In this paper, we study of the coherent Stokes generation in a transient Raman regime by Hydrogen gas-filled hollow-core photonic crystal fibres (HC-PCFs) configuration. The temporal and spatial evolution of the pump and Stokes field envelopes as well as the coherence and population inversion is numerically observed. The influence of the pump pulse width and gas pressure on the energy exchange along fiber and Stokes generation efficiency is investigated

Ho, Quy Quang

Nguyen, Thang Manh

Thai, Thanh Doan

English

Vietnam Academy of Science and Technology: Journals Online

Communications in Physics, Vol. 30, No. 2 (2020), pp. 143-150
DOI:10.15625/0868-3166/30/2/14460
EFFICIENT GENERATION OF COHERENT STOKES FIELD IN HYDROGEN
GAS-FILLED HOLLOW CORE PHOTONIC CRYSTAL FIBRES
THANH THAI DOAN1, QUY HO QUANG1,2 AND THANG NGUYEN MANH2,†
1Ho Chi Minh city University of Food Industry,
140 Le Trong Tan, Tan Phu, Ho Chi Minh City, Vietnam
2Academy of Military Science and Technology,
No. 17 Hoang Sam Street, Cau Giay, Hanoi, Vietnam
†E-mail: thangnm@jmst.info
Received 4 October 2019
Accepted for publication 20 February 2020
Published 11 May 2020
Abstract. We study the coherent Stokes generation in a transient stimulated Raman scattering
regime by Hydrogen gas-filled hollow-core photonic crystal fibres configuration. The temporal and
spatial evolution of the pump and Stokes field envelopes as well as the coherence and population
inversion are numerically calculated. The Stokes generation efficiency and the influence of pump
pulse width and gas pressure on the energy exchange along fibre are investigated.
Keywords: coherent Stokes generation; stimulated Raman scattering (SRS); gas filled HC-PCFs
(hollow-core photonic crystal fibres) .
Classification numbers: 42.65.Dr.
I. INTRODUCTION
The ability of remaining the high molecular coherence degree with the initial pump field in
the transient stimulated Raman scattering (SRS) regime [1] makes it become a promise candidate
for generating the ultrashort pulse compressed by coherent Raman frequency comb [2, 3]. How-
ever, the achievement of that regime in gas is difficult, it requires the applied pump pulse must
be intense, ultrashort [2, 4]. Gas filled HC-PCFs (hollow-core photonic crystal fibres) with the
excellent properties opens the opportunity to study the transient SRS regime in gas by very long
pump pulse duration [5, 6], and discover a lot of interesting processes in SRS [6–11]. In SRS, the
pump pulse width and the gas pressure filled inside HC-PCFs play an important role to optimize of
interaction Raman efficiency and to generate Stokes frequency, especially to choose input param-
eters for desired Stokes field. In this work, we study with numerical calculation the temporal and
c©2020 Vietnam Academy of Science and Technology
144 THANH THAI DOAN et al.
spatial evolution of the pump and Stokes field envelopes along Hydrogen gas-filled HC-PCFs. The
effects of active gas pressure and pump pulse width on the coherent Stokes generation efficiency
are also discussed.
II. COHERENT STOKES GENERATIONS IN H2 GAS-FILLED HC-PCFs
The scheme of coherent Stokes generation is described in Fig. 1, the coherent Raman inter-
action equations and its solution were presented in Ref. [12] where the pump, EP and Stokes, ES
Gaussian fields are in co-propagation in HC-PCFs filled with H2 gas. The pump pulse width is in
the range for transient SRS regime [5].
Fig. 1. The illustrated scheme of coherent Raman generation in H2 gas filled HC-PCFs.
In this model, gas pressure and pump pulse width are controllable. Because HC-PCFs
allows gas-laser intensity tight confinement in a small effective cross-section at relatively low
input pump powers, it could potentially increase the Raman linewidth, the dephasing times T2 (the
inverse value of Raman linewidth) on H2 gas pressure in HC-PCFs was shown in Fig. 2.
Fig. 2. The total Raman linewidth vs. H2 gas pressure filled into HC-PCFs [13].
EFFICIENT GENERATION OF COHERENT STOKES FIELD IN HYDROGEN GAS-FILLED . . . 145
