Third-order nonlinearity and saturable absorbed performance of Cr4+:Gd3Ga5O12 crystal

Yiran Wang; Zhitai Jia; Xiancui Su; Baitao Zhang; Ruwei Zhao; Xutang Tao; Jingliang He

doi:10.1364/OME.6.002600

1. Introduction

In recent years, diode-pumped passively Q-switched (PQS) lasers have attracted a great deal attention because of the advantages of high efficiency, simplicity, compactness and so on [1]. To Q-switch a laser passively need use a saturable absorber (SA), in which a material with nonlinear absorption at the laser wavelength and low saturable intensity. The nonlinearity of SA plays a key role for generation of passively pulsed lasers. There are various SAs that have been successfully used in PQS and passively Q-switching mode-locked (QML) lasers, for example, dyes, LiF:F₂^-, bulk semicondutors, two-dimensional materials and transition metal ion-doped crystals [2–9]. Among these SAs, Cr⁴⁺:YAG crystal has attracted much attention as passive Q-switchers. Compared with other SAs, it has a large absorption cross section, low saturable intensity, good thermal stabilities and higher damage threshold [10]. Be analogous to Cr⁴⁺:YAG, the saturable absorption was also discovered in Cr⁴⁺:GGG crystal. Thus, Cr⁴⁺:GGG crystal has the potential to be employed in the PQS and QML as a new kind of SA. Compared with YAG, GGG crystal can be grown in larger size and faster growth rate (5 mm/h) without growth core, and can support a high level concentration. The thermal conductivity of GGG crystal decreases slightly as the dopant concentration increases, while the YAG crystal decreases strongly so that YAG with high dopant concentration has a lower thermal conductivity than that of GGG [11]. Up to now, only Q-switching operation has been realized using the Cr⁴⁺:GGG. Z. Buurshtein et al. studied the excited-state absorption (ESA) of Cr⁴⁺ ions in details [12]. B. Lipavsky et al. demonstrated passive Q-switching flashlamp-pumped Nd:YAG laser by using Cr⁴⁺:GGG with the pulse duration of 150 ns [13]. Y. Kalisky et al. realized passively Q-switched operation by using Cr⁴⁺:GGG with the pulse width of 60 ns [14, 15]. In 2005, V. B. Tsvetkov grew Cr⁴⁺:GGG epitaxial films to achieve passively Q-switched laser, obtaining 0.5 W average output power with pulse duration of 500 ns and repetition rate of 100 kHz [16, 17]. However, to our best knowledge, there is no report about Q-switched mode-locked lasers using a Cr⁴⁺:GGG crystal as SA.

In this paper, using Z-scan technique, the optical Kerr nonlinearity of Cr⁴⁺:GGG crystal was analyzed systematically. The saturable absorption property was also investigated by using a nanosecond laser. In addition, the PQS and QML operations were demonstrated by using Nd:YAG as the gain medium and Cr⁴⁺:GGG crystal as the saturable absorber.

2. Spectroscopy and third-order nonlinearity

Figure 1 shows the absorption spectrum of the Cr⁴⁺:GGG crystal. From the spectrum, we can see the broadband absorption around 1.0 μm assigned to the ³A₂ -³T₂ transition of the Cr⁴⁺ ions. Meanwhile, the Cr⁴⁺:GGG has ESA around 1.0 μm assigned to the ³T₂ -³T₁ transition of Cr⁴⁺ ions. The upper level lifetime and the higher-lying level lifetime of Cr⁴⁺ ions were estimated to be 2.2 μs and picosecond range, respectively [18].

Fig. 1 Absorption spectrum of Cr⁴⁺:GGG crystal. The inset shows the detail information around 1 μm.

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In our experiment, the third-order nonlinear properties of Cr⁴⁺:GGG were investigated. The nonlinear refractive index (n₂) was measured by using Z-scan technique. In the Z-scan measurement we used a Ti:sapphire laser with pulse repetition rate of 80 MHz and a pulse width of 80 fs at 800 nm. In our Z-scan measurement, the open aperture and close aperture were both studied. The inset in Fig. 2(a) shows the experimental data of open aperture measurement. The open aperture Z-scan transmittance variations can be calculated following the fitting formula [19]

Fig. 2 (a) Normalized transmittance curves of Z-scan and (b) energy transmission corrected for Fresnel reflection versus energy density.

