pulses. Self-Similar (similariton) pulses are very promising high energy laser pulses due to its high immunity against wave breaking in normal dispersion fibers [1]. similariton pulses have parabolic profile in time and frequency domains and they have linear frequency chirp, so the pulse compression at the output will be very effective in compressing the pulses to its

Manuscript received February 25, 2013; revised April 19, 2013; accepted May 17, 2013. Date of publication May 30, 2013; date of current version June 14, 2013. The authors are with the University of Ottawa, Electrical Engineering and Computer Science, Ottawa, ON K1N 6N5, Canada (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2013.2264900

transform limit values [2]–[5]. Due to its robustness against optical wave breaking, the energy per pulse for similariton is much higher than that of the many other types like; soliton and stretched pulse regimes. The similariton has been very difficult to generate in fiber lasers due to its temporal and spectral widths monotonic increase which is not compatible with the periodic boundary condition of ring lasers. Ilday et al. succeeded to generate passive similariton from a fiber laser having positive dispersion by employing the diffraction gratings for pulse is used to produce compression in time. Short length of a sufficient gain and spectral filtering decoupled from any dispersion or nonlinear effect [2]. Normal dispersive gain medium of an adequate length can convert any pulse’s temporal shape into similariton (active similariton) [6]–[9]. Oktem et al. demonstrated that an active similariton is constructed after the Erbium-doped fiber section while a soliton is propagating in the rest of the laser cavity [10]. Renninger et al. were also able to generate active similariton using a long length of fiber in a laser cavity containing narrow spectral filter [11]. Another method to increase the pulse energy in fiber lasers is to increase the net cavity dispersion to widen the pulse in time domain and hence make it more robust against wave breaking [12]–[16]. These cavities generate dissipative soliton pulses having energy per pulse near to what is achieved by similariton lasers or even higher [13], [15], and [16]. In this paper, we show both theoretically and experimentally that we can use low-doped long fiber length to increase the peak power of the generated laser pulses. Conceptually, as the nonlinearity is gradually accumulated inside the low-doped fiber, the peak power of the generated pulse can reach a high value before hitting the threshold of multi pulsing or wave breaking. Two cavities were implemented; one used fiber while the other cavity high-doped short-length, of fiber. Passive similariton used low-doped long-length of femtosecond fiber laser is selected for two reasons: (1) to implement the laser cavity at different values of net group velocity dispersion (GVD) at fixed repetition Rate. (2) similariton pulses have pretty much linear chirp which results in narrow compressed pulse very near the transform limit [2]–[5]. The paper is organized as follows; the second section explains the concept of increasing the peak. Simulation results of the cavity are presented in the third section. The fourth section focuses on the experimental set-ups and the measurement results. In this section, the two experimental set-ups of the ring fiber cavity are demonstrated, both of them uses (SAM) as real mode-locker. Comparison between the low-doped long

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KOTB et al.: PEAK POWER OPTIMIZATION OF OPTICAL PULSES

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the cavity output is found to be higher for the low-doped fiber than that of the high-doped one. However, as will be shown in simulation and experimental results, the cavity with low-doped fiber can tolerate higher values of nonlinear phase shift than the one with high-doped fiber. Having equal , the ratio between the peak powers of the two cases after the gain medium is expressed as (4) Hence the following condition has to be satisfied to get higher peak power using lower doping gain fiber at the same cavity conditions; Fig. 1. Cartoon of peak power evolution in the cavity through the , , Saturable absorber (SA) and for the two cases. The short Yb has higher gain per unit length than long fiber fiber with length . The low-doped case can reach higher peak powers due with length to the slow accumulation of nonlinear phase shift. SA effect is neglected to emphasize on the proposed concept.

fibers and high-doped short section.

fibers is also reported in this

II. THEORETICAL BACKGROUND The accumulated nonlinear phase shift ( ) is the main obstacle that hinders the generation of high-energetic pulses and causes optical wave breaking. Its maximum value ( ) for single mode operation is [17]:

(5)

III. SIMULATION RESULTS A. Numerical Model Description The laser cavity structure used in the modeling and simulation is similar to that in [18], with the addition of gratings after the SA. It consists of an doped gain medium, followed by nonlinear-acting SMF and following linear acting SMF. The net cavity GVD is specified by the anomalous dispersion of the pair of diffraction gratings as well the total length of the fibers. Mode locking is obtained by using the SAM. The light propagating in gain fiber is modeled by scalar Ginzburg-Landau equation (GLE) [2], [17] and [18]:

