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A fiber grating Raman laser generating subpicosecond pulses
A FIBER GRATING RAMAN LASER GENERATING R. SCHULZ,
1 March 1989
OPTICS COMMUNICATIONS
Volume 70, number 3
M. KUCKARTZ
SUBPICOSECOND
PULSES
and H. HARDE
Vniversitiit der Bundeswehr Hamburg, Fachbereich Elektrotechnik, Holstenhojiveg 85, 2000 Hamburg 70, Fed. Rep. Germany
Received 11 July 1988
Successful operation of a fiber grating Raman laser delivering pulses of 0.8 ps duration at a wavelength of 1.1 Km is presented. The pulses are generated with a novel method taking advantage of stimulated perpendicular Raman scattering in conjunction with dispersion compensation in a birefringent fiber.
1. Introduction When powerful light pulses are launched into an optical fiber two nonlinear effects, self-phase modulation (SPM) and stimulated Raman scattering (SRS), have a dominant influence on their propagation [l-7]. SPM, in conjunction with group velocity dispersion (GVD), is commonly used to create a linear chirp in order to prepare pulses for compression by means of a grating pair [ 8,9]. SRS made possible the development of new, frequency shifted light sources [ 10,111. The associated broad Raman gain profile should offer the opportunity to generate ultrashort pulses. With the method of spectral windowing pulses of 46 ps were generated [ 121 and a dispersion shifted fiber Raman oscillator was shown to be capable of producing subpicosecond pulses but only at a relatively low average power of 20 mW [13]. In this paper we report a novel method for generating ultrashort Stokes pulses with a fiber grating Raman laser (FGRL). Essential for its feasability is the velocity matching of pump and first Raman Stokes wavelength on the two axes of a birefringent fiber. Such a fiber design supports an enhanced action of SRS and cross-phase modulation (XPM) of the Raman pulses travelling on the slow axis with the fundamental pulses propagating on the fast axis. These effects together with SPM and GVD produce a linear chirp of the Raman pulses. Hence the use of a grating pair as dispersive delay becomes possible. A similar technique of birefringent compensated 0 030-4018/89/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
dispersion was used for efficient phase-matched fourwave mixing in fibers [ 14 1. Another method for enhancing the interaction length is applied in fiber Raman soliton lasers [ 15 17 ] working around the minimum dispersion wavelength. Our system is shown to be capable of producing subpicosecond Stokes pulses at a wavelength of 1.1 pm with an average output power of 0.4 W. The experimental results are supported by a theoretical model.
2. Experimental set-up Fig. 1 shows a schematic of the FGRL together with the diagnostics. A cw actively mode-locked Nd:YAG laser emitting pulses of 70 ps duration at a rate of 84 MHz and a wavelength of 1064 nm is used as pump source. The.pulses are coupled into a 300 m polarization preserving fiber serving as the active me; dium. The core diameter of the fiber has a value of about 3.5 pm. The dispersion between pump pulse and first Raman component results in a walk-off value of 2.1 ps/m which is approximately identical to the value of the birefringence of the fiber for these wavelengths (6n= 7 x 10p4). After the fiber the Stokes light is collimated and directed through a grating pair ( 1700 lines/mm) in double pass configuration [ 181 serving as compressor as well as wavelength selector. The mirror M2 after the grating pair is slightly tilted so that the reflected beam is below the plane of fig. 1 to allow separation from the B.V.
239
Volume 70, number 3
1 March 1989
OPTICS COMMUNICATIONS
3. Results and discussion
DELAY
UNE
Fig. 1. Experimental scheme showing the FGRL with its diagnostics. Symbol key: PM photo multiplier, P prism, BS beam splitter, M mirror, SHG crystal for second harmonic generation.