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T = \sum_{m = 0}^{\infty} \frac{{[- q_{0} (z, 0)]}^{m}}{{(m + 1)}^{3 / 2}} (m \in N) q_{0} (z, 0) = \frac{β \cdot L_{e f f} \cdot I_{0}}{(1 + z^{2} / z_{0}^{2})}

where β is the nonlinear absorption coefficient, I₀ = 7.85 GW/cm² is the power fluence at focus, z₀ is Rayleigh range, $L_{e f f} = (1 - e^{- α L}) / α$ is the effective length, L is the length of Cr⁴⁺:GGG and α is the linear absorption coefficient. In the close aperture measurement, the nonlinear absorption and nonlinear refraction existed simultaneously. Figure 2(a) shows the close aperture experimental data divided by the open aperture. The transmission T can be estimated by the formula [19]

T = 1 + \frac{4 \cdot k \cdot L_{e f f} \cdot γ \cdot I_{0} \cdot x}{(x^{2} + 9) \times (x^{2} + 1)}

where $x = z / z_{0}$ , n₂ and γare the third-order nonlinear refractive index in esu and MSK, respectively. n₂ and γ are related through $n_{2} = c n_{0} γ / 40 π$ , c and n₀ are speed of light and linear refractive index. According to the Eqs. (1) and (2) we estimated the value of n₂ to be 5.34 × 10⁻¹³ (esu). The result is slightly smaller than that of 5.8 × 10⁻¹³ (esu) for pure GGG, but larger than that of 2.7 × 10⁻¹³ (esu) for pure YAG [20]. It indicated that Cr⁴⁺:GGG has the potential for realizing efficient kerr-lens mode-locked lasers.

For transmission saturation measurements we used 1064 nm pulses with a repetition rates of 5 kHz and duration about 10-20 ns. The energy density was varied by attenuating the output power or by moving the Cr⁴⁺:GGG along the focused beam axis using a lens of ƒ = 100 mm. Figure 2(b) displays the nonlinear transmission curve of a Cr⁴⁺:GGG sample (thickness 2.6 mm) at 1064 nm. For the “slow” absorber, the transmission T can be approximated by [10,21]

T \equiv \frac{E_{o u t}}{E_{i n}} ≅ T_{0} + \frac{T_{i} - T_{0}}{1 - T_{0}} (T_{m a x} - T_{0})

T_{i} = \frac{h v}{σ_{g s} {\bar{E}}_{i n}} l n {1 + T_{0} [e x p (σ_{g s} {\bar{E}}_{i n} / h v) - 1]}

where E_in and E_out are the incident and outgoing total pulse energies,

T_{0} = e x p (- N σ_{g s} L)

is the small-energy limit of the energy transmission,

T_{m a x} = e x p (- N σ_{gs} L)

is the saturated transmission limit, N is the concentration of tetrahedrally coordinated Cr⁴⁺ ions, L the sample thickness, σ_gs is the groud-state absorption cross section, σ_es is the excited-state absorption cross section, T_i is the energy transmission under no-loss conditions (σ_es = 0), and hv = 1.868 × 10⁻¹⁹ J is the photo energy. With Eqs. (3) and (4) shown above to fit the results in Fig. 2(b), the values of σ_gs and σ_es are determined by 4.92 × 10⁻¹⁸ cm² and 1.38 × 10⁻¹⁸ cm², respectively. The values of σ_gs and σ_es we measured are similar to the values in refer [22]. The σ_gs is slightly larger than that of Cr⁴⁺:YAG (3.2 × 10⁻¹⁸ cm²), Cr⁴⁺:YSGG (4.14 × 10⁻¹⁸ cm²) and Cr⁴⁺:YGG (4.14 × 10⁻¹⁸ cm²) [21,23]. The value of σ_gs/σ_es for Cr⁴⁺:GGG is determined to be 3.57, which is larger than that of Cr⁴⁺:YGG (1.43) but smaller than that of Cr⁴⁺:YSGG (7.2) and Cr⁴⁺:YAG (7.2) [21,23]. It indicates that Cr⁴⁺:GGG has relatively large σ_es. In combination with the short lifetime of second excited-state [18], Cr⁴⁺:GGG has the potential to be used for mode-locked lasers.

