- Email: [email protected]
Experimental and numerical investigation of short pulse propagation and amplification around 1.3 μm in a Nd3+-doped fluoride fiber
15 December 1994
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 113 (1994) 39--45
Experimental and numerical investigation of short pulse propagation and amplification around 1.3/xm in a Nd 3+-doped fluoride fiber H. Ammann, W. Hodel, H.P. Weber Institute of Applied Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland Received 24 May 1994
Abstract
We have investigated experimentally and theoretically the propagation and amplification characteristics of short optical pulses at A-- 1.3/zm in a neodymium-doped fluorozirconate fiber. We have found that psec pulses (4 ps) with sub-nJ energies can be propagated and amplified without appreciable temporal and spectral reshaping. The propagation and amplification of sub-psec pulses (300 fs) of comparable energy, however, is significantly affected by the dispersive and nonlinear properties of the fiber. The interplay between dispersion and nonlinear effects leads to a power dependent pulse broadening which is more pronounced when the pulses are amplified. The experimental results are in good agreement with numerical simulations based on an extended version of the nonlinear Schr'odinger equation. The comparison between experimental and numerical results allows to identify the pulse shaping mechanisms involved which is important in order to assess the potential of Nd 3 +-doped fluoride fibers as mode-locked fiber lasers and amplifiers.
1. Introduction
Short pulse generation and amplification is of considerable interest for high-capacity communications and ultrafast spectroscopy; In the third telecommunications window around 1.55/zm, both the generation and amplification of short pulses using Er a +-doped silica fibers is well established. Amplifiers with a single pass gain of over 40 dB are now commercially available, and the generation of sub-50 fs pulses has been demonstrated [ 1 ]. However, this success has not been matched so far in the important 1.3/xm telecommunications band. Neither of the two active ions most widely investigated as dopants, namely Neodymium (Nd 3 +) and Praseodymium (Pra + ), can be used in silica fibers for different reasons. The 4F 3 / 2 - 4I13/2 transition in Nd 3+ suffers from signal exited-state-absorption 0030-4018/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD10030-401 8 ( 9 4 ) 0 0 5 11-7
(ESA), which limits the gain to wavelengths longer than 1.36/xm. On the other hand, the 1G4 level of Pra + is quenched due to the large non-radiative decay rate. Both problems can be reduced by the use of fluoride instead of silica fibers. Up to now, Pr 3 +-doped fiber amplifiers with a maximum gain of 38.2 dB [2] and a mode-locked fiber laser generating 1.6 ps pulses [3] have been demonstrated at A = 1.3/xm. However, the demonstration of short pulse amplification and a profound investigation of pulse propagation in active fluoride fibers, which is important in order to assess the performance of fiber amplifiers or mode-locked fiber lasers, is still lacking. In this work we investigate experimentally and theoretically the propagation and amplification of short pulses in a bid 3+ :ZBLAN fiber. We demonstrate that 4 ps pulses with sub-nJ energies can be propagated and
40
1-1.Ammann et al. / Optics Communications 113 (1994) 39-45
./((3")
V ~ "/ Nd3+'ZBLAN* ' aut°c°rrelat°r~T~
I/ ~
, II
fibre#1(L=2m, ~fil
[monochromator['~-,d "LL ~ !:::1~ ('~ -! "II-- Nd3+_ ZBLAlq" fibre#2(L=2m) Fig. 1.Experimentalsetup
-
amplified (by up to 7 dB) in 4 m of active fiber without appreciable temporal or spectral reshaping. Pulses of 300 fs duration and comparable energy, on the other hand, experience a power dependent broadening which is due to the combined effects of dispersion and fiber nonlinearities. If the sub-ps pulses are amplified (by up to 6 dB) a gain induced enhancement of the temporal broadening is observed. The experimental results are compared with numerical calculations. The good agreement between theory and experiment demonstrates that pulse propagation and amplification in a Nd 3 ÷-doped ZBLAN fiber can be well understood on the basis of a modified nonlinear Schr/Sdinger equation which takes into account group-velocity dispersion (GVD), selfphase modulation (SPM), stimulated Raman scattering (SRS) and gain.
interference filter, which efficiently removed the competitive 1.05 /zm radiation [5]. The monochromator used for measuring the optical spectrum of the signal at the fiber input and output was a 0.5 m Czerny-Turner grating spectrograph. The background-free autocorrelation function obtained from the second harmonic signal of a LilO3 crystal was used to characterise the temporal pulse shapes.
3. Characterisation of the Nd a+-doped ZBLAN fiber In the experiments we used a commercially available Nd3+-dope d ZBLAN fiber (Le verre fluort, France) with an active ion concentration of 2000 ppm. The transmission loss was 0.075 dB/m at )t = 1.3/~m. The core diameter, outer diameter and cut-off wavelength were specified by the manufacturer to be 4/zm, 125 /zm and 1/~m, respectively. Since for our experiments with ultrashort pulses a knowledge of the dispersion and gain characteristics of the ZBLAN fiber is very important, we will in the following describe these properties in more detail.
3.1. The dispersive properties of the ZBLAN fiber 2. Experimental setup The experimental set-up used for all measurements presented in this paper is shown in Fig. 1. The short pulse source was a synchronously pumped dye laser which is described in more detail elsewhere [4]. Using either a Lyot filter or a pellicle of 7 / z m thickness as the tuning element, pulses with duration of approximately 4 ps and 300 fs, respectively, could be generated at a repetition rate of 82 MHz. The maximum average power was 100 mW and the centre wavelength of the pulses could be tuned between 1.25/zm and 1.35/xm. The Nd 3÷-doped fiber amplifier consisted of two 2 m pieces of non-polarisation preserving, Nd 3÷ :ZBLAN (ZrFa-BaF2-LaF3-AIF3-NaF) fiber. Two commercially available A1GaAs laser diodes (LD), which delivered 150 mW at A =0.82/xm each, were used as the pump. Signal and pump were combined by dichroic mirrors and coupled into the fibers by microscope objectives. Between the two pieces of active fiber we installed an
The group velocity dispersion (GVD) parameter D of the ZBLAN fiber is a sum of the material dispersion Dr, and the waveguide dispersion Dw. The waveguide contribution Dw can be calculated according to [ 6]
1
d2(Vb)
Dw= -Ac any dr-----7 ,
(1)
where V and b are the normalised frequency and propagation constant, respectively. Dw can be estimated using the approximation
d2(Vb) dV z
= 4.501 - 3.106V+ 0.547V 2,
(2)
which is valid in the range 1.3 < V< 2.4 [ 6]. The material dispersion contribution D~ of ZBLAN was measured by Monerie et al. and is presented in ReL [7]. We have used these values for Dr. and the values for Dw calculated with Eqs. (1) and (2) to get the total dispersion D of the ZBLAN fiber. Fig. 2 shows the individual contributions Dm and Dw and compares their
H. Ammann et al. /Optics Communications 113 (1994) 39-45
41
total dispersion is normal and rather high (in the order of - 30 p s / n m - km). The excellent agreement between calculated and measured data further indicates that the dopants have negligible influence on the GVD of the unpumped Z B L A N fiber.