incoming beam. Mirror M 1 deflects the beam out of the system. The FGRL output pulses are measured with standard background free autocorrelation techniques. The beam splitter 1 (BS 1) is removed from the set-up for these measurements. The intensity profiles of the pulses emerging from the fiber exit are determined by separating a portion of the power before the grating pair (BSl inserted and BS2 removed) and applying cross-correlation techniques. For this procedure the monochromator is by-passed. As test pulses the output of the FGRL or compressed pump pulses are used and controlled to have a duration of less than 2 ps. In order to measure the chirp, which the Stokes pulses receive in the fiber, the light beam is dispersed by the grating of a 1 m monochromator ( 1200 lines/ mm) and scanned across the exit slit adjusted to 0.1 mm width. This device acts as a bandpass of 0.1 nm transmission. The prism P allows the monochromator to operate in double-pass configuration and therefore ensures to compensate the spatial spreading across the beam profile caused by the grating. It is slightly tilted for the same reason that the mirror M2 is. The intensity profiles of these spectrally windowed pulses are measured by applying cross-correlation techniques as described above. The chirp is determined by measuring 16 windowed beam protiles while subsequently advancing the monochromator wavelength setting by 1 nm. 240
The conventional approach to design an FGRL would have been to launch the laser pulses into the fiber in such a way that the polarization is parallel to one of the principal fiber axis and that the input power is well above the threshold for SRS. Under these conditions the first Raman Stokes component appears at an average power of about 0.4 W. Between 0.7 W and 2 W we performed various measurements but no significant compression could be achieved. For example the resulting poor quality of the compressed pulses can be seen from the autocorrelation trace shown in fig. 2 which was taken at a power of 1.5 W resulting in a reduced width of 40 ps (assuming gaussian shape). Obviously the quality of the chirp fails to allow an efficient compression. A remarkable change of the situation occurs when introducing some small but far reaching modifications to the experimental set-up. The key element is the birefringent optical fiber which must be designed in such a way that the walk-off between the pump pulse, travelling on the fast axis, and the Raman component travelling on the slow axis is compensated. This fiber design offers the opportunity to enhance the effects of pulse interaction in an advantageous way. At first it becomes possible to generate the pulses utilized in the FGRL by stimulated perpendicular Raman scattering (SPRS). Here the Stokes light travelling on the slow axis is amplified by the pump I
I
I
I
1 .o0.80.60.40.20.0 -200
0
-100 Time
100
200
[psec]
Fig. 2. Autocorrelation trace of insufftcient FGRL output for pump pulses launched into one tiber axis only.
Volume 70, number 3
1 March 1989
OPTICS COMMUNICATIONS
pulse on the fast axis. Although the gain efficiency is more than one order of magnitude smaller compared to parallel SRS this disadvantage is easily compensated by the increased interaction length. To stimulate this process Raman photons may be ‘seeded’ on the slow axis by parallel SRS. Therefore input power is split between the two fiber axes. In addition the process of XPM may now be active between pump and Raman pulse throughout the entire fiber length, rather than only for the walk-off length as observed for the case of parallel Raman conversion [ 4,6 1. Together with GVD an improved linearity of the chirp is expected with increasing fiber length. For an experimental realization the polarization of the laser beam is rotated by 30 degrees to the fast axis. This way 25% of the power is launched for ‘seeding’ on the slow axis and 75% on the fast axis. The Raman output of the slow axis is directed through the grating pair. With this configuration the FGRL is capable of producing pulses with low substructure in the subpicosecond regime. The Raman component on the slow axis appears at an average input power of 0.7 W coupled into the fiber and is fully saturated at P= 1.4 W. For input powers up to 2.5 W, on the slow axis no conversion into higher Stokes components was found. Only higher Raman components on the fast axis could be observed. This prevents the Stokes light, that is used in the FGRL, from suffering depletion on its leading edge, which is the case for conventional Stokes generation [ 6 1. The further investigations were performed for an input power of 2 W. The power splitting therefore leaves an initial power of 0.5 W for the slow axis of wmch 0.1 W will be converted by parallel SRS for ‘seeding’. Fig. 3 shows a typical autocorrelation trace of the output of the FGRL for these conditions. Assuming gaussian shape the width is determined to be 0.8 ps with an average power of 0.4 W. The difference between the initial Raman power, generated by SRS on the slow axis, and the output power of the FGRL can clearly be attributed to the process of SPRS. In order to analyse the operation of the FGRL we performed measurements of the intensity profile and the chirp of the pulses emerging from the fiber exit. Fig. 4 shows the cross-correlation traces of the pump pulse (a) and the Raman pulse (b). The mono-
‘L-7-l 0
-I”
-L”
20
10
Time [ psec] Fig. 3. Autocorrelation trace of FGRL output for pump pulses launched into fiber at 30 degrees to the fast axis. 1
.o(4
.yl
0.s
s
0.6-
100
200
300
400
Time [psec]
b) _ 5
0.6-
s 0.6>r .; 5
0.4-
E 0.20.0
0
100
200
300
400
Time [ psec]
Fig. 4. Cross-correlation trace of pump pulse (a) guided by the fast axis and Raman pulse (b) guided by the slow axis after 300 m fiber length.