3. Q-switching operation

A plane-plane cavity was employed in the diode-pumped passively Q-switched laser. The pump source was a fiber-coupled 808 nm diode laser with a core diameter of 400 μm and numerical aperture of 0.22. The pump beam was focused into the gain medium with a waist radius of ~200 µm by a 1:1 coupling optics system. The Nd:YAG crystal was cut with the dimension of 3 × 3 × 5 mm³ and had a Nd-doping concentration of 1.0 at.%. Both sides of the Nd:YAG crystal were anti-reflection coated at 808 nm and 1064 nm. The input plane mirror M1 was high reflection coated at 1064 nm (R ≥ 99.9%) and high transmission coated at 808 nm (T ≥ 95%). Two flat mirror M2 with transmission of 10% and 4.2% were employed as the output coupler. An uncoated Cr⁴⁺:GGG crystal with the dimensions of 3 × 3 × 5 mm³ was used as the SA. The gain crystal and SA were wrapped with indium foil and held in a copper sink cooled by water at a temperature of 20 °C. The laser pulse profile was recorded by a Tektronix DPO7104 digital oscilloscope (1 GHz bandwidth, 5 Gs/s sampling rate) and a photodetector (New focus, model 1611).

Firstly, the CW operation was realized without SA in the cavity. With T = 10% output coupler, the maximum output power of 5.26 W was obtained at the absorbed pump power of 8.9 W, corresponding the slope efficiency of 62%. The passively Q-switched laser was achieved by inserting Cr⁴⁺:GGG SA into the cavity. Under the absorbed pump power of 8.9 W, the maximum output power of 0.6 W was achieved with the output coupler of 10%. The PQS output power was shown in the Fig. 3(a). The relationship between the pulse repetition rate and the pulse width versus the absorbed pump power was given in Fig. 3(b). As shown in Fig. 3(b), with the increase of absorbed pump power, the repetition rate increases and the pulse width declines linearly. The shortest pulse width of 4.76 ns with the repetition rate of 41.4 kHz was obtained under the absorbed pump power of 8.9 W, which was shorter than the previously reports [13, 14, 17]. The corresponding maximum pulse energy and pulse peak power were determined to be 14.5 μJ and 3 kW, respectively. The temporal pulse profiles and train of pulse under the absorbed pump power of 8.9 W were shown in Fig. 3(c).

Fig. 3 (a) Output power versus absorbed pump power; (b) repetition rate and pulse width versus the absorbed pump power; (c)and (d) measured and simulated pulse profile and pulse train under absorbed pump power of 8.9 W.

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We used the Q-switched rate equations to analyze the performance of Cr⁴⁺:GGG crystal in Q-switching operation. The rate equation can be written as [24]:

\frac{d ϕ}{d x} = \frac{ϕ}{t_{r}} [2 σ n l - 2 σ_{g s} n_{s 1} l_{s} - 2 σ_{e s} (n_{s 0} - n_{s 1}) l_{s} - \ln \frac{1}{R} - L]

\frac{dn}{dt} = R_{i n} - c σ ϕ n - \frac{n}{τ}

\frac{d n_{s 1}}{dt} = - c σ_{g s} ϕ n_{s 1} + \frac{n_{s 0} - n_{s 1}}{τ_{s}}

where ϕ is the total density in the cavity, c is speed of light, L_c is optical path of cavity, t_r = 2L_c/c is the round-trip time in cavity, n is the population-inversion density, ns1 is the ground-state population densities of Cr⁴⁺:GGG,

R_{i n} = P_{i n} / h v_{p} ω_{p}^{2} l

is the pump rate, ω_p is the radius of the pump light and hν_p is photon energy of the pump light. The captions and values of other parameters were shown in the Table 1.

Table 1. The parameters of the theoretical calcution.

View Table

Using the rate equation and parameters in the Table 1, we can obtain the simulated temporal Q-switched pulse shape. Figure 3(d) shows the calculated pulse profile and pulse train at the absorbed pump power of 8.9 W. The estimated width of the Q-switched pulse and the repetition rate of the pulse train are 3.55 ns and 43.46 kHz, which are well agreement with the experimental results (4.76 ns, 41.4 kHz).