-10 -20
-40
3.2. The gain properties o f the Z B L A N fiber -50
, 1100
,
,
,
i
. . . .
1200
t
,
,
•
1300
.
:
. . . .
1400
1500
Wavelength [nm]
Fig. 2. Wavegnide (a) and material (b) dispersion of ZBLANfibre. The dotted line represents the sum of (a) and (b) and the solid line is the measured total GVD.
--
6
B 3
_~
• 50
100
150
Total Launched Pump Power [mW]
Fig. 3. Small signal gain versus total launched pump power for a signal wavelength of A= 1.345 p.m. The dashed line represents the 1.05/xm fibre output radiation (ASE). 9 6
3
/
/
/
/' "-~-"
/ •;N
0
-3
/ 290
/
/
1310
1330
1350
Signal Wavelength [nm]
Fig. 4. Measured small signal gain versus signal wavelength for a launched pump power of 2 X 75 mW. sum with the measured total dispersion of the active fiber [ 8 ]. Excellent agreement between the theoretical and the experimental data was obtained by assuming a core diameter and a cut-off wavelength of d = 4.36 # m and Ac = 1.07 ~m, respectively, which are close to the specified values d = 4 / x m and Ac = 1/xm. Note that in the vicinity of 1300 nm the waveguide contribution is comparable to the material contribution and that the
The gain properties of the Z B L A N fiber were studied using ~ 4 ps pulses from the dye laser (note that because of the high repetition rate of 82MHz the output of the dye laser can be considered as cw radiation). The gain was evaluated by taking the pumped/unpumped output signal ratio and subtracting the transmission loss at A = 1.3/zm (0.3 dB). Fig. 3 shows the gain as a function of the total launched pump power (the gain provided by the individual pieces of active fiber was equal). The signal wavelength was A = 1.345/zm and the coupled signal power was held below - 20 dBm to ensure small signal behaviour. Assuming a coupling efficiency of 60% for the pump, the pump efficiency in the unsaturated regime was 0.3 d B / m W . The gain saturation at about 8 dB for a total pump power higher than approximately 2 X 50 m W is a consequence of the increasing 1.05/xm radiation [ 5 ], which is also shown in Fig. 3. We note that laser action at A = 1.05/xm was established in either piece of active fiber when the corresponding launched pump power was higher than 30 mW. In Fig. 4, the dependence of the small signal gain on the signal wavelength is depicted for a launched pump power of 2 × 75 mW. The gain is negative for wavelengths shorter than 1.31 /.tm due to ESA. For wavelengths longer than 1.32/zm the gain is relatively fiat with a maximum of 8 dB at A = 1.344 /zm. For completeness, we mention that the signal saturation input power (3 dB reduction of the unsaturated gain) was measured to be P = 16 mW.
4. The theoretical
model
Before we summarise the experimental results and compare them with theory we briefly describe the model used for the simulations. The numerical calculations are based on a modified nonlinear Schrrdinger (NLS) equation of the form
H. Ammannet al. /Optics Communications113 (1994)39-45
42
gx4 i i 11( , 62.4 i-~z + -~ a A - ~ g A - 2 8t2 -
n2k~°A((1 - Y) IAI 2 Aeff
+ dt'
(3)
0
which was solved using the standard split step Fourier algorithm. The last three terms on the left hand side represent the influence of linear losses ( a ) , gain (g) and GVD (k"), respectively. The linear loss was taken to be a = 0.075 d B / m as specified by the manufacturer. As the gain spectrum is quite flat in the range between 1.32/,m and 1.35/xm (see Fig. 4), g was taken to be independent of wavelength. The parameter k" is related to the GVD parameter D by k" = - D Az/27rc. Note that higher order dispersion terms have been omitted in Eq. (3). This is justified because for k" ---0.1 p s 3 / k m (estimated from the measured dispersion curve) and k" .~ 30 ps2/km, one gets k"/k"---3 fs, which is much shorter than the pulse widths used in our experiments. The terms on the right hand side of Eq. (3) describe SPM and SRS, respectively. The effective core area Aeff is approximated by A~ff= ~-d2ff/4, where d~ff is the mode field diameter dell= 1.4d [9]. The Kerr coefficient was taken to be n2 = 2.8 × 10-16 cm2/W [ 10], which is approximately 10% smaller than that of fused silica. This value contains the instantaneous (Kerr effect) as well as the delayed nonlinear response (Raman scattering) of the fiber material. The measured Raman gain spectrum for a typical fluoride glass was presented in Ref. [ 11 ]. The maximum gain occurs at a frequency shift of 600 c m - 1 corresponding to a wavelength shift of 110 nm, which is much larger than the spectral width of the pulses used in the experiments. The (maximum) gain for SRS is gR = 1.5 × 10 -13 m / W [ 12] at A -- 1.3 ~m, from which we calculated a critical power for significant SRS starting from noise of PSRS = 16A~rr/gRLeff= 800 W. For comparison, the maximum peak power in our experiments was in the order of Ppcak= 600 W (300 fs pulses, 25 mW average power). Therefore, SRS with frequency shifts much larger than the spectral bandwidth of the pulses is expected to have only a minor influence on pulse propagation. Within the spectral width of the pulses, how-
ever, SRS does not have to build up from noise. As this can lower the threshold power by as much as three orders of magnitude [ 13 ], we took intra-pulse Raman scattering into account in our calculations using the response function approach [ 14]. The parameter ,/in Eq. (3) describes the relative weight of Kerr and Raman nonlinearity and h(t) is the normalised Raman response function. From the fact that the Kerr coefficient nz in ZBLAN is smaller but, on the other hand, the Raman gain gR is approximately twice as large as in silicates [ 12], we conclude that the weighting factor 3' is larger in fluoride glasses. We have taken this into account by setting 3,=0.3 in the calculations (compared to 3,=0.18 for silicates [14]). The Raman response function h(t) was approximated by a single sided exponential with a decay time of 76 fs, which has been found suitable for silicates [ 14]. This choice was motivated by the fact that the normalised Raman gain spectra of these two hosts differ only slightly for frequency shifts smaller than 100 c m - 1 [ 11 ].