In the low gas pressure region (below 20 mbar), the linewidth for forward scattering is
dominant by Doppler broadening effect. When the gas density increases, molecular collision
begins to contribute to the spectral lineshape. If this collision is an elastic velocity-change process,
meaning that do not affect the internal state of molecules, the line shape will reduce when the
mean-free path of collisions is about the scattering wavelength (solid-curve in range gas pressure
< 0.1 bar). When the gas density increases significantly (above 500 mbar), the line shape is
broadened by the internal state-changing collisions of the gas molecules (solid-curve in the range
0.1 bar < gas pressure < 10 bar). Experimental measurements were shown by circles in Fig. 2 [13].
III. RESULTS AND DISCUSSIONS
III.1. Coherent wave propagation along fibre
Figure 3 shows the temporal and spatial evolution of the pump and Stokes field envelopes
along the HC-PCFs with length z = 4 m, filled H2 gas at pressure of 1 bar. The Stokes field
envelope’s growth (Fig. 3b) is caused by the decrease of pump envelope (Fig. 3a) along the fibre.
It is clear that the most of initial pump energy is transferred into the Stokes energy. The energy
transfer mechanism between pump - Stokes - coherence fields were explained in Ref. [11].
Fig. 3. Temporal and spatial evolution of pump (a) and Stokes (b) field envelopes along
the HC-PCFs at gas pressure of 1 bar and pump pulse width of 15 ns.
146 THANH THAI DOAN et al.
The formation and evolution, in the time-space phase plane (t, z), of the coherence and
population inversion are presented in Fig. 4. It shows that coherence and population inversion
slowly increase and achieve their maximum values when the Stokes is well generated at z∼1.2 m,
at which population inversion get a maximum value and saturates in time.
Fig. 4. Temporal and spatial evolution of absolute value of coherence (a) and population
inversion (b) at gas pressure of 1 bar and pump pulse width of 15 ns.
III.2. Efficiency of Stokes generation
Energy exchange between the pump and Stokes fields along a fibre length of 20 m filled of 1
bar H2 gas pressure, pump pulse width of 15 ns is calculated and presented in Fig. 5. At the input
position of fibre, z =0, the Stokes energy is quite small and the system energy is normalized to
coupled pump energy. The Stokes field is uniformly amplified or the spontaneous process appears
along fibre shorter 0.5 m, and then the energy exchanging process is strongly happened for longer
fibre and get 50% when fibre is 0.76 m length (at z = 0.76 m). More interestingly, Fig. 5 also
shows that optimal fibre length of about 3.5 m for the highest Stokes generation efficiency of 80%
exclusively exists. The optimization of fibre length is seem to be an important choice for Raman
generation experiments if gas pressure and pump pulse width are suitably given.
EFFICIENT GENERATION OF COHERENT STOKES FIELD IN HYDROGEN GAS-FILLED . . . 147
Fig. 5. Energy exchange between pump and Stokes along 20 m of HC-PCFs at gas pres-
sure of 2 bar and pump pulse width of 15 ns.
Effect of gas pressure
Now, we adjust the pressure of H2 active gas from 0.5 bar to 4 bar (T2 is calculated in
Fig. 2) at pump pulse width of 15 ns, the curves of pump - Stokes energy exchange are plotted in
the direction of black arrow in Fig. 6a. The output Stokes efficiency depends on the gas pressure
filled in 4 m of HC-PCFs is shown in Fig. 6b, in which output Stokes efficiency is presented by
the circles for the gas pressure 0.5 bar, 1 bar, 2 bar, 3 bar and 4 bar.
It also shows that coherent Stokes generation efficiency increases with gas pressure’s growth,
however, at the given pump pulse width and fibre length, it is not proportional to the gas pressure
that slowly increases to the limit energy line (dash line). The Stokes generation efficiency at out-
put surface of fibre archives approximately 93% at gas pressure of 4 bar and 65% at that of 0.5
bar. This causes by the robust increment of Raman linewidth resulting from the destroy of mol-
