s ..__ B3

@ ELSJ3VIER

1 July 1997

Optics Communications 139 (1997) 227-231

OPTICS COMMUNICATIONS

First Stokes pulse energy statistics for cascade Raman generation in optical fiber

Joseph Chang, David Baiocchi, Jovita Vas, John R. Thompson *

Physics Department, DePaul University, 2219 N. Kenmore Auenue, Chicago, IL 60614, USA

Received 27 November 1996; accepted 24 January 1997

Abstract

We present an experimental investigation of the pulse energy statistics of the first Stokes scattered light that is generated by spontaneous Raman scattering, and then amplified by stimulated scattering, for a wide range of input pump powers. We observe full-scale energy fluctuations for weak first Stokes scattering. The fist Stokes pulse energy fluctuations diminish for strong scattering, and local noise minima mark the onset of higher-order Stokes scattering. We also present measurements of the correlation between the input pump and first Stokes pulse energies for a wide range of input pump powers. This correlation coefficient starts out small for weak first Stokes scattering, then increases as the first Stokes pulse grows in energy, and then sharply decreases as the pump is depleted by the generation of multiple Stokes orders.

PACS: 42.5O.L~; 42.65.Dr; 42.65.Wi Keywords: Nonlinear optics; Quantum optics; Optical communications

Raman scattering in optical fibers has been the subject of intense research for over two decades. This prolonged attention has resulted because Raman scattering is relevant to many aspects of optical communication systems, and because the very broad Raman gain curve in glass can be used to construct widely tunable coherent light sources [ 11. Raman scattering in gases has also received much attention due to its potential to shift laser wavelengths to inaccessi- ble regions for spectroscopy, and due to sustained interest in the fundamental aspects of Raman scattering [2-61. Raman generation is a physical process in which zero-point fluctuations at the Stokes frequency are amplified to macroscopic proportions by stimulated scattering. It has been shown, in experiments in high pressure gas cells, that in the limit of weak scattering the macroscopic Stokes pulse energy has essentially the same statistical properties as the quantum noise from which it grew. The Stokes pulse energy fluctuations diminish once the scattering becomes strong enough to deplete the pump [3-S].

* Corresponding author. E-mail: jthompso@wppost.depaul.edu.

We believe that Raman generation provides an ideal system for investigating the evolution of the intensity statistics of light under the influence of nonlinearity, and it is this evolution in fiber-based Stokes Raman scattering that is the focus of our work. In particular, we will present a systematic study of the pulse energy statistics of the first Stokes scattered light as the pump power is varied from levels that produce only weak first Stokes scattering to levels where multiple Stokes orders are generated in the fiber. Over this range, we observe the transition from full-scale energy fluctuations to a narrow pulse energy distribution previously seen in gases; however, we also observe local minima in the first Stokes noise near the onset of higher-order scattering. In addition, we observe changes in the correlation between the input pump and first Stokes scattered light that are signatures of the transi- tion from weak first Stokes scattering to strong pump depletion when multiple Stokes orders are generated.

There has been little work on the statistical properties of spontaneously scattered light in optical fibers in com- parison to the work done in gases, even though there are important differences between the two physical systems. One key difference is the extremely broad Raman gain

0030-4018/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved. PZI SOO30-4018(97)00060-6

228 .I. Chang et al./ Optics Communications 139 (1997) 227-231

curve associated with glass fiber; another is the ease of generation of cascade Stokes orders and the ease of spatial mode control due to the waveguide geometry of the fiber [I]. Headley and Agrawal have recently reported numerical results on the statistics of the pulse energy and temporal width for the scattering of picosecond pump pulses in optical fibers [9]. There has also been experimental and theoretical work on spontaneous Brillouin scattering in optical fibers that primarily focused on the nonlinear dy- namics of the scattered light with varying levels of feed- back [IO-131, with more limited attention given to the statistical properties of the generated light [lo,1 11. To the best of our knowledge, our work is the first systematic experimental study of the statistics of light generated by Stokes Raman scattering in optical fibers.