(1) is the peak power Where is the nonlinear coefficient, varying with position ( ) inside the cavity. The peak power should increase when the low-doped long-length gain fiber is used because the rate of accumulation of the nonlinear phase shift gradually ramps inside the gain fiber. Fig. 1 is a cartoon depicting a comparison between the evolutions of peak power for the case of high and low-doped gain fiber operating on the edge of the single pulse operation. For simplicity, the input peak power of fibers after in the two cases is assumed to be equal. The small signal gain coefficient is used to derive a closed form relation for in the high- and low-doped cases, to be respectively: (2) (3) where, is the small signal gain coefficient for the high (low) fiber, is the length of the high (low) doped doped fiber and is the length of for the cavity fiber. with high (low) doped To have a fair comparison, it is assumed that, for single pulse operation hence the area under both curves should be the same, in this case the peak power before

(6) where is the complex field amplitude, is the propagation coordinate, is the retarding time, is the linear loss taken as 0.04 , is the GVD parameter taken as 24690.6 for SMF, and 24537.2 , and 23651.5 for highly and lowly doped fibers, respectively. The nonlinear parameter is taken as 0.0047 . is the small signal gain coefficient with parabolic frequency dependence and a bandwidth . is the pulse energy and is the gain medium saturation energy taken as 4 nJ. The same equation is used to model the pulse propagation inside SMF after omitting the gain term, and the solution of (6) is based on the well-known Split Step Fast Fourier Transform (SS-FFT) method [2], [17] and [18]. SAM is modeled as intensity dependence transmission medium, as described in [2], [14], and [18]: Where is the unsaturated loss and is the SAM‘s saturation power. Noteworthy, the relaxation time of the SAM has a negligible effect on such wide chirped pulse propagating inside the cavity. The total insertion loss of all cavity components including that of the gratings and the output part of light is taken as 10 dB. A very small noise pulse has been used to propagate through the

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Fig. 3. Pulse characteristics at net dispersion 0.02 (a) Normalized spectral power density (SPD) of the two cavities, the spectrum width of cavity with lowfiber is slightly higher than the one with high-doped fiber. doped This behavior is found in the measurement for the cavity with SAM, (b) Chirped . pulse profile of the two cavities at net dispersion 0.02

Fig. 2. Simulation results for the low and high-doped fibers; (a) max, (b) maximum energy per pulse, (c) maximum imum small signal gain peak power and (d) chirped FWHM pulse width ( ) versus net dispersion.

different cavity components for few thousands of roundtrips to reach a stable mode-locked pulse operation at certain cavity conditions. B. Numerical Results’ Discussion The maximum small signal gain coefficient for single pulse operation just before optical wave breaking at different values of net dispersion is plotted in Fig. 2(a). To ensure that the nonlinear phase shift is the same for both the low and high-doped cases, value is calculated from (2) through (4) based on the corresponding value at its maximum nonlinear phase shift . The threshold of multi-pulsing or wave breaking is higher for high values of net GVD as the pulse is widely chirped, so the cavity can operate at single pulse operation with higher values of . For comparison purposes, the variation of the max energy of the single pulse operation ( ) with different values of net dispersion for the two types of -doped fiber is plotted in Fig. 2(b), while Fig. 2(c) shows the variation of the max peak power ( ) with net dispersion. The cavity with low-doped fiber provides higher energy and peak power for single pulse operation than that of the highly-doped one. Although the maximum energy in Fig. 2(b) increases monotonically with the net dispersion, the peak power in Fig. 2(c) does not. This is because both the energy and chirped pulse width are increasing with net dispersion at different rates (see Fig. 2(d)). For the energy variation, a trend similar to these results is found in the work of Ilday, et al. [2]. The spectral and the temporal profiles of the laser pulses at after the for the two types of the fibers are plotted in Fig. 3(a) and (b) respectively. The steep-edges with parabolic top of the spectra as well as the positive chirp overall the cavity are signatures of similariton operation [2], [5]. At different values of net dispersion and on the edge of single pulse operation, and are also calculated based on (2) and plotted in Fig. 4(a). The cavity with

