Generation of 360 ps laser pulse with 3 J energy by stimulated Brillouin scattering with a nonfocusing scheme

Yulei Wang; Xuehua Zhu; Zhiwei Lu; Hengkang Zhang

doi:10.1364/OE.23.023318

1. Introduction

Inertial confinement fusion (ICF) has attracted attention all over the world because huge energy can be produced with this technique. It will become an important way to solve energy crisis. Hurricane and other researchers from American Lawrence Livermore National Laboratory observed fuel gain exceeded unity in an inertially confined fusion implosion in early 2014 [1]. That is the energy produced by fusion is higher than the energy injected into the fuel, which means the research of ICF has stepped into a new stage. Among the ignition methods for ICF in recent years, shock ignition raised by Betti’s research group in 2007 stood out [2]. The shock ignition can be achieved with multiple laser pulses whose pulse-durations are on the order of 10² ps, and pulse-energies are on the order of 10² kJ. Thus, producing laser pulses that meet the conditions becomes important, and a new amplification technology is desired.

The pulse compression effect of stimulated Brillouin scattering(SBS) provides a simple and efficient way to achieve hundred picosecond laser pulses. Since the first report in 1980s, this mechanism attracts the attentions of many research groups all around the world. In 1980, Hon discovered that pulse compression can be realized when laser pulses were injected into tapered waveguide or focusing cell filled with Brillouin active medium [3]. In his experiment, 20 ns pulses generated by a Nd:YAG laser are compressed to 2 ns in a tapered tube filled with methane, and a compression ratio of 1:10 is obtained. In 2008, Marcus et al. used quartz slab as nonlinear medium and compressed 2.5 ns laser pulses to 175 ps, which is considered the narrowest pulse obtained through SBS in solid medium [4]. Pulse compression in solid material is more stable than that in gas, but solid material cannot be used in high power lasers because of its low optical breakdown thershold. Permanent damage can easily happen in solid medium in the irradiation of high power laser. Thus, people started to pay attention to liquid medium for achieving high power pulse compression [5–8]. Heavy fluorocarbon liquids (e.g. FC-40, FC-72) is widely used in SBS research for its excellent optical property and high energy load capacity. The phonon lifetime of FC-40 is relatively brief, only 240 ps for pump irridiation at 1064 nm wavelength, which can lead to hundred picosecond compressed pulses generation [6]. Yoshida et al. achieved high-ratio pulse compression with heavy fluorocarbon FC-40 as nonlinear medium [6]. An 13 ns, 1064 nm pulse delivered by Nd:YAG laser was compressed to 160 ps and the corresponding SBS energy reflectivity was over 80%, without optical breakdown. However, as far as we know, almost all research about SBS pulse compression so far utilize the focusing scheme. The laser intensity in the focusing region is quite high in the focusing scheme, and the pump energy is limited even in liquid medium with high load capacity. Thus the pulse compression with a non-focusing scheme will enhance the load capacity of the system, and realize the genuine generation of high energy hundred picosecond laser pulses.

In recent years, some researchers reported that feedback propagating in the opposite direction of pump light would affect the process of SBS and lower the SBS threshold [9–15]. In reality, there is a band-width of the spectrum of laser pulse. If there is a Stokes component in the sideband, it will provide a weak feedback when the pump is reflected by an optical element in the light path. The feedback will be amplified by the subsequent laser pulse and speed up the progress of SBS [9,10]. Mahdi’s group presented theoretically and experimentally that SBS threshold would be halved by utilizing a reflector placed at the rear end of medium [11,12]. They claimed that SBS threshold is reduced because the counterpropagating feedback increases the interaction length, so a relatively lower pump power will be enough to excite SBS. Dement’ev et al. worked on the influence of the feedback provided by reflector behind the medium cell on pulse compression [14]. They experimentally compressed 1 ns laser pulses to less than 60 ps with counterpropagating pulses of the same carrier frequency and duration. This method is much more stable compared with pulse compression caused by spontaneous Brillouin scattering.

