Introduction

In [1] we have studied the generation of sub-nanosecond pulses with the sub-joule level of energy in gain-switched Ti:Sapphire lasers. The pulses with 460 ps duration, 1% pulse duration stability, and 300 mJ pulse energy were realized using (for pumping) 4–5 ns, 532 nm pulses from multimode Q-switched Nd:YAG laser, combined with microlens array homogenizer (MLA). To achieve a sub-nanosecond pulse duration in the Ti:Sapphire laser, we followed the idea suggested in [2], reducing the flat resonator length to several millimeters. To achieve sub-joule pulse energy, we significantly increased (10⁴ times in comparison with [2]) the area of the lasing spot, so that the lateral size of the spot was as large as 4–7 mm.

The Fresnel number (N_F) of such specific resonators is very large, exceeding 10³. In the case of low intracavity scattering the physical reasons for light coupling between particular areas of laser aperture in such flat resonators do not exist. So, in [1] we assumed that the laser generation field in similar resonators can split into several independent channels; and the characteristics of laser radiation from these channels will depend only on the local pump fluence W. The differences in the pulse build-up time of these channels could considerably increase the duration of the pulse, integrated over all the laser aperture (in the sequel we will call it as “integrated” pulse). It was reasonable to believe that the equalization of W for all channels, obtained due to a flattening of the pumping beam profile by a homogenizer, would result in the reduction of a channel build-up time spreading, thereby reducing integrated pulse duration.

In practice, MLA and DOE homogenizers (diffractive diffusers, or band-limited diffusers), when used in combination with high coherence pump sources (e.g., Nd:YAG laser), in addition to a flattening of W profile, produce small-scale interference modulation of W. In [1] we considered a similar modulation only as an unwanted process, which can be reduced by the appropriate choice and adjustment of homogenizer parameters. For example, a small shift of the Ti:Sapphire crystal towards the homogenizer’s condenser lens allowed us to reduce the amplitude of modulation below 25% of average W. Then we obtain the best values of pulse duration and stability, as indicated above. The good values of laser pulse duration obtained in these experiments were qualified only as a result of the good homogenization of pumping beam profile.

The subsequent investigation showed, however, that in the case of pumping with a multimode Nd:YAG laser pattern, which has an improved (in comparison with [1]) homogeneity, Ti: Sapphire laser integrated pulse duration is about 2 ns, which is much larger, than obtained in [1] with MLA homogenizer at the same level of W. We have suspected that only flattening of W profile is not sufficient to realize simultaneous generation over laser aperture thus obtain minimum available integrated pulse duration.

Indicated above observation leads us to start an intensive study of laser generation with different types of W distribution at Ti: Sapphire crystal. We study temporal and angular laser characteristics to discover the impact of pump light spatial modulation, obtained with and without homogenizers, on the process of laser generation. The main goal of this study is the better understanding of the conditions, required for stable generation of subnanosecond pulses with minimum integrated pulse duration in such lasers.

Experimental part

The optical scheme and the equipment, used in this work, in general, were the same as in [1]. Ti: Sapphire laser cavity had a flat mirrors with reflection 99.5% and 70% at 790 nm. The distance between mirrors was 6.5 mm. Mirror alignment precision was 6 angular seconds. Laser crystal diameter was 12 mm and thickness 3 mm. Pumping spot size was 4-5 mm.

Angular distribution of laser energy was measured using the set of diaphragms with different diameter, installed at 500 mm lens focal plane. All measurements were provided at low pulse repetition rate (1Hz) to eliminate the influence of thermal distortions in the both, Ti: Sapphire and Nd: YAG pumping lasers.

Four different patterns of spatially modulated light were used for pumping. They are shown at Fig. 1.

 

Fig. 1 Two-dimensional pump patterns (upper row) and their horizontal scans (lower row); a, c and d – obtained with multimode laser, b – with singlemode laser; a and b were obtained with no use of homogenizers, c and d – with MLA and DOE homogenizers correspondingly.

Download Full Size | PDF

Pattern “a” was produced using multimode Nd: YAG laser with improved in comparison with [1] beam homogeneity. One can see this pattern has good homogeneity of W almost over the all square except small spots at the peripheral area. The amplitude of W modulation, estimated from the scan, here does not exceed 15% at spatial frequencies below 2 mm⁻¹ and is less than 5% at higher frequencies.

