- Email: [email protected]
Second harmonic generation in optical fibers. Experimental study of the self-organised holographic grating length
Optics Communications 101 (1993) 391-396 North-Holland
OPTICS COMMUNICATIONS
Second harmonic generation in optical fibers. Experimental study of the self-organised holographic grating length G. D e m o u c h y 1 Laboratoire d'Optique Appliqude, Ecole Polytechnique-EcoleNationale Supdrieure des TechniquesAdvancdes, Chemin de la Hunibre, 91120 Palaiseau, France
Received 1 April 1993
We report experimental results concerningself-organisedholographicgrating length for second harmonicgeneration in optical fiber. By a cut-backmethod of the fiber and a comparisonbetween different laser regimeswe point out the limiting factorsto its extension. The gratinglength is found to be independent of the pulse duration. We have established experimental evidenceof the limitation of the grating length by self- and cross-phase modulations effects, spectral width of the pulses and central frequency fluctuation of the laser. With a stable Nd:YAG injected laser delivering transform-limited pulses we obtain for the first time to our knowledge,holographicgratinglengths above 60 cm.
1. Introduction
The discovery by Osterberg and Margulis [ 1 ] of the possibility of frequency doubling in germanosilicate optical fibers has received much attention and is currently the subject of many experimental and theoretical studies. Osterberg and Margulis have found that an optical fiber can generate green 532 nm second harmonic light after having been pumped by fundamental 1064 nm radiation during a preparation time of several hours. Second harmonic generation in optical fibers is not predicted by theory because of the symmetry of inversion of silica and is of considerable interest for practical applications due to the low cost of fibers relatively to frequency doubling crystals. In that view, the use of a fiber in a second harmonic generation (SHG) pulse autocorrelator [2 ] and as a frequency doubler for the synchronous pumping of a dye laser have been recently demonstrated [ 3 ]. Many attempt have been made to explain the anomalous second order process. It has been admitted that the inversion symmetry of the glass was broPresent address: Laboratoire d'Acoustique et Optique de la Matirre Condensre, Tour 13, Boite 86, 4 place Jussieu, 75252 Paris cedex05, France.
ken by photoinduced defects, but the origin of the reported efficiency conversion remained unexplained for some time. Stolen and Tom [4] have shown that the preparation time can be reduced from several hours to a few minutes if some externally second harmonic "seed" radiation is injected in the fiber along with fundamental pump light. The efficiency of this socalled seeding process has been interpreted as follows: if two harmonically related fields mixrin a thirdorder nonlinear medium, a static electric field is created by a third-order nonlinear process (~(3)(0, co, co, - 2 c o ) ); this field has the required periodicity for phase matching and has been believed for some time to be responsible for the orientation of the photoinduced defects and the creation of a holographic grating at the required phase matching periodicity [ 5 ]. Further studies have shown that this electrical field was of the order of a few V/m, what is insufficient to orient the defects. Experimental evidence has supported the view of a strong transverse photoinduced dc electric field that can be explained by the interference of the two harmonically related optical fields. These fields can give rise to ionizing transitions that have a phase-dependent electron direction of ejection. This idea is the basis of the model postulated by Baranova and
0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
391
Volume 101,number 5,6
OPTICS COMMUNICATIONS
Zel'dovich [6-9] and Anderson et al. [10], where interference effects between four-, three-, and twophotons ionization in the 5 eV conduction band are supposed to build-up the holographic grating by a phase dependent electron ejection direction that has the periodicity required to ensure phase matching. It is interesting to note that this model accounts for the limitation of the SHG efficiency and the limitation of the grating length. How long is the holographic grating responsible for SHG? What are the limiting factors to its extension? In this article, we point out experimentally the limiting parameters of interest. After a brief review of the physical phenomena, we present an experimental study based on the grating length measurement by a cut-back of the fiber for various (and hence decreasing) lengths and measuring the corresponding SHG.
2. Theory
Group velocity dispersion Group velocity dispersion (GDV) in optical fiber is of the order of 80 ps/m for pulses at 1064 nm and 532 nm. This effect is responsible for the limitation of the interaction length between the two pulses during the seeding process. For 100 ps pulses, the interaction length is theoretically limited to 125 cm.
