Generation of low repetition rate subnanosecond pulse in an optimal doubly QML Nd:Lu0.15Y0.85VO4 laser with EO and Cr4+:YAG

Haijuan Zhang; Jia Zhao; Kejian Yang; Shengzhi Zhao; Guiqiu Li; Dechun Li; Tao Li; Wenchao Qiao

doi:10.1364/OE.23.020176

1. Introduction

Pulsed lasers with high peak power and hundreds of microjoules of pulse energy enable numerous industrial, medical and scientific applications [1–5 ]. Pulse duration, per-pulse energy, peak power and amplitude stability are regarded as four most critical factors and have significant influence to the applications. For example, to the nonlinear frequency conversion, high intensity of the short laser pulses conduces to high conversion efficiency [1, 6 ]; subnanosecond laser pulses with high power can realize appropriate material removal rate and sufficient high precision in some micro-machining processes [7, 8 ]; highly stable picosecond lasers providing MW to GW peak powers can pump the optical parametric chirped-pulse amplifiers (OPCPAs).

The dual-loss-modulated QML technology means employing the active electro-optical (EO) Q-switch modulator and the passive saturable absorber simultaneously in one laser cavity [12]. By using the dual-loss-modulated QML technology, the Q-switched envelope could be compressed to contain only one mode-locking pulse [12]. In this way, all the energy of the Q-switched envelope was concentrated into one subnanosecond mode-locking pulse. The pulse energy and peak power were thus substantially improved. Benefitting from the introduction of the active modulator, the laser pulses had favorable stability and the repetition rate was optionally adjustable. The dual-loss-modulation technology was demonstrated to be a simple and effective method for generating subnanosecond pulses with high pulse energy and peak power.

Working as a traditional saturable absorber for QML, Cr⁴⁺:YAG has some advantages such as good photo-chemical and thermal stability, large absorption cross-section, low saturable intensity and high damage threshold. Because the Q-switched envelopes produced by the passively QML lasers with Cr⁴⁺:YAG usually have obviously sharper rising but gentler falling edges [13–15 ], Cr⁴⁺:YAG was deemed to be the non-preferred saturable absorber for compressing envelope width. Even when adopting EO/Cr⁴⁺:YAG dual-loss-modulator and high pump power, the shortest Q-switched envelope still contains several mode-locking pulses in it [13]. In fact, experiments proved that the rising time, falling time and pulse duration of the Q-switched envelope are variously influenced by output coupler (OC) transmission T and initial transmittance T₀ of Cr⁴⁺:YAG saturable absorber [14]. This indicates that symmetry of Q-switched envelopes generated from the QML laser with Cr⁴⁺:YAG could be optimized. Meanwhile, the envelope duration could be shortened by using appropriate transmission of output couplers and initial transmission of Cr⁴⁺:YAG saturable absorbers. In addition, mixed laser crystals have been approved to have better energy storage capacity in Q-switched lasers in comparison with the single crystals owing to the reduction of the stimulated emission cross sections and the extension of the fluorescence lifetime [16, 17 ]. Superior continuous wave (CW) mode-locked operation was also demonstrated for their broader gain spectrum [18, 19 ]. By using a mixed crystal as the gain medium, a larger pulse energy and shorter pulse duration could be expected. Based on the reasonable choice of T, T₀ and the gain medium, the EO/Cr⁴⁺:YAG dual-loss-modulated laser can be further improved. As a result, the expected single mode-locking pulse underneath one Q-switched envelope could be obtained.

