Calculation of stretching factor for optical pulse stretcher
A task of temporal stretching of pulses in an optical pulse stretcher of CPA-laser systems is considered. The output
 pulse profiles are obtained and the stretching factors are calculated on the foundation of the solution of the wave
 equation for a passage through an optical stretch...
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| Cite this: | Calculation of stretching factor for optical pulse stretcher / V.P. Leshchenko, A.I. Povrozin, S.Y. Karelin // Вопросы атомной науки и техники. — 2014. — № 3. — С. 214-217. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860248504423677952 |
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| author | Leshchenko, V.P. Povrozin, A.I. Karelin, S.Y. |
| author_facet | Leshchenko, V.P. Povrozin, A.I. Karelin, S.Y. |
| citation_txt | Calculation of stretching factor for optical pulse stretcher / V.P. Leshchenko, A.I. Povrozin, S.Y. Karelin // Вопросы атомной науки и техники. — 2014. — № 3. — С. 214-217. — Бібліогр.: 16 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | A task of temporal stretching of pulses in an optical pulse stretcher of CPA-laser systems is considered. The output
pulse profiles are obtained and the stretching factors are calculated on the foundation of the solution of the wave
equation for a passage through an optical stretcher of the ultrashort pulses with the different profiles. The calculations
for the optical stretcher of Offner triplet type had made.
Рассмотрена задача о временном расширении импульсов в оптическом расширителе импульсов CPAлазерной системы. На основе решения волнового уравнения для прохождения сверхкоротких импульсов различного профиля через оптический расширитель импульсов получены их выходные профили и рассчитаны коэффициенты расширения. Расчеты выполнены для оптического расширителя типа триплета Оффнера.
Розглянуто задачу про часове розширення імпульсів в оптичному розширювачі імпульсів CPA-лазерної системи. На основі рішення хвильового рівняння для проходження надкоротких імпульсів різного профiлю через оптичний розширювач отримано їх вихідні профілі та розраховано коефіцієнти розширення. Розрахунки виконанo для оптичного розширювача типу триплету Оффнера.
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ISSN 1562-6016. ВАНТ. 2014. №3(91) 214
CALCULATION OF STRETCHING FACTOR FOR OPTICAL PULSE
STRETCHER
V.P. Leshchenko, A.I. Povrozin, S.Y. Karelin
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
A task of temporal stretching of pulses in an optical pulse stretcher of CPA-laser systems is considered. The out-
put pulse profiles are obtained and the stretching factors are calculated on the foundation of the solution of the wave
equation for a passage through an optical stretcher of the ultrashort pulses with the different profiles. The calcula-
tions for the optical stretcher of Offner triplet type had made.
PACS: 42.60.Jf
An optical stretcher of pulses that stretches pulses of
a driving oscillator for the tens of femtoseconds to as
rule the hundreds of picoseconds [1] is an important
structural part of the CPA-laser systems. The stretching
of the femtosecond pulses performs in CPA-laser sys-
tems due to the phase modulation. A long-wavelength
component of the pulse passes a path shorter than short-
wavelength one due to this modulation and thus an out-
put pulse duration increases. This effect was achieved in
the first stretchers, consisting of two antiparallel diffrac-
tion gratings with a telescopic system between them,
introducing an additional dispersion in the entire optical
system [2 - 4]. Therefore the CPA-laser systems with
the stretchers, using only reflective optics, were created
[5 - 9]. These stretchers include the Offner triplet [10],
which in creating of the CPA-laser systems was often
preferable. The calculation method presented below is
applicable not only to the Offner triplet, but also for
other stretcher schemes. The consideration at an exam-
ple of the above type stretcher made to allow compari-
son of the obtaining results with published data [9].
An optical scheme of the Offner triplet includes the
minimum elements (Fig. 1): a diffraction grating 1, a
concave mirror M1, a convex mirror M2, a reflector M3
and a return mirror П.
Fig. 1.
An important task in a determining of the maximum
value for the stretching factor of the driving oscillator
pulse is to establish the connection between the stretcher
parameters and the temporal profile of this pulse. How-
ever, this problem has not considered in a literature.