In this paper, the generation of high energy hundred picosecond laser pulses using nonfocusing-pumped SBS is demonstrated. In the experiment, a narrow-band high power Nd:glass laser system delivers 5 ns super-Gaussian-shaped pulses with 527 nm wavelength is used as the light source. 3.02 J, 360 ps compressed pulse is obtained, when a 5.36 J pump pulse is introduced into the medium cell filled with heavy fluorocarbon liquid FC-40. This method of generating high energy hundred picosecond laser pulses has a simple structure and is easy to operate, and it can also be scaled to higher energy pulse compression.

2. Simulation and analysis

To numerically simulate the SBS initiated by Stokes component of pump light itself when propagating in the medium, we use the following coupled-wave equations describing this process [16]:

\frac{\partial A_{1}}{\partial z} + \frac{n}{c} \frac{\partial A_{1}}{\partial t} = i \frac{ω γ_{e}}{4 n c ρ_{0}} ρ A_{2}

- \frac{\partial A_{2}}{\partial z} + \frac{n}{c} \frac{\partial A_{2}}{\partial t} = i \frac{ω γ_{e}}{4 n c ρ_{0}} ρ^{*} A_{1}

\frac{\partial ρ}{\partial t} + \frac{Γ}{2} ρ = i \frac{γ_{e} q^{2}}{16 π Ω_{B}} A_{1} A_{2}^{*} + f

Where A₁, A₂ and ρ respectively indicates amplitude of pump light, Stokes light and acoustic wave; n is the refractive index of Brillouin medium; c is the velocity of light in vacuum; ω is angular frequency of pump light;

ρ_{0}

is medium density without laser injecting;

γ_{e}

is the electrostrictive constant; q is wave vector of acoustic wave;

Ω_{B}

and Γ donate the Brillouin frequency shift and Brillouin linewidth, respectively. With these parameters the gain factor can be calculated by

g_{B} = γ_{e}^{2} ω^{2} / n c^{3} V ρ_{0} Γ

, and V is velocity of sound in the medium. f represents the Langevin noise source that describes the random thermal noise in the medium, and it follows the relation

〈 f (z, t) 〉 = 0

and

〈 f (z, t) f^{*} (z^{'}, t^{'}) 〉 = Q δ (z - z^{'}) δ (t - t^{'})

, in which

Q = 2 k T ρ_{0} Γ / V^{2} A

, k is Boltzmann constant, T is the temperature of medium and A is cross-sectional area of the beam.

By numerically solving coupling wave equations consisting of (1)~(3), we can model the SBS process after laser is injected into the medium cell. In the algorithm, we use an implicit finite differencing in time and a backward differencing scheme in space simmilar as the model proposed by Chu [17]. By directly integrating the ρ phonon from Eq. (3) and substituting it into the remaining two equations, then the discreted form of the equations become

A_{1_{j + 1}}^{m + 1} - A_{1_{j}}^{m + 1} - \frac{n Δ z}{c Δ t} (A_{1_{j}}^{m + 1} - A_{1_{j}}^{m}) = G^{'} A_{2_{j}}^{m + 1} (p_{j}^{m} + A_{1_{j}}^{m + 1} A_{2_{j}}^{m + 1 *}) - {G^{'}}_{f} A_{2_{j}}^{m + 1} (q_{j}^{m} + f_{j}^{m + 1})

A_{2_{j + 1}}^{m + 1} - A_{2_{j}}^{m + 1} + \frac{n Δ z}{c Δ t} (A_{2_{j}}^{m + 1} - A_{2_{j}}^{m}) = G^{'} A_{1_{j}}^{m + 1} {(p_{j}^{m} + A_{1_{j}}^{m + 1} A_{2_{j}}^{m + 1 *})}^{*} + {G^{'}}_{f} A_{1_{j}}^{m + 1} {(q_{j}^{m} + f_{j}^{m + 1})}^{*}

where j, m discribe the spatial and temporal grid point, j = 0 corresponds to z = 0, m = 0 corresponds to t = 0;

Δ z

and

Δ t

are spatial and temporal step, respectivily;

