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Experiments on the co-propagation of ultra-short pulses with continuous wave radiation through optical fibres
1 October 1994
OPTICS COMMUNICATIONS Optics Communications 11 I ( 1994) 403-4 16
EISEVIEK
Full length article
Experiments on the co-propagation of ultra-short pulses with continuous wave radiation through optical Gbres J. Schlitz ‘, G.I. Onishchukov,
W. Hodel, H.P. Weber
Institute ofApplied Physics, University ofBern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
Received 3 1 January 1994; revised manuscript received 26 May 1994
Abstract
The superposition of a weak continuous wave to a train of ultra-short pulses propagating in an optical single-mode tibre can lead to strong interactions between the two co-propagating signals. These interactions result in considerable modifications of the propagated pulse spectrum. A systematic investigation of the dependence of these modifications on various input signal and tibre parameters is presented. It has been found that cw power levels typically 1O6times lower than the respective pulse peak power are strong enough to induce pronounced modifications in the output pulse spectrum.
1. Introduction
Nonlinear interactions between “differently coloured” optical waves during propagation in an optical fibre have been investigated by many authors [ l41. The characteristic features of such interactions, i.e. the resulting temporal and spectral modifications of the co-propagating signals, depend mainly on the nature of the nonlinear processes involved (crossphase modulation XPM, four-wave mixing FWM, self-phase modulation SPM, stimulated Raman scattering SRS) and on the dispersive properties of the libre used (group-velocity dispersion GVD). Whereas interactions between waves with different optical frequencies are relatively well understood provided that either continuous wave (cw) radiation or pulses are involved [ 5 1, the interactions between ultra-short optical pulses and cw radiation during propagation in optical tibres have - to the best of our ’ J. Schlitz is now with the Laser Physics Centre, Australian National University, Canberra ACT 0200, Australia.
knowledge - not been investigated up to now (Fig. 0). However, since this situation often occurs in practice (e.g. in Raman or rare-earth-doped fibreamplifiers [ 6,7] ) it is important to know under what circumstances such interactions occur and how they modify the co-propagating signals. In this work we study the interaction of ultra-short (pica- and sub-picosecond) pulses with weak cw radiation during the co-propagation through a singlemode tibre. We have found that for certain input pulse and tibre parameters the pulse spectrum is modified considerably already for very low power levels of the co-propagating cw radiation (for cw-to-pulse peak power ratios as low as 10p6). The properties of these modifications have been investigated for different fibre and signal parameters, such as the length and the dispersion of the fibre, the wavelength, power and polarization of the pulse and the cw light-wave, as well as the temporal width of the input pulse. The results indicate that the spectral modifications are primarily caused by parametric processes.
0030-4018/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0030-4018 (94)00345-U
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J. Schiitz et al. /Optics Communications I I I (1994) 403-416
Fig. 0. The joint adventures
2. Experimental setup The experimental setup is shown in Fig. 1. A laser diode with pigtail followed by an integrated 60 dB optical isolator served as the cw light source. Two laser diodes with the strongest emission lines located at 1297 nm and 1324 nm were used alternatively. The signal was transferred by optical connectors (of PCstandard type) to a fibre pigtail. A selfoc lens was used at the other end of this pigtail to collimate the radiation emerging from the fibre. The source of ultra-short pulses was a synchronously pumped dye laser which delivered pulses at 82 MHz pulse repetition rate with an average power of several tens of milliwatts. This
of elephant
Stokes and CW-Mouse.
system has been described in more detail in Ref. [ 8 1. The centre wavelength I, of the pulses could be tuned between 1250 nm and 1350 nm while the width could be changed between 0.4 ps and 4 ps fwhm (autocorrelation) using different tuning elements. As the determination of the temporal width of a pulse from the measured autocorrelation crucially depends on the knowledge of the pulse shape and the chirp, the subsequent fwhm values T,, always refer to the measured autocorrelation traces. The beams of the two sources were combined by a dielectric beam splitter of 68% reflection (at an angle of 45”) and coupled by a selfoc lens into a fibre pigtail of 80 cm length from where the signal was transferred to the fibre under
fibre
Fig. 1. The experimental setup. BS: dielectric beam splitter (68% reflection), CH: mechanical chopper, DA: disc attenuator,f,_,: lenses cf = 308 cm,f,= 148 cm,f,=40 cm), ISO: 60 dB fibre optical isolator, 1/2: halfwave plate, MI_,: fixed mirrors (100% reflection), OL: objective lens (10x ), PC: fibre-connector (of FC-PC type), PD: photodiode (InCaAs), PM: photomultiplier, RC: fibre-connector (Radial& 12” wedged), RM: removable mirror ( 100% reflection), SF:selfoc lens. The lock-in amplifier and the mechanical chopper were used for the measurements of the difference spectra only.
J. Schiitz et al. /Optics Communications lll(l994)
test via optical connectors. In order to achieve optimum coupling, weak lenses (fi and f2) were placed in the optical path between the two laser sources and the fibre pigtail. The relevant parameters of the fibres used are listed in Table 1. For the temporal analysis of the input pulses and of the signal at the output of the libre a backgroundfree autocorrelation trace was generated using the second harmonic signal obtained from a LiIOs crystal. The conversion efficiency of this crystal is strongly polarization dependent and drops to zero for wavelengths separated by more than ? 20 nm from the optimum phasematching wavelength which was set to the centre wavelength of the input pulses. The temporal resolution and the wavelength sensitivity of the autocorrelator were determined by the properties of the nonlinear crystal alone. The optical spectra of the input pulse and of the signal at the output of the fibre were measured using a 0.5 m Czerny-Turner monochromator which had been equipped at the output slit with an InGaAs-photodiode. The measured spectra were not sensitive to the polarization properties of the input signal. Provided the spectral modifications induced by the nonlinear interactions were strong, it was possible to determine the resulting modifications directly from a comparison of the measured output pulse spectra with and without co-propagating cw radiation. In order to be able to detect rather weak modifications in the spectrum, it was necessary to measure the resulting spectral differences induced by the co-propagating cw radiation directly. For these measurements the signal from the monochromator was processed using a lockin amplifier while the radiation from the cw source at the input of the fibre was modulated using a mechanical chopper (see Fig. 1). Therefore, the output signal of the lock-in amplifier was proportional to the magnitude of those changes in the pulse spectra, which
405
403-416
were induced by the co-propagating cw signal. In the following discussion, the spectra which were obtained using this technique will be referred to as “difference spectra”.
3. Experimental results 3.1. Types of observed modifications One of the observed effects which is due to interactions between picosecond pulses and cw radiation during propagation through an optical Iibre is a change of the noise characteristics of individual parts of the output spectrum. A narrow range of the optical spectrum at the output of the fibre was selected by the 0.5 m monochromator (see Fig. 1) and detected using an InGaAs-photodiode. The noise spectrum of the temporal fluctuations of the photodiode signal was measured by an electrical spectrum analyser in a frequency range from dc up to a few hundred kHz. The input wavelength A,= 1303 nm of the 4 ps input pulses was chosen close to the zero dispersion wavelength of the libre used. This choice resulted in the generation of a strong anti-Stokes band which was continuously shifting towards shorter wavelengths with increasing input power [ 91. Changes of the noise spectrum as well as modifications in the propagated pulse spectrum were found to occur as soon as the generated anti-Stokes band and the cw spectral lines started to overlap in the output spectrum. The magnitude of the changes in the noise spectrum also depended on the wavelength which was selected at the monochromator. In most cases, the noise in the spectrum obtained from the electrical spectrum analyzer was considerably reduced when cw radiation was added to the input pulses. This effect is illustrated in Fig. 2 by the optical pulse spectrum after
Table 1 Measured fibre parameters
Length L [m] Zero-GVD wavelength Lzd [ nm ] Attenuation (around 1320 nm) [dB/km] Spot size ( 1300 nm) [pm] ’
iibre #l
fibre #2
iibre #3-5
1183 1303 0.38 9.5
1000 1317 0.47 10.2
50,150,300 1300 0.37 9.5
a Diameter measured at 1/e* of the intensity. The fibres are monomode for all involved wavelengths.