The aim of this work is to create of a mathematical
model for the passage of the pulse through the stretcher
that is suitable for the engineering calculations of the
pulse stretching factors with the different time profiles.
An influence of the third and fourth orders dispersion in
the stretching of the pulse not previously considered in a
literature takes into account in this case. The wave equa-
tion for complex electric field amplitude A(z,t) of the
pulse passing through the stretcher with taking into ac-
count of this influence is in the form [11]:
2 3 4
2 3 42 3 4
1 0
2 6 24
∂ ∂ ∂ ∂
− − + =
∂ ∂ ∂ ∂
A i A A i AK K K
z t t t
, (1)
where K = 2π/λ is a wave vector; λ is a wave length;
2
2 2ω
∂
=
∂
KK is a dispersion of a group velocity of the
wave packet;
3 2
3 3 2
3 ;K K KK
Kω ω ω
∂ ∂ ∂
= +
∂ ∂ ∂
24 2 2
4 4 2 2
4 3 ;K K K KK
K Kω ω ω ω
∂ ∂ ∂ ∂
= + + ∂ ∂ ∂ ∂
ω is a frequency of a radiation.
Here and hereafter the digital codes “2” and higher
ones corresponds to the order dispersion. The values of
the wave vector and its derivatives had taken at the av-
erage frequency of the wave packet.
The solution of the equation (1) gives the opportuni-
ty to compare the influence on the pulse width and
shape of the second, third and fourth orders dispersion.
First, we consider the influence on the stretching factor
of only second order of the dispersion. The solution of
the equation (1) in such a representation founded by the
Fourier integral transforms method [12] is on the form:
0 1 1 1( , ) ( ) ( , )
∞
−∞
= −∫A t z A t G t t z dt , (2)
where A0(t1) = A(0,t1) − the electric field amplitude at
the input to the stretcher, G(t-t1,z) − influence function:
2
1
2
1
2
( )exp
2
( , )
2π
−
− =
i t t
K z
G t t z
iK z
. (3)
We assume, that at the input of the stretcher the
pulse electric field amplitude has a Gaussian temporal
profile:
2
1
1 0
0
( ) exp 2ln 2G G
G
tA t A
τ
= −
, (4)
where A0G − the maximum amplitude of the electric
field, the index “G” means “Gaussian”, 0Gτ − a pulse
duration determined at a level 2
0
1
2 GJ A= , that deter-
mines the specific form of the expression (4).
ISSN 1562-6016. ВАНТ. 2014. №3(91) 215
When the pulse passes through the stretcher, a spa-
tial coordinate z equals its effective length L. The se-
cond order dispersion is on the form:
2
2 22ω
∂ Φ
Φ = =
∂
K L , (5)
where K2 is given by expression [13]:
3
0
2 2 2 2
02 cos
λ
π θ
=K
c d
, (6)
where λ0 is the average wavelength of the wave packet;
θ0 is the diffraction angle at a wavelength λ0; d is a con-
stant of the grating; с is a velocity of a light in a vacuo.
The expression for the effective length of the Offner
triplet obtained on the basis of the theory of the optical
systems [14] and is on the form:
3 8 2 8 6
1 26 4 1,5
r R rR r R S
S r RL
R Rr
S R r S
− + + + −
=
+ − − −
, (7)
where R – a radius of the concave mirror, r – a radius of
the convex mirror, S – distance between the center of
the concave mirror and the middle of the diffraction
grating.
Substituting (3), (4) and (5) in (2) with followed
squaring a number gives an expression for the intensity
profile of the output stretcher pulse:
22
0
2 2 2
0 0 0
4 ln 2( , ) expG
G
G G G
A tJ t
V V τ
Φ = −
, (8)
where V0G − stretching factor of the pulse with a Gauss-
ian intensity distribution:
2
2
0 2
0
4 ln 21G
G
V
τ
Φ
= +
. (9)
As it is clear from a literature the driving oscillator
of the pulses with Gaussian temporal intensity profile
and the profile proportional to the square of the hyper-
bolic secant are in practice most often in the CPA-laser
systems. The electric field amplitude of this pulse is on
the form:
0
0
1.763( ) sechS S
S
tA t A
τ
= , (10)
where A0S – a peak amplitude of the electric field ,
τ0S − the pulse duration on the level 2
0
1
2 SA . Index “S”
means a belonging to the function "sech".