chromator was by-passed and the beam splitter BS2 was removed from the set-up for these measurements (see fig. 1). It is found that both pulses leave 241
Volume 70, number 3
the fiber at the same time as the result of birefringence compensated dispersion. The depletion of the pump pulse in its central region clearly reveals the effect of SPRS. A major part of it has been converted into Stokes light on the slow axis. While Stokes pulses generated by parallel SRS exhibit a strong trailing, a Raman pulse more concentrated in time and without trailing is created by the process of SPRS. This pulse is likely to experience SPM over its total profile in a well-defined way. Together with XPM the resulting chirp will be formed. The result of the chirp measurement is demonstrated in fig. 5a. It was derived by evaluating the temporal peak positions of spectrally windowed pulses and then relating the time shifts of subsequent cross-correlation measurements to the selected wavelengths. The graph shows an approximate linearity extending over major parts of the pulse length.
7
The measured chirp of pulses originating from parallel SRS, however, gives a quite similar result also with a fairly linear regime as can be seen in fig. Sb [ 12,191. On the other hand it had been shown that there is a major difference in the compressibility of the two Raman pulses. This indicates that the assessment of the chirp only from such a graph is insufficient. A look at the set of spectrally windowed pulse profiles discloses further information. For the component generated by parallel SRS we observed an increase in pulse duration from 60 to 90 ps with growing frequency. Likewise the asymmetry of the pulses increased, altogether indicating the existence of a nonlinear chirp (see also ref. [ 121). Fig. 6a displays a typical intensity profile for this case. It exhibits a strong side lobe on its trailing edge owing to decreasing Raman conversion during the walk-off
(a)
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1
: 1100
0
50
100
0.0,
200
150
0
.
1
100
Time [psec] 11251
1
.
200
,
300
.
,
400
.
I
l.O-
a
(b)
0
7
1120
l
b)
-
0 0
f,
O.B-
A
0
1105-l 0
.
50
100
150
I 200
Time [psec] Fig. 5. Chirp of Raman pulses generated by SPRS on the slow axis for pump pulses launched into the fiber at 30 degrees to the fast axis (a) and chirp of Raman pulses generated by parallel SRS (b).
242
500
Time [psec]
0.0
0
loo
200 Time
300
400
I
500
[psec]
Fig. 6. Typical cross-correlation traces of spectrally windowed Raman pulses (window width is 0.1 nm) after 300 m fiber length. In (a) the pump was launched into one fiber axis only and in (b) at 30 degrees to the fast axis.
Volume 70, number
3
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process as observed in the same way for the unwindowed pulse. This side lobe is prominent throughout the high frequency side and extends over more than 200 ps. Because of the vanishing derivative of this side lobe only little SPM is acting on that part of the pulse. This means that for a major part of the pulse all frequencies are present at all times making the use of a linear device for compression impossible. In contrast the Raman component generated by SPRS shows a clear symmetry after the bandpass (see fig. 6b). This is observable for all windowed pulses in the same manner within the entire frequency range. The duration of these pulses was approximately constant and had a value of about 55 ps. These results indicate the existence of a linear chirp as expected by the action of enhanced SPM and XPM.
