The chirped pulse amplification (CPA) technique[ are now achievable, and are expected to be boosted to the EW level
in the near future[
High Power Laser Science and Engineering, Volume. 2, Issue 4, 04000e38(2014)
Independent and continuous third-order dispersion compensation using a pair of prisms
The dispersion of a pair of prisms is analyzed by means of a ray-tracing method operating at other than tip-to-tip propagation of the prisms, taking into consideration the limited spectral bandwidth. The variations of the group delay dispersion and the third-order dispersion for a pair of prisms are calculated with respect to the incident position and the separation between the prisms. The pair of prisms can provide a wide range of independent and continuous third-order dispersion compensation. The effect of residual third-order dispersion on the pulse contrast ratio and pulse duration is also calculated. The residual third-order dispersion not only worsens the pulse contrast ratio, but also increases the pulse duration to the hundreds of femtosecond range for a tens of femtosecond pulse, even when the residual thirdorder dispersion is small. These phenomena are helpful in compensating for the residual high-order dispersion and in understanding its effect on pulse contrast ratios and pulse durations in ultrashort laser systems.
1. Introduction
The chirped pulse amplification (CPA) technique[ are now achievable, and are expected to be boosted to the EW level
in the near future[
In CPA ultrashort laser systems, the dispersion elements include stretcher, compressor and amplifier material[)[
The prism pair is an important element in dispersion compensation. In 1984, Fork
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In this study, we focus on independent and continuous TOD compensation using a pair of prisms. The dispersion of the pair of prisms is analyzed in detail using a ray-tracing method operating at other than tip-to-tip propagation of the prisms. The variations of GDD and TOD for the pair of prisms are calculated with respect to the incident position and the separation between the prisms. A pair of prisms can provide a wide range of independent and continuous TOD compensation. The effect of residual TOD (RTOD) on the pulse contrast ratio and pulse duration is calculated. The RTOD not only worsens the pulse contrast ratio, but also greatly increases the pulse duration to the hundreds of femtosecond range for a tens of femtosecond pulse, even when small RTOD is employed. These phenomena are helpful in compensating for residual high-order dispersion and in understanding its effect on the pulse contrast ratio in ultrashort laser systems.
2. Model
Figure
Based on Figure
To ensure high transmission efficiency of the prism pairs, Brewster angle incidence is adopted. The values of these angles can be calculated using ,
,
,
, where
is the central wavelength.
The total phase for the pair of prisms yields
According to Equation (
3. Numerical results
According to the model constructed in Section ,
, and
on GDD and TOD are determined. We then discuss independent and continuous TOD compensation by changing the distances
and
(or
and
) simultaneously. The effect of RTOD on the pulse contrast ratio and pulse duration is also discussed.
During the simulation, we adopted a typical Sellmeier series equation to describe glass material dispersion[
|
3.1. Influence of distances and
on dispersion
At the central wavelength, GDD and TOD change with distance or
(Figures
or
increases. For instance, when
, the value of GDD is reduced rapidly (Figure
, the value of GDD increases rapidly. Thus,
is the critical value; at
, the value of GDD is zero and the value of TOD is
. When
, the value of GDD reduces rapidly. However, when
, the value of GDD increases rapidly. Thus,
is the critical value; at
, the value of GDD is zero and the value of TOD is
.
Figures or
changes. Therefore, the prisms can compensate for GDD and TOD with the same signs, as well as GDD and TOD with different signs, by changing
or
.
In the simulation shown in Figure ,
,
,
,
, and
; material:
.
In the simulation shown in Figure ,
,
,
,
, and
; material:
.
3.2. Influence of distance on dispersion
At the central wavelength, GDD and TOD change with (Figure
. For instance, when
, the value of GDD reduces rapidly. However,
, the value of GDD increases rapidly. Thus
is the critical value; at
, GDD is zero and TOD is
.
During the simulation, the following parameters are employed: ,
,
,
,
, and
; material:
.
3.3. TOD independent and continuous compensation
Based on the analyses in Sections and
or
and
. At the central wavelength, TOD changes with
and
when
(Figures
that correspond to a particular TOD compensation value. Thus, the RTOD of the laser system is compensated by adjusting distances
and
simultaneously.
In the simulation shown in Figure ,
,
,
, and
; material:
. In the simulation shown in Figure
,
,
,
, and
; material: SF10. By comparison, we find that the
prism pair can provide a smaller TOD, which is suitable for small RTOD compensation (Figure
prisms are suitable for compensating RTOD under
, whereas the SF10 prisms are suitable for compensating RTOD under
.
3.4. Effect of RTOD on pulse contrast ratio and pulse duration
To demonstrate the effect of RTOD on the pulse contrast in CPA lasers, we employed a 30 fs compressed pulse laser system as a example. The central wavelength is and the spectral width is 140 nm. The spectral functions of the pulse exiting the compressor are assumed to have a Gaussian shape. The final output pulse contrast is calculated using a model in Ref. [
Figure , the output pulse contrast ratio in the 10 ps point is almost equal to the case when RTOD is zero (Figure
to 300 fs (Figure
), the RTOD not only affects the output contrast ratio, but also the pulse duration from
to 300 fs. When RTOD is
, the output pulse duration is increased from 30 to 36 fs (Figure
4. Conclusion
In summary, a ray-tracing model is presented to calculate the dispersion of a pair of prisms operating at other than tip-to-tip propagation of the prisms. The pair of prisms can provide a wide range of independent and continuous TOD compensation by employing appropriate values of and
or
and
simultaneously, which is helpful in compensating the residual high-order dispersion of the CPA laser system. RTOD not only worsens the pulse contrast ratio, but also increases the pulse duration to the hundreds of femtosecond range for a tens of femtosecond pulse, even at small RTOD. These phenomena are helpful in understanding the effect of residual high-order dispersion on the pulse contrast ratio in ultrashort pulse laser systems.
[6] E. B. Treacy.
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Qingwei Yang, Xinglong Xie, Jun Kang, Haidong Zhu, Ailin Guo, and Qi Gao. Independent and continuous third-order dispersion compensation using a pair of prisms[J]. High Power Laser Science and Engineering, 2014, 2(4): 04000e38
Category: regular articles
Received: Feb. 15, 2014
Accepted: Apr. 11, 2014
Published Online: Jan. 13, 2015
The Author Email: Qingwei Yang (yqwphy@siom.ac.cn)