The solution of the equation (1) taking into account
only the second order dispersion for the pulses with an
amplitude of electric field (10) at the stretcher input is
on the form:
2 2
2
1
0
2 1
1
02
( , )
( )exp
2 1,763sech .(11)
2
S
S
S
A t
i t tA
t dt
i τπ
∞
−∞
Φ =
−
Φ =
Φ∫
The squaring a number (11) gives the expression for
the intensity profile of the stretcher output:
2 2
22
1
0
2 1
1
02
( , )
( )exp
2 1,763sech
2
S
S
S
J t
i t tA
t dt
i τπ
∞
−∞
Φ =
−
Φ =
Φ∫
. (12)
The stretching factor in this case is defined:
VOS =τ2S/τ0S,
where τ2S − is determined by measuring at the level of
half J2S(t,Ф2).
A consistent taking into account of the influence of
the second and third orders dispersion and then the se-
cond, third and fourth orders dispersion for output pulse
with the input Gaussian profile (4) gives a solution of
the wave equation (1) on the form:
2
2
3 0 1 2 3 0
2 2
3 0
3 1 2
0
( , , , , ) exp{ [
2
1 3( ) ] } ,
6 8ln 2
G G
G
A t A i t
d
ωω
τ ωω ω
∞
−∞
Φ
Φ Φ Φ Φ = − +
− Φ + Φ Φ −
Φ
∫
(13)
4 0 1 2 3 4 0
2
32
3 1 2
0
2 2
2 4 0
4 1 3 2
0 0
( , , , , , ) exp{ [
1 3( )
2 6
1 4 3( ) ] } ,
24 8ln 2
G G
G
A t A i t
d
ω
ω ω
τ ωω ω
∞
−∞
Φ Φ Φ Φ Φ = − +
Φ
+ − Φ + Φ Φ +
Φ
+ Φ + Φ Φ + Φ −
Φ Φ
∫
(14)
here Φ0 is the phase shift acquired in the stretcher. It is
on the form [15]:
( )0
0 0 0cos cos cosω θ θ γΦ = − +
L
c
, (15)
where ω0 − average frequency of the wave packet, θ0 −
an angle of a diffraction at the frequency ω0, γ − an an-
gle of incidence of the pulse to the diffraction grating.
1 ω
∂Φ
Φ =
∂
− a first derivative with respect to fre-
quency of the phase. It is on the form [15]:
[ ]1 01 cos( )L
c
γ θΦ = − + − , (16)
3
3 3ω
∂ Φ
Φ =
∂
and
4
4 4ω
∂ Φ
Φ =
∂
– the third and fourth or-
ders dispersion, respectively. According to [13] the ex-
pressions for them are on the forms:
4
0 0 0
3 2 3 2 2 2
0 0
3 sin1
4 cos cos
λ λ θ
π θ θ
Φ = − +
L
c d d
, (17)
( )
5
0 0 0
4 3 4 2 2 2
0 0
2
2 20
0 02
3 sin{4 8
8 cos cos
1 6 5 }.
L
c d d
tg tg
d
λ λ θ
π θ θ
λ θ θ
Φ = + +
+ + +
(18)
The calculations Φ0, Φ1, Φ2, Φ3, Φ4 performed for
the Offner triplet with specific operating parameters:
ISSN 1562-6016. ВАНТ. 2014. №3(91) 216
R = 1024 mm, r = 512 mm, S = 774 mm, λ0 = 800 nm,
θ0 = 20.14°, d = 1/1200 mm (for the formulas (5) - (7),
taken from [8]). The calculations of the integrals (13)
and (14) performed numerically.