1 March
a@;*
kp 1
az
cOcnp
a@;*
kR 1
az
t0c nR
-=--
-=--
1989
4. Calculations
A first theoretical model for the operation of the FGRL considers the combined action of SPM, XPM and SRS on the fast and the slow axis, and first order dispersion. By following the procedure as outlined in ref. [ 6 ] we derived a set of 8 nonlinear differential equations coupled by the nonlinear electrical susceptibility xC3). The velocity of the pump pulse on the fast axis was assumed to be identical to the velocity of the Raman pulse on the slow axis. The reference system is transformed to move with the group velocity of these pulses, ?!&(+!-)!$
azpF* = az
T=
2
z;*,
(gRIz~*+gR,,z~*)
(gR,,z$*+gRIzp)
z;*
)
The symbols used in the equations have the following meaning: Z intensity, @ phase, g,,, parallel Raman gain coefftcient, gRI perpendicular Raman gain coefficient, n2,, parallel nonlinear refractive index, nzL perpendicular nonlinear refractive index, n linear refractive index, v group velocity, e. permittivity of free space, w frequency, k propagation constant, c vacuum velocity of light, and the super or subscripts denote the connection of the symbols with FA fast axis, SA slow axis, P pump pulse, R Raman pulse. The first set of equations describes the evolution of the intensity profiles along the optical fiber under the action of Raman scattering and the second set treats the evolution of the phases of the four pulses, thus accounting for the effects of SPM and XPM. The results of a numerical simulation based on the first set of equations with input values as chosen in the experiment, gR,,= 15 XgR, (see ref. [ 201 ) and gR,,= 1.0X lo-l3 m/W [21] are given in fig. 7. The pump pulse profiles are drawn as solid lines and the Raman pulse profiles as dashed lines. The Raman component on the fast axis appears out of proportion. Its intensity would be sufficient to generate the next Stokes pulse which has not been included into the theoretical model. The nonlinear coupling between velocity matched pulses over the entire fiber
~=(~-~)~+(gRIP*+gR,,z:*)z~*r and
243
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3
OPTICS
COMMUNICATIONS
1 March
1989
kW peak power. The technique of velocity matching, by using birefringence compensated dispersion, combined with nonlinear coupling offers an attractive and efficient alternative to fiber Raman oscillators [ 131 for the generation of frequency shifted ultrashort light pulses.
References Time
[ psec]
Fig. 7. Theoretical pulse profiles after 300 m fiber length and launching angle of 30 degrees to the fast axis. The pump pulses are represented by the solid traces and the Raman pulses by the dashed traces.
length amplifies the perpendicular Raman component at the cost of the pump pulse which suffers severe depletion in agreement with the experimental data (see fig. 4 ). The pulses at the fiber exit are completely determined by also calculating the phases. Therefore the second set of equations has to be integrated over the pulse duration and fiber length. The chirp is given by the time derivative of the phase function. While for shorter fiber lengths the applied model of pulse propagation can be assumed to give quite reliable results [ 4,6], in longer fibers, as they are used here, the influence of GVD becomes important and then leads to significant pulse shaping and chirping [ 71. For further improved calculations of the chirp the frequency dependency of the Raman gain has to be taken into account. Theoretical analyses with such an extended model will be the subject of another paper.
5. Conclusion We demonstrated the successful operation of an FGRL at a wavelength of 1.1 pm. Taking advantage of improved phase modulation in birefringent fibers output pulses of 0.8 ps duration and high average power of 0.4 W were obtained, corresponding to 5.5
244
[l .I. Auyeung and A. Yariv, IEEE J. Quantum