Fig. 4. (a) Plot of with net dispersion for the two cavities based on the simulation results. (b) Peak power evolution in the two cavities at net dispersion . 0.02

low-doped fiber can accumulate higher value of before wave breaking which is also seen in the experimental results (i.e., ). The most interesting part in the simulation is the ability to monitor the peak power evolution inside the fiber. Fig. 4(b) shows the peak power evolution inside the nonlinear part of the cavity including and at net dispersion of 0.02 . The peak power reduction in comes mainly from the dispersion; however this reduction is not large at high net dispersion due to small breathing ratio [2]. The peak power at the end of the is higher for the lowdoped fiber than the high-doped one. This also verifies that the increase in the peak power at the end of is mainly due to the low-doped fiber not due to the dispersion in the long after the high-doped fiber. Fig. 5(a) (Fig. 5(b)) shows the evolution of the temporal and the spectral root-mean square RMS pulse widths for high (low) doped fiber cavity at 0.02 net dispersion. The temporal breathing ratio (1.29 and 1.22 for low and high-doped fiber cavities, respectively) is higher than the spectral breathing ratio (1.016 for both low and high-doped fiber cavities), which matches with that previously illustrated for the passive similariton description [2], [19]. The comparison of the behavior of the temporal RMS pulse width in the two cavities reveals the followings. In the two cavities, the temporal RMS pulse width increases monotonically in the SMF preceding the gain fiber. While it decreases in the whole high-doped fiber section, it starts to increase after a plateau subsection in the low-doped fiber section. The temporal RMS pulse width increases in the SMF proceeding the doped fiber before


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Fig. 5. Evolution of the spectral and temporal RMS widths in the cavity at net dispersion for (a) high (b) low-doped fiber. (c) Evolution of 0.02 the excess kurtosis factor of the spectrum power density (SPD) for both cavities.

it is decreased by the saturable absorber and diffraction grating. The RMS spectral widths are 3.558 THz and 3.113 THZ for the low and high-doped fiber cavities, respectively, and their evolution is very similar to that reported in [2], [19]. The excess kurtosis factor is used to check the “parabolicness” of the spectrum through the cavity. The excess kurtosis is , 0, and 1.2 for ideal parabola, Gaussian, and profiles, respectively [19]. Apparently from Fig. 5(c), the spectral evolution is approaching the parabolic pulse through the whole cavity parts. IV. EXPERIMENTAL WORK A. Experimental Set-Up Description Fig. 6 depicts the experimental set-up employing a saturable absorber mirror (SAM, from Batop optoelectronic) as modelocker. It has 500 fs relaxation time, 120 saturation fluence, 10% non-saturable loss, 20% modulation depth and 30% absorbance. In this set-up, two 980 nm pump-sources are combined using a polarization combiner to increase the available pump power up to 590 mW. The gain medium ( fiber) is pumped through the output of the wave division multiplexer (WDM) and is followed by . The optical signal is coupled to/from the free space through angled-cleaved collimators. Free-space Faraday isolator (OFR, IO5-1030 HP) is inserted inside the cavity for unidirectional propagation. The net cavity GVD is adjusted by a pair of diffraction gratings and the output light is captured from the polarization beam splitter ( ). The energy fluence incident on the SAM is controlled by and HWP1 [20], [21]. acts as a polarization director [20], [21] which passes the horizontally-polarized light to the SAM and directs the reflected light from the SAM whose polarization being vertical to the . The polarization of the reflected light from the SAM is vertical due to the double effect of the on the incident horizontally light to the SAM (which is polarization insensitive). As the efficiency of the diffraction gratings is maximum for horizontally polarized beam, another

Fig. 6. Schematic diagram of the experimental set-up femtosecond fiber laser.

HWP ( ) is inserted to convert the polarization again to be horizontal before hitting the gratings. The SAM is inserted at the focal point of a converging lens to increase the fluence of the optical pulses incident on the SAM. The mode-locking is self-starting and the waveplates (QWP1 and HWP1) are used to adjust the value of the incident SAM’s fluence required to initiate the mode locking. The mode locking operation is lost when SAM is replaced by a mirror. This verifies that the waveplates’ angles cannot initiate any mode locking from nonlinear polarization rotation. The temporal and the spectral properties of the output chirped pulse are simultaneously monitored by (5 fs resolution, and 120 ps scanning range) Autocorrelator (AC, FR-103XL) and (0.05 nm resolution) optical spectrum analyzer (OSA), respectively. The pulse is dechirped outside the cavity and its temporal width is measured by another (5 fs resolution, 20 ps scanning range, FR103MN) AC. The optical pulse train is monitored through a large bandwidth photo-detector (30 GHz) connected to (10 ps resolution) sampled-based oscilloscope (OSC, Agilent 83480A) to ensure the single pulse operation. The zero order reflection of the intra-cavity grating is employed to capture the properties of the pulse circulating inside the cavity. The pump power is adjusted at each value of net dispersion to have a single pulse operation with the maximum output energy. B. Experimental Result’s Discussion To experimentally verify that low-doped long gain fiber length increase the peak power of the generated laser pulses, two available types of doped fibers (Coractive Yb214, and Coractive Yb501) having maximum doping concentration