J. Schiitz et al. / Optics Communications Ill (I 994) 403-416
Input
,,,, 1260
k 1280
,,,( 1300
Wavelength
0
1320
100
Frequency
1340
[nm]
200
[kHz]
Fig. 2. Upper graph: The cw and pulse spectra at the input of the fibre (the spectral intensity of the cw radiation and of the input pulses are not to scale) and after propagation through tibre #l. The overlaid traces show the output spectra without (black) and with (gray) cw radiation added. Lower graph: The low-frequency noise characteristics of the spectral intensity of the propagated pulse spectra (with and without cw) are shown for a selected spectral range (AA x 0.4 nm) centred at 13 I8 nm. The input wavelength of the pulses was centred near the zero-dispersion wavelength of the fibre at 1303 nm. The average power of the input pulses was Pavg= 5.7 mW and the pulse duration was 4 ps. The power of the added cw radiation was PC_=85 pW.
propagation through fibre #I and by the measured noise spectrum, when the centre wavelength of the selected spectral range of 0.4 nm width was set to 13 18
nm. The changes induced by the co-propagation of the weak cw-radiation are shown by the gray overlaid trace in the output spectrum and by the lower trace in the noise spectrum. It was found that the intensity noise of the selected spectral range was reduced by approximately a factor of ten for frequencies below 60 kHz. In a similar fashion, the intensity noise of the output spectrum was measured without spectral filtering. This was done by detecting the output signal from the Iibre directly using a photodiode. In this situation, the noise spectrum was not altered by the addition of the cw radiation. These results show, that the addition of weak cw radiation to a train of short pulses can considerably reduce the fluctuations of individual spectral components, but leaves the noise properties of the output signal as a whole unchanged. This may be explained by parametric processes which are “levelling out” the intensity fluctuations of individual spectral lines by a redistribution of the spectral energy. The second effect which has been observed in the experiments is substantial modifications in the propagated pulse spectrum which are induced by the copropagation of the cw radiation. Fig. 3 shows a typical experiment using 3.5 ps pulses with an average power of Pavg= 15.2 mW. The two overlaid traces at the top of the figure are measurements of the output spectra for pulses alone (black) and for pulses with co-propagating cw radiation (gray). With the addition of the cw radiation the frequency shift of the Stokes band is considerably reduced, even for cw power levels as low as 65 uW (corresponding to a cw power level 1O6times smaller than the respective pulse peak power!). In this case, the resulting spectrum forms an extended quasi-continuum with a width of about 60 nm. In order to make sure that these modifications do not originate from light which is reflected back into the laser cavity of the signal sources, we performed additional experiments with increased reverse isolation (by 30 dB) between the fibre coupling and each signal source. The experimental results showed no significant deviations from the described behaviour which indicates that the reflected light is not responsible for the observed changes. Thus we have observed two characteristic types of spectral modifications in our experiments. While the typical modifications shown in Fig. 2 affect only the
J. Schiitz et al. /Optics Communications 11 I (1994) 403-416
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nounced modifications occurred in the propagated pulse spectrum. These “default” values are listed in Table 2. In the following, we will refer to the default values as a whole as the default parameter set.
4. Dependence of spectral modifications in the output pulse spectrum on the experimental parameters 4.1. Dependence on the input pulse width Difference
1250
Spectrum
1300 Wavelength
1350
1400
[nm]
Fig. 3. Upper traces: Overlaid output spectra without (black) and with (gray) cw radiation added for a situation exhibiting pronounced cw-induced spectral modifications. Lower trace: The measured difference spectrum of the output spectra shown above for the following experimental parameters: Fibre #2, T,,= 3.5 ps, Pa,,=152 mW, A,=1332 nm, D=1.23 ps/(nm km), PC_=65 pW, I,= 1324 nm.
shape of the individual spectral bands (apart from the noise characteristics), the spectral modifications shown in Fig. 3 are characterized by a frequency shift occurring for some of these bands-where shifts towards longer as well as shorter wavelengths have been observed. Most apparent in this case is the change of the frequency shift of the well-separated Stokes band. We have chosen to address the type of modifications shown in Fig. 2 in a descriptive way as “respire’‘-type modifications and to refer to those shown in Fig. 3 as the modi’cation
of the Stokes frequency shift,
respectively. 3.2. Definition of a ‘default”parameter set
Fig. 4 shows the measured output spectra (left) and the corresponding difference spectra (right) for input pulses having comparable average power levels PaVg but different temporal widths T,, (the indicated values of T,, denote the fwhm of the measured autocorrelations). The wavelengths of the input pulses and ofthe cw radiation were&,= 1310 nm and&,= 1324 nm, respectively. Note that the spectra of the propagated pulses (black), which consist mainly of two well-separated spectral bands, look remarkably similar although the input pulse width (and therefore the resulting peak power) was changed by a factor of four. While the shape of the multiple peak spectrum in the vicinity of the centre wavelength of the input pulses 1, is changing with T,,, the shape and the centre wavelength of the spectrally separated Stokes band near 1380 nm remain approximately the same [lo]. A comparison with the output spectra for pulses with co-propagating cw radiation (gray) shows pronounced spectral modifications for 2.9 ps and 2.2 ps input pulses but nearly no changes for 0.74 ps input pulses (see the respective difference spectra on the right hand side of Fig. 4). Further experiments with 0.5 ps pulses also produced no measurable cw-induced spectral changes. This result indicates that the occurrence of any spectral modifications (within the parameter ranges available in the experiment ) is re-
stricted to input pulses longer than approximately
1
ps.
Since the described spectral modifications depend on a considerable number of experimental parameters (given by the properties of the interacting input signals and of the fibre used), it seems reasonable to characterize the development of these modifications systematically by varying one of these parameters while all others remain fixed. The values of the fixed parameters were chosen in such a way that pro-
For this reason no further measurements using sub-picosecond pulses will be presented in the following. 4.2. Dependence on the wavelength
TWO different laser diodes with main spectral peaks at ;I,,= 1297 nm and 1324 nm, respectively, were used for the investigation of the dependence of the
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Table 2 List of the default parameters
used for the investigation
of the spectral modifications
Parameter
Default value
Remarks
Length of fibre (L)
approx.
non-polarization communication
Zero dispersion wavelength (A,,) Input wavelength of pulses (A,) and cw radiation (A,,) Input pulse width (T.,) Average power of input pulse (Pa”,) Power of cw radiation (P,) Relative (linear) input polarization of pulses and cw radiation Reverse isolation of pulses Reverse isolation of cw radiation
1303 nm chosen to give the maximum effect approx. 3 ps approx. 15 mW 20-150 uw parallel
,
5,
I,,
1250
1 km
preserving monomode
standard fibre
consult Table 3 for the wavelength dependence of the effect fwhm of autocorrelation
none -6OdB
L
1300
I,,
1
I,
1,
1350 Wavelength
[nm]
Fig. 4. Output spectra (left) and difference spectra (right) for different input pulse widths T, after propagation through fibre #l. The exact values of Pavgare given on the left of each difference spectrum. Experimental parameters: T.,=O.74 ps: A,= 1312 nm, D=O.79 ps/(nmkm),P,=65 uW,1,=1324nm. T,=2.2and2.9ps:&=1310nm, 0=0.63ps/(nm km), Pm=65 uW,1,=1324nm.
spectral modifications on the input wavelength. The centre wavelength &, of the input pulses was tunable between 1250 nm and 1350 nm. A third important parameter is the zero dispersion wavelength Azdof the fibre used. In the experiment, we used two different fibres of comparable lengths but with different values for Lzd ( 1303 nm for tibre #l and 13 17 nm for fibre #2; see Table 1). This resulted in four different combinations for il,, and lzd while the continuous tuna-
bility of /2, was used to find the wavelength producing the maximum effect in the resulting output spectra as well as to determine the values of &, for which the spectral modifications vanished. Fig. 5 shows a typical example of the output spectra and the corresponding difference spectra for A = 1324 nm and Iz,,,= 1317 nm and for different cztre wavelengths /2, of the input pulses. From the figure we see that the maximum effect induced by the
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1.23
15.2
I
1350
1400 Wavelength
1250
1300
1350
1400
[nm]
Fig. 5. Output spectra (left) and difference spectra (right) for different 1, (marked by triangles) after propagation through fibre #2 (1,~ 1317 nm). The gray overlays (left) show the resulting spectra when cw radiation was added. The values of the dispersion paramparameters: T,= 3.5 ps, AP eter D at A, and of the average input power of the pulses Pay* are indicated in each spectrum. Experimental (frombottomtotop): 1310,1313, 1317,1323, 1332, 1337and 1340nm,P,=65pW,&,=1324nm.