Pattern “b” was produced by a single-mode Nd:YAG laser. W profile here has a flattened top due to gain saturation in amplifiers and is modulated in the radial direction due to the diffraction at the Nd:YAG laser rod aperture. The spatial frequency of this modulation is about 2.5 mm⁻¹ and the amplitude is about 50%.

Pattern “c” was produced by the multimode laser in combination with MLA homogenizer, like in [1]. Here we can see an interference structure, which consists of horizontal and vertical strips with spatial frequencies 17 – 26 mm⁻¹ and the amplitude of modulation 20-25% at central area (we already mentioned, that the amplitude of modulation was reduced by the shift of Ti: Sapphire crystal from focal plane of condenser lens). This light pattern structure corresponds to the structure of MLA, which is formed by two identical crossed arrays of cylinder lenses with 5 mm focal length and 0.5 mm pitch, fabricated at the opposite sides of thin fused silica plate.

Pattern “d” was produced by the multimode laser with DOE homogenizer. This DOE was also fabricated at thin fused silica plate. It has the diffusing angle 5.9 degrees and diffraction efficiency 76%. The pattern has a typical for DOE speckle structure [3]. At larger magnification one can see the speckles with various sizes. The prevailing spatial frequencies, which can be estimated from the scan, similar to the case of MLA, lie within ̴ 15-25 mm⁻¹. But the amplitude of W modulation here is 36 - 40%, which is larger than obtained with MLA. Also one can see a bright spot in the center of the pattern, related to DOE defocused zero diffraction order.

Results of the experiment

Temporal characteristics of Ti: Sapphire laser, obtained under pumping by multimode laser with MLA (pattern “c”) were scrutinized closely in [1]. It was shown, that the laser demonstrates very stable operation with pulse duration less than 500 ps. Pulse duration reduces with the increase of pump fluence W. The minimum available pulse duration 460 ps is restricted by the appearance of second pulse at high W, about 1.7-2.0 J/cm².

Similar behavior of temporal characteristics was observed in the case of pump pattern “d”. Generation was also very stable. Pulse duration here corresponds to that, obtained with MLA at reduced by ̴ 30% level of W, owing to the lower energy efficiency of DOE. Maximum level of W at DOE input here was restricted at ̴ 1.1 J/cm² by the damage of Ti: Sapphire crystal antireflection coatings from DOE zero diffraction order.

Another character of temporal characteristics was observed, when the pumping was produced by patterns “a” or “b”. Laser pulse, obtained with pattern “a” is shown at Fig. 2.

 

Fig. 2 Ti: Sapphire laser pulse at different levels of W: A – W = 0.8 J/cm²; B – W = 1.0 J/cm². Time scale is 2 ns/div.

Download Full Size | PDF

Here the pulses were relatively stable, but pulse duration was much larger than obtained with patterns “c” and “d”. At W = 0.8 J/cm² pulse duration was 2 +/−0.1 ns. After increasing of W to 1.0 J/cm² pulse duration reduces to 1.6 ns, but it was followed by second pulse generation (Fig. 2B). Mention that under pumping by pattern “c” at W = 1 J/cm², pulse duration was much shorter - 580 +/−15 ps.

Even worse temporal characteristics were obtained under pumping by pattern “b”.

At Fig. 3 one can see, that the oscillograms vary considerably from pulse to pulse, the main pulse is followed by secondary pulses and the total duration of the generation is close to the duration of the pump pulse (̴ 5 ns). The observed process is very similar to that, described earlier in [1] for pumping by the multimode laser with a very low homogeneity beam pattern.

 

Fig. 3 Series of Ti: Sapphire laser oscillograms, obtained with single-mode pump pattern “b” at average value of W = 1 J/cm². Time scale is 2 ns/div. Minimum duration of the main pulse here is 930 ps.

Download Full Size | PDF

Here we can conclude shortly that the conditions for the synchronous generation from all laser aperture have been realized for patterns “c” and “d”, but not realized for patterns “a” and “b”.

The angular distribution of the Ti: Sapphire laser energy is shown at Figs. 4 – 5. Here γ means a part of the total laser energy, irradiated within a cone with vertex angle φ.

 

Fig. 4 The angular distribution of Ti:Sapphire laser energy: A - for pumping by pattern “a”, B – by pattern “b”; 1 – at W = 0,78 J/cm²; 2 – at W = 1.5 J/cm².

