Precise measurement of group refractive indices and temperature dependence of refractive index for Nd-doped yttrium orthovanadate by intracavity spontaneous mode locking

Precise measurement of group refractive indices and

temperature dependence of refractive index for

Nd-doped yttrium orthovanadate by intracavity

spontaneous mode locking

Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan *Corresponding author: [email protected]

Received July 20, 2011; accepted August 27, 2011;

posted August 30, 2011 (Doc. ID 151452); published September 19, 2011

We report on a novel method based on intracavity spontaneous mode locking to precisely measure the group re-fractive indices and temperature dependence of rere-fractive index of Nd : YVO₄crystal at the wavelength of 1064 nm. All the experimental results are found to agree very well with the most recent measured values. We also confirm that the developed method is applicable to measuring the group refractive indices and the temperature dependence of the refractive indices of other vanadate crystals, as well as nonlinear crystals. © 2011 Optical Society of America

OCIS codes: 140.3380, 140.4050, 140.6810.

Phase and group refractive indices are among the most important properties of optical materials. The former and the latter are the ratios of the vacuum velocity of light to its phase and group velocities in the material, respectively. For dispersive media, these indices may differ substantially. Different approaches for measuring the phase refractive indices of various materials have been reviewed [1]. The group refractive index ngfor the

wavelength can be calculated mathematically from the phase refractive index np by use of [2]

ng¼ np− λ

∂np

∂λ : ð1Þ Alternatively, the group refractive index of a material can be measured directly by measuring the time of propagation of short pulses over a known distance. White-light interferometry based on the use of a white-light source in combination with a standard Michelson or Mach–Zehnder interferometer is by far the most widely used method for measuring the group refractive indices for different optical materials [3–5].

The temperature dependence of refractive index, dn=dT, is also an important physical quantity of an opti-cal material [6]. In solid-state lasers, the temperature dependence of refractive index of the laser gain media explicitly determines the focal power of the thermally induced thermal lens that significantly influences the cavity stability, the oscillation mode size, the maximum achievable average power, and the output beam quality [7]. Therefore, precise measurement of the temperature dependence of refractive index for laser gain media is practically important for designing high-power solid-state lasers.

In the past decade, Nd3þ_{-doped vanadate crystals have}

been confirmed to be promising gain medium due to their good laser properties, such as their large stim-ulated emission cross section and high absorption over a wide pumping wavelength bandwidth [8–11]. Re-cently it was verified that, under the condition of elimi-nating the internal and external unwanted reflection, a

diode-end-pumped Nd:YVO₄ laser could exhibit remark-able spontaneous mode locking [12,13]. In this work, we develop a novel method based on intracavity sponta-neous mode locking to precisely measure the group refractive indices and the temperature dependence of refractive index of Nd:YVO₄crystal at the wavelength of 1064 nm. The experimental results are found to be in good agreement with the most recent measured values [14]. The developed method is also confirmed to be applicable to measuring the group refractive indices and temperature dependence of refractive index of other vanadate crystals, as well as nonlinear crystals.

Figure1depicts the experimental setup for measuring the group refractive indices and the temperature depen-dence of refractive index. We used a simple concave-plano configuration to construct the laser cavity and obtained stable spontaneous mode locking by avoiding all unwanted reflection. The gain medium was a-cut 0:2 at:% Nd:YVO4 crystal with a length of 10 mm. Both

end surfaces of the Nd:YVO₄ crystal were antireflection coated at 1064 nm and wedged at 0:5° to suppress the Fabry–Perot etalon effect. The gain crystal was wrapped with indium foil and mounted in a water-cooled copper holder. The water temperature was maintained around 20 °C to ensure stable laser output. The input mirror was a 100 mm radius-of-curvature concave mirror with antire-flection coating at 808 nm on the entrance face and with high-reflectance coating at 1064 nm (>99:8%) and high transmittance coating at 808 nm on the second surface.

Nd:YVO4 Pumping beam Laser diode Focusing lens Cavity mirror Sample Stage Stage Output coupler Nd:YVO4 Pumping beam Laser diode Focusing lens Cavity mirror Sample Stage Stage Output coupler

Fig. 1. (Color online) Experimental setup for measuring the group refractive indices and temperature dependence of refractive index.

October 1, 2011 / Vol. 36, No. 19 / OPTICS LETTERS 3741

A flat wedged output coupler with 15% transmission at 1064 nm was used throughout the experiment. The pump source was a 2:5 W 808 nm fiber-coupled laser diode with a core diameter of 100 μm and an NA of 0.16. A focusing lens with 25 mm focal length and 85% coupling efficiency was used to reimage the pump beam into the laser crys-tal. The average pump size was approximately 150 μm, which was appropriate for mode-size matching. The mode-locked pulses were detected by a high-speed InGaAs photodetector (Electro-optics Technology Inc. ET-3500, with rise time 35 ps), whose output signal was connected to a digital oscilloscope (Agilent, DSO 80000) with 12 GHz electrical bandwidth and sampling interval of 25 ps. At the same time, the output signal of the photo-detector was also analyzed by an RF spectrum analyzer (Advantest, R3265A) with bandwidth of 8:0 GHz.

First of all, we set up the cavity without inserting the sample to be approximately 4:5 cm, corresponding to free spectral range of 3:337 GHz. As reported in the earlier study [12], the laser cavity could be optimized to exhibit stable mode locking by finely adjusting the cavity with the help of monitoring the real-time pulse train and the power spectrum. Figures2(a) and2(b) show the pulse trains on two different time scales, one with time span of 10 μs, demonstrating the amplitude stability, and the other with time span of 10 ns, demonstrating the mode-locked pulse train. It can be seen that the pulse train displays full modulation and complete mode locking is achieved. The corresponding power spectrum is depicted in Fig.2(c). The frequency deviation of the power spec-tra, Δυ=υ, is experimentally found to be significantly smaller than 10−4, whereυ is the center frequency of the power spectrum and Δυ is the frequency deviation of FWHM. The small frequency deviation enables us to mea-sure the change of the optical path length with precision. More importantly, the self-mode-locked emission is line-arly polarized because the Nd:YVO₄gain medium is a uni-axial crystal with a large birefringence.