The solutions of the equation (1) for the input pulse
having a temporal profile of the input field (10) pre-
pared similarly. The field amplitude of this pulse with
taking into account the second and third orders is on the
form:
0
3 0 1 2 3 0
2
32
3 1 2
0
( , , , , ) sech
3,526
1 3exp{ [ ( ) ]} .
2 6
S
S SA t A
i t d
πτ ω
ωω ω ω
∞
−∞
Φ Φ Φ Φ = ×
Φ
× − + − Φ + Φ Φ
Φ
∫
(19)
And the field amplitude of the same pulse with tak-
ing into account the second, third and fourth orders is on
the form:
0
4 0 1 2 3 4 0
2
32
3 1 2
0
2 4
4 1 3 2
0 0
( , , , , , ) sech
3,526
1 3exp{ [ ( )
2 6
1 4 3( ) ]} .
24
S
CS SA t A
i t
d
πτ ω
ωω ω
ω ω
∞
−∞
Φ Φ Φ Φ Φ = ×
Φ
× − + − Φ + Φ Φ +
Φ
+ Φ + Φ Φ + Φ
Φ Φ
∫
(20)
Fig. 2 shows the profiles of the pulses at the stretch-
er output with taking into account the second order dis-
persion for the input Gaussian pulse (8) and the input
pulses with a hyperbolic secant profile (12). Expression
(12) has been calculated numerically.
Fig. 2.
The results of calculations of Gaussian pulses pro-
files at the stretcher output with taking into account the
third (13) and fourth (14) orders dispersion have coin-
cided with the output Gaussian pulse profiles (8) calcu-
lated with taking into account only the second order
dispersion with the accuracy 0.6%. A similar coinci-
dence of the pulse profiles calculations with taking into
account the third (19) and fourth (20) orders dispersion
received in the comparison theirs with the pulse profile
(12) with taking into account only the second order dis-
persion for the case of the hyperbolic secant. Duration
of the input pulses in the calculations taken τ0G=τ0S
=30 fs.
As can be seen from Fig. 2 the duration of the
stretched input Gaussian pulse on the half intensity level
is 273 ps, and of the stretched input pulse with the pro-
file of the hyperbolic secant is 195 ps.
According to the formula (9) and Fig. 2 the stretch-
ing factor was V0 = 9118. This value is 9.7% lower than
the experimental one, obtained under the same parame-
ters of stretcher [9]. This discrepancy may be cause of
the fact that the calculations do not take into account the
phase shift caused by the spatial structure of the beam
[16].
The value of the stretching factor for the input pulse
with the profile of the hyperbolic secant is equal to
6500.
The following conclusions from the obtained solu-
tions of the wave equation for the passage of the pulses
with the input Gaussian profile and the input profile of
the hyperbolic secant through the stretcher taking into
account the second , third and fourth orders dispersion
have been made:
1. The negligible influence on the results of the cal-
culations of the profiles pulses passing through the
stretcher of the third and fourth orders dispersion allows
to simplify the calculation of the stretching factor. The
calculation of the stretching factor may be performed
with taking into account only the second order disper-
sion.
2. The discrepancy between the value calculation of
the stretching factor for the Gaussian shape pulse and
the value of the stretching factor experimentally deter-
mined in the range of 10% is acceptable and demon-
strates the possible applicability of the presented meth-
ods of the calculations for the practical purposes.
3. To achieve the largest stretching factor for the
same duration of the input pulses with the different pro-
files preferable to use a pulse with the Gaussian pro-
file, as in this case, the stretching factor in 1.4 times
larger than that of the pulse with the profile of hyperbol-
ic secant .
4. The maximum stretching factor of the output
pulse with the Gaussian profile at the input stretcher is
determined analytically and may be obtained by reduc-
ing its input duration and the increasing of the second
order dispersion of the stretcher. The maximum stretch-
ing factor of the pulse with temporal profile of the hy-
perbolic secant can be defined numerically by selection
of the specific initial data.
The authors are pleased to acknowledge useful dis-
cussion of the presented material with the candidate of
physical and mathematical sciences V.G. Sinitsyn.