5. Experimental results and comparison with theory
5.1. Propagation and amplification of ps pulses Propagation of picosecond pulses Using a Lyot filter as the tuning element the width of the autocorrelation function of the dye laser pulse was typically TAC = 6 ps (FWHM). After propagation through 2 × 2 m of the active fiber, no significant changes of the autocorrelation traces could be observed for coupled average powers up to 25 mW which corresponds to a pulse energy of 0.3 nJ. A close inspection of the pulse spectra on the other hand revealed a slight narrowing and a blue-shift of the output spectra. This is illustrated in Fig. 5 which shows the measured input and output spectrum (left) together with the numerically calculated input and output spectrum (right). In the calculations we have assumed an asymmetric Gaussian pulse shape with q'T= 2~'L, where ~'Land rv are the time constants of the leading and the trailing edge, respectively (this was motivated by measurements and numerical simulations presented in Ref. [ 15] ). The pulse duration was ~-p= 4.5 ps (TAc= 6.4 ps). Further, the input pulse was taken to be slightly chirped because the measured spectral width of A h = 0.66 nm is approx-
H. Ammann et al. /Optics Communications 113 (1994) 39--45
"7.
"7.
m m
g 1319
1320
1319
1321
1320
1321
Wavelength [nm]
Wavelength [nm]
0.69 nm
5.5 ps
0.71 nm
"~
e .
.
.
.
I
-8
.
.
0
.
.
I
.
8
'
I
I
1339
I
'
I
1340
I
I
A ~bspM= n2kLPp~ak= 1.1. The calculations have shown that the pulse asymmetry is responsible for the spectral blue-shift whereas the initial chirp of the pulse causes the spectral narrowing (this was also observed in Ref. [ 16] ). It is important to note that - as additional calculations have confirmed - unchirped and symmetric picosecond pulses with energies in the sub-nJ range would not experience any measurable temporal or spectral reshaping in the fluoride fiber.
Amplificationof picosecondpulses
Fig. 5. Fibre input (dashed) and output (solid) spectra of pulses with ~'p=4.5 ps (FWHM). Left: measurement, right: calculation.
5.5 p s
43
I
1341
Time Delay lpsl Wavelength lnm] Fig. 6. Autocorrelation traces and spectra of 3.9 ps input pulses. From bottom to top: fibre input, fibre output without pumping and fibre output for a launched pump power of 2 × 75 roW. Coupled average signal power and gain were 4 m W and 7 dB, respectively. All traces are normalised to unity. ¶,'
1.5 .,-"
~" 1.3 e~
Fig. 6 shows the measured autocorrelation traces and pulse spectra at the fiber output for the pumped and unpumped case, respectively. The coupled average signal power was 4 mW, which corresponds to a pulse energy of 50 pJ and a peak power of 12 W. The pump power and gain were 2 × 75 mW and 7 dB, respectively. The width of the autocorrelation trace of the input pulse was TAC= 5.6 ps (FWHM). It can be seen from Fig. 6 that the shape of the autocorrelation trace did not change when the pump was turned on. On the other hand, the modifications of the spectra which were discussed in more detail above, were slightly more pronounced with the pump on owing to the gain induced enhancement of the nonlinear effects. These results could be well reproduced by numerical simulations, which in addition showed that the spectral changes are absent when bandwidth limited, symmetric pulses are amplified. We therefore conclude that propagation and moderate amplification of picosecond pulses with input pulse energies up to 50 pJ is possible without noticeable pulse distortions.
5.2. Propagationand amplificationof sub-pspulses ..
Propagationof subpicosecondpulses
*. , . . *
0.9 5
10
15
20
Coupled Signal Power ImW] Fig. 7. Width of the output autocorrelation function TAC (FWHM) versus coupled average signal power after propagation through 4 m of fibre. The dotted line represents the calculated power dependence of TAC.
imately 20% larger than that corresponding to a bandwidth limited pulse (0.55 nm). The maximum SPM induced phase shift which corresponds to an average signal power of 25 mW was estimated to be
Using a pellicle as the tuning element the width of the autocorrelation trace of the dye laser pulses was typically TAC= 700 fs (FWHM). Whereas the spectral reshaping of the sub-ps pulses after propagation through the ZBLAN fiber was in general negligibly small, the temporal reshaping was very pronounced. We have found that the width of the autocorrelation function after propagation of the sub-ps pulses through the ZBLAN fiber was distinctly power dependent. The increase of the autocorrelation width with increasing power coupled into the ZBLAN fiber is illustrated in Fig. 7. The experimental results (points) are compared
44
H. Ammann et al./ Optics Communications 113 (1994) 39--45
i m
i
-4
0
Time Delay [psi
i
4
-4
0
Time Delay [psl
Fig. 8. Left: autocorrelation functions (measured and calculated) at fibre input (bottom) and fibre output (middle: Pay=4 mW, top: P~v = 20 mW). Right: corresponding pulse shapes (calculated).