4. Q-switched mode-locking operation

To realize mode locking operation, a V-type cavity shown in Fig. 4(a) was used. The pump system, gain medium and SA are the same as that in Q-switching operation. The input concave mirror M1 (R = 150 mm) and folded concave mirror M2 (R = 515 mm) were high reflection coated at 1064 nm (R ≥ 99.9%) and high transmission coated at 808 nm (T ≥ 95%) . The flat mirror M3 with the transmittance of T = 10% at 1064 nm was employed as the output coupler. The lengths of L1 and L2 were 578 mm and 465 mm, and the total length of the V-type cavity was 1043 mm.

Fig. 4 (a) Experimental setup of the V-type cavity. (b) Temporal traces of QML laser pulses with scale of 100 ns/div and 10 ns/div.

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When the pump power was around the threshold, Nd:YAG laser was operated in the Q-switching regime because of the low photon density in the Cr⁴⁺:GGG crystal. The ESA of Cr⁴⁺ plays a key role in the QML operation. To generate a QML pulse, the photon density in the Cr⁴⁺:GGG crystal must be high enough thus the ESA would be strong. The relatively large excited-state absorption cross section of Cr⁴⁺:GGG is also beneficial for ESA. In our experiment, we used a V-type cavity to make a proper spot size in the SA. Base on the ABCD theory and considering the thermal-lensing effect of the gain medium, we calculate that the intracavity beam waist was about ~40 μm in radius in the SA. The average output power increased linearly with the augment of absorbed pump power, and the maximum output power of 468 mW was obtained at the absorbed pump power of 11.8 W. Figure 4(b) displays the temporal traces of a single Q-switched pulse envelops obtained at the maximum absorbed pump power. As shown in Fig. 4(b), the modulation depth of the mode-locking pulse train was nearly 100%. The inset in Fig. 4(b) shows the expanded mode-locked pulse train within the Q-switched envelope. The pulses were separated by 7 ns, matching exactly with the cavity roundtrip time and corresponding to a repetition rate of 141.2 MHz.

5. Conclusion

In summary, the optical nonlinear refraction and saturable absorption properties of Cr⁴⁺:GGG were measured and analyzed. The results show that Cr⁴⁺:GGG has a large excited-state absorption cross section compared to Cr⁴⁺:YAG. And the large nonlinear refractive index indicates that Cr⁴⁺:GGG has potential for realizing kerr-lens mode-locked laser. By using Cr⁴⁺:GGG as saturable absorber, the Q-switched operation and Q-switched mode-locking operation were realized. In the Q-switched operation, the maximum average output power of 0.6 W was obtained with T = 10% output coupler under the absorbed pump power of 8.9 W. The shortest pulse width was 4.76 ns with the repetition rate of 41.4 kHz, corresponding to signal pulse energy and pulse peak power of 14.5 µJ and 3 kW, respectively. For the Q-switching mode-locking operation, the maximum output power of 468 mW was obtained with a repetition rate of 141.2 MHz. The results in this work indicate that the Cr⁴⁺:GGG crystal can be used as saturable absorber in the PQS and QML lasers.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Contract No. 61275142, 61308042, 51321091, 51227002, 51323002) and Young Scholars Program of Shandong University (2015WLJH36).

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Parameters	Caption	values
σ	the stimulated emission section of gain medium	2.8 × 10⁻¹⁹ cm⁻²
σ_gs	the ground-state absorption cross section of Cr⁴⁺:GGG	4.9 × 10⁻¹⁸ cm⁻²
σ_es	the excited-state absorption cross section of Cr⁴⁺:GGG	13.8 × 10⁻¹⁹ cm⁻²
τ	the stimulated-state lifetime of gain medium	230 μs
τ_s	the excited-state lifetime of Cr⁴⁺:GGG	2.2μs
l	the length of laser crystal	5 mm
l_s	The length of Cr⁴⁺:GGG	5 mm
L	theontrinsic loss of cavity	0.08
n_s0	the total density of Cr⁴⁺:GGG	1.57 × 10¹⁷ cm⁻³

Third-order nonlinearity and saturable absorbed performance of Cr⁴⁺:Gd₃Ga₅O₁₂ crystal

Abstract

1. Introduction

2. Spectroscopy and third-order nonlinearity

3. Q-switching operation

4. Q-switched mode-locking operation

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (4)

Tables (1)

Equations (7)

Optical Materials Express