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Group delay dispersion measurement of Yb:Gd2SiO5, Yb:GdYSiO5 and Yb:LuYSiO5crystal with white-light interferometry
Optics Express, Vol. 15, Issue 13, pp. 8486-8491 (2007)
http://dx.doi.org/10.1364/OE.15.008486
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– Abstract
1. Introduction
2. White-light Interferometer
3. Data Processing
4. Conclusions
– References and links
– Abstract
1. Introduction
2. White-light Interferometer
3. Data Processing
4. Conclusions
– References and links
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Abstract
We report the measured group delay dispersion (GDD) of new crystals Yb:Gd2SiO5 (Yb:GSO), Yb:GdYSiO5 (Yb:GYSO) and Yb:LuYSiO5 (Yb:LYSO) over wavelengths from 1000nm to 1200nm, with a white-light interferometer. Those GDD data should be useful for the dispersion compensation for femtosecond pulse generation in the lasers with these new crystals as the gain media.
© 2007 Optical Society of America
1. Introduction
Ytterbium-doped material crystals have received a great interest in recent years, mainly
for its broadband fluorescence spectrum, simple energy structure, and favorable
absorption wavelength for diode pumping. However, its quasi-three-level operating scheme
has a rigorous requirement on the pumping rate, and the thermal populating in the ground
state laser level would cause strong re-absorption around the emission wavelengths.
These defects have restricted their application in mode locked laser systems.
Recently, several newly developed Yb-doped material crystals such as Yb:GSO, Yb:GYSO and
Yb:LYSO have been demonstrated to be able to overcome these problems [1–4]. Yb:GSO crystal has a quasi-four-level
system, high absorption cross-sections and particularly broad emission bandwidth (about
72 nm) [1]. Yb:GYSO not only retains the high
laser performance of Yb:GSO, but also contains the good mechanical properties of
Yb:Y2SiO5 (Yb:YSO) [3].
In the continuous-wave laser operation of Yb:LYSO, a maximal slope efficiency of 96% and
output power of 7.8 W have been achieved [4]. All
these properties with their ultra-broad fluorescence bands indicate that they are
excellent media for the femtosecond lasers. Pulses as short as 343 fs have already been
achieved in the diode-pumped Yb:GSO femtosecond laser [2]. However, there have not been reliable dispersion data available for these
three new crystals. For further shortening the pulse width, accurate dispersion data are
required. Therefore, measurement for the GDD of these crystals becomes necessary.
C. Yan, G. Zhao, L. Su, X. Xu, L. Zhang, and J. Xu, “Growth and spectroscopic characteristics of Yb:GSO single crystal,” J. Phys.: Condens. Matter 18,1325–1333 (2006). [CrossRef]
C. Yan, G. Zhao, L. Su, X. Xu, L. Zhang, and J. Xu, “Growth and spectroscopic characteristics of Yb:GSO single crystal,” J. Phys.: Condens. Matter 18,1325–1333 (2006). [CrossRef]
J. Du, X. Liang, Y. Xu, R. Li, Z. Xu, C. Yan, G. Zhao, L. Su, and J. Xu, “Tunable and efficient diode-pumped Yb3+:GYSO laser,” Opt. Express 14, 3333–3338 (2006). [CrossRef] [PubMed]
W. Li, S. Xu, H. Pan, L. Ding, H. Zeng, W. Lu, C. Guo, G. Zhao, C. Yan, L. Su, and J. Xu, “Efficient tunable diode-pumped Yb:LYSO laser,” Opt. Express 14, 6681–6686 (2006). [CrossRef] [PubMed]
W. Li, Q. Hao, H. Zhai, H. Zeng, W. Lu, G. Zhao, L. Zheng, L. Su, and J. Xu, “Diode-pumped Yb:GSO femtosecond laser,” Opt. Express 15, 2354–2359 (2007). [CrossRef] [PubMed]
In this paper, we report the GDD of these new crystals (10%-doped Yb:GSO, 5%-doped
Yb:GSO, 5%-doped Yb:GYSO and 5%-doped Yb:LYSO) measured by a home-made white-light
interferometer. The measured GDD data are highly precise for the wavelengths of 1000nm
to 1200nm, covering the tuning bands of those lasers. The GDD data should be useful in
developing diode pumped femtosecond lasers using those new promising crystals.