Electron. QE14 (1978) 347. 12 J.I. Gersten, R.R. Alfano and M. Belie, Phys. Rev. A 21 (1980) 1222. A.Ya. Karasik, P.G. Mamyshev, A.M. I3 I E.M. Dianov, Prokhorov and V.N. Serkin, Sov. Phys. JETP 62 (1985) 448. D. Schadt, B. Jaskorzynska and U. oesterberg, J. Opt. Sot. Am.B3(1986) 1257. D. Schadt and B. Jaskorzynska, J. Opt. Sot. Am. B 4 ( 1987) 856. M. Kuckartz, R. Schulz and H. Harde, Optical and Quantum Electron. 19 (1987) 237. M. Kuckartz, R. Schulz and H. Harde, J. Opt. Sot. Am. B 5 (1988). [ 81 D. Grischkowsky and A.C. Balant, Appl. Phys. Lett. 41 (1982) 1. [9] W.J. Tomlinson, R.H. Stolen and C.W. Shank, J. Opt. Sot. Am. B 1 (1984) 139. [ lo] R.H. Stolen, Chinlon Lin and R.K. Jain, Appl. Phys. Lett. 30 (1977) 340. ChinIon Lin, IEEE J. Lightwave Technol. LT-4 ( 1986) 1103. A.S.L. Gomes, V.L. da Silva and J.R. Taylor, J. Opt. Sot. Am. B 5 (1988) 373. J.D. Kafka, D.F. Head and T. Baer, Ultrafast Phenomena V, eds. G.R. Fleming and A.E. Siegman (Springer, Heidelberg 1986) p. 5 1. R.H. Stolen, M.A. Bosch and Chinlon Lin, Optics Lett. 6 (1918) 213. [15]J.D.KatkaandT.Baer,OpticsLett. 12 (1987) 181. [ 161 A.S. Gouveia-Neto, A.S.L. Gomes and J.R. Taylor, Electron. Lett. 23 (1987) 537. [ 17 ] M.N. Islam, L.F. Mollenauer, R.H. Stolen, J.R. Simpson and H.T. Shang, Optics Lett. 12 (1987) 814. [ 181 A.M. Johnson, R.H. Stolen and W.M. Simpson, Appl. Phys. Lett. 44 ( 1984) 729. [19 I A.M. Johnson, R.H. Stolen and W.M. Simpson, Ultrasfast Phenomena V, eds. G.R. Fleming and A.E. Siegman (Springer, Heidelberg, 1986 ) p. 160. 120 M.C. Tobin and T. Baak, J. Opt. Sot. Am. 58 (1968) 1459. [21 R.H. Stolen and E.P. Ippen, Appl. Phys. Lett. 22 (1973) 276.
1 March 1989
OPTICS COMMUNICATIONS
Volume 70, number 3
M. KUCKARTZ
SUBPICOSECOND
PULSES
and H. HARDE
Vniversitiit der Bundeswehr Hamburg, Fachbereich Elektrotechnik, Holstenhojiveg 85, 2000 Hamburg 70, Fed. Rep. Germany
Received 11 July 1988
Successful operation of a fiber grating Raman laser delivering pulses of 0.8 ps duration at a wavelength of 1.1 Km is presented. The pulses are generated with a novel method taking advantage of stimulated perpendicular Raman scattering in conjunction with dispersion compensation in a birefringent fiber.
1. Introduction When powerful light pulses are launched into an optical fiber two nonlinear effects, self-phase modulation (SPM) and stimulated Raman scattering (SRS), have a dominant influence on their propagation [l-7]. SPM, in conjunction with group velocity dispersion (GVD), is commonly used to create a linear chirp in order to prepare pulses for compression by means of a grating pair [ 8,9]. SRS made possible the development of new, frequency shifted light sources [ 10,111. The associated broad Raman gain profile should offer the opportunity to generate ultrashort pulses. With the method of spectral windowing pulses of 46 ps were generated [ 121 and a dispersion shifted fiber Raman oscillator was shown to be capable of producing subpicosecond pulses but only at a relatively low average power of 20 mW [13]. In this paper we report a novel method for generating ultrashort Stokes pulses with a fiber grating Raman laser (FGRL). Essential for its feasability is the velocity matching of pump and first Raman Stokes wavelength on the two axes of a birefringent fiber. Such a fiber design supports an enhanced action of SRS and cross-phase modulation (XPM) of the Raman pulses travelling on the slow axis with the fundamental pulses propagating on the fast axis. These effects together with SPM and GVD produce a linear chirp of the Raman pulses. Hence the use of a grating pair as dispersive delay becomes possible. A similar technique of birefringent compensated 0 030-4018/89/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
dispersion was used for efficient phase-matched fourwave mixing in fibers [ 14 1. Another method for enhancing the interaction length is applied in fiber Raman soliton lasers [ 15 17 ] working around the minimum dispersion wavelength. Our system is shown to be capable of producing subpicosecond Stokes pulses at a wavelength of 1.1 pm with an average output power of 0.4 W. The experimental results are supported by a theoretical model.
2. Experimental set-up Fig. 1 shows a schematic of the FGRL together with the diagnostics. A cw actively mode-locked Nd:YAG laser emitting pulses of 70 ps duration at a rate of 84 MHz and a wavelength of 1064 nm is used as pump source. The.pulses are coupled into a 300 m polarization preserving fiber serving as the active me; dium. The core diameter of the fiber has a value of about 3.5 pm. The dispersion between pump pulse and first Raman component results in a walk-off value of 2.1 ps/m which is approximately identical to the value of the birefringence of the fiber for these wavelengths (6n= 7 x 10p4). After the fiber the Stokes light is collimated and directed through a grating pair ( 1700 lines/mm) in double pass configuration [ 181 serving as compressor as well as wavelength selector. The mirror M2 after the grating pair is slightly tilted so that the reflected beam is below the plane of fig. 1 to allow separation from the B.V.