REFERENCES
1. P.G. Kryukov. Lazery ul’trakorotkikh impul’sov //
Kvantovaya electronika. 2001, 31, № 2, p. 95-119
(in Russian).
2. O.E. Martinez. 3000 times grating compressor with
positive group velocity dispersion: application to fi-
ber compensation in 1.3…1.6 µm region // IEEE
Journal of Quantum E Electronics. 1987, QE-23,
№ 1, p. 59-64.
3. C. Fiorimi, C. Sauteret, C. Rouyer, N. Blanchot,
S. Sgnec and A. Migus. Temporal aberrations due to
misalignments of a stretcher-compressor system and
compensation // IEEE Journal of Quantum E Elec-
tronics. 1994, v. 30, № 7, p. 1662-1670.
ISSN 1562-6016. ВАНТ. 2014. №3(91) 217
4. J.P. Kmetec, J.J. Mackin and J.F. Young. 0.5TW
125-fs Ti: sapphire laser // Optics Letters. 1991,
v. 16, № 13, p. 1001-1003.
5. C.P.J. Barty, C.L. Gordon, and B.E. Lemoff.
Multiterawatt 30-fs Ti: sapphire laser system //
Optics Letters. 1994, v. 19, № 18, p. 1442-1444.
6. D. Du, J. Squier, S. Kane, G. Korn, G. Mouron,
C. Bogush, C.T. Cotton. Terawatt Ti: sapphire laser
with spherical reflective-optic pulse expander // Op-
tics Letters. 1995, v. 20, № 20, p. 2114-2116.
7. B.E. Lemoff and C.P. Batry. Quantic-phase-limited,
spatially uniform expansion and recopression of ul-
trashort optical pulses // Optics Letters. 1993, v. 18,
№ 19, p. 1651-1653.
8. G. Gheriaux, P. Rousseau, F. Salin, J.P. Chambaret,
B. Walker, L. F. Dimauro. Aberration-free stretcher
design for ultrashort pulses amplification // Optics
Letters. 1996, v. 21, № 6, p. 414-416.
9. J.P. Chambaret, C. Le Blanc, G. Cheriaux, P.
Gurley, G. Darpentigny, P. Rousseau,
G. Hamoniaux, A. Antonetti and F. Salin. Generator
of 25 TW, 32-fs pulses at 10 Hz // Optics Letters.
1996, v. 21, № 23, p. 1921-1923.
10. A. Offner U. S. Patent 3, 748, 015 (1971).
11. S.А. Akhmanov, Yu.Е. D’yakov, А.S. Chirkin.
Vvedenie v statisticheskuyu radiofiziku i optiku.
Moskva: «Nauka». 1981, p. 271-277 (in Russian).
12. G. Korn, Т. Korn. Spravochnik po matematike.
Moskva: «Nauka». 1973, p. 329-332 (in Russian).
13. G.A. Mourou. Optics in the relativistic regime //
Reviews of modern physics. 2006, v. 78, April-June,
p. 309-371.
14. N.P. Gvozdeva, К.I. Korkina. Teoriya opticheskikh
system i opticheskie izmereniya. Moskva: «Mashi-
nostroenie». 1981, p. 61-64 (in Russian).
15. E.B. Treacy. Optical pulse compression with diffrac-
tion grating // IEEE Journal of Quantum Electron-
ics. 1969, QE-5, № 9, p. 454-458.
16. H. Kogelnik and T. Li. Laser beams and resonators
// Applied Optics. 1966, v. 5, № 10, p. 1550-1567.
See also: H. Kogelnik, T. Li. Rezonatory i svetovye
puchki lazerov // Trudy instituta ingenerov po el-
ektotekhnike i radiotekhnike (ТIIER). 1966, v. 54,
№ 10, p. 95-113 (in Russian).