2. White-light Interferometer
The GDD measurement was performed with a white-light interferometer which was proposed
by Naganuma et al. [5], and we
made some modifications. The schematic of the interferometer is shown in Fig. 1. The interferometer was basically a
Michelson. The white-light source was a fiber-coupled metal-halogen lamp and was
polarized by a polarization beam splitter cube. The scanner was composed of a solenoid
and an iron rod, and was driven by a waveform generator and a power amplifier. To make
precise calibration, another Michelson interferometer was built on the back of the
scanner and the light source was a helium-neon (He-Ne) laser. Two silver mirrors were
glued on both ends of the rod. A triangle current wave was used to drive the scanner and
to generate the interferograms. The repetition frequency of the scanner was about 40Hz
and the scan range was adjusted to best cover the full fringe. The interferograms were
recorded with two InGaAs photodiodes on both sides of the system.
K. Naganuma, K. Mogi, and H. Yamada, “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett. 15, 393–395 (1990). [CrossRef] [PubMed]
Fig. 1. Schematic of the white-light interferometer. SM: single mode fiber; BS: cubic beam
splitter; PBS: polarization beam splitter; M1~M4: Silver mirrors in the Michelson
interferometers; M5~M9: Silver mirrors for optical axes alignment. The GDD of the
apparatus on a blank sample condition would first be measured and would be
subtracted from the subsequent measurement on samples.
The key problem was that the scanner could not translate precisely and linearly with
respect to the scanning time. Although two parallel Michelsons had already been used to
correct the nonlinearity of the scanner, the translation of the scanner should be as
linear as possible, so that the interference fringe could be sampled uniformly in the
temporal axis. Both piezo translator and the solenoid were tried as the scanner and the
linearity of the piezo translator was found much worse than that of the solenoid. Thus
the solenoid was employed in this experiment as the scanner. Slight adjustment of the
repetition frequency and the driving current was still necessary to ensure the He-Ne
interference fringes to look equally spaced in time.
3. Data Processing
Yb:GSO, Yb:GYSO and Yb:LYSO are all biaxial monoclinic crystals. The direction that the
light propagates through our sample is determined as the b-axis. With
unpolarized light when the PBS in the white-light interfermometer was removed, we could
identify two white-light interferograms due to the different group delay of orthogonal
polarizations. The interferogram at the early delay corresponds to the polarization that
sees a smaller refractive index.
The interferograms from both Michelson were recorded simultaneously. The He-Ne laser
interference fringe should be uniformly spaced in the temporal axis, with which we could
calibrate the delay axis and apply to the white-light fringe. However, by checking the
time interval between the neighboring sampled points in the delay axis, we found that
the spacing was not exactly the same, because of the residual nonlinearity of the
scanner translation. Therefore, based on the original sampled data, we used piecewise
cubic Hermite interpolation [6] to rebuilt the
data sets and made the delay axis uniform. The procedure was, for every half-period of
the fringes of He-Ne laser, the horizontal axis was calibrated by taking arccosine of
the normalized amplitude and the phase angle was projected on to the horizontal axis in
from 0 to π. Then the horizontal axis was re-arranged in equal space by cubic
Hermite interpolation. This new horizontal axis was then applied to calibrate the delay
axis of the white-light interference fringes. In this way, the delay axis of the
white-light fringe became uniform in time. Because our original data were densely
sampled with respect to time (about 30 points per period), we had quite enough data
points for ensuring the accurate interpolation in the new time frame. Then the Fourier
transform of the calibrated fringes in cross correlation yields:
F. Fritsch and R. Carlson, “Monotone piecewise cubic interpolation,” SIAM J. Numer. Anal. 17, 238–246 (1980). [CrossRef]
where Ẽs
(ω) was the Fourier transform of the electric field
transmitting through the sample arm and Ẽr
*(ω) was the complex conjugate of the signal in the
reference arm. The phase φ(ω) was
expressed as φ(ω) =
φs
(ω) + φsystem
(ω) - ωτ
0, where φs
(ω) was the phase shift due to the crystal and
φsystem
(ω) was caused by the apparatus inherent bias in group
delay, while τ
0 was the delay representing the path length offset between the two arms in
the interferometer. GDD of the crystal was the second derivative of
φs
(ω) with respect to ω where
τ
0 would be vanished:
In practice, φ(ω) was fitted with a
4th order polynomial from ω =
1.5708fs-1 to 1.8850fs-1, correspondent to wavelength from
1200nm to 1000nm. Then the second derivative was taken, and d
2
φsystem
(ω)/dω
2 would be subtracted through another measurement on a blank sample
condition. Thirty data sets were taken and the phase was averaged before the curve
fitting. To estimate the accuracy, we calculated the root mean squared error (RMSE) for
the fitted curve of the phase, where the phase was normalized in the arithmetic mean
sense. The RMSE was very small, ranging from 1.5326×10-5 to
6.3445×10-5 for these four crystals. We also calculated the
standard deviation of these thirty data sets for each point. The average standard
deviation of these four crystals was ranged from 0.66264fs2/mm to
3.4308fs2/mm, indicating the consistency of our measurement.