In this paper, the dependence of duration and symmetry of the Q-switched envelope, generated by Cr⁴⁺:YAG passively QML Nd:Lu_0.15Y_0.85VO₄ laser, on T and T₀ was investigated firstly. A series of OCs with T = 20, 40, and 60% were utilized to crossly match Cr⁴⁺:YAG saturable absorbers with T0 = 88%, 79% and 60%. To ensure a higher output power of the laser, OCs with T>60% and saturable absorbers with T₀<60% were eliminated in the experiment. Among the 9 groups of T₀/T, groups T₀ = 79%/T = 40%, T₀ = 79%/T = 60% and T₀ = 60%/T = 60% were proved to be able to generate Q-switched envelopes possessing either good symmetry or short duration. Based on this, these three T₀/T groups were introduced to dual-loss-modulated QML Nd:Lu_0.15Y_0.85VO₄ laser with the EO/Cr⁴⁺:YAG, and the Q-switched envelope was finally compressed until containing only one mode-locking pulse. The largest mode-locking pulse energy of 1.15 mJ and the highest peak power of 3.15 MW were reached using groups T₀ = 79%/T = 40% and T₀ = 79%/T = 60%, respectively. The experimental results were analyzed utilizing the rate equation theory, and the theoretical simulation was basically in accordance with the experimental data.

2. Experimental setup

The schematic setup for the low repetition rate sub-nanosecond Nd:Lu_0.15Y_0.85VO₄ laser with EO and Cr⁴⁺:YAG is shown in Fig. 1 , where a Z-type folded cavity is employed. To ensure a high mode matching efficiency, the laser cavity was designed to supply a mode diameter not larger than 300 μm inside the laser crystal by using the ABCD matrix. As the time interval between two adjacent mode-locking pulses underneath one Q-switching envelope is $2 L^{'} / c$ , where c is the speed of light in vacuum, the cavity length $L^{'}$ has a direct influence to the pulse width of the Q-switched envelope, as well as the number of mode-locking pulses a Q-switched envelope can cover. A longer cavity results in a larger time interval between two adjacent mode-locking pulses, which seems to be propitious to reduce mode-locking pulses in a Q-switched envelope; however, a too long cavity also leads to a broadening of the Q-switched envelope, and vice versa. In this experiment, the cavity length was optimized theoretically and experimentally for generating fewest mode-locking pulses underneath a Q-switched envelope. The whole length of the folded cavity used in this experiment is 142.5 cm, with the three cavity arms L₁, L₂ and L₃ as 570, 770 and 85 mm, respectively. The corresponding roundtrip transit time is 9.5 ns. A flat mirror M₁, anti-reflection (AR) coated at 808 nm on its outside surface nearing the focusing optics and high-reflection (HR) coated at 1064 nm on the inside surface, was adopted as the input mirror. Spherical concave mirrors M₂ and M₃ with radii of curvature (ROC) of 500 mm and 150 mm, respectively, were both HR coated at 1064 nm. Flat mirrors with three different transmissions of T = 20, 40, and 60% were employed as output mirrors (M₄). A commercial fiber-coupled laser diode (FAP system, Coherent Inc., USA), working at the maximum absorption wavelength (808 nm) of the Nd ions, was used as the pump source. An a-cut mixed laser crystal Nd:Lu_0.15Y_0.85VO₄ (0.38 at.% Nd-doped, 3 × 3 × 10 mm³), AR coated at 808 nm and 1064 nm on both surfaces, was employed as the laser media. The laser crystal was wrapped with indium foil and mounted in a copper block cooled by a thermo-electric cooler to efficiently dissipate the heat deposition, and the cooling temperature was set as 16 °C. An EO modulator (BBO crystal, modulated repetition rate from 1 to 5 kHz) with a polarizer and a λ/4 plate was adopted as the active Q-switcher. Considering that shorter Q-switched envelope can be obtained at a lower modulated repetition rate [13], the modulated frequency of the EO modulator was fixed at 1 kHz in this experiment. Three Cr⁴⁺:YAG crystals with different initial transmissions of T₀ = 88%, 79% and 60% were used as the passive saturable absorbers. Both sides of the Cr⁴⁺:YAG were AR coated at 1064 nm. The pulse characteristics were recorded by a 16 GHz digital oscilloscope (Keysight MSOV164A) and a fast pin photodiode detector (New Focus 1414) with a rise time of 14 ps. The output power was measured by a PM100D Energy/Power Meter (Thorlabs Inc., USA).