with the numerically calculated power dependence of TAC (dashed line). The simulations were again carried out using parameters obtained from the experimental data (fit of the autocorrelation and spectrum). In the calculations we assumed an asymmetric doubled sided exponential pulse shape with ~'L= 3~'T,where % and ~'Tare the time constants of the leading and the trailing edge, respectively. The pulse duration was ~-p= 310 fs (TAc=700 fs). Further, the input pulse was taken to be strongly chirped because the measured spectral width of AA = 9.3 nm is approximately 4 times larger than that corresponding to a bandwidth limited pulse (2.3 nm). The maximum SPM induced phase shift was estimated to be A thspM= 0.45 per mW of coupled average power. With these parameters, the power dependent broadening observed in the experiment could be well reproduced by the numerical simulations as shown in Fig. 7. For low input powers, the autocorrelation trace was broadened from 700 fs to approximately 970 fs due to the influence of GVD only. The power dependent broadening of the output autocorrelation traces clearly observed for pulse energies higher than 0.1 nJ (8 mW average power) is due to the combined effects of GVD and fiber nonlinearities. The measured autocorrelation traces for two specific cases (average input powers of 4 mW and 20 mW) are shown in Fig. 8 together with the calculated autocorrelation functions and the corresponding output pulse shapes. It can be seen that the transmitted pulses were not only broadened but also exhibited some modulation at the leading edge. It should be mentioned that the calculated pulse evolution along the ZBLAN fiber actually was quite complex: in
the first half of the fiber, the pulses evolved into squarelike shapes typical for the presence of GVD and SPM, whereas in the second half no further broadening occurred. Instead, the pulses experienced a slight recompression, which was accompanied by the formation of the modulation at the leading edge. Although the details of the pulse evolution (temporally and spectrally) strongly depend upon the input pulse parameters (shape, chirp and asymmetry of the pulse), the calculations confirmed that the propagation of sub-ps pulses is significantly affected by the nonlinear and dispersive properties of the ZBLAN fiber.
Amplification of subpicosecondpulses Fig. 9 shows the measured and calculated (smooth solid lines) autocorrelation traces and pulse spectra at the fiber input as well as at the fiber output for the pumped and unpumped case, respectively. The coupled average signal power was 9 mW corresponding to a pulse energy of 110 pJ and a peak power in the order of 200 W. The pump power and gain were 2 × 75 mW and 6 dB, respectively. The width of the autocorrelation trace of the input pulse was 700 fs (FWHM). It can be seen from Fig. 9 that the spectrum was only slightly modified when the pump was turned on, whereas the changes in the autocorrelation trace are much more pronounced. The width of the autocorrelation was increased from 1.2 ps to approximately 1.7 ps in the presence of the pump which is again due to the gain induced enhancement of the nonlinear effects. The temporal broadening could be well reproduced by the calculations (see Fig. 9). The comparatively poor
"7".
m 0
,.r, ct~
-3
0
Time Delay [psi
3
1320
1335
1350
Wavelength [nm]
Fig. 9. Autocorrelation traces and spectra of 310 fs input pulses. From bottom to top: fibre input, fibre output without pumping and fibre output for a launched pump power of 2 X 75 mW. Coupled average signal power and gain were 9 mW and 6 dB, respectively. All traces are normalised to unity. The smooth traces are calculated.
H. Ammann et al. /Optics Communications 113 (1994) 39-45
agreement between the measured and calculated spectra could not be clarified conclusively but is probably due to the uncertainty of the input pulse parameters.
45
in the fs regime will be affected by the fiber dispersion and nonlinearities. The numerical investigation of possible limitations for the case of a high gain fiber amplifier will be the subject of a forthcoming publication.
6. Conclusions Acknowledgements We have investigated the propagation and amplification characteristics of short pulses with central wavelengths in the vicinity of A = 1.3/.tm in a Nd3+-doped ZBLAN fiber. Calculation of the GVD parameter (the calculated values are in excellent agreement with measured data) and an estimation of the strength of the different nonlinear effects in fluoride fibers allowed to perform numerical simulations, which could well explain the main experimental findings. It has been demonstrated experimentally that 4 ps pulses transmitted through 4 m of active fluoride fiber do not experience any measurable temporal reshaping, whereas the spectra were slightly blue shifted and narrowed. The numerical simulations have shown, however, that the occurrence of these spectral modifications was due to the asymmetry and the chirp of the input pulses. Therefore, symmetric, bandwidth limited pulses with a duration of several picoseconds and sub-nJ energies would propagate essentially distortionless through short active fluoride fibers. Furthermore, we have demonstrated that moderate amplification (7 dB) of picosecond pulses is feasible without pulse distortions. For sub-picosecond pulses of comparable pulse energy, on the other hand, the dispersive and nonlinear effects significantly affected pulse propagation. The combination of GVD, SPM and SRS led to a power dependent temporal broadening which became more pronounced when the pulses were amplified (by up to 6 dB). These results indicate that the performance of both fiber amplifiers as well as mode-locked fiber lasers
We thank Dr. B. Deutsch from the University of Kaiserslautern for carrying out the dispersion measurements.
References [ 1 ] D.J. Richardson, A.B. Grudinin and D.N. Payne, Electron. Lett. 28 (1992) 778. [2] Y. Miyajima, T. Sugawa and Y. Fukasaku, Electron. Lett. 27 (1991) 1706. [3] T. Sugawa, E. Yoshida, Y. Miyajima and M. Nakazawa, Electron. Lett. 29 (1993) 902. [4] P. Beaud, B. Zysset, A.P. Schwarzenbach and H.P. Weber, Optics Lett. I 1 (1986) 24. [5] M. Obro, B. Pedersen, A. Bjarklev, J.H. Povlsen and J.E. Pedersen, Electron. Lett. 27 ( 1991 ) 470. [6] A.E. Comyns (Wiley, New York, 1989). [7] M. Monerie, F. Alard and G. Maze, Electron. Lett. 21 (1985) 1179. [8] B. Deutsch, University of Kaiserslautem, private communication. [9] D. Marcuse, The Bell System Techn. J. 56 (1977) 703. [ 10] I.D. Aggarwal and G. Lu (Academic, New York, 1991 ). [ 11 ] A. Saissy, J. Botineau, L. Macon et G. Maze, J. Physique Lett. 46 (1985) L289. [ 12] M. Monerie, SPIE Vol. 799 (1987) 123. [ 13] D. Cotter, Opt. Quantum Electron. 19 (1987) 1. [ 14] R.H. Stolen, J.P. Gordon, W.J. Tomlinson and H.A. Hans, J. Opt. Soc. Am. B 6 (1989) I159. [ 15 ] J. Schiitz, W. Hodel and H.P. Weber, Optics Comm. 95 (1993) 357. [ 16] M. Oberthaler and R.A. Hfpfel, Appl. Phys. Lett. 63 (1993) 1017.