Article received 18.10.2013
РАСЧЕТ КОЭФФИЦИЕНТА РАСШИРЕНИЯ ДЛЯ ОПТИЧЕСКОГО РАСШИРИТЕЛЯ
ИМПУЛЬСОВ
В.П. Лещенко, А.И. Поврозин, С.Ю. Карелин
Рассмотрена задача о временном расширении импульсов в оптическом расширителе импульсов CPA-
лазерной системы. На основе решения волнового уравнения для прохождения сверхкоротких импульсов
различного профиля через оптический расширитель импульсов получены их выходные профили и рассчита-
ны коэффициенты расширения. Расчеты выполнены для оптического расширителя типа триплета Оффнера.
РОЗРАХУНОК КОЕФІЦІЄНТА РОЗШИРЕННЯ ДЛЯ ОПТИЧНОГО РОЗШИРЮВАЧА ІМПУЛЬСІВ
В.П. Лещенко, А.І. Поврозін, С.Ю. Карелін
Розглянуто задачу про часове розширення імпульсів в оптичному розширювачі імпульсів CPA-лазерної
системи. На основі рішення хвильового рівняння для проходження надкоротких імпульсів різного профiлю
через оптичний розширювач отримано їх вихідні профілі та розраховано коефіцієнти розширення. Розраху-
нки виконанo для оптичного розширювача типу триплету Оффнера.
|
| id | nasplib_isofts_kiev_ua-123456789-80288 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:40:19Z |
| publishDate | 2014 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Leshchenko, V.P. Povrozin, A.I. Karelin, S.Y. 2015-04-14T16:02:38Z 2015-04-14T16:02:38Z 2014 Calculation of stretching factor for optical pulse stretcher / V.P. Leshchenko, A.I. Povrozin, S.Y. Karelin // Вопросы атомной науки и техники. — 2014. — № 3. — С. 214-217. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 42.60.Jf https://nasplib.isofts.kiev.ua/handle/123456789/80288 A task of temporal stretching of pulses in an optical pulse stretcher of CPA-laser systems is considered. The output
 pulse profiles are obtained and the stretching factors are calculated on the foundation of the solution of the wave
 equation for a passage through an optical stretcher of the ultrashort pulses with the different profiles. The calculations
 for the optical stretcher of Offner triplet type had made. Рассмотрена задача о временном расширении импульсов в оптическом расширителе импульсов CPAлазерной системы. На основе решения волнового уравнения для прохождения сверхкоротких импульсов различного профиля через оптический расширитель импульсов получены их выходные профили и рассчитаны коэффициенты расширения. Расчеты выполнены для оптического расширителя типа триплета Оффнера. Розглянуто задачу про часове розширення імпульсів в оптичному розширювачі імпульсів CPA-лазерної системи. На основі рішення хвильового рівняння для проходження надкоротких імпульсів різного профiлю через оптичний розширювач отримано їх вихідні профілі та розраховано коефіцієнти розширення. Розрахунки виконанo для оптичного розширювача типу триплету Оффнера. The authors are pleased to acknowledge useful discussion
 of the presented material with the candidate of
 physical and mathematical sciences V.G. Sinitsyn. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Применение ускорителей в радиационных технологиях Calculation of stretching factor for optical pulse stretcher Расчет коэффициента расширения для оптического расширителя импульсов Розрахунок коефіцієнта розширення для оптичного розширювача імпульсів Article published earlier |
| spellingShingle | Calculation of stretching factor for optical pulse stretcher Leshchenko, V.P. Povrozin, A.I. Karelin, S.Y. Применение ускорителей в радиационных технологиях |
| title | Calculation of stretching factor for optical pulse stretcher |
| title_alt | Расчет коэффициента расширения для оптического расширителя импульсов Розрахунок коефіцієнта розширення для оптичного розширювача імпульсів |
| title_full | Calculation of stretching factor for optical pulse stretcher |
| title_fullStr | Calculation of stretching factor for optical pulse stretcher |
| title_full_unstemmed | Calculation of stretching factor for optical pulse stretcher |
| title_short | Calculation of stretching factor for optical pulse stretcher |
| title_sort | calculation of stretching factor for optical pulse stretcher |
| topic | Применение ускорителей в радиационных технологиях |
| topic_facet | Применение ускорителей в радиационных технологиях |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/80288 |
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