Second harmonic radiation Second harmonic radiation itself is a limiting factor. Anderson et al. [ 10 ] have shown that SHG evolution during propagation is given by O---7 =Go
Pump pulse spectral width The short pulses delivered by a mode-locked laser have a nonzero spectral extend and each pulse spectral component gives rise to its own elementary holographic grating with its own periodicity. For some so-called maximum coherence length, the total resuiting grating is blurred and the SHG saturates. The coherence length is given by [ 11 ] Z e _-
2 (a-b)Aco'
with a=ldk(to)/dtol~o,
1-I2`o/I.t l+fllz`o/i.t+(i2,o/i.t)212`o,
(1)
with
Ato is the pump pulse spectral width, a = 1.462/c and b = 1.485/c. Assuming Fourier transform-limited gaussian pulses of 100 ps full-width-at-half-maximum, the coherence length is equal to
Third-order nonlinear effects Glass optical fibers are Kerr-like media. For sufficiently high pulse peak power, self-phase (SPM) and cross-phase modulation (XPM) induce a broadening of the pump and probe pulses spectra, respectively [ 12 ]. Assuming Fourier transform-limited gaussian pulses of Ah = 100 ps duration at 21= 1064 nm and At2= 70 ps at 22= 532 nm, at the fiber input the initial spectral widths are AATF- 22 0.44 =0.017 nm c Atl AA~r_ 22 0.4___4=0.0059 n m . c At2 After a distance L of propagation in the fiber the spectral width are given by
--[
A Z t ( L ) = 0.442~
Co=
en2o,c \/¢4/~
cat1
] "t'r
1
\
I J
'
"
As the second harmonic intensity 12,ogrows along the fiber, the numerator of eq. ( 1 ) vanishes and the SHG saturates.
392
b=ldk(og)/dtol2~o,
Lc = 94.5 c m .
The relevant phenomena for the limitation to the holographic grating amplitude along the fiber are:
012,o
1 September1993
A22(L)= 0.4422
[l+(4rcn[IiL'~2T/2 k
/_1
'
with L the propagation length, n~ the nonlinear refractive index for SPM, n~ the nonlinear refractive
Volume 101, number 5,6
OPTICS COMMUNICATIONS
index for XPM and I, the input ir peak power. In this equation we have neglected the effect of the green beam which is too weak to induce such a thirdorder nonlinear effect. The spectral width A21 of the ir pulse is broadened by SPM and the spectral width A22 of the green seed pulse by XPM. In the Q-switched mode-locked regime the ir peak power in the fiber is in the order of 11 = 5 × 101° W / cm 2, for a propagation length of 1 m, and by taking n ~ = n [ = 4.19 × 10 - ~6 cm2/W, we obtain the ir and green spectral width of the order of 4.2 nm and 3 nm, a factor of 250 and 500 superior to the initial Fourier transform-limited case. In mode-locked regime the ir peak power in the fiber is much smaller (in the order of 1.5× 10 9 W / cm2); in this regime SPM and XPM can be neglected. We will show experimentally that in the Q-switched mode-locked regime the interplay of these two thirdorder nonlinear effects with GVD induces a blurring of the holographic grating. The physics of these phenomena is by now well understood, but in our case their numerical analysis is not straightforward because the pulses have not the same peak intensity in the pulse train.
Phase fluctuations between the pump and harmonic seed light In the model of Anderson et al. the relative phase difference between the 1064 nm pump field and the 532 nm seed field is of crucial importance for the di-
1 September 1993
rection of the electrical charge migration. Random phase fluctuations between these two field would induce different holographic gratings with different relative phase. This phenomena would induce a blurring of the holographic grating and limit the grating length and the SHG efficiency. This result has been experimentally observed by Krol and co-workers [13].
Laser frequency emission fluctuations As the grating period depends on the laser frequency, a drift of the laser central frequency emission during the seeding process would induce some other grating with different period. It would be another limiting factor to the grating length.