The fitted GDD formulae valid in the wavelength range of 1.0μm~1.2μm are
summarized in Table 1, and plotted in Fig. 2 – Fig. 5.
Table 1. Fitted single pass GDD in the wavelength range of 1.0μm~1.2μm
In Fig. 2–Fig. 5, axis x
1 and axis x
2 are the two principal axes in Fresnel’s ellipsoid. They are
orthogonal to the biaxial monoclinic crystal’s b-axis and are
also perpendicular to each other. Axis x
1 corresponds to the polarization parallel to the axis with smaller
refractive index, and its GDD is also smaller. All the GDD decreases with increasing
wavelength, and would reach zero at a longer wavelength, indicating these crystals have
high refractive indices.
The GDD of 5%-doped Yb:GSO is a bit smaller than that of 10%-doped Yb:GSO. We then
measured the refractive index of Yb:GSO by optical transmission measurements in the
1000~1200nm region according to methodology described by J. C. Manifacier et
al. [7]. The result showed that
5%-doped Yb:GSO had a smaller refractive index than the 10%-doped Yb:GSO. This is
consistent with our common sense that the higher refractive index material has a higher
GDD. We concluded that the higher concentration of the Yb3+ ion in the
substrate would lead to a higher refractive index and also a higher GDD in Yb:GSO.
J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E: Sci. Instrum. 9, 1002–1004 (1976). [CrossRef]
It can also be seen that the GDD of these crystals is quite large and drops rapidly
(from 100 to 75 fs2/ mm for Yb:GSO, 95 to 70 fs2/mm for Yb:GYSO
and 95 to 60 fs2/mm for Yb:LYSO, respectively). The rapid drop of GDD implies
a large third order dispersion (TOD). For example, by taking derivative of the formulae
listed in Table 1, we obtained the TOD for
axis x
1 of Yb:GSO which was approximately 101fs3/mm at the wavelength of
1064nm, and the TOD for axis x
2 of Yb:LYSO was even larger, approximately 170fs3/mm at 1064nm.
Therefore, the dispersion compensation should include TOD for femtosecond pulse
generation.
4. Conclusions
We have measured the GDD of Yb:GSO, Yb:GYSO and Yb:LYSO crystal along the two orthogonal
axes with respect to b-axis, over the wavelengths from 1000nm to
1200nm, which is positive and decreases with increasing wavelength. The measured GDD
provided here is convincing and reliable, and would be useful for the dispersion
compensation and for further short pulse generation in femtosecond lasers where these
new crystals are used as laser media.
Acknowledgments
This research was supported in part by the National Basic Research Program (973) of
China under grant number of 2006CB806000, Major Program of National Science Foundation
of China under grant number of 60490280, National Science Foundation of China under
grant number of 60578007 , NSFC-JSPS International Cooperation Program under grant
number of 60611140297, National Natural Science Foundation of China under grant number
of 60544003, Science and Technology department of Shanghai under grant number of
05JC14082, National Outstanding Youth Foundation under grant number of 60425516 and the
Principal Grant of Peking University. The authors wish to thank Kai Guo for lending us
the 5%-doped Yb:GSO crystal and Cheng Xu for the assistance in the measurement of the
refractive indices of the crystals.