G^{'} = ω γ_{e}^{2} q^{2} Δ z Δ t / 128 π n c ρ_{0} Ω_{B} Γ

and

{G^{'}}_{f} = i ω γ_{e} Δ z Δ t / 16 n c ρ_{0}

are two constants. And the two terminal variables are iterated with the following relations:

p^{m + 1} = (p^{m} + 2 A_{1}^{m + 1} A_{2}^{m + 1 *}) e^{- Γ Δ t / 2}

,

p^{0} = A_{1}^{0} A_{2}^{0 *} e^{- Γ Δ t / 2}

,

q^{m + 1} = (q^{m} + 2 f^{m + 1}) e^{- Γ Δ t / 2}

,

q^{0} = f^{0} e^{- Γ Δ t / 2}

. The amplitute of the noise term

f_{j}^{m}

is treated as a complex Gaussian random distribution function with zero mean and variance of

\sqrt{n Q / {(Δ t)}^{2} c}

[18]. When the initial and boundry conditions are given, amplitutes of the pump and the Stokes light can be calculated with Eq. (4) and Eq. (5).

Initial conditions of the three feilds are given below. Initial conditions of pump light are $A_{1} (j = 0, m) = A_{0}$ and $A_{1} (j > 0, m = 0) = 0$ , where A₀ represents the waveform of incident pump light. For the Stokes light, the reflection of rear cell window should be introduced, assume the reflectivity is r and the ratio of Stokes component among pump light is η, the initial conditions of Stokes light can be described as:

\begin{array}{l} A_{2} (j = J, m) = {\begin{cases} r η A_{1} (j = 0, m - [T_{t} / Δ t]) m > [T_{t} / Δ t] \\ 0 o t h e r s \end{cases} \\ A_{2} (j < J, m) = 0 \end{array}

in which T_t represents propagation time of laser pulse in medium, J corresponds to z = L and [ ] represents round numbers. Eventually, initial conditions of acoustic wave are given as:

ρ (j = 0, m) = f_{0, m}

ρ (j, m = 0) = f_{j, 0}

The parameters used in above numerical calculation are shown in Table 1, and the parameters of Brillouin medium come from heavy fluorocarbon FC-40. In [6], Yoshida et al mentioned the parameters of FC-40 at 1064 nm wavelength. With the wavelength related equations, the corresponding paremeters can be calculated at 527 nm.

Table 1. Simulation parameters

View Table

According to the Fourier Transform, in the sideband spectrum of super-Gaussian-shaped pump laser pulse whose duration is 5 ns, the ratio (η) of Stokes components is approximately 6.4 × 10⁻⁵. In the medium cell, the reflectivity coefficient of the rear window calculated from Fresnel formula is approximately 10⁻³, so among reflected light from the rear cell window, the intensity of Stokes component is 6.4 × 10⁻⁸ times that of pump light.

With the numerical model and parameters detailed above, we simulated the pulse compression process. The pump energy increases from 2.4 J to 14 J, with 100 energy steps. Typical waveforms of the pump with different energies used in the numerical calculation are shown in Fig. 1(a). The pulses are 20th-order super-Gaussian-shaped with 5 ns pulse-duration. Figure 1(b) shows waveforms of the reflected light corresponding to those of the pump light shown in Fig. 1(a). When pump energy is relatively low, the waveform of the corresponding reflected light is a typical steep-fronted Stokes pulse, which means the reflected light in this situation is an amplified component of the feedback from the rear end of medium cell. And this kind of reflected pulse is hereinafter refered to as feedback-initiated SBS pulse. However, when pump energy exceeds a certain value (~10 J), another pulse component appearing at the bottom of the rising edge of the reflected pulse, whose intensity increases with the further increment of pump energy. Note that when laser pulse propagates in medium cell, not only the feedback at the rear window, but thermal noise in the medium contributes to the excitation of SBS. The evolution of the output pulses in the above two cases are shown in Fig. 2. When pump energy is relatively low, gain of rear window’s feedback is much higher than that of spontaneous scattering in the cell, and the feedback-initiated SBS pulse is the dominant component of reflected light. The waveform of the output pulse is shown as ① in Fig. 2. In contrast, when pump energy is relatively high, spontaneous scattering in the cell can be amplified effectively, and generates noise-initiated SBS pulse as shown in Fig. 2. This kind of pulse overlaps with the feedback-initiated SBS pulse, and results in the waveform shown as ② in Fig. 2.