3. Experiments
The experimental set-up is represented on fig. 1. The Nd: YAG laser is able to operate in mode-locked, Q-switched, and Q-switched mode-locked regime. The beam passes through a polarizing prism and is focused with a 10 X microscope objective at the fiber input. A KDP crystal placed at the laser output was used to generate a small amount of green seed light that was focused together with the pump. At the fiber end, a 10 × microscope objective collimates the green and infrared beams that are separated by a dichroic mirror and directed on a two-channel optical
Nd:YAG Laser
/
I RG695 fdter
Photodiode
Glan prism
!~339 filter
Optkai fiber
lox Microsoope objective
Dichrffic mirror Rmax 532am Tmax 1064nm
Fig. 1. Experimental set-up: the pulses of an Nd: YAG laser are injected in an optical fiber with a small amount of second harmonic seed
light during the preparation time. After the preparation time SHG is measured by launching in the fiber ir light 0nly. At the output, a dichro'/cmirror separates the fundamental and second harmonic radiation. The effectivegratinglength is measuredby makingsuccessive cuts of the prepared fiber end. 393
Volume 101, number 5,6
OPTICS COMMUNICATIONS
power meter. For SHG intensity measurements, an infrared RG695 filter was placed on the laser output beam. A green BG39 filter placed on the beam refleeted by the dichroic mirror was used to remove residual fundamental light along the second harmonic direction. During the fiber preparation, green and infrared lights were used together, while infrared was used alone for SHG measurements. To measure the effective grating length we chose to make successive cuts of the fiber end, and to record the corresponding SHG. This method gives a plot of the SHG as a function of the fiber length; the grating length is given by the length where a growth of SH is observed. Batdorf and co-workers [ 14 ] have shown that the grating length decreases with the seed green ratio g= 12,o/lo,. This observation is in agreement with the model of Anderson et al. In order to compare our results, a constant proportion of seed light ( g = I2o,/Io, = 0.15 × 10- a) was used in the experiments presented in this article. We used germanosilicate fibers that were drawn to be monomode for 1064 nm; the cutoff wavelength was 0.8 I~m, the core diameter was of the order of 5 I~m and the step index ws 5.4× 10 -a. The concentration in germanium of the fiber core was 5%. In a first set of experiments we used our laser in the Q-switched mode-locked regime, delivering trains of 40 pulses of 100 ps duration separated by 10 ns at the repetition rate of 1 kHz and a peak power of 9.5 kW. We have plotted on fig. 2 the ratio l(2oJ)/I2(to) as a function of fiber length. This ratio is proportional to the square of the effective second order nonlinear susceptibility (X~t~)2= (fo~Xt2~ (z) dz) 2. For this mode of operation, our measurements show that the effective length of the grating is of the order of 9 cm. We have show that in this regime, for a propagation length of 1 m, the ir spectral width and the green spectral width are increased by a factor of 250 and 500, respectively. The short grating length can be attributed to the spectral broadening of the p u m p pulses by self-phase and cross-phase modulation effects. Another increase in the blurring of the holographic grating is caused by the fact that the laser pulses have not the same peak intensity in the pulse train (the spectral broadening is not the same for each pulses). 394
1 September 1993
I(2w)/P(w)
2.~E-06 2E-06 1,5E-06 IE-06 5E-07
# #
0
10
20
30
40
50
60
Length (cm) Fig. 2. 12o,/12 or reduced SHG as a function of the fiber length for the laser operating in mode-lockedQ-switchedregime.
I(2w)/F(w)
1,6E-06 1,4E-06 1,2E-06
1E.06 8E.07 6E-07
/ //
4E.07 2E.07 j" ; .....
~.........
10
r .........
20
I .........
30
i .........
40
I ......
50
60
Length (era) Fig. 3. 12~,/12 or reduced SHG as a function of the fiber length for the laser operating in mode-lockedregime. In a second set of experiments, our laser was operated in the mode-locked regime, delivering pulses of 100 ps, 300 W of peak power at the repetition rate of 76 MHz. Such peak power enables us to neglect self- and cross-phase modulation effects. As shown by fig. 3, the grating length is found to be of the order of 18 cm, a factor of two superior to the Q-switched mode-locked case. This demonstrates the limitation of the grating length caused by nonlinear phase modulation effects.