References and links
C. Yan, G. Zhao, L. Su, X. Xu, L. Zhang, and J. Xu, “Growth and spectroscopic characteristics of Yb:GSO single crystal,” J. Phys.: Condens. Matter 18,1325–1333 (2006). [CrossRef] | |
W. Li, Q. Hao, H. Zhai, H. Zeng, W. Lu, G. Zhao, L. Zheng, L. Su, and J. Xu, “Diode-pumped Yb:GSO femtosecond laser,” Opt. Express 15, 2354–2359 (2007). [CrossRef] [PubMed] | |
J. Du, X. Liang, Y. Xu, R. Li, Z. Xu, C. Yan, G. Zhao, L. Su, and J. Xu, “Tunable and efficient diode-pumped Yb3+:GYSO laser,” Opt. Express 14, 3333–3338 (2006). [CrossRef] [PubMed] | |
W. Li, S. Xu, H. Pan, L. Ding, H. Zeng, W. Lu, C. Guo, G. Zhao, C. Yan, L. Su, and J. Xu, “Efficient tunable diode-pumped Yb:LYSO laser,” Opt. Express 14, 6681–6686 (2006). [CrossRef] [PubMed] | |
K. Naganuma, K. Mogi, and H. Yamada, “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett. 15, 393–395 (1990). [CrossRef] [PubMed] | |
F. Fritsch and R. Carlson, “Monotone piecewise cubic interpolation,” SIAM J. Numer. Anal. 17, 238–246 (1980). [CrossRef] | |
J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E: Sci. Instrum. 9, 1002–1004 (1976). [CrossRef] |
OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(140.3380) Lasers and laser optics : Laser materials
(140.7090) Lasers and laser optics : Ultrafast lasers
ToC Category:
Lasers and Laser Optics
History
Original Manuscript: May 10, 2007
Revised Manuscript: June 13, 2007
Manuscript Accepted: June 13, 2007
Published: June 22, 2007
Citation
Weijian Yang, Jing Li, Fan Zhang, Yuanyang Zhang, Zhigang Zhang, Guangjun Zhao, Lihe Zheng, Jun Xu, and Liangbi Su, "Group delay dispersion measurement of Yb:Gd2SiO5, Yb:GdYSiO5 and Yb:LuYSiO5crystal with white-light interferometry," Opt. Express 15, 8486-8491 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8486
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References
- C. Yan, G. Zhao, L. Su, X. Xu, L. Zhang, and J. Xu, "Growth and spectroscopic characteristics of Yb:GSO single crystal," J. Phys.: Condens. Matter 18, 1325-1333 (2006). [CrossRef]
- W. Li, Q. Hao, H. Zhai, H. Zeng, W. Lu, G. Zhao, L. Zheng, L. Su, and J. Xu, "Diode-pumped Yb:GSO femtosecond laser," Opt. Express 15, 2354-2359 (2007). [CrossRef] [PubMed]
- J. Du, X. Liang, Y. Xu, R. Li, Z. Xu, C. Yan, G. Zhao, L. Su, and J. Xu, "Tunable and efficient diode-pumped Yb3+:GYSO laser," Opt. Express 14, 3333-3338 (2006). [CrossRef] [PubMed]
- W. Li, S. Xu, H. Pan, L. Ding, H. Zeng, W. Lu, C. Guo, G. Zhao, C. Yan, L. Su, and J. Xu, "Efficient tunable diode-pumped Yb:LYSO laser," Opt. Express 14, 6681-6686 (2006). [CrossRef] [PubMed]
- K. Naganuma, K. Mogi, and H. Yamada, "Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light," Opt. Lett. 15, 393-395 (1990). [CrossRef] [PubMed]
- F. Fritsch and R. Carlson, "Monotone piecewise cubic interpolation," SIAM J. Numer. Anal. 17, 238-246 (1980). [CrossRef]
- J. C. Manifacier, J. Gasiot and J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E: Sci. Instrum. 9, 1002-1004 (1976). [CrossRef]
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