addition of cw radiation to the input pulses appears for I,=1332 nm (0~1.23 ps/(nm km)) whereas the effect vanishes for wavelengths above 1340 nm and below 13 10 nm. We can further observe a distinct change in the characteristics of the spectral modifications which occurs for 2, in the vicinity of the zero dispersion wavelength Azd. For input pulses with wavelengths &, in the region of anomalous GVD (D > 0) the resulting spectra show pronounced “respire”-type modifications and changes of the Stokes frequency shift (see Sect. 3.1). “Respire’‘-type modifications appear in the difference spectra as a number of narrow spikes which coincide (roughly) with the respective structures in the optical spectrum, while the changes of the Stokes frequency shift can be iden-
titied by the broad sinusoidal-like structures. On the low-wavelength side of &, in the region of normal GVD (D < 0), we have never observed significant changes of the Stokes frequency shift, i.e. the changes are entirely of “respire’‘-type. Another interesting feature which can be observed in the difference spectra of Fig. 5 is the tendency of these spectra to maintain a certain symmetry, “Respire’‘-type moditications typically show an axial symmetry with respect to A,,. The changes of the Stokes frequency shift, on the other hand, are accompanied by corresponding changes on the anti-Stokes side which resemble a mirror image with respect to the zero-dispersion wavelength ;Izd of the tibre [ 111. The remaining combinations of LCwand Lzd have
J. Schlitz et al. /Optics Communications I1 1 (1994) 403-416
4 IO
also been investigated experimentally and two of them (namely/I,,= 1303nm/l,,= 1324nmand&,= 1303 nm/).,,= 1297 nm, respectively) showed a behaviour very similar to the situation we have just discussed. The respective values of 1, for which the modifications in the output spectrum were maximal or vanishing were shifted, however, to other wavelength ranges. In contrast, the last of the four possible combinations of Lzd and A,, (i.e. Azd= 13 17 nm and A,,,,= 1297 nm) showed no effect throughout the tuning range of the dye laser, except for ;i, = 132 1 nm where a rather weak effect was found (notably a change of the Stokes frequency shift and no “respire”-type modifications, very similar to the spectrum for D = 0.48 in Fig. 5 ) . A summary of these experimental findings is given in Table 3. 4.3. Dependence on the power
4.3. I. Averagepulsepower Fig. 6 illustrates the dependence of the output spectra on the average pulse power for 3.9 ps pulses after propagation through libre #l (the values of PaVg are indicated in the figure). The input wavelengths A,= 1309 nm and A,,.,= 1297 nm were chosen in accordance with the default parameter set defined in Table 2. The minimal average pulse power PaVgfor which (“respire’‘-type) spectral modifications have been observed was approximately 6 mW. For PaVg=20 mW, however, the Stokes frequency shift is changed as well. In this case, a large spectral quasi-continuum extending over nearly 80 nm is formed with the ad-
dition of the cw radiation, while the spectrum of “plain” input pulses consists of two well-separated spectral bands (i.e. one spectral band near LP exhibiting multiple peaks, and a frequency shifted Stokes band). 4.3.2. Cw pa wer In the spectra of Fig. 7 the input power PCWwas changed while PaVgof the 3 ps pulses was kept at a constant level of 20.5 (left) and 38.0 mW (right), respectively. For 20.5 mW average pulse power and low cw power levels, the cw-induced spectral modifications are mainly restricted to the multi-peak spectral band in the vicinity of 1,. Only at the highest cw power of 13 1 uW the distinct separation of the symmetrical Stokes band is destroyed and an extended quasi-continuum is formed instead. This result indicates that the spectral modifications exhibit threshold behaviour with respect to the variation of the cw power. For PaVg=38 mW the same behaviour can be observed for considerably lower cw power levels of only a few microwatts. Note, that there are only minor changes in the output spectrum for power levels of PCWbetween 17 uW and 136 uW, which corresponds to a variation of the cw power by nearly one order of magnitude. 4.3.3. Determination of the threshold power levels In order to determine the minimal power levels for the input pulses and the cw radiation which are required to produce detectable modifications in the propagated pulse spectrum, we have reduced the
Table 3 The characterization of the spectral modifications for cw radiation with different wavelengths I,, and for two tibres of comparable length but different zero dispersion wavelengths &. The characterization is given by the values of ,I, resulting in the strongest spectral modifications (maximum effect) and by the lower and upper limit of 1, for which an effect is still visible. In addition, the characteristic type (as defined in Sect. 3.1) and the magnitude of the modifications are indicated in the last three columns
L
[nml
L lnml
Spectral modifications
1, lnml Lower limit
Maximal effect
Upper limit
1332 1316 1308 1311 1321
1340
1324
1317
1310
1297 1324 1297
1303 1303 1317
1295 1283
1314 1333 _
“Respire”type
yes yes yes yes no
Change of Stokes freq. shift
Strength of the moditications
yes no
pronounced medium pronounced pronounced weak
yes yes yes
J. Schlitz et al. /Optics Communications I1 I (1994) 403-416
2.4
411
served in the output spectrum for power levels higher than PC,.,= 15 pW. From these experimental results we derive that the occurrence of any modifications scales with the product of the pulse power times the cw power. Thus, if the power level of one of the two signals is increased (e.g. Pavp)the minimum required power for the other signal ( PCw) will be lowered and vice versa. This change of the threshold power can be observed best in the spectra of Fig. 7 by comparing the results for P,,,=20.5 mW and 38.0 mW with respect to changes of the Stokes frequency shift.
/
4.4. Dependence onJbre length
0.45
I
6
i
,I /~
Input _L 1200
1400
1300 Wavelength
[nm]
Fig. 6. Output spectra for different Pay8(values indicated on the left) after propagation through fibre #l. The gray overlays show the spectrum after cw radiation at 1297 nm wavelength had been added. Experimental parameters: T,=3.9 ps, ,I,= 1309 nm, P,=llOpW,1,=1297nm.
power levels of both signal sources until the modifications vanished (apart from the use of libre #2 in the measurements all other experimental parameters were chosen in accordance with the default parameter set defined in Table 2). Fig. 8 shows the output and difference spectra which result from a variation of PaVgwhile PC, was kept at a constant power level of 62 pW. The results indicate that “respire’‘-type modifications occur for values of Pavgin the order of 4-5 mW while for a change of the Stokes frequency shift approximately 7 mW are required. Analogous measurements are presented in Fig. 9 for a fixed level of P,,=7.9 mW and different levels of PCw.In this case, “respire’‘-type modifications are observed for PC,.,as low as 400 nW (which corresponds to a cw power lo8 times lower than the pulse peak power) while changes of the Stokes frequency shift are ob-
In order to study the dependence on the fibre length, pieces of L= 50, 150 and 300 m length were cut from the same fibre in order to ensure that all other fibre parameters were identical (the most important parameters are listed in Table 1). The resulting output spectra after propagation through the different fibre pieces are shown in the left part of Fig. 10. The right part of the figure shows measurements of the corresponding autocorrelations where the phase-matching angle of the nonlinear crystal had been adjusted to result in the highest conversion efficiency at Ap. The input parameters were chosen to give maximum interaction between the pulses and the cw radiation. The output spectrum for L=50 m propagation-length is relatively narrow and exhibits a typical modulation due to SPM. The distinct asymmetry of the spectrum is the result of an asymmetry of the input pulse shape 2. The addition of cw radiation to the input pulses leads to no significant changes in the output spectrum for this fibre length. With increasing fibre length the influence of stimulated Raman scattering grows and leads eventually to the formation of a broad frequency shifted Stokes band. This development is illustrated by the spectra for L= 150 m and 300 m. In this situation, however, the addition of cw radiation to the train of input pulses leads to a considerable reduction of the frequency shift of the generated Stokes band. The magnitude of the modifications is large enough to result in visible changes ’ This has been verified by numerical simulations
using the wellknown split-step Fourier method [ 5,9]. Additionally it was found, that the influence of third-order dispersion (TOD) on the symmetry of the spectrum can be neglected in this case.
J. Schiitz et al. /Optics Communications 111 (1994) 403-416
412
P avg = 20.5 mW
I ”
1200
1250
7 ,I r
1300
P avg = 38.0 mW
7I
”
1350
r
1400 1200
Wavelength
1300
1400
[nm]
Fig. 7. Spectral changes induced by different levels o~P,~ (values indicated on the left) of the cw radiation pulses with P,,,=20.5 mW (left) and 38 mW (right) after propagation through fibre #l. Experimental T.,=3.6 ps,+1308.5 nm,A,,=1297nm. P,,=38mW: T,=3.Ops,A,=1309 nm,l,,=1297nm.
in the respective autocorrelation of Fig. 10).
traces (see right part
4.5. Dependence on the input polarization We have also investigated how the spectral modifications depend on the respective input polarization states of the interacting signals. The experimental parameters were chosen in accordance to the “default parameter set” of Table 2. We restricted our investigations to initially linearly polarised signals which were oriented either parallel or perpendicular to each other. The adjustment of the respective polarization directions of the cw radiation and of the pulse train was established by means of halfwave plates which were inserted into the beams. The resulting output spectra for parallel and perpendicular relative input polarizations are shown in Fig. 11 (note in this respect, that the spectra obtained from the mono-
added to the ultra-short parameters: P,,,=20.5
input mW:
chromator depend only weakly on the polarization of the analyzed radiation). By comparing the results for input pulses alone with those for pulses with co-propagating cw radiation it becomes obvious that the interaction crucially depends on the relative orientation of the input polarizations. While pronounced spectral modifications are observed for parallel input polarizations, the corresponding spectra for perpendicular input polarizations are practically identical. This indicates that the initial polarization states of the two signals have to be equal in order to induce spectral modifications. This fact is inasmuch astonishing as the tibre used was not polarization preserving and the polarization states of the different spectral components in the propagated spectrum were varying strongly.