Fig. 1 Experimental configuration for the kHz sub-nanosecond Nd:Lu_0.15Y_0.85VO₄ laser with EO and Cr⁴⁺:YAG.

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3. Experimental results and discussion

When the EO Q-switcher is turned off, the laser is a passively Q-switched mode-locked with Cr⁴⁺:YAG. As is mentioned in [13–15 ], Q-switched pulses and envelopes from this passively QML lasers always have slow falling times, which is the main factor to block the EO/ Cr⁴⁺:YAG dual-loss-modulator from compressing the Q-switched envelope. It is reported that the shapes of the Q-switched envelopes somehow reply on the output coupler transmission T and the initial transmittance T₀ of Cr⁴⁺:YAG saturable absorber [14]. Thus, in the first step of the experiment, the dependence of Q-switched envelope duration and symmetry, generated by Cr⁴⁺:YAG passively QML Nd:Lu_0.15Y_0.85VO₄ laser, on T and T₀ was investigated. A series of OCs with T = 20, 40, and 60% were utilized to crossly match Cr⁴⁺:YAG saturable absorbers with T₀ = 88%, 79% and 60%. Short pulse duration and good symmetry of Q-switched envelopes generated in the passively QML regime are important prerequisites for further pulse compression using the dual-loss-modulated QML technology. Better symmetry and shorter envelope width make it relatively easier to realize the expected single mode-locking pulse operation of the dual-loss-modulated QML laser. Thus, appropriate combinations of T and T₀, which can generate Q-switched envelopes with short pulse duration and good symmetry, will be picked out for the next step research. Figure 2 exhibits expanded Q-switched envelopes obtained at the pump power of 8.76 W using different groups of output couplers and Cr⁴⁺:YAG saturable absorbers. Three different initial transmittances of Cr⁴⁺:YAG, T₀ = 60%, 79%, and 88%, as three columns match with three different transmissions of OC, T = 20%, 40%, and 60%, as three rows. By fitting the envelopes, rising time t₁ and falling time t₂ of the Q-switched envelopes can be obtained. Therefore, the widths and asymmetric factors of these Q-switched envelopes can be estimated by the definition of $τ = (t_{1} + t_{2}) / 2$ and $t_{1} / t_{2}$ , as summarized in Fig. 2. The results indicate that, among the 9 combinations of T and T₀, combination T₀ = 79%/T = 40% generates Q-switched envelopes with the best symmetry. Groups T₀ = 60%/T = 60% and T₀ = 79%/T = 60% generate envelopes with a little worse symmetry but shorter widths in comparison with group T₀ = 79%/T = 40%. Other groups yield either poor symmetry or long pulse width. As a consequence, groups T₀ = 79%/T = 40%, T₀ = 79%/T = 60% and T₀ = 60%/T = 60% were employed for further research of the dual-loss-modulated QML laser with EO/Cr⁴⁺:YAG. Actually, OCs with T>60% and saturable absorbers with T₀<60% were also tried and shorter Q-switched envelopes were obtained. But because of the relatively low average output power generated by them, they were subsequently eliminated.

Fig. 2 QML pulse shapes output by different groups of T₀/T at the pump power of 8.76 W.