Fig. 1 Calculated waveform of pump light (a) and reflected light (b), output pulse-width (c) and energy reflectivity (d) with different pump energy

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Fig. 2 Schematic of generation progress of reflected pulse. The pump pulse incidents into the Brillouin cell from the left side and the excited Stokes light transmits in the opposite direction. The waveforms shown in the left represent the reflected pulses with the pump intensity below (①) and above (②) the “Noise-initiated” SBS threshold.

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In the reflected light, pulse durations of feedback-initiated SBS with different pump energies are shown in Fig. 1(c). With the increase of pump energy, pulse duration gradually decreases. After pump energy exceeds a certain value (~10 J), pulse duration tends to be a constant. The reason is that noise-initiated SBS extracts part of pump energy, weakens the intensity of the pump used to generate feedback-initiated SBS, thus further compression of pulse duration is limited. As shown in Fig. 1(d), noise-initiated SBS in the medium also affects energy reflectivity. The solid line is related to the energy reflectivity of the feedback-initiated SBS which supports the generation of the compressed pulse. The dash line shows the total energy reflectivity which contains both the feedback-initiated SBS and the noise-initiated SBS. When the pump energy is relatively low, the two lines overlap each other because there is no noise-initiated SBS exists and energy reflectivity gradually increases with the increase of pump energy. After pump energy exceeds the threshold of noise-initiated SBS, total energy reflectivity continues to increase, but the reflectivity related to feedback-initiated SBS drops owing to the energy extraction of the noise-initiated SBS. It indicates that keeping the pump energy lower than the threshold of SBS initiated from noise is essential to the application of our scheme.

3. Experimental setup

An experiment is carried out on the generation of hundred picosecond laser pulses based on stimulated Brillouin scattering with a nonfocusing scheme. The experimental setup is shown in Fig. 3. A narrow-band high power Nd:glass laser system is used as the light source. The duration of the pulse is 5 ns, beam diameter is approximately 60 mm, wavelength is 527 nm, and single pulse energy is over 10 J. The front-end of the laser system begins with a CW Yb-doped DFB fiber laser with linear polarization. The output of fiber oscillator then proceeds with a fiber intensity modulator, which chops the CW beam into packets of 5 ns. The waveform of the chopped pulse is controlled by an arbitrary waveform generator (AWG) which is used to drive the intensity modulator. And the temporal shape of the output pulse depends on AWG linearly. The output waveform of the front-end is pre-compensated to a pulse structure with increasing intensity from its rising edge to the falling edge according to the nonlinear gain of the subsequent main amplifier system. The output energy of the front-end system is 10 nJ at 5 ns in a single pulse. The fiber output of the front-end system is collimated into a freely propagating beam that is then injected into the preamplifier system. The pulse was typically amplified to energy up to a few millijoules with the beam diameter of 6 mm. After passing through a spatial beam shaping module, the beam is transported into the main amplifier section. The main amplifier is comprised of 4 Nd:phosphate glass amplifier rods (measured one 20 mm, one 40 mm and two 70 mm in diameter). The beam profile is shaped by the spatial beam shaping module to a nearly flat-toped beam, the detailed compensation process is presented in another paper published recently [19]. The beam ejected from the main amplifier system is then introduced into the frequency converter section. It provides the pulse with over 10 J at 527 nm. To increase the laser intensity, a 3:1 beam-contracting system is used to reduce the beam diameter to 20 mm, and the laser intensity is magnified 9 times. The p-polarized laser beam passes through a polarizer, a quarter wave plate and turns into circularly-polarized light. Then the beam is introduced into the medium cell to induce stimulated Brillouin scattering. The length of the medium cell is 600 mm which equals to the effect gain length of the pump pulse. The usage of a shorter cell may lower the compression efficiency and the choice of a longer cell may leads to some other nonlinear effects (e.g. small scale self-focusing), which are harmful for pulse compression. Both quartz windows of the cell are anti-reflection coated on the outer side, because superposition of the reflected pulse from the two plane of the rear window may leads to spreading of the output pulses. The cell is filled with FC-40, and the reflection on the interface between quartz and medium provides feedback. Careful light path adjustment is conducted, and the reflected light of the rear window overlaps well with the pump in the medium cell. The compressed pulse leaves the cell at the front window. Then it is turned into s-polarized light after passing through the quarter wave plate again, and outputs from the polarizer. The waveform of the output compressed pulses are detected by a photodetector (Alphalas UPD-40-UVIR-D; rise time, < 40 ps), and the measured waveform is recorded with a digital oscilloscope (Tektronix DPO71254C; bandwidth, 12.5 GHz; sample rate, 100 Gsamples/s). At the same time, an energy detector (PE50DIF-ER, Ophir) is used to measure the compressed pulse energy. The energy detector and photoelectric detector used to measure parameters of pump light are the same as those for measuring reflected light.