J. Schiitz et al. / Optics Communications 1 I1 (1994) 403-416
Wavelength
[nm]
Fig. 8. Output spectra (left) and difference spectra (right) for 3.5 ps input pulses with different Pays (indicated in the figure) after propagation through fibre #2. The power level of the added cw radiation was 62 uW for all the measured spectra except for the bottom most trace where no cw radiation was added. Experimental parameters: I,= 1332 nm, ,A,,= 1324 nm.
5. Discussion
The presented results illustrate that the occurrence of spectral modifications show a complicated dependence on the input pulse and fibre parameters used in the experiment. For a theoretical analysis it is necessary to be able to identify the nonlinear processes which are involved in the generation of the observed spectral modifications. We have investigated numerically the propagation of picosecond pulses through single-mode tibres using an extended version of the modified non-linear Schrijdinger (NLS) equation [ 9 ] and by solving this equation with the well-known split-step Fourier method [ 5 1. It was found that the numerical results are in good agreement with the measurements for relatively low input power levels and short tibres. This, however, is not the case for the power levels and fibre lengths which are required for spectral modifications to occur in the present experiments. This discrepancy may be due to insufficient knowl-
edge about the experimental parameters, especially about the symmetry and chirp of the input pulses (in the calculations the symmetry of the input pulses was treated as a free parameter and we have further assumed that the input pulses are bandwidth limited and sech or Gaussian shaped). On the other hand the discrepancy may also be caused by the fact, that the NLS equation implicitly assumes that the polarization is preserved. This assumption is not justified if a standard non-polarization preserving fibre is used (as in our experiment). Because nonlinear processes such as the stimulated Raman effect or parametric processes are inherently polarization dependent, the pulse spectra (and temporal shapes) generated in a standard communication fibre might be different from those which are calculated using the NLS equation. In fact there are several indications that lead us to assume that parametric processes are involved: (i) The experimental results show that spectral modifications occur only for very specific combinations of the signal wavelengths. This wavelength de-
414
J. Schiitz et al. /Optics Communications 1I I (1994) 403-416
Wavelength
[nm]
Fig. 9. Output spectra (left) and difference spectra (right) of 4 ps input pulses after propagation through fibre #2 for different Pewof the co-propagating cw radiation (indicated in the figure) and a relatively low average pulse power of Pa,,*= 7.9 mW. Experimental parameters: I,=
133?nm,
A,=
1324 nm.
pendence might be a manifestation of the phase matching condition between the interacting signals. (ii) The modifications of the output pulse spectra show a strong dependence on the polarization of both input signals. The interaction is maximal for parallel (linear) input polarizations and becomes negligible for perpendicular polarizations. Inoue [ 12 ] has studied four-wave mixing (FWM) processes in non-polarization preserving fibres for general polarization states of the interacting cw light. His results show that there exists one specific case for which the FWM efficiency is zero for orthogonal polarization states. This case is characterized by an interaction of the form wq=w, + o, -wZ, where o, and o2 are the optical frequencies of the interacting signals (i.e. of the pulses and of the cw radiation in our case) and where w4 is the idler frequency.
(iii) The threshold power for the occurrence of spectral modifications was found to scale with the product of the pulse power times the cw power. This is compatible with the assumption that these modifications are induced by a FWM process, because the FWM gain shows a similar power dependence. (iv) The difference spectra obtained for “respire”type modifications are fairly symmetrical with respect to the input wavelength A,,,, of the cw radiation (see Fig. 5 ). This symmetry is typical for the sidebands generated by any mixing processes. (v) In Section 3.1 it was found that the intensity noise of a narrow spectral range (which was filtered from the output spectrum by a monochromator) may be considerably reduced by the co-propagation of the cw radiation, while the noise spectrum of the output spectrum as a whole remains unchanged. We believe
J. Schiitz et al. /Optics Communications 11 I (1994) 403-416
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Autocorrelation
Spectra
P,,,= 16.3 mW il
mj ____A-J
c-,._
16.9
16.6
i”\
.._____ _, ,I
1
.._ .._..
Ai_____ I
1300
1250
Wavelength
1350 [nm]
-20
I,
I
I
-10 Time
I
0 Delay
I
I
I
I,
IO
20
[ps]
Fig. 10. Output spectra (left) and autocorrelation traces (right) for differentfibre lengths L as indicated in the figures (fibres #3, #4 and #5 of Table 1). The exact values for Pgvgare given on the right side of the respective autocorrelations. Experimental parameters: T,=2.9 ps,1,=1306nm,0=0.47ps/(nmkm),~,,=1297nm,P,,=120~W.
that parametric processes lead to a redistribution of energy between individual spectral lines which reduces the intensity fluctuations in the respective spectral range.
6. Conclusions
1250
1300
Wavelength
1350
[nm]
spectra on the relative orientation of the (linear) input polarizations of the pulses and of the cw radiation. The black curves show the propagated spectra for pulses alone whereas the resulting spectra with cw added are overlaid as gray traces. The results for parallel (orthogonally) polarized input signals are shown at the top (bottom) of the figure. Experimental parameters: Fibre # 1, T,,= 3.1 ps, A, = 1307 nm, P,,,=20.8 mW, A,= 1297 nm, P,= 19 pW. Fig. 11. Dependence
of the output
We have investigated the experimental conditions that lead to interactions between a train of ultra-short optical pulses and weak cw radiation during co-propagation in an optical fibre. These interactions were found to result in modifications in the output pulse spectra which show two different characteristics (referred to as “respire-type modifications” and “changes of the Stokes frequency-shift”). The observed spectral modifications in general show a complicated dependence on the input signal and fibre parameters but exhibit a distinct threshold behaviour with respect to pulse and cw power, pulse width and fibre length. Finally, it was found that the input polarization states of the interacting signals have to be equal, because the effect vanishes for orthogonal input polarizations. There are several indications (noise
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J. Schiitz et al. / Optics Communications lll(l994)
characteristics, difference spectra, power dependence. wavelength dependence, input polarization dependence) which lead us to assume that these effects are caused by parametric interactions during copropagation of the picosecond pulses and the cw radiation through the optical fibre. The most important result of our work is that a very weak disturbance (namely the addition of weak cw radiation) can lead to considerable changes in the output spectrum of picosecond input pulses. The extremely low cw power level (typically 1O-6 of the input pulse peak power) required to change the resulting frequency shift of Raman-generated Stokes bands makes this effect interesting e.g. for optical switching. On the other hand, it could be a problem for ultra-high bitrate communication systems using remotely powered amplifiers, because it is likely to occur in situations where a weak signal is co-propagating with strong cw radiation.
Acknowledgements We would like to address our special thanks to Dr. Paul A. Beaud and Dr. Henry H. Gilgen for their constructive feedback and discussions, and thanks also to Reto Santschi for the creation of Fig. 0. This work was supported by the Swiss PTT who provided finances and valuable experimental equipment.
403-416
References [ 1] A.R. Chraplyvy and J. Stone, Electron. Lett. 20 ( 1984) 996. [ 21 M.N. Islam, L.F. Mollenauer, R.H. Stolen, J.R. Simpson and H.T. Shang, Optics Lett. 12 (1987)
625.