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Turn the EO Q-switcher on, and the laser can be doubly Q-switched mode-locked by EO modulator and Cr⁴⁺:YAG saturable absorber. Figure 3 shows pulse widths of Q-switched envelopes as functions of incident pump power. For three T₀/T groups, Q-switched envelope pulse widths all decrease as the rise of the incident pump power. Adopting the same pump power, the T₀ = 60%/T = 60% group generates the shortest envelope. In other words, the fewest mode-locking pulses exist in an envelope. Figure 4 illustrates 6 QML envelopes corresponding to the 6 points circled by ellipses in Fig. 3. As shown in Fig. 4, when the pump power is 6.52 W, Q-switched envelopes generated by groups T₀ = 79%/T = 40%,T₀ = 79%/T = 60% and T₀ = 60%/T = 60% cover 9, 4 and 3 mode-locking pulses, respectively. Rising the incident pump power constantly, the Q-switched envelope becomes shorter and shorter. The higher the pump power is, the more inversion population density the gain medium can get in unit time, the shorter Q-switched envelope can be generated. Because the time interval between two adjacent mode-locking pulses underneath one Q-switching envelope is $2 L^{'} / c$ , when the Q-switched envelope is compressed even shorter than $2 L^{'} / c$ , only one mode-locking pulse can exist underneath a Q-switched envelope. We defined the threshold power for observation of single mode-locking pulse as the pump power at which the pulse width of the Q-switched envelope is less than or equal to $2 L^{'} / c$ . The threshold pump powers of single mode-locking pulse operation for groups T₀ = 79%/T = 40%, T₀ = 79%/T = 60% and T₀ = 60%/T = 60% are 9.24, 7.69 and 7.09 W, respectively. For the Q-switched envelope generated by group T₀ = 79%/T = 40% at 9.24 W, the main pulse was followed by a small peak, which continues to decrease, and then disappears as the increasing pump power. For the dual-loss-modulated QML laser, the repetition rate of the Q-switched envelopes is controlled by the EO modulator, which is fixed at 1 kHz in this experiment. Thus, mode-locking pulses with repetition rate of 1 kHz were obtained.

Fig. 3 Pulse width of Q-switched envelope (at Q-switched mode-locking stage) and mode-locking pulse (at single mode-locking stage) generated with different T₀ and T as a function of incident pump power.

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Fig. 4 QML pulse shapes output by the EO/Cr⁴⁺:YAG dual-loss-modulated laser with different T₀ and T at pump power of (a) 6.52 and (b) 9.24 W.

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The laser spectrum of this dual-loss-modulated Nd:Lu_0.15Y_0.85VO₄ laser was measured. The central wavelength was 1064.8 nm with a full width at half-maximum (FWHM) of about 5.1 nm. No obvious change of the spectrum was observed when the laser switched from the Q-switched mode-locking stage to the single mode-locking pulse operation.

The shortest mode-locking pulse was generated by the T₀ = 60%/T = 60% group at the pump power of 10.5 W. The pulse width was measured to be 310 ps. In comparison with the passively Q-switched and QML lasers, mode-locking pulses by the dual-loss-modulated QML laser have a good amplitude stability, as shown in Fig. 5 , which is attributed to the employment of the active Q-switcher [22, 23 ].

Fig. 5 Mode-locking pulse at time scale of 20 ms.

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Figure 6(a) shows the average output powers obtained by the three lasers as functions of incident pump power. It was measured that about 83% of the incident pump light was absorbed by the Nd:Lu_0.15Y_0.85VO₄ crystal. The average powers output by groups T₀ = 79%/T = 40% and T₀ = 79%/T = 60% are close, but much higher than that generated by group T₀ = 60%/T = 60%. This indicates that the initial transmission of the saturable absorber is one of the main factors for the output power. The maximum output power of 1.15 W was reached by group T₀ = 79%/T = 40%, corresponding to an optic-to-optical conversion efficiency of 13.2% and a slope efficiency of 16%, which was only about 1/4 of the slope efficiency under the CW operation. Such low power transfer efficiency from the CW to the QML operation is mainly caused by the insertion loss of the Cr⁴⁺:YAG saturable absorber and the EO modulator. For groups T₀ = 79%/T = 60% and T₀ = 60%/T = 60%, the highest output powers were 1.07 and 0.65 W, respectively. Since the modulation frequency is fixed at 1 kHz, owing to the relationship $E n v e l o p e E n e r g y = \frac{A v e r a g e O u t p u t P o w e r}{R e p e t i t i o n R a t e}$ , the Q-switched envelope energy has the same tendency as the average output power, as shown in Fig. 6(b).

Fig. 6 (a) Average output power and (b) Q-switched envelope energy as a function of incident pump power. Symbol, experimental data; Solid curve, theoretical result.