The experimental setup for the measurements described in this article is shown in Fig. 1. The pump pulses were produced by a repetitively Q-switched, diode-pumped, Nd:YAG laser with a pulse repetition rate of 1 kHz. The pulse width was typically 32 ns (full-width at half-maxi- mum), and the pulses typically contained multiple longitu- dinal modes. The temporal pulse-width and the total pulse energy were quite stable. Details of the pump pulse energy statistics will be discussed below. The laser crystal had one

NDF IS0

M LY /‘30/7Q BS

SO/50 BS c7Hwp

NDF

AP

7 LP

FCP

Fig. 1. Experimental setup for the measurement of fust Stokes

pulse energy statistics: PLSA, pulsed laser spectrum analyzer; PD,

photodiode; NDF, neutral density filter; ISO, isolator; ES, beam- splitter: M, mirror; HWP, half-wave plate: FCP, fiber coupler; P,

dispersing prism; L, positive lens; LP, linear polarizer; AP, aper- ture. The Si and InGaAs photodiodes are both connected to gated

integrators.

face cut at Brewster’s angle so that the output pulses were linearly polarized. A combination of a half-wave plate and a linear polarizer was used to control the amount of light coupled into the fiber so that it was not necessary to change the mechanical alignment of the fiber or the pump laser power. The 71 m optical fiber supported a single transverse mode at the pump wavelength (hn = 1.06 pm), and it was polarization maintaining. The input pump pulse polarization was aligned parallel to one of the principal axes of the fiber so that linear polarization was maintained throughout propagation. At the fiber output, two dispersing prisms were used to physically separate the pump and generated Stokes orders. The output polarization was in the plane of incidence so that there were low reflection losses associated with the prisms. There was a long propagation distance between the prisms and the aperture so that the different frequency components were well separated spa- tially, and the first Stokes was selected by the aperture. A low noise InGaAs fast photodiode (t, = 500 ps) was used to monitor the energy in the first Stokes pulse at the fiber output. A Si fast photodiode (t, = 1 ns> was used to monitor the input pump pulse energy, and the average input pump spectrum was monitored using a Burleigh pulsed laser spectrum analyzer. Neutral density filters were used to prevent saturation of the photodiodes.

The signals from the input pump and output first Stokes photodiodes were each routed to fast gated integrators, and the two integrators were connected to a common computer interface. The integrator system was triggered by the Q- switch driver for the acousto-optic Q-switch. For each trigger the input pump and corresponding output first Stokes pulse areas were stored in a buffer in the computer interface. For each input pump power level, a total of 1800 pulse pairs were stored before the buffer contents were transferred to a personal computer via a general purpose interface bus (GPIB) for subsequent statistical analysis.

Fluctuations in the first Stokes pulse energy at the fiber output are the result of two types of noise: amplified quantum noise that initiates the spontaneous Raman scat- tering, and amplified classical pump noise. Thus, it is important to know the statistics of the pump pulse energy at the fiber input. The input pump pulse energy was approximately Gaussian distributed, and it had a standard deviation that was 2.5% of the mean pump pulse energy. The tails of this distribution extended a couple of standard deviations on either side of the mean. To reduce the effects of amplified pump pulse energy noise, we filtered the collected data pairs. We accepted only those pump/first Stokes pairs for which the pump pulse energy fell within a pre-specified window centered on the mean pump pulse energy. The window width for the measurements reported in this article was +2.1% of the mean, and this width resulted in the retention of roughly 1000 of the 1800 collected pairs. The standard deviation for the filtered pump pulse energy was 1.1% of the mean. We have also tried a more restrictive window width with virtually identi-

J. Chang et al./Optics Communications 139 (1997) 227-231 229

cal results for the first Stokes noise, as will be discussed later in the article.

Fig. 2 shows the first Stokes pulse energy relative noise versus input pump power. The relative noise is the stan- dard deviation expressed as a percentage of the mean pulse energy. Each data point in the figure is based upon the results of five different trials. In each trial, we collected 1800 input pump/first Stokes pulse pairs for each of the input pump power levels that fell within the range shown in the figure. We then calculated relative noise figures based upon the filtered data sets from each trial. The horizontal and vertical error bars represent the standard deviations that resulted from the five trials, and in most cases the size of the error bar is close to the point size used in the figure. For the lowest pump power shown in Fig. 2 there was only a weak first Stokes pulse generated, while for the highest pump powers four Stokes orders were generated. We will refer to the generation of multiple Stokes orders as cascade scattering. As can be seen, the first Stokes pulse energy shows essentially full scale fluc- tuations for the lowest power where the relative noise is

0’ 10 40 70 100 130

Pump Power (Watts Peak)

@I

J,

10 40 70 100 130

Pump Power (Watts Peak) Fig. 2. First Stokes relative noise versus input pump peak power.