I P.L. Baldeck and R.R. Alfano, Appl. Phys. Lett. 52 ( 1988) 1939. J.M. Hickmann, H.R. da Cruz and A.S. Gouveia-Neto, Optics Lett. 17 (1992) 478. G.P. Agrawal, Nonlinear fiber optics (Academic, New York, 1989). ‘I K. Aida, S. Nishi, Y. Sato, K. Hagimoto and K. Nakagawa, 15th European Conference on Optical Communication (ECOC ‘89), 3, PDA-7,29. [7] W. Hodel, J. Schtltz and H.P. Weber, Optics Comm. 88 (1992) 173. [ 81 P. Beaud, B. Zysset, A.P. Schwarzenbach and H.P. Weber, Optics Lett. 11 (1986) 24; P. Beaud, B. Zysset and H.P. Weber, Proc. ECOOSA ‘86, SPIE 701 (1986) 466. [9] J. Schlitz, W. Hodel and H.P. Weber, Optics Comm. 95 (1993) 357. [lo] J. Schiitz, W. Hodel and H.P. Weber, Optics Comm. 107 (1994) 170; J. Schlitz, H. Ammann, G.I. Onishchukov, W. Hodel and H.P. Weber, Optics Comm. 107 (1994) 287. [ 111 P. Beaud, W. Hodel, B. Zysset and H.P. Weber, IEEE J. Quantum Electron. QE-23 (1987) 1938. [ 121 K. Inoue, IEEE J. Quantum Electron. QE-28 4 ( 1992) 883.
OPTICS COMMUNICATIONS Optics Communications 11 I ( 1994) 403-4 16
EISEVIEK
Full length article
Experiments on the co-propagation of ultra-short pulses with continuous wave radiation through optical Gbres J. Schlitz ‘, G.I. Onishchukov,
W. Hodel, H.P. Weber
Institute ofApplied Physics, University ofBern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
Received 3 1 January 1994; revised manuscript received 26 May 1994
Abstract
The superposition of a weak continuous wave to a train of ultra-short pulses propagating in an optical single-mode tibre can lead to strong interactions between the two co-propagating signals. These interactions result in considerable modifications of the propagated pulse spectrum. A systematic investigation of the dependence of these modifications on various input signal and tibre parameters is presented. It has been found that cw power levels typically 1O6times lower than the respective pulse peak power are strong enough to induce pronounced modifications in the output pulse spectrum.
1. Introduction
Nonlinear interactions between “differently coloured” optical waves during propagation in an optical fibre have been investigated by many authors [ l41. The characteristic features of such interactions, i.e. the resulting temporal and spectral modifications of the co-propagating signals, depend mainly on the nature of the nonlinear processes involved (crossphase modulation XPM, four-wave mixing FWM, self-phase modulation SPM, stimulated Raman scattering SRS) and on the dispersive properties of the libre used (group-velocity dispersion GVD). Whereas interactions between waves with different optical frequencies are relatively well understood provided that either continuous wave (cw) radiation or pulses are involved [ 5 1, the interactions between ultra-short optical pulses and cw radiation during propagation in optical tibres have - to the best of our ’ J. Schlitz is now with the Laser Physics Centre, Australian National University, Canberra ACT 0200, Australia.
knowledge - not been investigated up to now (Fig. 0). However, since this situation often occurs in practice (e.g. in Raman or rare-earth-doped fibreamplifiers [ 6,7] ) it is important to know under what circumstances such interactions occur and how they modify the co-propagating signals. In this work we study the interaction of ultra-short (pica- and sub-picosecond) pulses with weak cw radiation during the co-propagation through a singlemode tibre. We have found that for certain input pulse and tibre parameters the pulse spectrum is modified considerably already for very low power levels of the co-propagating cw radiation (for cw-to-pulse peak power ratios as low as 10p6). The properties of these modifications have been investigated for different fibre and signal parameters, such as the length and the dispersion of the fibre, the wavelength, power and polarization of the pulse and the cw light-wave, as well as the temporal width of the input pulse. The results indicate that the spectral modifications are primarily caused by parametric processes.
0030-4018/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0030-4018 (94)00345-U
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J. Schiitz et al. /Optics Communications I I I (1994) 403-416
Fig. 0. The joint adventures
2. Experimental setup The experimental setup is shown in Fig. 1. A laser diode with pigtail followed by an integrated 60 dB optical isolator served as the cw light source. Two laser diodes with the strongest emission lines located at 1297 nm and 1324 nm were used alternatively. The signal was transferred by optical connectors (of PCstandard type) to a fibre pigtail. A selfoc lens was used at the other end of this pigtail to collimate the radiation emerging from the fibre. The source of ultra-short pulses was a synchronously pumped dye laser which delivered pulses at 82 MHz pulse repetition rate with an average power of several tens of milliwatts. This
of elephant
Stokes and CW-Mouse.
system has been described in more detail in Ref. [ 8 1. The centre wavelength I, of the pulses could be tuned between 1250 nm and 1350 nm while the width could be changed between 0.4 ps and 4 ps fwhm (autocorrelation) using different tuning elements. As the determination of the temporal width of a pulse from the measured autocorrelation crucially depends on the knowledge of the pulse shape and the chirp, the subsequent fwhm values T,, always refer to the measured autocorrelation traces. The beams of the two sources were combined by a dielectric beam splitter of 68% reflection (at an angle of 45”) and coupled by a selfoc lens into a fibre pigtail of 80 cm length from where the signal was transferred to the fibre under
fibre
Fig. 1. The experimental setup. BS: dielectric beam splitter (68% reflection), CH: mechanical chopper, DA: disc attenuator,f,_,: lenses cf = 308 cm,f,= 148 cm,f,=40 cm), ISO: 60 dB fibre optical isolator, 1/2: halfwave plate, MI_,: fixed mirrors (100% reflection), OL: objective lens (10x ), PC: fibre-connector (of FC-PC type), PD: photodiode (InCaAs), PM: photomultiplier, RC: fibre-connector (Radial& 12” wedged), RM: removable mirror ( 100% reflection), SF:selfoc lens. The lock-in amplifier and the mechanical chopper were used for the measurements of the difference spectra only.
J. Schiitz et al. /Optics Communications lll(l994)
test via optical connectors. In order to achieve optimum coupling, weak lenses (fi and f2) were placed in the optical path between the two laser sources and the fibre pigtail. The relevant parameters of the fibres used are listed in Table 1. For the temporal analysis of the input pulses and of the signal at the output of the libre a backgroundfree autocorrelation trace was generated using the second harmonic signal obtained from a LiIOs crystal. The conversion efficiency of this crystal is strongly polarization dependent and drops to zero for wavelengths separated by more than ? 20 nm from the optimum phasematching wavelength which was set to the centre wavelength of the input pulses. The temporal resolution and the wavelength sensitivity of the autocorrelator were determined by the properties of the nonlinear crystal alone. The optical spectra of the input pulse and of the signal at the output of the fibre were measured using a 0.5 m Czerny-Turner monochromator which had been equipped at the output slit with an InGaAs-photodiode. The measured spectra were not sensitive to the polarization properties of the input signal. Provided the spectral modifications induced by the nonlinear interactions were strong, it was possible to determine the resulting modifications directly from a comparison of the measured output pulse spectra with and without co-propagating cw radiation. In order to be able to detect rather weak modifications in the spectrum, it was necessary to measure the resulting spectral differences induced by the co-propagating cw radiation directly. For these measurements the signal from the monochromator was processed using a lockin amplifier while the radiation from the cw source at the input of the fibre was modulated using a mechanical chopper (see Fig. 1). Therefore, the output signal of the lock-in amplifier was proportional to the magnitude of those changes in the pulse spectra, which
405
403-416
were induced by the co-propagating cw signal. In the following discussion, the spectra which were obtained using this technique will be referred to as “difference spectra”.
3. Experimental results 3.1. Types of observed modifications One of the observed effects which is due to interactions between picosecond pulses and cw radiation during propagation through an optical Iibre is a change of the noise characteristics of individual parts of the output spectrum. A narrow range of the optical spectrum at the output of the fibre was selected by the 0.5 m monochromator (see Fig. 1) and detected using an InGaAs-photodiode. The noise spectrum of the temporal fluctuations of the photodiode signal was measured by an electrical spectrum analyser in a frequency range from dc up to a few hundred kHz. The input wavelength A,= 1303 nm of the 4 ps input pulses was chosen close to the zero dispersion wavelength of the libre used. This choice resulted in the generation of a strong anti-Stokes band which was continuously shifting towards shorter wavelengths with increasing input power [ 91. Changes of the noise spectrum as well as modifications in the propagated pulse spectrum were found to occur as soon as the generated anti-Stokes band and the cw spectral lines started to overlap in the output spectrum. The magnitude of the changes in the noise spectrum also depended on the wavelength which was selected at the monochromator. In most cases, the noise in the spectrum obtained from the electrical spectrum analyzer was considerably reduced when cw radiation was added to the input pulses. This effect is illustrated in Fig. 2 by the optical pulse spectrum after
Table 1 Measured fibre parameters
Length L [m] Zero-GVD wavelength Lzd [ nm ] Attenuation (around 1320 nm) [dB/km] Spot size ( 1300 nm) [pm] ’
iibre #l
fibre #2
iibre #3-5
1183 1303 0.38 9.5
1000 1317 0.47 10.2
50,150,300 1300 0.37 9.5
a Diameter measured at 1/e* of the intensity. The fibres are monomode for all involved wavelengths.