Volume 101, number 5,6
OPTICS COMMUNICATIONS
We have shown that for 100 ps p u m p pulses, the interaction length due to G V D is of 125 cm and the coherence length of 94 cm for Fourier transformlimited gaussian pulses. Despite the fact that these measured grating lengths are much lower than the theoretical, one cannot definitely rule out the pump pulse spectral width because in mode-locked regime the pulses are not necessary Fourier transform-limited gaussian pulses. We have made a set of experiments using the laser in the Q-switched mode. The p u m p pulses were of 600 ns duration and of 90 W peak power. In this case the self- and cross-phase modulation effects and GVD effects are negligible for the fiber lengths we used (typically 1 m ) . The results on fig. 4 show a grating length of 18 cm for this regime, what is very similar to the results obtained in the mode-locked regime. The theoretical coherence length for transform-limited pulses of 600 ns duration is 5.7 km. This suggest that this large discrepancy may be caused by nontransform-limited pulses, a n d / o r by low frequency variations of the central frequency of the laser. To reduce these detrimental effects, we have used a frequency stabilised injected laser delivering 1064 nm, 6 ns pulses at the repetition rate of 1 kHz. For these quasi transform-limited pulses Av At~ 0.44, the injected peak power was of the order of 400 W and the g ratio was kept constant. The results obtained with this laser are on fig. 5 where it is clearly shown that the measured holo-
I(2w)/l=(w) 5E-06
t
tt .......
.............t ..................
.~"
1E-06
I(~)/I=(w) 5E-06 4E-06
./"""i.....
3E-06
/~/
2E-06 1E-06 00=..... i0
.,." ............
20
30
40
50
"60
Length (cm) Fig. 5. l~/I 2 or reduced SHG as a function of the fiber length for a frequencystabilised injected laser operating in Q-switched regime. graphic grating length is of 60 cm. This represents a substantial improvement compared to the mode locked-regime that can be attributed to the greater central frequency stability and the better spectral purity of the injected pump pulses. Note that we could not reach the saturation of SHG during the preparation process owing to the relatively low repetition rate of our laser and to long-term mechanical unstability of our set-up. We estimate that better results could be obtained by an improvement of the experimental conditions.
4. Conclusion
4E-06
2E-06
1 September 1993
.i =
Oo, ..... i'6 ...... 20 ...... gO ...... 40 ...... gO ....... 60 L e n g t h (era)
Fig. 4. 12o,/12 or reduced SHG as a function of the fiber length for the laser operating in Q-switchedregime.
We have experimentally demonstrated that the selforganized holographic grating is not significantly affected by the pump pulses duration. We have established experimental evidence of the limitation of the grating length by self- and cross-phase modulations effects by a comparison between Q-switched modelocked and mode-locked pump pulses. To reduce the spectral width of the pump pulses, the central frequency fluctuations of the laser and the subsequent limitations for holographic grating length, we have used a stable N d : Y A G injected laser delivering transform-limited pulses. This allowed us to obtain, with same other experimental conditions, and 395
Volume 101, number 5,6
OPTICS COMMUNICATIONS
for the first time to our knowledge, holographic grating lengths above 60 cm.
References [ 1 ] U. Osterberg and W. Margulis, Optics Lett. 11 (1986) 516. [2] U. Osterberg and W. Margulis, IEEE J. Quantum Electron. 24 (1988) 2127. [3 ] N.M. Lawandy, J.P. Bernardin, G. Demouchy and R.L. Mc Donald, Electron. Lett. 27 ( 1991 ) 1264. [4] R.H. Stolen and H.W.K. Tom, Optics Lett. 12 (1987) 585. [5] A. Kamal, D.A. Weinberger and W.H. Weber, Optics Lett. 15 (1990) 613. [ 6 ] B.Ya. Zel'dovich, Yu.E. Kapitskii and V.M. Churikov, JETP Lett. 53 (1991) 78.
396
1 September 1993
[7]Yu.E. Kapitzloy and B.Ya. Zcl'dovich, Optics Lctt. 15 (1990) 1236. [ 8 ] N.B. Baranova, A.N. C"hudinovand B.Ya. Zcl'dovich, Optics Comm. 79 (1990) 116. [ 9 ] B.Ya. Zcl'dovich and A.N. Chudinov, JErP Lctt. 50 (1989) 439. [ 10] D.Z. Anderson, V. Mizrahi and .I.E. Sipe, Optics Lett. 16 (1991) 796. [ 11 ] H.W.K. Tom, R.H. Stolen, G.D. Aumiller and W. Pleibel, Optics Lett. 13 (1988) 512. [ 12] F. Ouellette, Optics Lett. 14 (1989) 964. [ 13 ] D.M. Krol, M.M. Broer, K.T. Nelson, R.H. Stolen, H.W.K. Tom and W. Pleibel, Optics Lett. 16 ( 1991 ) 211. [ 14] B. Batdorf, C. Krautschik, U. Osterberg and G. Stegeman, Optics Comm. 73 (1989) 393.