239
Volume 70, number 3
1 March 1989
OPTICS COMMUNICATIONS
3. Results and discussion
DELAY
UNE
Fig. 1. Experimental scheme showing the FGRL with its diagnostics. Symbol key: PM photo multiplier, P prism, BS beam splitter, M mirror, SHG crystal for second harmonic generation.
incoming beam. Mirror M 1 deflects the beam out of the system. The FGRL output pulses are measured with standard background free autocorrelation techniques. The beam splitter 1 (BS 1) is removed from the set-up for these measurements. The intensity profiles of the pulses emerging from the fiber exit are determined by separating a portion of the power before the grating pair (BSl inserted and BS2 removed) and applying cross-correlation techniques. For this procedure the monochromator is by-passed. As test pulses the output of the FGRL or compressed pump pulses are used and controlled to have a duration of less than 2 ps. In order to measure the chirp, which the Stokes pulses receive in the fiber, the light beam is dispersed by the grating of a 1 m monochromator ( 1200 lines/ mm) and scanned across the exit slit adjusted to 0.1 mm width. This device acts as a bandpass of 0.1 nm transmission. The prism P allows the monochromator to operate in double-pass configuration and therefore ensures to compensate the spatial spreading across the beam profile caused by the grating. It is slightly tilted for the same reason that the mirror M2 is. The intensity profiles of these spectrally windowed pulses are measured by applying cross-correlation techniques as described above. The chirp is determined by measuring 16 windowed beam protiles while subsequently advancing the monochromator wavelength setting by 1 nm. 240
The conventional approach to design an FGRL would have been to launch the laser pulses into the fiber in such a way that the polarization is parallel to one of the principal fiber axis and that the input power is well above the threshold for SRS. Under these conditions the first Raman Stokes component appears at an average power of about 0.4 W. Between 0.7 W and 2 W we performed various measurements but no significant compression could be achieved. For example the resulting poor quality of the compressed pulses can be seen from the autocorrelation trace shown in fig. 2 which was taken at a power of 1.5 W resulting in a reduced width of 40 ps (assuming gaussian shape). Obviously the quality of the chirp fails to allow an efficient compression. A remarkable change of the situation occurs when introducing some small but far reaching modifications to the experimental set-up. The key element is the birefringent optical fiber which must be designed in such a way that the walk-off between the pump pulse, travelling on the fast axis, and the Raman component travelling on the slow axis is compensated. This fiber design offers the opportunity to enhance the effects of pulse interaction in an advantageous way. At first it becomes possible to generate the pulses utilized in the FGRL by stimulated perpendicular Raman scattering (SPRS). Here the Stokes light travelling on the slow axis is amplified by the pump I
I
I
I
1 .o0.80.60.40.20.0 -200
0
-100 Time
100
200
[psec]
Fig. 2. Autocorrelation trace of insufftcient FGRL output for pump pulses launched into one tiber axis only.