J. Schiitz et al. / Optics Communications Ill (I 994) 403-416
Input
,,,, 1260
k 1280
,,,( 1300
Wavelength
0
1320
100
Frequency
1340
[nm]
200
[kHz]
Fig. 2. Upper graph: The cw and pulse spectra at the input of the fibre (the spectral intensity of the cw radiation and of the input pulses are not to scale) and after propagation through tibre #l. The overlaid traces show the output spectra without (black) and with (gray) cw radiation added. Lower graph: The low-frequency noise characteristics of the spectral intensity of the propagated pulse spectra (with and without cw) are shown for a selected spectral range (AA x 0.4 nm) centred at 13 I8 nm. The input wavelength of the pulses was centred near the zero-dispersion wavelength of the fibre at 1303 nm. The average power of the input pulses was Pavg= 5.7 mW and the pulse duration was 4 ps. The power of the added cw radiation was PC_=85 pW.
propagation through fibre #I and by the measured noise spectrum, when the centre wavelength of the selected spectral range of 0.4 nm width was set to 13 18
nm. The changes induced by the co-propagation of the weak cw-radiation are shown by the gray overlaid trace in the output spectrum and by the lower trace in the noise spectrum. It was found that the intensity noise of the selected spectral range was reduced by approximately a factor of ten for frequencies below 60 kHz. In a similar fashion, the intensity noise of the output spectrum was measured without spectral filtering. This was done by detecting the output signal from the Iibre directly using a photodiode. In this situation, the noise spectrum was not altered by the addition of the cw radiation. These results show, that the addition of weak cw radiation to a train of short pulses can considerably reduce the fluctuations of individual spectral components, but leaves the noise properties of the output signal as a whole unchanged. This may be explained by parametric processes which are “levelling out” the intensity fluctuations of individual spectral lines by a redistribution of the spectral energy. The second effect which has been observed in the experiments is substantial modifications in the propagated pulse spectrum which are induced by the copropagation of the cw radiation. Fig. 3 shows a typical experiment using 3.5 ps pulses with an average power of Pavg= 15.2 mW. The two overlaid traces at the top of the figure are measurements of the output spectra for pulses alone (black) and for pulses with co-propagating cw radiation (gray). With the addition of the cw radiation the frequency shift of the Stokes band is considerably reduced, even for cw power levels as low as 65 uW (corresponding to a cw power level 1O6times smaller than the respective pulse peak power!). In this case, the resulting spectrum forms an extended quasi-continuum with a width of about 60 nm. In order to make sure that these modifications do not originate from light which is reflected back into the laser cavity of the signal sources, we performed additional experiments with increased reverse isolation (by 30 dB) between the fibre coupling and each signal source. The experimental results showed no significant deviations from the described behaviour which indicates that the reflected light is not responsible for the observed changes. Thus we have observed two characteristic types of spectral modifications in our experiments. While the typical modifications shown in Fig. 2 affect only the
J. Schiitz et al. /Optics Communications 11 I (1994) 403-416
401
nounced modifications occurred in the propagated pulse spectrum. These “default” values are listed in Table 2. In the following, we will refer to the default values as a whole as the default parameter set.
4. Dependence of spectral modifications in the output pulse spectrum on the experimental parameters 4.1. Dependence on the input pulse width Difference
1250
Spectrum
1300 Wavelength
1350
1400
[nm]
Fig. 3. Upper traces: Overlaid output spectra without (black) and with (gray) cw radiation added for a situation exhibiting pronounced cw-induced spectral modifications. Lower trace: The measured difference spectrum of the output spectra shown above for the following experimental parameters: Fibre #2, T,,= 3.5 ps, Pa,,=152 mW, A,=1332 nm, D=1.23 ps/(nm km), PC_=65 pW, I,= 1324 nm.
shape of the individual spectral bands (apart from the noise characteristics), the spectral modifications shown in Fig. 3 are characterized by a frequency shift occurring for some of these bands-where shifts towards longer as well as shorter wavelengths have been observed. Most apparent in this case is the change of the frequency shift of the well-separated Stokes band. We have chosen to address the type of modifications shown in Fig. 2 in a descriptive way as “respire’‘-type modifications and to refer to those shown in Fig. 3 as the modi’cation
of the Stokes frequency shift,
respectively. 3.2. Definition of a ‘default”parameter set
Fig. 4 shows the measured output spectra (left) and the corresponding difference spectra (right) for input pulses having comparable average power levels PaVg but different temporal widths T,, (the indicated values of T,, denote the fwhm of the measured autocorrelations). The wavelengths of the input pulses and ofthe cw radiation were&,= 1310 nm and&,= 1324 nm, respectively. Note that the spectra of the propagated pulses (black), which consist mainly of two well-separated spectral bands, look remarkably similar although the input pulse width (and therefore the resulting peak power) was changed by a factor of four. While the shape of the multiple peak spectrum in the vicinity of the centre wavelength of the input pulses 1, is changing with T,,, the shape and the centre wavelength of the spectrally separated Stokes band near 1380 nm remain approximately the same [lo]. A comparison with the output spectra for pulses with co-propagating cw radiation (gray) shows pronounced spectral modifications for 2.9 ps and 2.2 ps input pulses but nearly no changes for 0.74 ps input pulses (see the respective difference spectra on the right hand side of Fig. 4). Further experiments with 0.5 ps pulses also produced no measurable cw-induced spectral changes. This result indicates that the occurrence of any spectral modifications (within the parameter ranges available in the experiment ) is re-
stricted to input pulses longer than approximately
1
ps.
Since the described spectral modifications depend on a considerable number of experimental parameters (given by the properties of the interacting input signals and of the fibre used), it seems reasonable to characterize the development of these modifications systematically by varying one of these parameters while all others remain fixed. The values of the fixed parameters were chosen in such a way that pro-
For this reason no further measurements using sub-picosecond pulses will be presented in the following. 4.2. Dependence on the wavelength
TWO different laser diodes with main spectral peaks at ;I,,= 1297 nm and 1324 nm, respectively, were used for the investigation of the dependence of the
408
J. Schiitz et al. / Optics Communications I I1 (1994) 403-416
Table 2 List of the default parameters
used for the investigation
of the spectral modifications
Parameter
Default value
Remarks
Length of fibre (L)
approx.
non-polarization communication
Zero dispersion wavelength (A,,) Input wavelength of pulses (A,) and cw radiation (A,,) Input pulse width (T.,) Average power of input pulse (Pa”,) Power of cw radiation (P,) Relative (linear) input polarization of pulses and cw radiation Reverse isolation of pulses Reverse isolation of cw radiation
1303 nm chosen to give the maximum effect approx. 3 ps approx. 15 mW 20-150 uw parallel
,
5,
I,,
1250
1 km
preserving monomode
standard fibre
consult Table 3 for the wavelength dependence of the effect fwhm of autocorrelation
none -6OdB
L
1300
I,,
1
I,
1,
1350 Wavelength
[nm]
Fig. 4. Output spectra (left) and difference spectra (right) for different input pulse widths T, after propagation through fibre #l. The exact values of Pavgare given on the left of each difference spectrum. Experimental parameters: T.,=O.74 ps: A,= 1312 nm, D=O.79 ps/(nmkm),P,=65 uW,1,=1324nm. T,=2.2and2.9ps:&=1310nm, 0=0.63ps/(nm km), Pm=65 uW,1,=1324nm.
spectral modifications on the input wavelength. The centre wavelength &, of the input pulses was tunable between 1250 nm and 1350 nm. A third important parameter is the zero dispersion wavelength Azdof the fibre used. In the experiment, we used two different fibres of comparable lengths but with different values for Lzd ( 1303 nm for tibre #l and 13 17 nm for fibre #2; see Table 1). This resulted in four different combinations for il,, and lzd while the continuous tuna-
bility of /2, was used to find the wavelength producing the maximum effect in the resulting output spectra as well as to determine the values of &, for which the spectral modifications vanished. Fig. 5 shows a typical example of the output spectra and the corresponding difference spectra for A = 1324 nm and Iz,,,= 1317 nm and for different cztre wavelengths /2, of the input pulses. From the figure we see that the maximum effect induced by the
409
J. Schiitz et al. /Optics Communications 1 I1 (1994) 403-416
1.23
15.2
I
1350
1400 Wavelength
1250
1300
1350
1400
[nm]
Fig. 5. Output spectra (left) and difference spectra (right) for different 1, (marked by triangles) after propagation through fibre #2 (1,~ 1317 nm). The gray overlays (left) show the resulting spectra when cw radiation was added. The values of the dispersion paramparameters: T,= 3.5 ps, AP eter D at A, and of the average input power of the pulses Pay* are indicated in each spectrum. Experimental (frombottomtotop): 1310,1313, 1317,1323, 1332, 1337and 1340nm,P,=65pW,&,=1324nm.