OPTICS COMMUNICATIONS
Second harmonic generation in optical fibers. Experimental study of the self-organised holographic grating length G. D e m o u c h y 1 Laboratoire d'Optique Appliqude, Ecole Polytechnique-EcoleNationale Supdrieure des TechniquesAdvancdes, Chemin de la Hunibre, 91120 Palaiseau, France
Received 1 April 1993
We report experimental results concerningself-organisedholographicgrating length for second harmonicgeneration in optical fiber. By a cut-backmethod of the fiber and a comparisonbetween different laser regimeswe point out the limiting factorsto its extension. The gratinglength is found to be independent of the pulse duration. We have established experimental evidenceof the limitation of the grating length by self- and cross-phase modulations effects, spectral width of the pulses and central frequency fluctuation of the laser. With a stable Nd:YAG injected laser delivering transform-limited pulses we obtain for the first time to our knowledge,holographicgratinglengths above 60 cm.
1. Introduction
The discovery by Osterberg and Margulis [ 1 ] of the possibility of frequency doubling in germanosilicate optical fibers has received much attention and is currently the subject of many experimental and theoretical studies. Osterberg and Margulis have found that an optical fiber can generate green 532 nm second harmonic light after having been pumped by fundamental 1064 nm radiation during a preparation time of several hours. Second harmonic generation in optical fibers is not predicted by theory because of the symmetry of inversion of silica and is of considerable interest for practical applications due to the low cost of fibers relatively to frequency doubling crystals. In that view, the use of a fiber in a second harmonic generation (SHG) pulse autocorrelator [2 ] and as a frequency doubler for the synchronous pumping of a dye laser have been recently demonstrated [ 3 ]. Many attempt have been made to explain the anomalous second order process. It has been admitted that the inversion symmetry of the glass was broPresent address: Laboratoire d'Acoustique et Optique de la Matirre Condensre, Tour 13, Boite 86, 4 place Jussieu, 75252 Paris cedex05, France.
ken by photoinduced defects, but the origin of the reported efficiency conversion remained unexplained for some time. Stolen and Tom [4] have shown that the preparation time can be reduced from several hours to a few minutes if some externally second harmonic "seed" radiation is injected in the fiber along with fundamental pump light. The efficiency of this socalled seeding process has been interpreted as follows: if two harmonically related fields mixrin a thirdorder nonlinear medium, a static electric field is created by a third-order nonlinear process (~(3)(0, co, co, - 2 c o ) ); this field has the required periodicity for phase matching and has been believed for some time to be responsible for the orientation of the photoinduced defects and the creation of a holographic grating at the required phase matching periodicity [ 5 ]. Further studies have shown that this electrical field was of the order of a few V/m, what is insufficient to orient the defects. Experimental evidence has supported the view of a strong transverse photoinduced dc electric field that can be explained by the interference of the two harmonically related optical fields. These fields can give rise to ionizing transitions that have a phase-dependent electron direction of ejection. This idea is the basis of the model postulated by Baranova and
0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
391
Volume 101,number 5,6
OPTICS COMMUNICATIONS
Zel'dovich [6-9] and Anderson et al. [10], where interference effects between four-, three-, and twophotons ionization in the 5 eV conduction band are supposed to build-up the holographic grating by a phase dependent electron ejection direction that has the periodicity required to ensure phase matching. It is interesting to note that this model accounts for the limitation of the SHG efficiency and the limitation of the grating length. How long is the holographic grating responsible for SHG? What are the limiting factors to its extension? In this article, we point out experimentally the limiting parameters of interest. After a brief review of the physical phenomena, we present an experimental study based on the grating length measurement by a cut-back of the fiber for various (and hence decreasing) lengths and measuring the corresponding SHG.
2. Theory
Group velocity dispersion Group velocity dispersion (GDV) in optical fiber is of the order of 80 ps/m for pulses at 1064 nm and 532 nm. This effect is responsible for the limitation of the interaction length between the two pulses during the seeding process. For 100 ps pulses, the interaction length is theoretically limited to 125 cm.