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Using the Q-switched envelope width and $2 L^{'} / c$ we can obtain the number of mode-locking pulses covered by one envelope. By employing the Q-switched envelope energy and the mode-locking pulse number, the average mode-locking pulse energy at different incident pump powers can be estimated, as illustrated in Fig. 7(a) . In the low pump power region, as the group which yields higher envelope energy also generates wider Q-switched envelope, mode-locking pulse energies obtained by the three T₀/T groups were nearly the same until the three lasers realized single mode-locking pulse operation in succession. In the 7.09-9.27 W region, the difference of the pulse energies mainly comes from the different threshold pump powers of three lasers for single mode-locking pulse operation. For instance, at the pump power of 8.25 W, there are three mode-locking pulses in one Q-switched envelope generated by group T₀ = 79%/T = 40%, while there is only one pulse for envelope yielded by group T₀ = 79%/T = 60%, but their envelope energies are nearly the same. As a result, group T₀ = 79%/T = 60% generates much higher mode-locking pulse energy. After then, the difference is attributed to the distinct average output powers. When three lasers all run at single mode-locking status, the group which generates larger envelope energy generates higher mode-locking pulse energy. The largest pulse energies obtained by groups T₀ = 79%/T = 40%, T₀ = 79%/T = 60% and T₀ = 60%/T = 60% were 1.15, 1.07 and 0.65 mJ.

Fig. 7 (a) Average pulse energy and (b) peak power of mode-locking pulses as a function of incident pump power.

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Using the mode-locking pulse energy and pulse width, the mode-locking pulse peak power can be calculated, as exhibited in Fig. 7(b). The peak powers grow exponentially as the rise of the incident pump power. In the single mode-locking stage, although the group T₀ = 79%/T = 40% yields the largest pulse energy, it has no advantage in generating high peak power limited by its broad pulse duration. T₀ = 79%/T = 60% group generates the highest peak power over the whole pump power range and a peak power up to 3.15 MW can be reached at 10.5 W pump power.

Higher repetition rates (2, 3 kHz and so on) were tried and a single mode-locking pulse underneath one Q-switch envelope was also obtained in these conditions. However, the higher the repetition rate was, the higher the threshold pump power was for the realization the single mode-locking pulse operation. Furthermore, the rise of the repetition rate leads to a sharp decrease of the pulse energy and peak power, since it only results in a slight increase of the average output power.

4. Theoretical analysis

The generation of picosecond pulses in a simultaneously Q-switched and mode-locked laser could be explained by the fluctuation mechanism [24]. According to this mechanism, the ultra-short pulse formation process includes the linear stage, as well as the nonlinear stage, which can be further divided into the nonlinear absorption and nonlinear amplification stage. During the linear and the nonlinear absorption stages, it is difficult to give the quantitatively theoretical description. Only in the nonlinear amplification process, because the pulse shape is not compressed, can the photon intensity shape be mathematically given [24]. Based on the fluctuation mechanism and considering the Gaussian spatial distribution of the intracavity photon intensity, the coupled rate equations for a dual-loss-modulated QML Nd:Lu_0.15Y_0.85VO₄ laser with EO/Cr⁴⁺:YAG can be described as [24–26 ]:

l_{A}

\begin{array}{l} n (r, t_{k}) = \exp (- \frac{t_{k}}{τ_{a}}) \prod_{m = 0}^{k - 1} \exp [- \frac{w_{l}^{2}}{w_{G}^{2}} \exp (- \frac{2 r^{2}}{w_{G}^{2}}) Φ_{m}] \\ \times {R_{i n} (r) \exp (\frac{t_{k}}{τ_{a}}) \int_{0}^{t_{_{k}}} \prod_{m = 0}^{k - 1} \exp [\frac{w_{l}^{2}}{w_{G}^{2}} \exp (- \frac{2 r^{2}}{w_{G}^{2}}) Φ_{m}] d t + n_{i} \exp (- \frac{2 r^{2}}{w_{p}^{2}})} \end{array}