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 113 (1994) 39--45
Experimental and numerical investigation of short pulse propagation and amplification around 1.3/xm in a Nd 3+-doped fluoride fiber H. Ammann, W. Hodel, H.P. Weber Institute of Applied Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland Received 24 May 1994
Abstract
We have investigated experimentally and theoretically the propagation and amplification characteristics of short optical pulses at A-- 1.3/zm in a neodymium-doped fluorozirconate fiber. We have found that psec pulses (4 ps) with sub-nJ energies can be propagated and amplified without appreciable temporal and spectral reshaping. The propagation and amplification of sub-psec pulses (300 fs) of comparable energy, however, is significantly affected by the dispersive and nonlinear properties of the fiber. The interplay between dispersion and nonlinear effects leads to a power dependent pulse broadening which is more pronounced when the pulses are amplified. The experimental results are in good agreement with numerical simulations based on an extended version of the nonlinear Schr'odinger equation. The comparison between experimental and numerical results allows to identify the pulse shaping mechanisms involved which is important in order to assess the potential of Nd 3 +-doped fluoride fibers as mode-locked fiber lasers and amplifiers.
1. Introduction
Short pulse generation and amplification is of considerable interest for high-capacity communications and ultrafast spectroscopy; In the third telecommunications window around 1.55/zm, both the generation and amplification of short pulses using Er a +-doped silica fibers is well established. Amplifiers with a single pass gain of over 40 dB are now commercially available, and the generation of sub-50 fs pulses has been demonstrated [ 1 ]. However, this success has not been matched so far in the important 1.3/xm telecommunications band. Neither of the two active ions most widely investigated as dopants, namely Neodymium (Nd 3 +) and Praseodymium (Pra + ), can be used in silica fibers for different reasons. The 4F 3 / 2 - 4I13/2 transition in Nd 3+ suffers from signal exited-state-absorption 0030-4018/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD10030-401 8 ( 9 4 ) 0 0 5 11-7
(ESA), which limits the gain to wavelengths longer than 1.36/xm. On the other hand, the 1G4 level of Pra + is quenched due to the large non-radiative decay rate. Both problems can be reduced by the use of fluoride instead of silica fibers. Up to now, Pr 3 +-doped fiber amplifiers with a maximum gain of 38.2 dB [2] and a mode-locked fiber laser generating 1.6 ps pulses [3] have been demonstrated at A = 1.3/xm. However, the demonstration of short pulse amplification and a profound investigation of pulse propagation in active fluoride fibers, which is important in order to assess the performance of fiber amplifiers or mode-locked fiber lasers, is still lacking. In this work we investigate experimentally and theoretically the propagation and amplification of short pulses in a bid 3+ :ZBLAN fiber. We demonstrate that 4 ps pulses with sub-nJ energies can be propagated and
40
1-1.Ammann et al. / Optics Communications 113 (1994) 39-45
./((3")
V ~ "/ Nd3+'ZBLAN* ' aut°c°rrelat°r~T~
I/ ~
, II
fibre#1(L=2m, ~fil
[monochromator['~-,d "LL ~ !:::1~ ('~ -! "II-- Nd3+_ ZBLAlq" fibre#2(L=2m) Fig. 1.Experimentalsetup
-
amplified (by up to 7 dB) in 4 m of active fiber without appreciable temporal or spectral reshaping. Pulses of 300 fs duration and comparable energy, on the other hand, experience a power dependent broadening which is due to the combined effects of dispersion and fiber nonlinearities. If the sub-ps pulses are amplified (by up to 6 dB) a gain induced enhancement of the temporal broadening is observed. The experimental results are compared with numerical calculations. The good agreement between theory and experiment demonstrates that pulse propagation and amplification in a Nd 3 ÷-doped ZBLAN fiber can be well understood on the basis of a modified nonlinear Schr/Sdinger equation which takes into account group-velocity dispersion (GVD), selfphase modulation (SPM), stimulated Raman scattering (SRS) and gain.
interference filter, which efficiently removed the competitive 1.05 /zm radiation [5]. The monochromator used for measuring the optical spectrum of the signal at the fiber input and output was a 0.5 m Czerny-Turner grating spectrograph. The background-free autocorrelation function obtained from the second harmonic signal of a LilO3 crystal was used to characterise the temporal pulse shapes.
3. Characterisation of the Nd a+-doped ZBLAN fiber In the experiments we used a commercially available Nd3+-dope d ZBLAN fiber (Le verre fluort, France) with an active ion concentration of 2000 ppm. The transmission loss was 0.075 dB/m at )t = 1.3/~m. The core diameter, outer diameter and cut-off wavelength were specified by the manufacturer to be 4/zm, 125 /zm and 1/~m, respectively. Since for our experiments with ultrashort pulses a knowledge of the dispersion and gain characteristics of the ZBLAN fiber is very important, we will in the following describe these properties in more detail.
3.1. The dispersive properties of the ZBLAN fiber 2. Experimental setup The experimental set-up used for all measurements presented in this paper is shown in Fig. 1. The short pulse source was a synchronously pumped dye laser which is described in more detail elsewhere [4]. Using either a Lyot filter or a pellicle of 7 / z m thickness as the tuning element, pulses with duration of approximately 4 ps and 300 fs, respectively, could be generated at a repetition rate of 82 MHz. The maximum average power was 100 mW and the centre wavelength of the pulses could be tuned between 1.25/zm and 1.35/xm. The Nd 3÷-doped fiber amplifier consisted of two 2 m pieces of non-polarisation preserving, Nd 3÷ :ZBLAN (ZrFa-BaF2-LaF3-AIF3-NaF) fiber. Two commercially available A1GaAs laser diodes (LD), which delivered 150 mW at A =0.82/xm each, were used as the pump. Signal and pump were combined by dichroic mirrors and coupled into the fibers by microscope objectives. Between the two pieces of active fiber we installed an
The group velocity dispersion (GVD) parameter D of the ZBLAN fiber is a sum of the material dispersion Dr, and the waveguide dispersion Dw. The waveguide contribution Dw can be calculated according to [ 6]
1
d2(Vb)
Dw= -Ac any dr-----7 ,
(1)
where V and b are the normalised frequency and propagation constant, respectively. Dw can be estimated using the approximation
d2(Vb) dV z
= 4.501 - 3.106V+ 0.547V 2,
(2)
which is valid in the range 1.3 < V< 2.4 [ 6]. The material dispersion contribution D~ of ZBLAN was measured by Monerie et al. and is presented in ReL [7]. We have used these values for Dr. and the values for Dw calculated with Eqs. (1) and (2) to get the total dispersion D of the ZBLAN fiber. Fig. 2 shows the individual contributions Dm and Dw and compares their
H. Ammann et al. /Optics Communications 113 (1994) 39-45
41
total dispersion is normal and rather high (in the order of - 30 p s / n m - km). The excellent agreement between calculated and measured data further indicates that the dopants have negligible influence on the GVD of the unpumped Z B L A N fiber.
