Studies on transmitted beam modulation effect from laser induced damage on fused silica optics

Yi Zheng; Ping Ma; Haibo Li; Zhichao Liu; Songlin Chen

doi:10.1364/OE.21.016605

1. Introduction

In high power laser facility, a great number of optics is applied to compose the beam path. It’s inevitable to introduce defects in them during manufacturing, transporting, assembling and operating. To date, the interactions between high power laser beam and those imperfections or impurities in optics have been studied a lot [1–6]. Research findings reveal that the interaction would result in obscuration that degrades the beam quality, and moreover, generate localized intensification (or “hot spot”) that is very hazardous to the downstream optics. It has been demonstrated that this modulation effect are greatly associated with the nature of the defects such as size, transparency, refractive index, thick, etc [3,4], and the explanations have been provided based on the diffraction model of transmitted beam whose amplitude and phase distributions are locally disturbed by those defects [2].

Fused silica is widely applied as UV functional optics owing to its excellent optical transparency and uniformity. However, it’s likely to be damaged by the irradiation of high power UV laser pulses [7–11]. The emergent damage spots on the exit surface will further induce modulation effect to transmitted beam. Here we name it DIME (Damage Induced Modulation Effect). As same as the modulation effect from defects, beam quality degradation and intensification risk would also be caused by DIME, but the modeling is more complex because the damage region usually presents various surface morphologies. To our knowledge, although DIME is universally recognized by laser optics community, only few studies go in deep. In fact, the investigation on DIME is of particular importance for evaluating the performance of on-line optical components, guiding the mitigation of damage regions [12–14], and understanding the beam quality of high power laser pulse [15–17]. It’s necessary to find a method to characterize and describe DIME phenomenon.

This paper presents our studies on this topic. In part 2, experimental setup is introduced. An improved LID testing bench is designed with a series of instruments for DIME characterization. After that, in part 3, experimental investigation is performed. UV laser damage is created on fused silica sample, and the characterization results are exhibited and discussed. Next, in part 4, in order to give a theoretical description on DIME principle, analytical modeling and numerical simulation are performed. We design a polygon crater pattern to model the actual damage site. And finally in part 5, jobs and fruits are summarized in brief.

2. Experimental setup

Generally, DIME could be regarded as the amplitude and phase disturbances on the wavefront of transmitted beam. Therefore, for experimental characterization on this effect, a series of measurement instruments are set in our standard LID testing bench. Figure 1 shows the structure. The UV pump laser is provided by Beam-tech SGR-EXTRA-10. It’s a Q-switched Nd:YAG laser whose maximum 3ω (355nm) output achieves 3 Joule. The pulse duration is alternative between 3ns and 10ns. UV laser shot is delivered to a properly mounted fused silica sample, and LID could be created on exit surface. After that, the instruments, including beam profiler, interferometer, OCT, and microscope, are set respectively. The 1st part is the beam profiler. It’s applied for measuring the intensity modulation effect. A continuous-wave probe laser with 3ω wavelength is adopted to illuminate the damage region. It’s a DPSSL with fiber-tailed output. A quasi-planar-wave beam with 20mm diameter is generated by a fiber-laser collimator. This aperture is large enough to cover the whole damaged region. The transmitted beam modulated by damage is then acquired by Spiricon SP-620U. It’s a CCD designed as a laser beam profiler. The active area is 7.1*5.4mm size. It’s mounted on a motorized linear stage, which is custom-made by Newport Micro-Controle. The travel range reaches 1000mm. The stage enables a dynamic position change of CCD along Z axis and therefore the beam profiles at different propagation distances could be detected conveniently. Intensity distribution, peak value, and X-Y cross-section could be obtained by software named “Beamgage 6.5”, and thus the intensity modulation properties could be quickly extracted.

Fig. 1 Sketch map of experimental setup. A series of measurement instruments are applied for DIME characterization.

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In order to check the phase modulation effect of DIME, we use ZYGO “DynaFiz” interferometer to measure the concerned damage region. It’s the 2nd part [18]. The surface form data could be detected based on Fizeau principle. It’s helpful for understanding the phase disturbance induced by damage. The 3rd part is OCT. It could measure the lateral damage morphology without contact and cut. Some hints under the surface could be discovered, and they are very valuable for morphology analysis [19]. The last part is a microscope, composed of a C-mount zoom lens and an industrial camera. It’s used for the general observation of damage region. In order to implement an in situ characterization on the interested region, we design a mechanical slip-rail structure. Instruments are fixed in beam path, and the sample holder is mounted on the rail. Sample could be freely switched to the wanted measurement part.