\begin{array}{l} n_{s 1} (r, t_{k}) = [^{\prod_{m = 0}^{k - 1} \exp [- \frac{w_{l}^{2}}{w_{A}^{2}} \exp (- \frac{2 r^{2}}{w_{A}^{2}}) Φ_{m}]] (σ_{g s} + σ_{e s}) / σ} \times {\int_{0}^{k} {[\prod_{m = 0}^{k - 1} \exp [\frac{w_{l}^{2}}{w_{A}^{2}} \exp (- \frac{2 r^{2}}{w_{A}^{2}}) Φ_{m}]]}^{^{(σ_{g s} + σ_{e s}) / σ}} \\ \times \frac{σ_{e s} n_{s 0}}{2 σ τ_{p}} \times \sum_{m = 0}^{k - 1} Φ_{m} \frac{w_{l}^{2}}{w_{A}^{2}} \exp (- \frac{2 r^{2}}{w_{A}^{2}}) {sech}^{2} (\frac{t - m t_{r}}{τ_{p}}) d t + n_{0}} \end{array}

Where

Φ_{k}

is the relative amplitude of the mode-locked pulses at the

k

th round trip,

t_{k} = k t_{r}

,

t_{r} = \frac{2 [n_{1} l + n_{2} l_{A} + n_{3} d + (L^{'} - l - l_{A} - d)]}{c}

is the cavity round-trip time,

n_{1}

,

n_{2}

, and

n_{3}

are the refractive indices of the laser gain medium, the Cr⁴⁺:YAG saturable absorber and the BBO crystal in the EO modulator, respectively, and

l

,

l_{A}

and

d

are the lengths of them.

r

is the distance from the axis in a Gaussian beam,

w_{l}

is the mean radius of the Gaussian beam in the cavity.

n (r, t_{k})

is the average population-inversion density and

n_{s 1} (r, t_{k})

is population density of the ground state of Cr⁴⁺:YAG saturable absorber at the

k

th round trip,

n_{s 0}

is the total population density of Cr⁴⁺:YAG.

σ

is the stimulated emission cross section of the gain medium.

σ_{g s}

and

σ_{e s}

are the ground state and exited state absorption cross section of Cr⁴⁺:YAG.

w_{A}

and

w_{G}

are the beam radii at the position of laser crystal and saturable absorber, respectively.

R

is the reflectivity of the output mirror and

L

is the intrinsic optical loss.

δ_{e} (t)

is the loss function of the EO modulator, which can be expressed as [27]

δ_{e} (t) = \cos^{2} (\frac{π}{2} \frac{V (t)}{V_{λ / 4}})

, where

V_{λ / 4}

is the quarter-wave voltage and

V (t)

is the voltage on the electro-optic crystal, which can be described as a step function:

V (t) = {\begin{cases} 0 t \leq 0 \\ V_{λ / 4} t > 0 \end{cases}

.

R_{i n} (r) = \frac{2 α P_{i n} \exp (- 2 r^{2} / w_{p}^{2}) [1 - \exp (- α l)]}{h ν_{p} π w_{p}^{2} l}

is the pump rate, where

P_{i n}

is the pump power,

h ν_{p}

is the single-photon energy of the pump light,

w_{p}

is the average radius of the pump beam, and

α

is the absorption coefficient of the gain medium.

τ_{a}

is the emission lifetime of the upper laser level of the gain medium and

τ_{s}

is the upper level lifetime of Cr⁴⁺:YAG.

τ_{p}

is related to the FWHM mode-locked pulse duration

τ

by

τ = 1.76 τ_{p}

[24].

The initial population-inversion density for doubly QML laser can be expressed as:

n_{i} = R_{i n} τ_{a} [1 - \exp (- 1 / f_{p} τ_{a})]

where

f_{p}

is the modulation frequency of EO. Using the parameters shown in Table 1 and a given initial value of

Φ_{0}

, by numerically solving Eqs. (1), (5) and (6) ,

Φ_{k}

can be obtained and temporal shapes of Q-switched envelopes can be simulated.