-10 -20
-40
3.2. The gain properties o f the Z B L A N fiber -50
, 1100
,
,
,
i
. . . .
1200
t
,
,
•
1300
.
:
. . . .
1400
1500
Wavelength [nm]
Fig. 2. Wavegnide (a) and material (b) dispersion of ZBLANfibre. The dotted line represents the sum of (a) and (b) and the solid line is the measured total GVD.
--
6
B 3
_~
• 50
100
150
Total Launched Pump Power [mW]
Fig. 3. Small signal gain versus total launched pump power for a signal wavelength of A= 1.345 p.m. The dashed line represents the 1.05/xm fibre output radiation (ASE). 9 6
3
/
/
/
/' "-~-"
/ •;N
0
-3
/ 290
/
/
1310
1330
1350
Signal Wavelength [nm]
Fig. 4. Measured small signal gain versus signal wavelength for a launched pump power of 2 X 75 mW. sum with the measured total dispersion of the active fiber [ 8 ]. Excellent agreement between the theoretical and the experimental data was obtained by assuming a core diameter and a cut-off wavelength of d = 4.36 # m and Ac = 1.07 ~m, respectively, which are close to the specified values d = 4 / x m and Ac = 1/xm. Note that in the vicinity of 1300 nm the waveguide contribution is comparable to the material contribution and that the
The gain properties of the Z B L A N fiber were studied using ~ 4 ps pulses from the dye laser (note that because of the high repetition rate of 82MHz the output of the dye laser can be considered as cw radiation). The gain was evaluated by taking the pumped/unpumped output signal ratio and subtracting the transmission loss at A = 1.3/zm (0.3 dB). Fig. 3 shows the gain as a function of the total launched pump power (the gain provided by the individual pieces of active fiber was equal). The signal wavelength was A = 1.345/zm and the coupled signal power was held below - 20 dBm to ensure small signal behaviour. Assuming a coupling efficiency of 60% for the pump, the pump efficiency in the unsaturated regime was 0.3 d B / m W . The gain saturation at about 8 dB for a total pump power higher than approximately 2 X 50 m W is a consequence of the increasing 1.05/xm radiation [ 5 ], which is also shown in Fig. 3. We note that laser action at A = 1.05/xm was established in either piece of active fiber when the corresponding launched pump power was higher than 30 mW. In Fig. 4, the dependence of the small signal gain on the signal wavelength is depicted for a launched pump power of 2 × 75 mW. The gain is negative for wavelengths shorter than 1.31 /.tm due to ESA. For wavelengths longer than 1.32/zm the gain is relatively fiat with a maximum of 8 dB at A = 1.344 /zm. For completeness, we mention that the signal saturation input power (3 dB reduction of the unsaturated gain) was measured to be P = 16 mW.
4. The theoretical
model
Before we summarise the experimental results and compare them with theory we briefly describe the model used for the simulations. The numerical calculations are based on a modified nonlinear Schrrdinger (NLS) equation of the form
H. Ammannet al. /Optics Communications113 (1994)39-45
42
gx4 i i 11( , 62.4 i-~z + -~ a A - ~ g A - 2 8t2 -
n2k~°A((1 - Y) IAI 2 Aeff
+ dt'
(3)
0
which was solved using the standard split step Fourier algorithm. The last three terms on the left hand side represent the influence of linear losses ( a ) , gain (g) and GVD (k"), respectively. The linear loss was taken to be a = 0.075 d B / m as specified by the manufacturer. As the gain spectrum is quite flat in the range between 1.32/,m and 1.35/xm (see Fig. 4), g was taken to be independent of wavelength. The parameter k" is related to the GVD parameter D by k" = - D Az/27rc. Note that higher order dispersion terms have been omitted in Eq. (3). This is justified because for k" ---0.1 p s 3 / k m (estimated from the measured dispersion curve) and k" .~ 30 ps2/km, one gets k"/k"---3 fs, which is much shorter than the pulse widths used in our experiments. The terms on the right hand side of Eq. (3) describe SPM and SRS, respectively. The effective core area Aeff is approximated by A~ff= ~-d2ff/4, where d~ff is the mode field diameter dell= 1.4d [9]. The Kerr coefficient was taken to be n2 = 2.8 × 10-16 cm2/W [ 10], which is approximately 10% smaller than that of fused silica. This value contains the instantaneous (Kerr effect) as well as the delayed nonlinear response (Raman scattering) of the fiber material. The measured Raman gain spectrum for a typical fluoride glass was presented in Ref. [ 11 ]. The maximum gain occurs at a frequency shift of 600 c m - 1 corresponding to a wavelength shift of 110 nm, which is much larger than the spectral width of the pulses used in the experiments. The (maximum) gain for SRS is gR = 1.5 × 10 -13 m / W [ 12] at A -- 1.3 ~m, from which we calculated a critical power for significant SRS starting from noise of PSRS = 16A~rr/gRLeff= 800 W. For comparison, the maximum peak power in our experiments was in the order of Ppcak= 600 W (300 fs pulses, 25 mW average power). Therefore, SRS with frequency shifts much larger than the spectral bandwidth of the pulses is expected to have only a minor influence on pulse propagation. Within the spectral width of the pulses, how-
ever, SRS does not have to build up from noise. As this can lower the threshold power by as much as three orders of magnitude [ 13 ], we took intra-pulse Raman scattering into account in our calculations using the response function approach [ 14]. The parameter ,/in Eq. (3) describes the relative weight of Kerr and Raman nonlinearity and h(t) is the normalised Raman response function. From the fact that the Kerr coefficient nz in ZBLAN is smaller but, on the other hand, the Raman gain gR is approximately twice as large as in silicates [ 12], we conclude that the weighting factor 3' is larger in fluoride glasses. We have taken this into account by setting 3,=0.3 in the calculations (compared to 3,=0.18 for silicates [14]). The Raman response function h(t) was approximated by a single sided exponential with a decay time of 76 fs, which has been found suitable for silicates [ 14]. This choice was motivated by the fact that the normalised Raman gain spectra of these two hosts differ only slightly for frequency shifts smaller than 100 c m - 1 [ 11 ].