After optimizing the self-mode-locked laser, the sample crystal was inserted into the cavity to measure the change of the pulse repetition rate. The sample crystal was an a-cut Nd:YVO₄ crystal with a doping concentra-tion of 0:2 at:% and length of 12:4 mm. We initially set the c axis of the sample crystal to be along the output polarization. Figure 3 depicts the experimental results for the pulse repetition rate before and after inserting the sample crystal. The optical path difference can be

precisely calculated from the variation of the pulse repe-tition rate.

The measured optical path difference was then em-ployed to determine the group refractive index for ne.

Since the YVO₄ crystal is a positive uniaxial crystal with no¼ na¼ nb and ne¼ nc, the group refractive index

for no can be determined by turning the sample crystal

90° around the longitudinal axis. It was found that the group refractive indices for no and ne are 1.9987 and

2.2222, respectively. Recently, Zelmon et al. [14] reported new measurements of the phase refractive indices for the Nd:YVO₄crystal and expressed the Sellmeier equation as

n2 o¼ 2:3409 þ 1:4402λ 2 λ2_{− 0:04825}þ 1:8698λ2 λ2_{− 171:27}; ð2Þ n2 e¼ 2:7582 þ 1:853λ 2 λ2_{− 0:056986}þ 3:0749λ2 λ2_{− 195:06}: ð3Þ

With Eqs. (1)–(3), the group refractive indices for noand

ne are calculated to be 1.9984 and 2.2221, respectively.

The differences between our and Zelmon et al.’s results are as significantly small as 0.0003 and 0.0001 for the group refractive indices of no and ne, respectively. The

principal sources of error in the measurements are from the frequency uncertainty of the pulse repetition rate. The frequency uncertainty is estimated to be approxi-mately
50 kHz. Consequently, the errors induced by the frequency uncertainty in the measurement of group refractive indices are generally less than
10−4.

Zelmon et al. [14] recently measured the temperature dependences of refractive indices of the Nd:YVO₄crystal and found the values to be dno=dT ¼ 14:0 × 10−6K−1and

dne=dT¼ 9:0 × 10−6K−1. Their values are larger by a

factor of 3 for dno=dT and a factor of 2 for dne=dT

at 1064 nm than those often cited in the literature [15]. This large discrepancy deserves further investigation. To measure the temperature dependence of refractive index, we employ a heater and a temperature control to vary the temperature of the sample crystal between 30 °C and 200 °C. The optical path difference ΔL caused by the temperature change ΔT can be expressed as ΔL ¼ ½ðdn=dTÞ þ αT×ðn − 1Þ × lc×ΔT, where lc is

the length of the sample crystal andαT is the linear

ther-mal expansion coefficient. The optical path difference leads to a variation of the pulse repetition rateΔυ to be

1µ s/div 1ns/div Frequency (GHz) 3.335 3.336 3.337 3.338 3.339 3.340 Sp ect ra l pow er densi ty ( d B m ) -80 -70 -60 -50 -40 -30 -20 -10 1µ s/div 1ns/div (a) (b) (c) Span: 5MHz, Res. BW: 1kHZ

Fig. 2. (Color online) Pulse trains on two different time scales: (a) time span of 10 μs, demonstrating mode-locked pulses; (b) time span of 10 ns, demonstrating the amplitude oscillation. (c) Corresponding power spectrum.

Frequency (GHz) 2.6 2.8 3.0 3.2 3.4 In te n sity (d Bm ) -80 -70 -60 -50 -40 -30 -20 -10

Crystal inside cavity Crystal outside cavity

720 MHz

Fig. 3. (Color online) Experimental results for the pulse repe-tition rate before and after inserting the sample crystal. 3742 OPTICS LETTERS / Vol. 36, No. 19 / October 1, 2011

given by Δυ ¼ −½2 × υ2_{=c × ΔL. As a consequence, the}

temperature dependence of refractive index can be determined by recording the variation of the pulse repetition rate as a function of the temperature change. Figure 4 shows the experimental results for the fre-quency shift versus the temperature change. With the experimental data andα_T ¼ 4:43 × 10−6K−1, the tempera-ture dependences of refractive indices are derived to be dno=dT ¼ 14:6 × 10−6K−1 and dne=dT ¼ 9:0 × 10−6K−1.

Our results can be found to agree very well with those Zelmon et al. reported [14]. Furthermore, we confirmed that the present method can be used to measure the temperature dependences of refractive indices for other laser crystals.

In conclusion, we have exploited intracavity sponta-neous mode locking to measure the group refractive indices and the temperature dependence of refractive in-dex of Nd:YVO_{4crystal at the wavelength of 1064 nm with} high accuracy. All the experimental results are found

to be in good agreement with the most recent measured values. This method can be further employed to measure the group refractive indices and temperature depen-dences of refractive indices of other laser crystals, as well as nonlinear crystals.

The authors thank the National Science Council of Taiwan (NSCT) for their financial support of this re-search under Contract No. NSC-97-2112-M-009-016-MY3.

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Temperature difference (K)

0 20 40 60 80 100 120 140 160 180

Pulse repetiton rate shift (MHz)

-1000 -800 -600 -400 -200 0 a-axis c-axis

Fig. 4. (Color online) Pulse repetition rate shift versus temperature.