First of all, the stable self-mode-locked are established for operating at 1064 nm and 1342 nm. The pulse repetition rates are measured at the frequency of 2.748 GHz.
The relative frequency deviation of the power spectrum, v/v, is smaller than 6 10 5, where v is the center frequency of the power spectrum and v is the frequency deviation of full width at half maximum. After the sample inserts into the optical resonator, the pulse repetition rates are observed a finite shit corresponding the change of optical path length and can be expressed as:
'
2 'opt 2 opt
c c
f f f
L L
, (4.3.1) )
where Lopt is the optical path length with a sample inside. By measuring the shift of pulse repetition rate, the change of optical path length Lopt L'opt Lopt can be estimate. However, the difference of the optical path length is associated with the length and refractive index of crystal. Therefore, the refractive index will be obtained with a given crystal length. However the refractive index which estimated by a mode-locked pulse is called group index n [16], a convenient way for determining g the refractive index n according to p
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Here, we have measured three kinds of Nd3+-doped crystals with different host materials including Nd:YVO4, Nd:GdVO4, and Nd:YGdVO4 and the self-mode- locked lasers are not only operating at 1064 nm but also operating at 1342 nm. Table 4.3.1 shows the experimental results for the measurement of ordinary refractive indexes and extraordinary refractive indexes at 1064 nm and 1342 nm. The refractive indexes measuring in this method are found to be agreement with the values that reported in the literatures [9-15]. Figure 4.3-1 demonstrates the experimental results for measuring the ordinary refractive index (n ) and extraordinary refractive index o (n ) of Nd:YVOe 4 with different doped concentration in the range of 0.2 - 0.8 at. %.
There are three samples for each doped concentration. The ordinary refractive indexes are found in the range of 1.9997 - 2.0002 and the extraordinary refractive indexes are found in the range of 2.2232 - 2.2240 as a function of doped concentration.
It can be seen that the crystals exhibit higher refractive index with the higher doped concentration and the variation are observed in the order of 104..
In the second part, we have measured the thermal optical coefficient of 0.1 at. % Nd:YVO4 crystal with a length of 12 mm. In the experimental system, an oven is used for heating the crystal inside the optical cavity. By heating the crystal form 30 °C to 200 °C, the pulse repetition rate of the mode-locked laser was found to decrease gradually. The frequency shifts are resulted from the increase of the optical path
by:
( 1)
opt cav c
L L (4.3.3) n l
where Lcav is the cavity length and n is the refractive index of the crystal. As the crystal is heated, the optical length path has changed and can be written as
' ( 1) (1 )
where dn dT is the thermal optical coefficient, is the thermal expansion coefficient, and T is the increase of temperature. Thus, the difference of the optical path length is obtained by
1
2However, the last term in Eq. (4.3.4) is quite small usually and can be neglect. With the frequency shifts which were obtained experimentally, the difference of optical path length would be carrying out. Therefore, with the parameterslc 12 mm ,
1.996
no , 2.223ne , and 4.43 10 6 K, the thermal optical coefficient can be found to be 7.6 10 6 K and 4.2 10 6 K for the direction perpendicular and parallel to the c-axis of crystal respectively. The experimental results are in good
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agreement with that reported in the literature (the value of thermal optical coefficient are 8.5 10 6 K and 3 10 6 K, respectively, for a-axis and c-axis of Nd:YVO4
crystal) [12].
Table. 4.3.1. The experimentally measuring refractive indexes for different material at operating wavelength of 1064 nm and 1342 nm.
Materials 1064 nm 1342 nm
1.7958 1.8872 [15] 1.7685 1.8536 [15]
ny nz ny nz
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Fig. 4.3-1. The experimental results for measuring refractive indexes of Nd:YVO4 with different doped concentrations. (a) For ordinary refractive indexes. (b) For extraordinary refractive indexes.
(b) (a)
Fig. 4.3-2. Frequency shift versus the temperature of oven.
Temperature (K)
300 320 340 360 380 400 420 440 460 480
Frequency shift f (KHz)
-1000 -800 -600 -400 -200 0 200
a-axis crystal c-axis of crystal
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4.4 Conclusion
In summary, we have demonstrated a novel method to estimate the refractive indexes of several crystals. The ideal is based on the shift of pulse repetition rate as a crystal is placed inside the optical cavity. The ordinary and extraordinary refractive indexes of Nd:YVO4 crystals with different doped concentration are experimentally found that the refractive indexes increasing as the doped concentration increasing in the range from 0.2 at.% to 0.8 at.%. Besides, the Nd:YVO4 crystal, we also measuring the Nd:GdVO4 and Nd:GdYVO4 crystals. The experimental results are consist with the value which have reported. By heating the crystal, the thermal optical coefficient of Nd:YVO4 crystal are experimentally observed. The thermal optical coefficients are 7.6 10 6 K and 4.2 10 6 K at different axis of Nd:YVO4 crystal and are in good agreement with the results in other reports.
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