5. Experimental results and comparison with theory
5.1. Propagation and amplification of ps pulses Propagation of picosecond pulses Using a Lyot filter as the tuning element the width of the autocorrelation function of the dye laser pulse was typically TAC = 6 ps (FWHM). After propagation through 2 × 2 m of the active fiber, no significant changes of the autocorrelation traces could be observed for coupled average powers up to 25 mW which corresponds to a pulse energy of 0.3 nJ. A close inspection of the pulse spectra on the other hand revealed a slight narrowing and a blue-shift of the output spectra. This is illustrated in Fig. 5 which shows the measured input and output spectrum (left) together with the numerically calculated input and output spectrum (right). In the calculations we have assumed an asymmetric Gaussian pulse shape with q'T= 2~'L, where ~'Land rv are the time constants of the leading and the trailing edge, respectively (this was motivated by measurements and numerical simulations presented in Ref. [ 15] ). The pulse duration was ~-p= 4.5 ps (TAc= 6.4 ps). Further, the input pulse was taken to be slightly chirped because the measured spectral width of A h = 0.66 nm is approx-
H. Ammann et al. /Optics Communications 113 (1994) 39--45
"7.
"7.
m m
g 1319
1320
1319
1321
1320
1321
Wavelength [nm]
Wavelength [nm]
0.69 nm
5.5 ps
0.71 nm
"~
e .
.
.
.
I
-8
.
.
0
.
.
I
.
8
'
I
I
1339
I
'
I
1340
I
I
A ~bspM= n2kLPp~ak= 1.1. The calculations have shown that the pulse asymmetry is responsible for the spectral blue-shift whereas the initial chirp of the pulse causes the spectral narrowing (this was also observed in Ref. [ 16] ). It is important to note that - as additional calculations have confirmed - unchirped and symmetric picosecond pulses with energies in the sub-nJ range would not experience any measurable temporal or spectral reshaping in the fluoride fiber.
Amplificationof picosecondpulses
Fig. 5. Fibre input (dashed) and output (solid) spectra of pulses with ~'p=4.5 ps (FWHM). Left: measurement, right: calculation.
5.5 p s
43
I
1341
Time Delay lpsl Wavelength lnm] Fig. 6. Autocorrelation traces and spectra of 3.9 ps input pulses. From bottom to top: fibre input, fibre output without pumping and fibre output for a launched pump power of 2 × 75 roW. Coupled average signal power and gain were 4 m W and 7 dB, respectively. All traces are normalised to unity. ¶,'
1.5 .,-"
~" 1.3 e~
Fig. 6 shows the measured autocorrelation traces and pulse spectra at the fiber output for the pumped and unpumped case, respectively. The coupled average signal power was 4 mW, which corresponds to a pulse energy of 50 pJ and a peak power of 12 W. The pump power and gain were 2 × 75 mW and 7 dB, respectively. The width of the autocorrelation trace of the input pulse was TAC= 5.6 ps (FWHM). It can be seen from Fig. 6 that the shape of the autocorrelation trace did not change when the pump was turned on. On the other hand, the modifications of the spectra which were discussed in more detail above, were slightly more pronounced with the pump on owing to the gain induced enhancement of the nonlinear effects. These results could be well reproduced by numerical simulations, which in addition showed that the spectral changes are absent when bandwidth limited, symmetric pulses are amplified. We therefore conclude that propagation and moderate amplification of picosecond pulses with input pulse energies up to 50 pJ is possible without noticeable pulse distortions.
5.2. Propagationand amplificationof sub-pspulses ..
Propagationof subpicosecondpulses
*. , . . *
0.9 5
10
15
20
Coupled Signal Power ImW] Fig. 7. Width of the output autocorrelation function TAC (FWHM) versus coupled average signal power after propagation through 4 m of fibre. The dotted line represents the calculated power dependence of TAC.
imately 20% larger than that corresponding to a bandwidth limited pulse (0.55 nm). The maximum SPM induced phase shift which corresponds to an average signal power of 25 mW was estimated to be
Using a pellicle as the tuning element the width of the autocorrelation trace of the dye laser pulses was typically TAC= 700 fs (FWHM). Whereas the spectral reshaping of the sub-ps pulses after propagation through the ZBLAN fiber was in general negligibly small, the temporal reshaping was very pronounced. We have found that the width of the autocorrelation function after propagation of the sub-ps pulses through the ZBLAN fiber was distinctly power dependent. The increase of the autocorrelation width with increasing power coupled into the ZBLAN fiber is illustrated in Fig. 7. The experimental results (points) are compared
44
H. Ammann et al./ Optics Communications 113 (1994) 39--45
i m
i
-4
0
Time Delay [psi
i
4
-4
0
Time Delay [psl
Fig. 8. Left: autocorrelation functions (measured and calculated) at fibre input (bottom) and fibre output (middle: Pay=4 mW, top: P~v = 20 mW). Right: corresponding pulse shapes (calculated).