Frame (b) gives an expanded view of the local noise minima that

appear near the onset of higher Stokes orders.

over 90%. As the pump pulse power increases, the first Stokes relative noise rapidly drops to comparatively low

levels. This drop in relative noise is the natural outcome of two factors: the increased importance of stimulated scatter- ing compared with spontaneous scattering as the mean first Stokes pulse energy increases, and the effects of gain saturation for the first Stokes near the onset of cascade scattering. These results are consistent with similar experi- ments in gas cells [3--S].

At the onset of cascade scattering some interesting structures appear in the first Stokes pulse energy noise. This is illustrated by frame (b) of Fig. 2 where the high noise points have been excluded. The first minimum in the first Stokes relative noise appears near the onset of second Stokes generation. A possible explanation for this structure is that while the first Stokes relative noise drops as it grows in energy and saturates, the first Stokes eventually becomes strong enough to pump the second Stokes. The newly generated second Stokes pulse will fluctuate from shot to shot, taking highly variable amounts of energy from the first Stokes pulse. Because of this, the first Stokes relative noise increases from the local minimum until a pump power is reached that-is sufficient to saturate the second Stokes. The next minimum in the first Stokes relative energy noise appears near the onset of third Stokes generation, and can be explained by similar arguments. It should be noted, however, that there is no evidence for a local minimum near the onset of the fourth Stokes pulse. A possible reason for this is that the generation of higher Stokes orders is a predominantly sequential process, mean- ing that a particular higher-order Stokes pulse is primarily pumped by the preceding order [14]. Thus, one might expect that the statistics of the first Stokes pulse energy would become insensitive to fluctuations in sufficiently high Stokes orders. These are physically plausible argu- ments for the observed structures in the first Stokes noise versus pump power, but further experiments and modeling are needed to test their validity.

Fig. 3 provides two examples of first Stokes pulse energy histograms: one at the lowest pump power, and one near the onset of second Stokes generation. The shape of the first Stokes histogram for the lowest pump power, Fig. 3(a), resembles the negative exponential distribution that characterizes the quantum noise from which the first Stokes pulse grows [3-61. The relative noise at this point is over 90%; however, the distribution does peak on a small nonzero pulse energy. By the onset of cascade scattering, Fig. 3(b), the distribution has narrowed considerably but is still not a symmetric Gaussian, and it is now skewed in the opposite direction to the low power distribution. The shape of the histograms showed a systematic change in shape with increasing pump power. The details of this evolution of the pulse energy distribution will be reported in a subsequent article.

Another interesting way of illustrating the transition from statistics dominated by spontaneous scattering to

230 J. Chang et al. /Optics Communications 139 (1997) 227-231

"0 2 4 6 8 10 Pulse Area

60

s? 40

!3 0

o 20

0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Pulse Area Fig. 3. Typical first Stokes pulse energy histograms for very weak scattering (a), and near to the onset of second Stokes scattering (b). The relative noise is 90.8% in frame (a) and only 6.7% in frame (b).

statistics dominated by stimulated scattering and gain satu- ration is by looking at the correlation between the input pump pulse energy and the output first Stokes energy. This correlation coefficient is shown as a function of pump pulse power in Fig. 4 for the same data sets used to generate Fig. 2. For weak scattering there is a small positive correlation between the pump and first Stokes pulse energies. This is to be expected since for weak scattering of stable pump pulses the dominant factor deter- mining the output energy of the individual first Stokes pulses is the location in the fiber where the first pump photons are spontaneously scattered into a guided mode and then amplified through stimulated scattering [9]. As the mean first Stokes pulse energy grows due to increased stimulated scattering, so also does the correlation between the pump and first Stokes. However, when the first Stokes pulse energy begins to saturate the correlation rapidly drops. The correlation between the pump and first Stokes deep into the saturation region is quite small, which is to be expected since the output of a saturated amplifier will be insensitive to variations in pump power [7].