Volume 70, number 3
1 March 1989
OPTICS COMMUNICATIONS
pulse on the fast axis. Although the gain efficiency is more than one order of magnitude smaller compared to parallel SRS this disadvantage is easily compensated by the increased interaction length. To stimulate this process Raman photons may be ‘seeded’ on the slow axis by parallel SRS. Therefore input power is split between the two fiber axes. In addition the process of XPM may now be active between pump and Raman pulse throughout the entire fiber length, rather than only for the walk-off length as observed for the case of parallel Raman conversion [ 4,6 1. Together with GVD an improved linearity of the chirp is expected with increasing fiber length. For an experimental realization the polarization of the laser beam is rotated by 30 degrees to the fast axis. This way 25% of the power is launched for ‘seeding’ on the slow axis and 75% on the fast axis. The Raman output of the slow axis is directed through the grating pair. With this configuration the FGRL is capable of producing pulses with low substructure in the subpicosecond regime. The Raman component on the slow axis appears at an average input power of 0.7 W coupled into the fiber and is fully saturated at P= 1.4 W. For input powers up to 2.5 W, on the slow axis no conversion into higher Stokes components was found. Only higher Raman components on the fast axis could be observed. This prevents the Stokes light, that is used in the FGRL, from suffering depletion on its leading edge, which is the case for conventional Stokes generation [ 6 1. The further investigations were performed for an input power of 2 W. The power splitting therefore leaves an initial power of 0.5 W for the slow axis of wmch 0.1 W will be converted by parallel SRS for ‘seeding’. Fig. 3 shows a typical autocorrelation trace of the output of the FGRL for these conditions. Assuming gaussian shape the width is determined to be 0.8 ps with an average power of 0.4 W. The difference between the initial Raman power, generated by SRS on the slow axis, and the output power of the FGRL can clearly be attributed to the process of SPRS. In order to analyse the operation of the FGRL we performed measurements of the intensity profile and the chirp of the pulses emerging from the fiber exit. Fig. 4 shows the cross-correlation traces of the pump pulse (a) and the Raman pulse (b). The mono-
‘L-7-l 0
-I”
-L”
20
10
Time [ psec] Fig. 3. Autocorrelation trace of FGRL output for pump pulses launched into fiber at 30 degrees to the fast axis. 1
.o(4
.yl
0.s
s
0.6-
100
200
300
400
Time [psec]
b) _ 5
0.6-
s 0.6>r .; 5
0.4-
E 0.20.0
0
100
200
300
400
Time [ psec]
Fig. 4. Cross-correlation trace of pump pulse (a) guided by the fast axis and Raman pulse (b) guided by the slow axis after 300 m fiber length.
chromator was by-passed and the beam splitter BS2 was removed from the set-up for these measurements (see fig. 1). It is found that both pulses leave 241
Volume 70, number 3
the fiber at the same time as the result of birefringence compensated dispersion. The depletion of the pump pulse in its central region clearly reveals the effect of SPRS. A major part of it has been converted into Stokes light on the slow axis. While Stokes pulses generated by parallel SRS exhibit a strong trailing, a Raman pulse more concentrated in time and without trailing is created by the process of SPRS. This pulse is likely to experience SPM over its total profile in a well-defined way. Together with XPM the resulting chirp will be formed. The result of the chirp measurement is demonstrated in fig. 5a. It was derived by evaluating the temporal peak positions of spectrally windowed pulses and then relating the time shifts of subsequent cross-correlation measurements to the selected wavelengths. The graph shows an approximate linearity extending over major parts of the pulse length.
7
The measured chirp of pulses originating from parallel SRS, however, gives a quite similar result also with a fairly linear regime as can be seen in fig. Sb [ 12,191. On the other hand it had been shown that there is a major difference in the compressibility of the two Raman pulses. This indicates that the assessment of the chirp only from such a graph is insufficient. A look at the set of spectrally windowed pulse profiles discloses further information. For the component generated by parallel SRS we observed an increase in pulse duration from 60 to 90 ps with growing frequency. Likewise the asymmetry of the pulses increased, altogether indicating the existence of a nonlinear chirp (see also ref. [ 121). Fig. 6a displays a typical intensity profile for this case. It exhibits a strong side lobe on its trailing edge owing to decreasing Raman conversion during the walk-off
(a)
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1
: 1100
0
50
100
0.0,
200
150
0
.
1
100
Time [psec] 11251
1
.
200
,
300
.
,
400
.
I
l.O-
a
(b)
0
7
1120
l
b)
-
0 0
f,
O.B-
A
0
1105-l 0
.
50
100
150
I 200
Time [psec] Fig. 5. Chirp of Raman pulses generated by SPRS on the slow axis for pump pulses launched into the fiber at 30 degrees to the fast axis (a) and chirp of Raman pulses generated by parallel SRS (b).
242
500
Time [psec]
0.0
0
loo
200 Time
300
400
I
500
[psec]
Fig. 6. Typical cross-correlation traces of spectrally windowed Raman pulses (window width is 0.1 nm) after 300 m fiber length. In (a) the pump was launched into one fiber axis only and in (b) at 30 degrees to the fast axis.