addition of cw radiation to the input pulses appears for I,=1332 nm (0~1.23 ps/(nm km)) whereas the effect vanishes for wavelengths above 1340 nm and below 13 10 nm. We can further observe a distinct change in the characteristics of the spectral modifications which occurs for 2, in the vicinity of the zero dispersion wavelength Azd. For input pulses with wavelengths &, in the region of anomalous GVD (D > 0) the resulting spectra show pronounced “respire”-type modifications and changes of the Stokes frequency shift (see Sect. 3.1). “Respire’‘-type modifications appear in the difference spectra as a number of narrow spikes which coincide (roughly) with the respective structures in the optical spectrum, while the changes of the Stokes frequency shift can be iden-
titied by the broad sinusoidal-like structures. On the low-wavelength side of &, in the region of normal GVD (D < 0), we have never observed significant changes of the Stokes frequency shift, i.e. the changes are entirely of “respire’‘-type. Another interesting feature which can be observed in the difference spectra of Fig. 5 is the tendency of these spectra to maintain a certain symmetry, “Respire’‘-type moditications typically show an axial symmetry with respect to A,,. The changes of the Stokes frequency shift, on the other hand, are accompanied by corresponding changes on the anti-Stokes side which resemble a mirror image with respect to the zero-dispersion wavelength ;Izd of the tibre [ 111. The remaining combinations of LCwand Lzd have
J. Schlitz et al. /Optics Communications I1 1 (1994) 403-416
4 IO
also been investigated experimentally and two of them (namely/I,,= 1303nm/l,,= 1324nmand&,= 1303 nm/).,,= 1297 nm, respectively) showed a behaviour very similar to the situation we have just discussed. The respective values of 1, for which the modifications in the output spectrum were maximal or vanishing were shifted, however, to other wavelength ranges. In contrast, the last of the four possible combinations of Lzd and A,, (i.e. Azd= 13 17 nm and A,,,,= 1297 nm) showed no effect throughout the tuning range of the dye laser, except for ;i, = 132 1 nm where a rather weak effect was found (notably a change of the Stokes frequency shift and no “respire”-type modifications, very similar to the spectrum for D = 0.48 in Fig. 5 ) . A summary of these experimental findings is given in Table 3. 4.3. Dependence on the power
4.3. I. Averagepulsepower Fig. 6 illustrates the dependence of the output spectra on the average pulse power for 3.9 ps pulses after propagation through libre #l (the values of PaVg are indicated in the figure). The input wavelengths A,= 1309 nm and A,,.,= 1297 nm were chosen in accordance with the default parameter set defined in Table 2. The minimal average pulse power PaVgfor which (“respire’‘-type) spectral modifications have been observed was approximately 6 mW. For PaVg=20 mW, however, the Stokes frequency shift is changed as well. In this case, a large spectral quasi-continuum extending over nearly 80 nm is formed with the ad-
dition of the cw radiation, while the spectrum of “plain” input pulses consists of two well-separated spectral bands (i.e. one spectral band near LP exhibiting multiple peaks, and a frequency shifted Stokes band). 4.3.2. Cw pa wer In the spectra of Fig. 7 the input power PCWwas changed while PaVgof the 3 ps pulses was kept at a constant level of 20.5 (left) and 38.0 mW (right), respectively. For 20.5 mW average pulse power and low cw power levels, the cw-induced spectral modifications are mainly restricted to the multi-peak spectral band in the vicinity of 1,. Only at the highest cw power of 13 1 uW the distinct separation of the symmetrical Stokes band is destroyed and an extended quasi-continuum is formed instead. This result indicates that the spectral modifications exhibit threshold behaviour with respect to the variation of the cw power. For PaVg=38 mW the same behaviour can be observed for considerably lower cw power levels of only a few microwatts. Note, that there are only minor changes in the output spectrum for power levels of PCWbetween 17 uW and 136 uW, which corresponds to a variation of the cw power by nearly one order of magnitude. 4.3.3. Determination of the threshold power levels In order to determine the minimal power levels for the input pulses and the cw radiation which are required to produce detectable modifications in the propagated pulse spectrum, we have reduced the
Table 3 The characterization of the spectral modifications for cw radiation with different wavelengths I,, and for two tibres of comparable length but different zero dispersion wavelengths &. The characterization is given by the values of ,I, resulting in the strongest spectral modifications (maximum effect) and by the lower and upper limit of 1, for which an effect is still visible. In addition, the characteristic type (as defined in Sect. 3.1) and the magnitude of the modifications are indicated in the last three columns
L
[nml
L lnml
Spectral modifications
1, lnml Lower limit
Maximal effect
Upper limit
1332 1316 1308 1311 1321
1340
1324
1317
1310
1297 1324 1297
1303 1303 1317
1295 1283
1314 1333 _
“Respire”type
yes yes yes yes no
Change of Stokes freq. shift
Strength of the moditications
yes no
pronounced medium pronounced pronounced weak
yes yes yes
J. Schlitz et al. /Optics Communications I1 I (1994) 403-416
2.4
411
served in the output spectrum for power levels higher than PC,.,= 15 pW. From these experimental results we derive that the occurrence of any modifications scales with the product of the pulse power times the cw power. Thus, if the power level of one of the two signals is increased (e.g. Pavp)the minimum required power for the other signal ( PCw) will be lowered and vice versa. This change of the threshold power can be observed best in the spectra of Fig. 7 by comparing the results for P,,,=20.5 mW and 38.0 mW with respect to changes of the Stokes frequency shift.
/
4.4. Dependence onJbre length
0.45
I
6
i
,I /~
Input _L 1200
1400
1300 Wavelength
[nm]
Fig. 6. Output spectra for different Pay8(values indicated on the left) after propagation through fibre #l. The gray overlays show the spectrum after cw radiation at 1297 nm wavelength had been added. Experimental parameters: T,=3.9 ps, ,I,= 1309 nm, P,=llOpW,1,=1297nm.
power levels of both signal sources until the modifications vanished (apart from the use of libre #2 in the measurements all other experimental parameters were chosen in accordance with the default parameter set defined in Table 2). Fig. 8 shows the output and difference spectra which result from a variation of PaVgwhile PC, was kept at a constant power level of 62 pW. The results indicate that “respire’‘-type modifications occur for values of Pavgin the order of 4-5 mW while for a change of the Stokes frequency shift approximately 7 mW are required. Analogous measurements are presented in Fig. 9 for a fixed level of P,,=7.9 mW and different levels of PCw.In this case, “respire’‘-type modifications are observed for PC,.,as low as 400 nW (which corresponds to a cw power lo8 times lower than the pulse peak power) while changes of the Stokes frequency shift are ob-
In order to study the dependence on the fibre length, pieces of L= 50, 150 and 300 m length were cut from the same fibre in order to ensure that all other fibre parameters were identical (the most important parameters are listed in Table 1). The resulting output spectra after propagation through the different fibre pieces are shown in the left part of Fig. 10. The right part of the figure shows measurements of the corresponding autocorrelations where the phase-matching angle of the nonlinear crystal had been adjusted to result in the highest conversion efficiency at Ap. The input parameters were chosen to give maximum interaction between the pulses and the cw radiation. The output spectrum for L=50 m propagation-length is relatively narrow and exhibits a typical modulation due to SPM. The distinct asymmetry of the spectrum is the result of an asymmetry of the input pulse shape 2. The addition of cw radiation to the input pulses leads to no significant changes in the output spectrum for this fibre length. With increasing fibre length the influence of stimulated Raman scattering grows and leads eventually to the formation of a broad frequency shifted Stokes band. This development is illustrated by the spectra for L= 150 m and 300 m. In this situation, however, the addition of cw radiation to the train of input pulses leads to a considerable reduction of the frequency shift of the generated Stokes band. The magnitude of the modifications is large enough to result in visible changes ’ This has been verified by numerical simulations
using the wellknown split-step Fourier method [ 5,9]. Additionally it was found, that the influence of third-order dispersion (TOD) on the symmetry of the spectrum can be neglected in this case.