Download Full Size | PDF

 

Fig. 5 The angular characteristics of Ti:Sapphire laser for pumping with pattern “d”: A – angular distribution at W = 0.51 J/cm² (1), and W = 1.25 J/cm²; B – the dependence of angular divergence on W: (1) – angular divergence measured at 10% level, (2) – measured at 1/e level.

Download Full Size | PDF

Figure 4 shows the angular distribution under pumping by patterns “a” and “b” at two different W. Angular divergence, determined at the (1/e) level (when 63% of laser energy are irradiated within this angle and 37% (or 1/e) - outside), was 6.3 mrad for “a” and 8 mrad for “b” at W = 1 J/cm² . In the both cases the divergence did not increase with the increase of W (at least, when W˂ 1.5 J/cm²). The wings of the angular distribution are very slight; more than 90% of laser energy is concentrated within 10 mrad (“a”) and 12–15 mrad (“b”).

Another character of the angular distribution was observed with patterns “c” and “d”. In the both cases the angular divergence and the wings considerably increased with W. At Fig. 5 one can see angular characteristics, measured with pattern “d”. When W is 0.51 J/cm², the angular distribution (Fig. 5A (1)) is very similar to that, obtained with patterns “a” and “b”. But when W is increased to 1.25 J/cm2, the distribution considerably changes (Fig. 5A (2)). Angular divergence increases and the wings grow. From Fig. 5B (2) one can see, that angular divergence at 1/e level increases more than 2 times. Measurement of angular divergence at 10% level (90% of laser energy are irradiated within angle φ) allows estimation of wings intensity. Rapid growth of the wings begins at W ≥ 1 J/cm² (Fig. 5B (1)).

At Fig. 6 one can see far-field intensity distribution of Ti: Sapphire laser radiation, obtained with pump pattern “c”.

 

Fig. 6 Far-field distribution of the Ti:Sapphire laser radiation with pattern “c” pump. Two-dimensional patterns and the appropriate intensity profiles were recorded at the focal plane of 800 mm lens at different levels of pump fluence: left – W = 1 a. u., middle – W = 1.7 a. u., right – W = 2.9 a. u.

Download Full Size | PDF

All three patterns of far-field distribution were recorded at equal optical attenuation and electronic gain of beam profiler CMOS camera. We see, that when W increases, the profile width also increases, but the axial intensity remains practically unchanged. Thus Fig. 6 reflects the process of laser light energy redistribution from the axial direction to the wings, described in [6].

Above, we described the main results obtained during the experimental study of Ti:Sapphire laser temporal characteristics and angular distribution, registered for 4 pump patterns with different spatial W distribution. Below we will analyze the reasons of the observed laser generation behavior.

Analysis and discussion of experimental results

We operate with the laser resonators, which have the flat mirrors and large N_F. Some properties of such specific resonators and the characteristics of solid-state lasers with such resonators have been investigated for the first time in 1967–1977 [4–7]. To explain the processes, observed in our experiments we will proceed from the results described in these publications. Below is a brief summary of these results.

It was shown, that a weak small-angle light scattering (in the sequel referred as scattering) in such resonators can increase the angular divergence of the laser radiation by many times. The reason for the high sensitivity of such resonators to a scattering is the very small frequency difference between the transversal modes of the different order. As a result, even a weak coupling between such modes due to the scattering leads to the junction of the generated light into the complexes of the modes with the same frequency. Such complexes, which consist of a large number of the undistorted flat cavity high order transversal modes, with the random phase and the intensity, are the real modes of large N_F flat resonators with the intracavity scattering. At the high pump level, these complexes predominate in the laser generation, resulting in the large angular divergence of the radiation.

The mode structure and the angular distribution of the laser radiation here depend on the characteristics of the scattering: the intensity and the width 2ϑ₀ of the scattering diagram. Scattering intensity and the width of scattering diagram, the both should be large enough to produce intermodal coupling.

In [6] A. Siegman wrote:” The far-field on-axis intensity of the laser very seriously decrease with increasing scattering. This occures because the energy scattered out of the lowest order mode is not simply lost out of the cavity, but rather is coupled into the higher order modes. These modes are then regeneratively amplified…”.