Second harmonic radiation Second harmonic radiation itself is a limiting factor. Anderson et al. [ 10 ] have shown that SHG evolution during propagation is given by O---7 =Go
Pump pulse spectral width The short pulses delivered by a mode-locked laser have a nonzero spectral extend and each pulse spectral component gives rise to its own elementary holographic grating with its own periodicity. For some so-called maximum coherence length, the total resuiting grating is blurred and the SHG saturates. The coherence length is given by [ 11 ] Z e _-
2 (a-b)Aco'
with a=ldk(to)/dtol~o,
1-I2`o/I.t l+fllz`o/i.t+(i2,o/i.t)212`o,
(1)
with
Ato is the pump pulse spectral width, a = 1.462/c and b = 1.485/c. Assuming Fourier transform-limited gaussian pulses of 100 ps full-width-at-half-maximum, the coherence length is equal to
Third-order nonlinear effects Glass optical fibers are Kerr-like media. For sufficiently high pulse peak power, self-phase (SPM) and cross-phase modulation (XPM) induce a broadening of the pump and probe pulses spectra, respectively [ 12 ]. Assuming Fourier transform-limited gaussian pulses of Ah = 100 ps duration at 21= 1064 nm and At2= 70 ps at 22= 532 nm, at the fiber input the initial spectral widths are AATF- 22 0.44 =0.017 nm c Atl AA~r_ 22 0.4___4=0.0059 n m . c At2 After a distance L of propagation in the fiber the spectral width are given by
--[
A Z t ( L ) = 0.442~
Co=
en2o,c \/¢4/~
cat1
] "t'r
1
\
I J
'
"
As the second harmonic intensity 12,ogrows along the fiber, the numerator of eq. ( 1 ) vanishes and the SHG saturates.
392
b=ldk(og)/dtol2~o,
Lc = 94.5 c m .
The relevant phenomena for the limitation to the holographic grating amplitude along the fiber are:
012,o
1 September1993
A22(L)= 0.4422
[l+(4rcn[IiL'~2T/2 k
/_1
'
with L the propagation length, n~ the nonlinear refractive index for SPM, n~ the nonlinear refractive
Volume 101, number 5,6
OPTICS COMMUNICATIONS
index for XPM and I, the input ir peak power. In this equation we have neglected the effect of the green beam which is too weak to induce such a thirdorder nonlinear effect. The spectral width A21 of the ir pulse is broadened by SPM and the spectral width A22 of the green seed pulse by XPM. In the Q-switched mode-locked regime the ir peak power in the fiber is in the order of 11 = 5 × 101° W / cm 2, for a propagation length of 1 m, and by taking n ~ = n [ = 4.19 × 10 - ~6 cm2/W, we obtain the ir and green spectral width of the order of 4.2 nm and 3 nm, a factor of 250 and 500 superior to the initial Fourier transform-limited case. In mode-locked regime the ir peak power in the fiber is much smaller (in the order of 1.5× 10 9 W / cm2); in this regime SPM and XPM can be neglected. We will show experimentally that in the Q-switched mode-locked regime the interplay of these two thirdorder nonlinear effects with GVD induces a blurring of the holographic grating. The physics of these phenomena is by now well understood, but in our case their numerical analysis is not straightforward because the pulses have not the same peak intensity in the pulse train.
Phase fluctuations between the pump and harmonic seed light In the model of Anderson et al. the relative phase difference between the 1064 nm pump field and the 532 nm seed field is of crucial importance for the di-
1 September 1993
rection of the electrical charge migration. Random phase fluctuations between these two field would induce different holographic gratings with different relative phase. This phenomena would induce a blurring of the holographic grating and limit the grating length and the SHG efficiency. This result has been experimentally observed by Krol and co-workers [13].
Laser frequency emission fluctuations As the grating period depends on the laser frequency, a drift of the laser central frequency emission during the seeding process would induce some other grating with different period. It would be another limiting factor to the grating length.