Fig. 3 Schematic diagram of the experimental setup

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4. Experimental results and discussion

Waveform of pump light used in the experiment is shown in Fig. 4(a). The pulse duration of the pump is 5 ns and the waveform is in a nearly flat-top shape. There exists Stokes component in spectrum of such kind of pulse, which can provide seed for generation of hundred picosecond pulse when receiving feedback from the rear end of the medium cell. Waveforms of reflected light measured in the experiment are shown in Fig. 4(b), similar to the calculated results in Fig. 1. When pump energy is relatively low, only feedback-initiated Stokes pulse exists. However, when pump energy exceeds 5.36 J, the noise-initiated Stokes pulse appears. The higher pump energy, the earlier this kind of pulse builds and the longer its duration is. The reason is that with the increase of pump energy, medium length needed to reach noise-initiated SBS threshold decreases. That is to say, this component among reflected light starts from place more close to the front end of medium cell. It can also be seen from Fig. 4(b) that the time jitter of the peak time of the compressed pulse is insignificant, which means the compressed pulse has a good stability. The main reason for the small time jitter is that the location of the feedback mirror is fixed. The inset of Fig. 4(b) shows the detail of compressed pulse with pump energy of 5.36 J, the generated pulse duration is 360 ps. It should be pointed out that the experiment is conducted with a single shot at each pump energy, and the error of the measured data mainly comes from the uncertainty of the measurement system. The system uncertainty of the energy detector is about 1.05%, and the response time of the total temporal measurement system is about 40 ps.

Fig. 4 Typical waveforms of pump light (a) and Stokes light (b) with different energy in our experiment. Inset: waveform of the compressed pulse with pump energy of 5.36 J.

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For large-aperture laser beams, the uniformity of transverse intensity distribution directly affects the SBS process. Backscattering initiates mainly in the spots with high intensity (hot-spots) in the beam aperture. The laser intensity in hot-spots exceeds the average intensity of the whole beam aperture by far. Thus, estimating SBS progress with the average intensity will lead to low accuracy. Skeldon and Bahr claimed that the practical intensity should be equal to the product of average intensity multiplied and a hot-spot parameter [20]. The near-field pattern and its gray-scale histogram of the incident light beam are shown in Fig. 5. According to the method of Skeldon, the calculated hot-spot parameter is about 1.76, which means the practical laser intensity is 1.76 times of the average intensity. Hereinafter, we divide the energy in calculated results by 1.76 as the practical laser energy.

Fig. 5 The near-field pattern (a) and its gray-scale histogram (b) of the incident light

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Kerr effect, self-focusing effect and other nonlinear effects may occur in the propagation process of high power laser. The strength of these nonlinear effects depends on the nonlinear refractive index n₂ of the medium, n₂ of FC-40 was measured by Z-scan technology to be 7 × 10⁻¹⁶ cm²/GW. Small scale self-focusing is the easiest to happen among those nonlinear effects. B integral is a critical parameter for measuring small scale self-focusing. The expression of B integral is as follow [21]:

B = \frac{2 π}{λ} \int_{0}^{L} n_{2} I (x, y) d z

When the value of B is greater than 1.0, small scale self-focusing will occur obviously [21]. With parameters used in the experiment substituted into this equation, the value of B is calculated to be 0.25. According to the near field distribution shown in Fig. 5(a), the hot-spot parameter can be calculated as 1.76, then the spatially local value of B is approximately 0.44, which is below the level of generating small scale self-focusing obviously.