J. Schiitz et al. /Optics Communications 111 (1994) 403-416
412
P avg = 20.5 mW
I ”
1200
1250
7 ,I r
1300
P avg = 38.0 mW
7I
”
1350
r
1400 1200
Wavelength
1300
1400
[nm]
Fig. 7. Spectral changes induced by different levels o~P,~ (values indicated on the left) of the cw radiation pulses with P,,,=20.5 mW (left) and 38 mW (right) after propagation through fibre #l. Experimental T.,=3.6 ps,+1308.5 nm,A,,=1297nm. P,,=38mW: T,=3.Ops,A,=1309 nm,l,,=1297nm.
in the respective autocorrelation of Fig. 10).
traces (see right part
4.5. Dependence on the input polarization We have also investigated how the spectral modifications depend on the respective input polarization states of the interacting signals. The experimental parameters were chosen in accordance to the “default parameter set” of Table 2. We restricted our investigations to initially linearly polarised signals which were oriented either parallel or perpendicular to each other. The adjustment of the respective polarization directions of the cw radiation and of the pulse train was established by means of halfwave plates which were inserted into the beams. The resulting output spectra for parallel and perpendicular relative input polarizations are shown in Fig. 11 (note in this respect, that the spectra obtained from the mono-
added to the ultra-short parameters: P,,,=20.5
input mW:
chromator depend only weakly on the polarization of the analyzed radiation). By comparing the results for input pulses alone with those for pulses with co-propagating cw radiation it becomes obvious that the interaction crucially depends on the relative orientation of the input polarizations. While pronounced spectral modifications are observed for parallel input polarizations, the corresponding spectra for perpendicular input polarizations are practically identical. This indicates that the initial polarization states of the two signals have to be equal in order to induce spectral modifications. This fact is inasmuch astonishing as the tibre used was not polarization preserving and the polarization states of the different spectral components in the propagated spectrum were varying strongly.
J. Schiitz et al. / Optics Communications 1 I1 (1994) 403-416
Wavelength
[nm]
Fig. 8. Output spectra (left) and difference spectra (right) for 3.5 ps input pulses with different Pays (indicated in the figure) after propagation through fibre #2. The power level of the added cw radiation was 62 uW for all the measured spectra except for the bottom most trace where no cw radiation was added. Experimental parameters: I,= 1332 nm, ,A,,= 1324 nm.
5. Discussion
The presented results illustrate that the occurrence of spectral modifications show a complicated dependence on the input pulse and fibre parameters used in the experiment. For a theoretical analysis it is necessary to be able to identify the nonlinear processes which are involved in the generation of the observed spectral modifications. We have investigated numerically the propagation of picosecond pulses through single-mode tibres using an extended version of the modified non-linear Schrijdinger (NLS) equation [ 9 ] and by solving this equation with the well-known split-step Fourier method [ 5 1. It was found that the numerical results are in good agreement with the measurements for relatively low input power levels and short tibres. This, however, is not the case for the power levels and fibre lengths which are required for spectral modifications to occur in the present experiments. This discrepancy may be due to insufficient knowl-
edge about the experimental parameters, especially about the symmetry and chirp of the input pulses (in the calculations the symmetry of the input pulses was treated as a free parameter and we have further assumed that the input pulses are bandwidth limited and sech or Gaussian shaped). On the other hand the discrepancy may also be caused by the fact, that the NLS equation implicitly assumes that the polarization is preserved. This assumption is not justified if a standard non-polarization preserving fibre is used (as in our experiment). Because nonlinear processes such as the stimulated Raman effect or parametric processes are inherently polarization dependent, the pulse spectra (and temporal shapes) generated in a standard communication fibre might be different from those which are calculated using the NLS equation. In fact there are several indications that lead us to assume that parametric processes are involved: (i) The experimental results show that spectral modifications occur only for very specific combinations of the signal wavelengths. This wavelength de-
414
J. Schiitz et al. /Optics Communications 1I I (1994) 403-416
Wavelength
[nm]
Fig. 9. Output spectra (left) and difference spectra (right) of 4 ps input pulses after propagation through fibre #2 for different Pewof the co-propagating cw radiation (indicated in the figure) and a relatively low average pulse power of Pa,,*= 7.9 mW. Experimental parameters: I,=
133?nm,
A,=
1324 nm.
pendence might be a manifestation of the phase matching condition between the interacting signals. (ii) The modifications of the output pulse spectra show a strong dependence on the polarization of both input signals. The interaction is maximal for parallel (linear) input polarizations and becomes negligible for perpendicular polarizations. Inoue [ 12 ] has studied four-wave mixing (FWM) processes in non-polarization preserving fibres for general polarization states of the interacting cw light. His results show that there exists one specific case for which the FWM efficiency is zero for orthogonal polarization states. This case is characterized by an interaction of the form wq=w, + o, -wZ, where o, and o2 are the optical frequencies of the interacting signals (i.e. of the pulses and of the cw radiation in our case) and where w4 is the idler frequency.
(iii) The threshold power for the occurrence of spectral modifications was found to scale with the product of the pulse power times the cw power. This is compatible with the assumption that these modifications are induced by a FWM process, because the FWM gain shows a similar power dependence. (iv) The difference spectra obtained for “respire”type modifications are fairly symmetrical with respect to the input wavelength A,,,, of the cw radiation (see Fig. 5 ). This symmetry is typical for the sidebands generated by any mixing processes. (v) In Section 3.1 it was found that the intensity noise of a narrow spectral range (which was filtered from the output spectrum by a monochromator) may be considerably reduced by the co-propagation of the cw radiation, while the noise spectrum of the output spectrum as a whole remains unchanged. We believe
J. Schiitz et al. /Optics Communications 11 I (1994) 403-416
415
Autocorrelation
Spectra
P,,,= 16.3 mW il
mj ____A-J
c-,._
16.9
16.6
i”\
.._____ _, ,I
1
.._ .._..
Ai_____ I
1300
1250
Wavelength
1350 [nm]
-20
I,
I
I
-10 Time
I
0 Delay
I
I
I
I,
IO
20
[ps]
Fig. 10. Output spectra (left) and autocorrelation traces (right) for differentfibre lengths L as indicated in the figures (fibres #3, #4 and #5 of Table 1). The exact values for Pgvgare given on the right side of the respective autocorrelations. Experimental parameters: T,=2.9 ps,1,=1306nm,0=0.47ps/(nmkm),~,,=1297nm,P,,=120~W.
that parametric processes lead to a redistribution of energy between individual spectral lines which reduces the intensity fluctuations in the respective spectral range.
6. Conclusions
1250
1300
Wavelength
1350
[nm]
spectra on the relative orientation of the (linear) input polarizations of the pulses and of the cw radiation. The black curves show the propagated spectra for pulses alone whereas the resulting spectra with cw added are overlaid as gray traces. The results for parallel (orthogonally) polarized input signals are shown at the top (bottom) of the figure. Experimental parameters: Fibre # 1, T,,= 3.1 ps, A, = 1307 nm, P,,,=20.8 mW, A,= 1297 nm, P,= 19 pW. Fig. 11. Dependence
of the output
We have investigated the experimental conditions that lead to interactions between a train of ultra-short optical pulses and weak cw radiation during co-propagation in an optical fibre. These interactions were found to result in modifications in the output pulse spectra which show two different characteristics (referred to as “respire-type modifications” and “changes of the Stokes frequency-shift”). The observed spectral modifications in general show a complicated dependence on the input signal and fibre parameters but exhibit a distinct threshold behaviour with respect to pulse and cw power, pulse width and fibre length. Finally, it was found that the input polarization states of the interacting signals have to be equal, because the effect vanishes for orthogonal input polarizations. There are several indications (noise
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J. Schiitz et al. / Optics Communications lll(l994)
characteristics, difference spectra, power dependence. wavelength dependence, input polarization dependence) which lead us to assume that these effects are caused by parametric interactions during copropagation of the picosecond pulses and the cw radiation through the optical fibre. The most important result of our work is that a very weak disturbance (namely the addition of weak cw radiation) can lead to considerable changes in the output spectrum of picosecond input pulses. The extremely low cw power level (typically 1O-6 of the input pulse peak power) required to change the resulting frequency shift of Raman-generated Stokes bands makes this effect interesting e.g. for optical switching. On the other hand, it could be a problem for ultra-high bitrate communication systems using remotely powered amplifiers, because it is likely to occur in situations where a weak signal is co-propagating with strong cw radiation.
Acknowledgements We would like to address our special thanks to Dr. Paul A. Beaud and Dr. Henry H. Gilgen for their constructive feedback and discussions, and thanks also to Reto Santschi for the creation of Fig. 0. This work was supported by the Swiss PTT who provided finances and valuable experimental equipment.
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