3. Experiments
The experimental set-up is represented on fig. 1. The Nd: YAG laser is able to operate in mode-locked, Q-switched, and Q-switched mode-locked regime. The beam passes through a polarizing prism and is focused with a 10 X microscope objective at the fiber input. A KDP crystal placed at the laser output was used to generate a small amount of green seed light that was focused together with the pump. At the fiber end, a 10 × microscope objective collimates the green and infrared beams that are separated by a dichroic mirror and directed on a two-channel optical
Nd:YAG Laser
/
I RG695 fdter
Photodiode
Glan prism
!~339 filter
Optkai fiber
lox Microsoope objective
Dichrffic mirror Rmax 532am Tmax 1064nm
Fig. 1. Experimental set-up: the pulses of an Nd: YAG laser are injected in an optical fiber with a small amount of second harmonic seed
light during the preparation time. After the preparation time SHG is measured by launching in the fiber ir light 0nly. At the output, a dichro'/cmirror separates the fundamental and second harmonic radiation. The effectivegratinglength is measuredby makingsuccessive cuts of the prepared fiber end. 393
Volume 101, number 5,6
OPTICS COMMUNICATIONS
power meter. For SHG intensity measurements, an infrared RG695 filter was placed on the laser output beam. A green BG39 filter placed on the beam refleeted by the dichroic mirror was used to remove residual fundamental light along the second harmonic direction. During the fiber preparation, green and infrared lights were used together, while infrared was used alone for SHG measurements. To measure the effective grating length we chose to make successive cuts of the fiber end, and to record the corresponding SHG. This method gives a plot of the SHG as a function of the fiber length; the grating length is given by the length where a growth of SH is observed. Batdorf and co-workers [ 14 ] have shown that the grating length decreases with the seed green ratio g= 12,o/lo,. This observation is in agreement with the model of Anderson et al. In order to compare our results, a constant proportion of seed light ( g = I2o,/Io, = 0.15 × 10- a) was used in the experiments presented in this article. We used germanosilicate fibers that were drawn to be monomode for 1064 nm; the cutoff wavelength was 0.8 I~m, the core diameter was of the order of 5 I~m and the step index ws 5.4× 10 -a. The concentration in germanium of the fiber core was 5%. In a first set of experiments we used our laser in the Q-switched mode-locked regime, delivering trains of 40 pulses of 100 ps duration separated by 10 ns at the repetition rate of 1 kHz and a peak power of 9.5 kW. We have plotted on fig. 2 the ratio l(2oJ)/I2(to) as a function of fiber length. This ratio is proportional to the square of the effective second order nonlinear susceptibility (X~t~)2= (fo~Xt2~ (z) dz) 2. For this mode of operation, our measurements show that the effective length of the grating is of the order of 9 cm. We have show that in this regime, for a propagation length of 1 m, the ir spectral width and the green spectral width are increased by a factor of 250 and 500, respectively. The short grating length can be attributed to the spectral broadening of the p u m p pulses by self-phase and cross-phase modulation effects. Another increase in the blurring of the holographic grating is caused by the fact that the laser pulses have not the same peak intensity in the pulse train (the spectral broadening is not the same for each pulses). 394
1 September 1993
I(2w)/P(w)
2.~E-06 2E-06 1,5E-06 IE-06 5E-07
# #
0
10
20
30
40
50
60
Length (cm) Fig. 2. 12o,/12 or reduced SHG as a function of the fiber length for the laser operating in mode-lockedQ-switchedregime.
I(2w)/F(w)
1,6E-06 1,4E-06 1,2E-06
1E.06 8E.07 6E-07
/ //
4E.07 2E.07 j" ; .....
~.........
10
r .........
20
I .........
30
i .........
40
I ......
50
60
Length (era) Fig. 3. 12~,/12 or reduced SHG as a function of the fiber length for the laser operating in mode-lockedregime. In a second set of experiments, our laser was operated in the mode-locked regime, delivering pulses of 100 ps, 300 W of peak power at the repetition rate of 76 MHz. Such peak power enables us to neglect self- and cross-phase modulation effects. As shown by fig. 3, the grating length is found to be of the order of 18 cm, a factor of two superior to the Q-switched mode-locked case. This demonstrates the limitation of the grating length caused by nonlinear phase modulation effects.