ecule system’s coherence (see Fig. 4a). Therefore, it requires longer fibre for lower gas pressure
to archive higher Stokes efficiency. Consequently, we can control the Stokes generation efficiency
in the range of certain gas pressure at a given fibre length. Interestingly, the intersection point
between the Stokes efficiency curve and pump one seems to be on the Stokes efficiency straight
line of 50%.
148 THANH THAI DOAN et al.
Fig. 6. Dependence of coherent Stokes generation on H2 gas pressure filled into HC-
PCFs at pump pulse width of 15 ns, fibre length of 4 m: a) Energy exchange between
pump and Stokes with gas pressure variation (0.5 bar, 1 bar, 2 bar, 3 bar and 4 bar) , b)
Output Stokes generation efficiency vs. gas pressure.
EFFICIENT GENERATION OF COHERENT STOKES FIELD IN HYDROGEN GAS-FILLED . . . 149
Effect of pump pulse width
Fig. 7. Dependence of coherent Stokes generation on the pump pulse width at gas pres-
sure of 1 bar, fibre legth of 8 m: a) Energy exchange between pump and Stokes change
with the change of pump pulse width, b) Output Stokes geration efficiency vs. pump
pulse width (10 ns, 12 ns, 15 ns, 18 ns, 20 ns, 22 ns).
When the pump pulse width is changed in the range of 10 ns -22 ns, at 1 bar gas pressure and
constant peak power, the energy exchange curves are calculated and shown in Fig. 7a, the direction
of arrow shows the pump pulse width’s growing direction. Fig. 7b shows the dependence of the
150 THANH THAI DOAN et al.
Stokes generation efficiency on pump pulse width in the range of 10 ns -22 ns. Larger pump pulse
width gives higher Stokes generation efficiency at the given length of fibre and gas pressure. This
efficiency increment is gradually slower when the pump pulse width becomes larger, this could
be caused by the increase of collisional dephasing rate for larger pump pulse widths and reach a
steady state (saturation). Of course, it is not linearly proportional to the pump pulse width that
slowly increases to the limit energy line. Stokes generation efficiency gets approximately 86%
at pump pulse width of 22 ns and 65% at that of 10 ns. Hence, in order to archive the highest
efficiency, it is necessary to choose a suitable length of fibre for a given pump pulse width.
Consequently, we also control the Stokes generation efficiency in the range of certain pump
pulse width at the given gas pressure and fibre length. The intersection point between the Stokes
efficiency curve and pump one also seem to be on the Stokes efficiency straight line of 50%,
like the case of gas pressure change. These give us another simple way to enhance the Raman
generation efficiency instead of using other complex Raman generation system with special hollow
fibre structure [14, 15] or tailor polarization [16].
IV. CONCLUSIONS
We study with numerical calculation the coherent Stokes generation in a transient SRS
regime by Hydrogen gas-filled HC-PCFs configuration. The temporal and spatial evolution of the
pump and Stokes fields along Hydrogen gas-filled HC-PCFs, as well as the effects of gas pressure
and pump pulse width on the coherent Stokes generation efficiency have been investigated and
discussed. Interestingly, we prove that coherent Stokes generation efficiency can be controlled
and, therefore, optimized by changing of gas pressure and pump pulse width at a given length of
HC-PCFs. In this process, the intersection point between the Stokes efficiency curve and pump
one seems to be on the Stokes efficiency straight line of 50%. These obtained results are useful
for predicting the processes of coherent Raman generation and reducing experimental works.
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Efficient Generation of Coherent Stokes Field in Hydrogen Gas-Filled Hollow Core Photonic Crystal Fibres

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Efficient Generation of Coherent Stokes Field in Hydrogen Gas-Filled Hollow Core Photonic Crystal Fibres

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