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TABLE I PHYSICAL PARAMETERS OF THE YB FIBER

Fig. 8. Comparison of dispersion contributed from intra-cavity grating and fiber. de-chirping grating for cavity with high and low-doped

Fig. 9. Output pulse characteristics of the cavity at a net dispersion of 0.02 ; (a) parabolic spectrum with spectral BW 17.92 nm (20.88 nm) for cavity with fiber (b) autocorrelation of the chirped pulse of width high (low) doped fiber, Insert is the 8.25 ps (5.676 ps) for cavity with high (low) doped de-chirped pulse of width 221.76 fs (205.7 fs) for cavity with high (low) doped fiber.

Fig. 7. (a) Pump power ( ) (b) Maximum pulse energy ( ) (c) Max) (d) Chirped pulse width versus net dispersion. imum peak power (

contrast are selected in the experimental set-up shown in Fig. 6. The single mode fiber was varied to ensure equal cavity length and hence the same repetition rate. The first one is based on high-doped fiber (Coractive Yb214) of length 25 cm followed by a 143 cm while the second one utilizes 73 cm of low-doped fiber (Coractive Yb501), followed by 97 cm of and the average repetition rate for the two cases is about 30.21 MHz. The length of is 352.5 cm. Detailed specifications of the Yb-doped fiber used are reported in Table I, as provided from CorActive Inc. Fig. 7(a) shows the max pump power that can be used for single pulse operation at each net dispersion value, for the two fiber types. The cavity with low-doped fiber needs lower pump power than the cavity with high-doped fiber. The energy and the peak power of the output pulse at different values of net dispersion are shown in Fig. 7(b) and (c), respectively. Obviously, the max energy monotonically increases with net dispersion. The cavity with a low-doped fiber results in a higher energy and peak power than that with a high-doped fiber.

The enhancement factor in this specific case is around 2. The chirped pulse width increases with net dispersion as shown in Fig. 7(d). Our experimental results in Fig. 8 are in agreement with the simulation results presented in Fig. 2. The pulses are confirmed to be similariton by checking the relation between the anomalous dispersion required to de-chirp the pulses compared to the intra-cavity grating dispersion. Fig. 8 shows that the pulses are similariton because the magnitude of the anomalous dispersion required to de-chirp the output pulse near the transform limit is larger than the intra-cavity grating dispersion. The spectral profile of the chirped pulse, the temporal profile of the chirped and de-chirped pulse at 0.02 net dispersion (as that numerically studied) for the two cavities is presented in Fig. 9. The spectrum width of the pulse generated from high-doped fiber cavity is slightly lower than that generated from the low-doped one. The two spectra are fitted to and parabolic curves in Fig. 10. It is clear that the parabolic fitting is very near to the measured spectra. The Fourier transform limited pulse profiles are calculated from the measured spectra for the two cavities at 0.02 net dispersion. They are also fitted to and parabolic curves as shown in Fig. 11, the pulses are more parabolic especially at their edges. This proves the parabolic pulse profile in the two cavities. The de-chirped parabolic pulse widths calculated from the autocorrelation are 193.29 fs and 179.29 fs for the cavity with high and low-doped fiber, respectively. The time bandwidth


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V. CONCLUSION

Fig. 10. Output spectrum fitted to and parabolic curves at net dispersion for the cavity with (a) high (b) low-doped fiber. 0.02

Fig. 11. Calculated intensity fitted to and parabolic curves at net disperfor the cavity with (a) high (b) low-doped fiber. sion 0.02