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process as observed in the same way for the unwindowed pulse. This side lobe is prominent throughout the high frequency side and extends over more than 200 ps. Because of the vanishing derivative of this side lobe only little SPM is acting on that part of the pulse. This means that for a major part of the pulse all frequencies are present at all times making the use of a linear device for compression impossible. In contrast the Raman component generated by SPRS shows a clear symmetry after the bandpass (see fig. 6b). This is observable for all windowed pulses in the same manner within the entire frequency range. The duration of these pulses was approximately constant and had a value of about 55 ps. These results indicate the existence of a linear chirp as expected by the action of enhanced SPM and XPM.
1 March
a@;*
kp 1
az
cOcnp
a@;*
kR 1
az
t0c nR
-=--
-=--
1989
4. Calculations
A first theoretical model for the operation of the FGRL considers the combined action of SPM, XPM and SRS on the fast and the slow axis, and first order dispersion. By following the procedure as outlined in ref. [ 6 ] we derived a set of 8 nonlinear differential equations coupled by the nonlinear electrical susceptibility xC3). The velocity of the pump pulse on the fast axis was assumed to be identical to the velocity of the Raman pulse on the slow axis. The reference system is transformed to move with the group velocity of these pulses, ?!&(+!-)!$
azpF* = az
T=
2
z;*,
(gRIz~*+gR,,z~*)
(gR,,z$*+gRIzp)
z;*
)
The symbols used in the equations have the following meaning: Z intensity, @ phase, g,,, parallel Raman gain coefftcient, gRI perpendicular Raman gain coefficient, n2,, parallel nonlinear refractive index, nzL perpendicular nonlinear refractive index, n linear refractive index, v group velocity, e. permittivity of free space, w frequency, k propagation constant, c vacuum velocity of light, and the super or subscripts denote the connection of the symbols with FA fast axis, SA slow axis, P pump pulse, R Raman pulse. The first set of equations describes the evolution of the intensity profiles along the optical fiber under the action of Raman scattering and the second set treats the evolution of the phases of the four pulses, thus accounting for the effects of SPM and XPM. The results of a numerical simulation based on the first set of equations with input values as chosen in the experiment, gR,,= 15 XgR, (see ref. [ 201 ) and gR,,= 1.0X lo-l3 m/W [21] are given in fig. 7. The pump pulse profiles are drawn as solid lines and the Raman pulse profiles as dashed lines. The Raman component on the fast axis appears out of proportion. Its intensity would be sufficient to generate the next Stokes pulse which has not been included into the theoretical model. The nonlinear coupling between velocity matched pulses over the entire fiber
~=(~-~)~+(gRIP*+gR,,z:*)z~*r and
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Volume 70, number
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OPTICS
COMMUNICATIONS
1 March
1989
kW peak power. The technique of velocity matching, by using birefringence compensated dispersion, combined with nonlinear coupling offers an attractive and efficient alternative to fiber Raman oscillators [ 131 for the generation of frequency shifted ultrashort light pulses.
References Time
[ psec]
Fig. 7. Theoretical pulse profiles after 300 m fiber length and launching angle of 30 degrees to the fast axis. The pump pulses are represented by the solid traces and the Raman pulses by the dashed traces.
length amplifies the perpendicular Raman component at the cost of the pump pulse which suffers severe depletion in agreement with the experimental data (see fig. 4 ). The pulses at the fiber exit are completely determined by also calculating the phases. Therefore the second set of equations has to be integrated over the pulse duration and fiber length. The chirp is given by the time derivative of the phase function. While for shorter fiber lengths the applied model of pulse propagation can be assumed to give quite reliable results [ 4,6], in longer fibers, as they are used here, the influence of GVD becomes important and then leads to significant pulse shaping and chirping [ 71. For further improved calculations of the chirp the frequency dependency of the Raman gain has to be taken into account. Theoretical analyses with such an extended model will be the subject of another paper.
5. Conclusion We demonstrated the successful operation of an FGRL at a wavelength of 1.1 pm. Taking advantage of improved phase modulation in birefringent fibers output pulses of 0.8 ps duration and high average power of 0.4 W were obtained, corresponding to 5.5
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[l .I. Auyeung and A. Yariv, IEEE J. Quantum
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