It was noted earlier that there are two types of noise that appear in the output first Stokes pulse: amplified quantum noise, and amplified classical pump noise. A natural question to ask is the following: to what extent does each noise source determine the observed first Stokes pulse energy statistics? We offer the following experimen- tal results to address this question. Suppose we compare the relative noise versus pump power, as shown in Fig. 2, for different levels of input pump energy noise. If ampli- fied pump energy noise plays a prominent role, then the relative noise for a particular pump power should change significantly for different levels of input pump noise. We have made such a comparison for the unfiltered pump (2.5% relative noise, Gaussian distribution), a filtered pump with the same window width used for the results reported in this article (1.1% relative noise), and a more restrictive window width (0.6% relative noise). The results for these three pump noise levels are shown in Fig. 5, and all three curves lie virtually on top of one another. There is very little spread in the points for a particular pump power even in the high-noise, weak-scattering limit. We conclude that amplified pump pulse energy noise does not play a signifi- cant role in our experiments. We have also performed numerical modeling for the first Stokes generation that indicates that amplified classical pump noise cannot ac- count for the observed large scale fluctuations in the weak scattering limit of our experiments. The results of these simulations will be reported in a subsequent article.

In conclusion, we have performed a systematic study of the statistical properties of the first Stokes scattered light for fiber-based Raman scattering, from the onset of first Stokes scattering through strong cascade scattering. The general trends are in good agreement with previous work on Raman generation in gases, even though the bandwidth of the Raman gain in glass is several orders of magnitude larger than in gases [1,3-5,141. The breadth of the Raman gain curve suggests that a spectrally narrow pump scatters

10 30 50 70 90 110 130 Pump Power (Watts Peak)

Fig. 4. Normalized correlation coefficient between the input pump and output first Stokes pulse energies as a function of input pump peak power. The correlation is quite small near to the onset of first Stokes scattering and also for strong cascade scattering.

J. Chng et al./ Optics Communications 139 (19971227-231 231

-100. S

g 75

Ej

.l+ z !$ 50

‘-F! I

2 29 Ic, I@mmmmmm m m m m q m m m

0' 10 40 70 100 130

Pump Power (Watts Peak)

Fig. 5. First Stokes relative noise versus input pump peak power

for variable amounts of pump energy noise. The circles corre-

spond to the unfiltered data, triangles to a + 2.1% window width,

and squares to a + 1% window width. The relative noise curves

are virtually identical for all three pump energy noise levels.

into a broad range of frequencies, and arguments based on the central limit theorem would suggest that an exponential distribution for the scattered light would be difftcult to observe, even for low pump powers [3-S]. We have observed essentially full-scale fluctuations in the first Stokes pulse energy in our experiments, even though the full-width of the pump pulse spectrum is between 2 and 3 orders of magnitude smaller than the full-width of the spontaneous Raman gain curve for silica. A possible expla- nation for this observation is that for weak scattering the only appreciable contributions to the first Stokes pulse energy come from frequencies very near the gain peak, so that the Stokes pulse spectrum is much narrower than the

gain curve would suggest. We are currently designing experiments to explore this and other questions.

Acknowledgements

This work is supported by the National Science Foun- dation under grant number PHY-9515240.

References

[l] G.P. Agrawal, Nonlinear Fiber Optics, second edition

(Academic Press, San Diego, 1995) Ch. 8, and references

therein.

[2] P.R. Battle, J.G. Wessel, J.L. Carlsten, Phys. Rev. A 47

(1993) 4308.

[3] IA. Walmsley, M.G. Raymer, Phys. Rev. Lett. 50 (1983)

962.

[4] N. Fabricins, K. Nattermann, D. von der Linde, Phys. Rev.

Lett. 52 (1984) 113.

[5] D.C. MacPherson, R.C. Swanson, J.L. Carlsten, Phys. Rev.

Lett. 61 (1988) 66.

[6] M. Scalora, J.W. Haus, Optics Comm. 87 (1992) 267.

[7] I.A. Walmsley, M.G. Raymer, T. Sizer II, I.N. Duling III,

J.D. Kafka, Optics Comm. 53 (1985) 137.

[8] M. Lewenstein, 2. Phys. B 56 (1984) 69.

[9] C. Headley III, G.P. Agrawal, IEEE J. Quantum Electron. 31

(1995) 2058.

[lo] A.L. Gaeta, R.W. Boyd, Phys. Rev. A 44 (1991) 3205.

[ll] M. Dammig, G. Zinner, F. Mitschke, H. Welling, Phys. Rev.

A 48 (1993) 3301.

1121 R.G. Harrison, P.M. Ripley, W. Lu, Phys. Rev. A 49 (1994)

R24.

[13] D. Yu, W. Lu, R.G. Harrison, Phys. Rev. A 51 (1995) 669.

[14] K.X. Liu, E. Garmire, IEEE J. Quantum Electron. 27 (1991)

1022.