Volume 101, number 5,6
OPTICS COMMUNICATIONS
We have shown that for 100 ps p u m p pulses, the interaction length due to G V D is of 125 cm and the coherence length of 94 cm for Fourier transformlimited gaussian pulses. Despite the fact that these measured grating lengths are much lower than the theoretical, one cannot definitely rule out the pump pulse spectral width because in mode-locked regime the pulses are not necessary Fourier transform-limited gaussian pulses. We have made a set of experiments using the laser in the Q-switched mode. The p u m p pulses were of 600 ns duration and of 90 W peak power. In this case the self- and cross-phase modulation effects and GVD effects are negligible for the fiber lengths we used (typically 1 m ) . The results on fig. 4 show a grating length of 18 cm for this regime, what is very similar to the results obtained in the mode-locked regime. The theoretical coherence length for transform-limited pulses of 600 ns duration is 5.7 km. This suggest that this large discrepancy may be caused by nontransform-limited pulses, a n d / o r by low frequency variations of the central frequency of the laser. To reduce these detrimental effects, we have used a frequency stabilised injected laser delivering 1064 nm, 6 ns pulses at the repetition rate of 1 kHz. For these quasi transform-limited pulses Av At~ 0.44, the injected peak power was of the order of 400 W and the g ratio was kept constant. The results obtained with this laser are on fig. 5 where it is clearly shown that the measured holo-
I(2w)/l=(w) 5E-06
t
tt .......
.............t ..................
.~"
1E-06
I(~)/I=(w) 5E-06 4E-06
./"""i.....
3E-06
/~/
2E-06 1E-06 00=..... i0
.,." ............
20
30
40
50
"60
Length (cm) Fig. 5. l~/I 2 or reduced SHG as a function of the fiber length for a frequencystabilised injected laser operating in Q-switched regime. graphic grating length is of 60 cm. This represents a substantial improvement compared to the mode locked-regime that can be attributed to the greater central frequency stability and the better spectral purity of the injected pump pulses. Note that we could not reach the saturation of SHG during the preparation process owing to the relatively low repetition rate of our laser and to long-term mechanical unstability of our set-up. We estimate that better results could be obtained by an improvement of the experimental conditions.
4. Conclusion
4E-06
2E-06
1 September 1993
.i =
Oo, ..... i'6 ...... 20 ...... gO ...... 40 ...... gO ....... 60 L e n g t h (era)
Fig. 4. 12o,/12 or reduced SHG as a function of the fiber length for the laser operating in Q-switchedregime.
We have experimentally demonstrated that the selforganized holographic grating is not significantly affected by the pump pulses duration. We have established experimental evidence of the limitation of the grating length by self- and cross-phase modulations effects by a comparison between Q-switched modelocked and mode-locked pump pulses. To reduce the spectral width of the pump pulses, the central frequency fluctuations of the laser and the subsequent limitations for holographic grating length, we have used a stable N d : Y A G injected laser delivering transform-limited pulses. This allowed us to obtain, with same other experimental conditions, and 395
Volume 101, number 5,6
OPTICS COMMUNICATIONS
for the first time to our knowledge, holographic grating lengths above 60 cm.
References [ 1 ] U. Osterberg and W. Margulis, Optics Lett. 11 (1986) 516. [2] U. Osterberg and W. Margulis, IEEE J. Quantum Electron. 24 (1988) 2127. [3 ] N.M. Lawandy, J.P. Bernardin, G. Demouchy and R.L. Mc Donald, Electron. Lett. 27 ( 1991 ) 1264. [4] R.H. Stolen and H.W.K. Tom, Optics Lett. 12 (1987) 585. [5] A. Kamal, D.A. Weinberger and W.H. Weber, Optics Lett. 15 (1990) 613. [ 6 ] B.Ya. Zel'dovich, Yu.E. Kapitskii and V.M. Churikov, JETP Lett. 53 (1991) 78.
396
1 September 1993
[7]Yu.E. Kapitzloy and B.Ya. Zcl'dovich, Optics Lctt. 15 (1990) 1236. [ 8 ] N.B. Baranova, A.N. C"hudinovand B.Ya. Zcl'dovich, Optics Comm. 79 (1990) 116. [ 9 ] B.Ya. Zcl'dovich and A.N. Chudinov, JErP Lctt. 50 (1989) 439. [ 10] D.Z. Anderson, V. Mizrahi and .I.E. Sipe, Optics Lett. 16 (1991) 796. [ 11 ] H.W.K. Tom, R.H. Stolen, G.D. Aumiller and W. Pleibel, Optics Lett. 13 (1988) 512. [ 12] F. Ouellette, Optics Lett. 14 (1989) 964. [ 13 ] D.M. Krol, M.M. Broer, K.T. Nelson, R.H. Stolen, H.W.K. Tom and W. Pleibel, Optics Lett. 16 ( 1991 ) 211. [ 14] B. Batdorf, C. Krautschik, U. Osterberg and G. Stegeman, Optics Comm. 73 (1989) 393.