All our experimental results can be explained, if we suppose the appearance of the scattering in Ti: Sapphire crystals that depends on W. To our opinion, the main features of the observed laser angular characteristics, such as the increase of the angular divergence with W, the appearance and the growth of the wings with W (Fig. 5) and the restriction of the axial light intensity, when W increases (Fig. 6), in accordance with given above summary, are indicative of intracavity scattering.

This scattering, we suppose, is caused by the optical nonuniformities δn(x, y), induced in Ti: Sapphire crystals by the pumping light due to refraction index change (RIC)-effect [8,9]. The spatial structure of the nonuniformities is determined by the structure of the pumping light. In the case of the uniform pumping the refraction index changes uniformly within the illuminated area, so the nonuniformities and the scattering do not appear, even at large W. But when W is properly modulated, then the induced nonuniformities in the crystal will cause the scattering. It explains the difference between the characteristics, obtained with pumping by uniform pattern “a”, where scattering does not reveals, and patterns “c” and “d”. The scattering also does not reveals for pattern “b”. We guess there W modulation frequencies are too low (<2.5 mm⁻¹), that`s why scattering diagram angles 2ϑ₀ are too small for the efficient coupling of the laser radiation within the aperture.

The coupling, caused by the scattering, also is favorable for the synchronization of the generation within the laser aperture. When the scattering leads to the junction of laser radiation into the mode complexes, the spreading of build-up time reduces, resulting in the reduction of integrated pulse duration. That`s why the conditions, when we observe the generation with maximum angular divergence, correspond to the most stable temporal characteristics with the minimum integrated pulse duration, and vice versa.

The supposed physical origin of this scattering is RIC-effect. Below we will estimate the phase shift, produced by RIC for the light at generating wavelengths, which passes through the Ti: Sapphire crystal.

In [8] was shown that the pump-induced RIC is determined by two factors – by the thermal effect (δn_t) and by the polarizability difference in the excited and the ground state of Ti – ions (δn_e). Recently in [9] was shown, that δn_e is wavelength-dependent. For π-polarization, where our Ti: Sapphire laser operates, δn_e reduces to zero at 788-790 nm, just at the center of the laser generation spectrum. So, the generation at the central wavelengths will be influenced only by the thermal component δn_t. Unfortunately the data of δn_t are not indicated at [9].

Nevertheless, the thermal component can be estimated as [10]: δn_t = (dn/dT) * [(N * hν * Φ)/(C * ρ)]. Here dn/dT is the temperature coefficient of the refraction index for π-polarization, N is the inversion population, hν is 532 nm photon energy, Φ is the relative part of the pump energy, converted into the heat, C is the heat capacity and ρ is the density of the crystal.

We can determine N using the well-known relation: K₀ = σ * N, where σ = 4.1* 10⁻¹⁹ cm² [11] is the stimulated emission cross section. Ti: Sapphire gain coefficient, measured in our experiments, K₀ = 3 cm⁻¹ at W = 1.5 J/cm². For this K₀ we obtain N = 7.3*10¹⁸ cm⁻³. Then, using a literature data for dn/dT = 2 * 10⁻⁵ K⁻¹ [12], C = 0.76 J/g.K [11], ρ = 4 g/cm³ [11] and calculating Φ as a relative difference of the pumping and the generating photon energies, we can calculate δn_t = 6 * 10⁻⁶.

The appropriate phase shift Ψ at the generating wavelengths, caused due to RIC-effect for the light, passing through pumped Ti: Sapphire crystal at W = 1.5 J/cm² is: Ψ = (2π/λ) * δn * t, where t = 3 mm is the laser crystal thickness. Finally we obtain Ψ = 0.14 rad (8°).

The results of the measurements of the phase shift, caused by δn_e only, in the neighborhood of 790 nm at W = 0.4-1.3 J/cm², are indicated in [9]. The data of Ψ, obtained there, are very similar to ours, calculated above. Mention, that Ψ is proportional to the gain increment K₀ * t. In our case K₀ * t = 0.9, which is relatively small. Under the strong pumping at the thicker crystals the gain increment can be as large as 5.2 [13]. So, the RIC-induced phase shift, the scattering level and the impact of these factors on the laser generation can be larger, than observed in our investigation.

Conclusion

The main results, obtained in our study are the following:

Mention that, to our best knowledge, this study is the first detailed experimental investigation of the angular distribution of solid-state lasers with large N_F flat resonators. Our findings are in good agreement with the predictions made over 50 years ago without connection to any given laser type.