The relationship between output pulse-duration and pump energy is shown in Fig. 6. In the diagram the solid dots represent reflected pulse-duration measured in the experiment, and the solid line represents the numerically calculated results. It can be seen from the picture that the reflected pulse-duration decreases gradually with the increase of pump energy, and tends to be a constant when the pump energy exceeds a certain value. The numerical calculation and experimental results agree reasonably well with each other.

Fig. 6 Output pulse-width (FWHM) with different pump energy

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The measured energies of the compressed pulses at different pump energies are shown in Fig. 7(a), and the related energy conversion efficiency is shown in Fig. 7(b). The solid dots in the picture represent measured energies of laser pulses in the experiment, and the solid line represents calculated results. Note that in the non-focusing scheme, the noise-initiated SBS has a certain angle of divergence [22]. For measuring the output energy, reflected light enters energy detector after passing through an aperture to filter out the noise. It is shown that output energy and the related energy reflectivity increase rapidly with the increase of pump energy when the pump energy is lower than 5.36 J. In contrast, when the pump energy exceeds 5.36 J, with the increase of pump energy, the growth of output energy slows down and the corresponding energy conversion efficiency decreases, as shown in Fig. 7(b). The experimental measurement matches the numerical calculation well.

Fig. 7 Output energy (a) and energy conversion efficiency (b) with different pump energy

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Because the SBS progress depends on the intensity of incident laser, a simple and convenient method to obtain narrow pulses with high energies is to expand the beam diameter of pump light. In our experiment, if the beam-contracting system were absent and the laser beam with aperture of 60 mm were introduced into the medium cell as the pump light, the optimized energy of compressed pulses would reach 30 J.

5. Conclusion

A novel technique for high energy hundred picosecond laser pulses generation on the basis of nonfocusing-pumped stimulated Brillouin scattering is presented in this paper. The spectrum of super-Gaussian-shaped laser pulses has a complex structure. And the components that fulfill the Brillouin frequency shift in its sideband will work as the seed of exciting the progress of SBS when feedback exists, which results in efficient compression of incident pump pulse. An experiment is carried out with a high power frequency-doubled Nd:glass laser system of 527 nm wavelength used as light source. The laser system delivers 5 ns super-Gaussian-shaped pulses. Heavy fluorocarbon liquid FC-40 is used as the active medium and the corresponding cell length is 600 mm. When the energy of pump pulse is 5.36 J, 3.02 J compressed pulse with pulse-width of 360 ps is obtained. The experimental results agree well with the numerically calculated results. It is worth noting that the time jitter of the compressed pulses is small because the pulse compression derives from the feedback of rear window of the medium cell but not from the randomly distributed thermal noise, which shows a good stability. This technique of generating hundred picosecond laser pulses can be scaled to higher energy pulse compression. It should be pointed out that this technique is fit for compressing super-Gaussian temporally shaped laser pulses. On the contrary, temporally Gaussian shaped laser pulses cannot be well compressed for its relatively weak Stokes component. In addition, for the intensity of a frequency component in the spectrum is inversely proportional to its interval with the central frequency, material with a relatively small Brillouin frequency shift is preferred to obtain strong Stokes component. In the future, efforts may be concentrated on optimizing the experimental setup and weakening the noise-initiated SBS for generating higher energy hundred picosecond laser pulses.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 61138005 and No.61378007).

References and links

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Description	Parameter
Laser wavelength λ	527 nm
Pulse-width t_p	5 ns
Beam diameter D	20 mm
Refractive index n	1.28
Cell length L	60 cm
Brillouin gain coefficient g	2 cm/GW
Brillouin shift $Ω_{B}$	2162 MHz
Brillouin bandwidth $Γ_{B}$	410 MHz
Phonon lifetime $τ_{B}$	60 ps

Generation of 360 ps laser pulse with 3 J energy by stimulated Brillouin scattering with a nonfocusing scheme

Abstract

1. Introduction

2. Simulation and analysis

3. Experimental setup

4. Experimental results and discussion

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (9)

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