Table 1. Parameters for theoretical calculation [28, 29].

View Table

According to the relationship of output power and the photon intensity, the average output power generated by the laser can be expressed as:

P (t) = \frac{h ν π w_{l}^{2}}{8 σ τ_{p}} (\ln \frac{1}{R}) \sum_{k = 0}^{\infty} ϕ_{k} \sec h^{2} (\frac{t - t_{k}}{τ_{p}})

By integrating (13) over time from zero to infinity, the pulse energy of a Q-switched envelope can be obtained:

E = \frac{h ν π w_{l}^{2}}{8 σ} (\ln \frac{1}{R}) \sum_{k = 0}^{\infty} ϕ_{k}

The calculated envelope energies are illustrated in Fig. 6(b) as the solid curves, which are on good agreement with the experimental results. The simulated temporal shapes of the Q-switched envelopes are shown in Fig. 8 , correspond to experimental pulse shapes illustrated in Fig. 4. In the numerical simulation, because of the absence of the quantitative description for the linear and the nonlinear absorption stages, the value of

τ_{p}

, which is related to the FWHM mode-locked pulse duration

τ

by

τ = 1.76 τ_{p}

, cannot be numerically simulated. According to the experimentally measured mode-locking pulse duration,

τ_{p}

was assumed to be 200 ps, which means the mode-locking pulse duration was supposed to be a constant value in the theoretical analysis. So, the evolution of mode-locking pulse duration in the experimental process was not modeled. In general, the theoretical data are basically in accordance with the experimental results.

Fig. 8 Calculated temporal shapes of Q-switched envelopes corresponding to pulses illustrated in Fig. 4.

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5. Conclusion

Considering the poor symmetry of Q-switched envelopes produced by Cr⁴⁺:YAG passively QML laser, which makes Cr⁴⁺:YAG a non-preferred saturable absorber for envelope compression in dual-loss-modulated QML lasers, different T₀/T groups was employed to optimize the Q-switched envelope shape. Based on this, the EO/Cr⁴⁺:YAG dual-loss-modulated laser can be further improved. As a result, single mode-locking pulse underneath one Q-switched envelope can be obtained from the EO/Cr⁴⁺:YAG dual-loss-modulated QML Nd:Lu_0.15Y_0.85VO₄ laser .The achieved mode-locking pulse energy and peak power can reach to 1.15 mJ and 3.15 MW, respectively. The rate equation theory was utilized to analyze the experimental results, and the theoretical results were basically in accordance with the experimental data.

Acknowledgment

This work was supported by the National Natural Science Foundation of China (61378022, 61205145), the Science and Technology Development Program of Shandong Province (2012G0020126), and the Independent Innovation Foundation of Shandong University (2012JC025).

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Generation of low repetition rate subnanosecond pulse in an optimal doubly QML Nd:Lu_0.15Y_0.85VO₄ laser with EO and Cr⁴⁺:YAG

Abstract

1. Introduction

2. Experimental setup

3. Experimental results and discussion

4. Theoretical analysis

5. Conclusion

Acknowledgment

References and links

Cited By

Figures (8)

Tables (1)

Equations (6)

Optics Express

Parameters	Values	Parameters	Values
$σ$	8.7 × 10⁻¹⁹ cm²	$τ_{s}$	3.2 μs
$σ_{g s}$	4.3 × 10⁻¹⁸ cm²	$l$	10 mm
$σ_{e s}$	8.2 × 10⁻¹⁹ cm²	$d$	50 mm
$n_{s 0}$	2.0 × 10¹⁷ cm⁻³	$n_{1}$	2.045
$w_{p}$	200 μm	$n_{2}$	1.82
$w_{l}$	90 μm	$n_{3}$	1.65
$w_{G}$	106 μm	$V_{λ / 4}$	3.8 kV
$w_{A}$	80 μm	$L$	0.04
$τ_{a}$	124 μs	$τ_{p}$	200 ps