In conclusion, for the first time to the best of our knowledge, we found that decreasing the doping level and increasing the length of the gain medium results in an increase in the peak power. A comparison between high-doped short-length and low-doped long-length gain medium in fiber laser cavity is carried out both theoretically and experimentally. Moreover, we demonstrate that the ability of the low-doped gain medium to generate high peak power in the fiber laser cavity is attributed to two reasons, one is direct and the other is indirect. The direct reason is due to the gradual increase of the nonlinear phase shift accumulated during the pulse propagation in the gain medium. The indirect reason is that the ability of the low-doped fiber to tolerate higher maximum nonlinear phase shift for single pulse operation. The indirect reason arises from the larger effect of the nonlinearity per unit length in the highly doped fiber compared to that of the low-doped fiber as a function of the dispersion. In the high-doped gain medium, the nonlinearity effect per unit length dominates the dispersion effect on the pulse propagation while in the low-doped gain medium, their effect per unit length might be similar. As a result the threshold nonlinear phase shift for single mode-operation has higher value in low-doped-fiber than that of the highly-doped fiber cavity. Subsequently the available output peak power is higher in the case of the low-doped fiber. So generally speaking, the selection of the lowest doped fiber results in the highest peak power of the generated pulse provided that the cross-sections of all fibers are the same. REFERENCES

Fig. 12. The variation of Yb501 and Yb214.

with net dispersion for the cavities having

product is found to be 0.84 and 0.92 for high and low-doped fiber, respectively. The transform limit to the parabolic pulse is exceeded by and , respectively. These values are close to the values reported in [3], [4] and indicate linearly chirped pulse to great extent. for the two cavities is calculated for each value of net dispersion using the (1) through (3), and plotted in Fig. 12. is higher for the cavity with low-doped fiber (Yb501) than for the other cavity with fiber (Yb214), (i.e., ). So this cavity can support higher values of for single pulse operation before the onset of multi pulsing or wave breaking.

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(NTI), Cairo, Egypt. From September 2007 until June 2009, he worked as a Teacher Assistant in French University, Cairo, Egypt (UFE). From February 2008 until August 2010, he worked as a researcher in Laboratory for Lasers and Optical Communications at Ain Shams University, Cairo, Egypt. He is a student member of International Society for Optics and Photonics (SPIE) and Institute of Electrical and Electronics Engineers (IEEE).

Hussein E. Kotb (S’07) received the B.Sc. and M.A.Sc. degrees from Electronics and Communication department, Faculty of Engineering, Ain Shams University, Cairo, Egypt, in 2002 and 2006, respectively. He is currently working towards his Ph.D. degree in the School of Electrical Engineering and Computer Science, Faculty of Engineering, University of Ottawa, Ontario, Canada. His current research interests include the implementation of femtosecond Fiber Laser for biomedical application. He was born in Cairo, Egypt in 1980. In September 2002, he worked as a Teacher Assistant in Engineering Physics and Mathematics department at Ain Shams University, Cairo, Egypt. In October 2003, he joined National Telecommunication Institute

Hanan Anis is an Associate Professor at the School of Electrical Engineering and Computer Science, Faculty of Engineering, University of Ottawa, Ontario, Canada. Prior to that, Hanan was the co-founder and Chief Technology Officer at Ceyba, an optical long-haul networking company that employed 250 people at its peak. From 1994 to 2000, Hanan worked at Nortel Networks in different positions conducting research in various areas of photonics, ranging from device physics to optical networking. Hanan holds a B.Sc from Ain-Shams University (1987), a M.A.Sc (1991) and a Ph.D. (1996) from University of Toronto both in Electrical and Computer Engineering. She has numerous journal and conference publications and patents.

Mohamed A. Abdelalim received B.Sc. degree in electrical engineering from Ain Shams University, Cairo, Egypt, in 1996, and M.A.Sc. degree in electrical engineering from Cairo University, Egypt, in 2003, and Ph.D. degree from Ain Shams University, Egypt, in 2010. He is currently a Research Associate in Photonics Innovation Laboratory at School of Electrical Engineering and Computer Science, Faculty of Engineering, University of Ottawa, Ontario, Canada. His current research interests are in femtosecond fiber laser. His research interests also include fiber sensors, nonlinear optics applications, and photonic crystals. He is a member of International Society for Optics and Photonics (SPIE) and Optical Society of America (OSA).

Katherine J. Bock received her degree in engineering physics from Carleton University, Ottawa, Canada in 2009 and an M.A.Sc. in biomedical engineering from the University of Ottawa, Ottawa, Canada in 2012. She is currently working towards her Ph.D. in electrical engineering in the Department of Electronics at Carleton University. Her research interests include tilted fibre Bragg grating sensor devices and plasmonics.