with the numerically calculated power dependence of TAC (dashed line). The simulations were again carried out using parameters obtained from the experimental data (fit of the autocorrelation and spectrum). In the calculations we assumed an asymmetric doubled sided exponential pulse shape with ~'L= 3~'T,where % and ~'Tare the time constants of the leading and the trailing edge, respectively. The pulse duration was ~-p= 310 fs (TAc=700 fs). Further, the input pulse was taken to be strongly chirped because the measured spectral width of AA = 9.3 nm is approximately 4 times larger than that corresponding to a bandwidth limited pulse (2.3 nm). The maximum SPM induced phase shift was estimated to be A thspM= 0.45 per mW of coupled average power. With these parameters, the power dependent broadening observed in the experiment could be well reproduced by the numerical simulations as shown in Fig. 7. For low input powers, the autocorrelation trace was broadened from 700 fs to approximately 970 fs due to the influence of GVD only. The power dependent broadening of the output autocorrelation traces clearly observed for pulse energies higher than 0.1 nJ (8 mW average power) is due to the combined effects of GVD and fiber nonlinearities. The measured autocorrelation traces for two specific cases (average input powers of 4 mW and 20 mW) are shown in Fig. 8 together with the calculated autocorrelation functions and the corresponding output pulse shapes. It can be seen that the transmitted pulses were not only broadened but also exhibited some modulation at the leading edge. It should be mentioned that the calculated pulse evolution along the ZBLAN fiber actually was quite complex: in
the first half of the fiber, the pulses evolved into squarelike shapes typical for the presence of GVD and SPM, whereas in the second half no further broadening occurred. Instead, the pulses experienced a slight recompression, which was accompanied by the formation of the modulation at the leading edge. Although the details of the pulse evolution (temporally and spectrally) strongly depend upon the input pulse parameters (shape, chirp and asymmetry of the pulse), the calculations confirmed that the propagation of sub-ps pulses is significantly affected by the nonlinear and dispersive properties of the ZBLAN fiber.
Amplification of subpicosecondpulses Fig. 9 shows the measured and calculated (smooth solid lines) autocorrelation traces and pulse spectra at the fiber input as well as at the fiber output for the pumped and unpumped case, respectively. The coupled average signal power was 9 mW corresponding to a pulse energy of 110 pJ and a peak power in the order of 200 W. The pump power and gain were 2 × 75 mW and 6 dB, respectively. The width of the autocorrelation trace of the input pulse was 700 fs (FWHM). It can be seen from Fig. 9 that the spectrum was only slightly modified when the pump was turned on, whereas the changes in the autocorrelation trace are much more pronounced. The width of the autocorrelation was increased from 1.2 ps to approximately 1.7 ps in the presence of the pump which is again due to the gain induced enhancement of the nonlinear effects. The temporal broadening could be well reproduced by the calculations (see Fig. 9). The comparatively poor
"7".
m 0
,.r, ct~
-3
0
Time Delay [psi
3
1320
1335
1350
Wavelength [nm]
Fig. 9. Autocorrelation traces and spectra of 310 fs input pulses. From bottom to top: fibre input, fibre output without pumping and fibre output for a launched pump power of 2 X 75 mW. Coupled average signal power and gain were 9 mW and 6 dB, respectively. All traces are normalised to unity. The smooth traces are calculated.
H. Ammann et al. /Optics Communications 113 (1994) 39-45
agreement between the measured and calculated spectra could not be clarified conclusively but is probably due to the uncertainty of the input pulse parameters.
45
in the fs regime will be affected by the fiber dispersion and nonlinearities. The numerical investigation of possible limitations for the case of a high gain fiber amplifier will be the subject of a forthcoming publication.
6. Conclusions Acknowledgements We have investigated the propagation and amplification characteristics of short pulses with central wavelengths in the vicinity of A = 1.3/.tm in a Nd3+-doped ZBLAN fiber. Calculation of the GVD parameter (the calculated values are in excellent agreement with measured data) and an estimation of the strength of the different nonlinear effects in fluoride fibers allowed to perform numerical simulations, which could well explain the main experimental findings. It has been demonstrated experimentally that 4 ps pulses transmitted through 4 m of active fluoride fiber do not experience any measurable temporal reshaping, whereas the spectra were slightly blue shifted and narrowed. The numerical simulations have shown, however, that the occurrence of these spectral modifications was due to the asymmetry and the chirp of the input pulses. Therefore, symmetric, bandwidth limited pulses with a duration of several picoseconds and sub-nJ energies would propagate essentially distortionless through short active fluoride fibers. Furthermore, we have demonstrated that moderate amplification (7 dB) of picosecond pulses is feasible without pulse distortions. For sub-picosecond pulses of comparable pulse energy, on the other hand, the dispersive and nonlinear effects significantly affected pulse propagation. The combination of GVD, SPM and SRS led to a power dependent temporal broadening which became more pronounced when the pulses were amplified (by up to 6 dB). These results indicate that the performance of both fiber amplifiers as well as mode-locked fiber lasers
We thank Dr. B. Deutsch from the University of Kaiserslautern for carrying out the dispersion measurements.
References [ 1 ] D.J. Richardson, A.B. Grudinin and D.N. Payne, Electron. Lett. 28 (1992) 778. [2] Y. Miyajima, T. Sugawa and Y. Fukasaku, Electron. Lett. 27 (1991) 1706. [3] T. Sugawa, E. Yoshida, Y. Miyajima and M. Nakazawa, Electron. Lett. 29 (1993) 902. [4] P. Beaud, B. Zysset, A.P. Schwarzenbach and H.P. Weber, Optics Lett. I 1 (1986) 24. [5] M. Obro, B. Pedersen, A. Bjarklev, J.H. Povlsen and J.E. Pedersen, Electron. Lett. 27 ( 1991 ) 470. [6] A.E. Comyns (Wiley, New York, 1989). [7] M. Monerie, F. Alard and G. Maze, Electron. Lett. 21 (1985) 1179. [8] B. Deutsch, University of Kaiserslautem, private communication. [9] D. Marcuse, The Bell System Techn. J. 56 (1977) 703. [ 10] I.D. Aggarwal and G. Lu (Academic, New York, 1991 ). [ 11 ] A. Saissy, J. Botineau, L. Macon et G. Maze, J. Physique Lett. 46 (1985) L289. [ 12] M. Monerie, SPIE Vol. 799 (1987) 123. [ 13] D. Cotter, Opt. Quantum Electron. 19 (1987) 1. [ 14] R.H. Stolen, J.P. Gordon, W.J. Tomlinson and H.A. Hans, J. Opt. Soc. Am. B 6 (1989) I159. [ 15 ] J. Schiitz, W. Hodel and H.P. Weber, Optics Comm. 95 (1993) 357. [ 16] M. Oberthaler and R.A. Hfpfel, Appl. Phys. Lett. 63 (1993) 1017.