3. Experiments and results

In experiment, fused silica disks (Corning 7980) with 2 inch diameter and 8mm thick are adopted. The samples are prepared by processes including fine polishing and HF-based etching. Damage sites are created and measured on the experimental setup.

3.1 DIME characterization

In order to make the measurement results clear, we take a grown damage site as an object. It’s created by a sequence of 3ns laser pulses with 15J/cm². DIME characterization results are shown in Fig. 2.

Fig. 2 DIME characterizations: (a) microscope observation, (b) surface form measured by interferometer, (c) OCT image of lateral morphology, and (d) Transmitted beam profile at 5mm downstream distance.

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The blue and red panels in Figs. 2(a)-2(d) mark out the same regions observed by different characterization approaches. Here we sort them as amplitude and phase regions respectively, according to their particular modulation features. The details are described in following:

■ Blue panel: The nature of this region is opaque, so it looks dark in microscope (2.a). In interferometer, error surface date is obtained because light signal in this area is missed (2.b). In OCT image, the lateral contour looks clear and bright, because the light scattering from the bottom is very strong. (2.c), and in transmitted beam profile, intensity in this region is blocked (2.d).
■ Red panel: From the microscope we can see that laser shots have peeled a piece of material off the surface (2.a), but the transparent nature of this region hasn’t been destroyed. Sub-surface crack induces OPD (Optical Path Distance) shift to the transmitted beam and therefore phase modulation effect emerges. The interferometer result demonstrates a local phase protuberance with near λ/5 magnitude (2.b). In OCT image, lateral contour in sub-surface layer indicates the location of crack and fractured structure (2.c). In beam profile, a bright spot shows up in the center of this region (2.d). The red pixels are attributed to the intensity saturation of CCD sensor. It’s the hot spot which has been widely referred [1–4]. The peeled transparent piece functions as a lens. It focuses the transmitted beam via the phase diffraction effect.

3.2 Discussion

Based on the characterization results, we can conclude that DIME has a close connection with damage morphology. In order to get a further understanding, we use scanning electron microscope (SEM) to observe the microstructures in these two regions. Figure 3 shows the detail. It has been acknowledged that typical LID morphology on fused silica could be expressed as “crater”, particularly, a molten core region surrounded by fractured ring region [18]. This morphological feature mainly comes from the thermal explosion in center and shock wave radiation all around. The microstructures in these regions play different roles in DIME: the molten core usually contains a great number of sub-micron structures, for example, digs, pits, fibers, etc.. They are light-scattering and function as beam block. This feature could be regarded as amplitude-type morphology (AM). In fractured ring region, pieces of surface material are peeled off. They are still transparent, but the sub-surface separation could add OPD shift into the transmitted beam. Therefore, this region presents a phase modulation effect and is regarded as phase-type morphology (PM). In actual damage events, the appearances of these two morphologies are highly random and various. For the initial damage with small size, three typical morphologies are summarized in [20]. Here we take them as examples: the morphology Hazlet is AM type because it looks gray and opaque. The laser-triggered explosion hasn’t caused prominent fracture around this baby-size structure. For morphology Mussel, PM feature is more significant. A piece of surface material has been peeled off, and the “shell” area looks smooth and transparent. The morphology Pansy is relatively large and thus it forms a mixed status with both two type morphologies.

Fig. 3 SEM micrograph of the damage site. In center, crater core with sub-micron structures is formed. Around, the cracks and flaws indicate the existence of sub-surface fracturing and peeling.

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For the grown damage, the two kinds of morphologies are usually not isolated but present together. One general law is that AM is usually more dominant, and PM can hardly form a large size because the fractured piece is likely to explode or shell before it grows into a big and unstable structure. Therefore, although PM may induce great downstream intensification, it has low chance to cause a catastrophic damage chain-reaction, because hot spots arise in a very short range while PM is in small size, and for the damage existing on the exit surface, downstream hot spots won’t take place inside the bulk but in the space between fused silica optics. Therefore, comparing the serious beam modulation problem induced by the defects and flaws on the entrance side, DIME appears not so hazardous, and the blocking effect would be more significant than intensification. Under this condition, the damage size is an important factor because it determines the aperture diffraction effect. Here we have created two damage sites with different size and then measured the corresponding transmitted beam profiles at different downstream distances. The results are shown in Fig. 4.

Fig. 4 Modulated profiles of transmitted beam at different downstream distances.

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We can see that in both instances Airy disk and diffraction rings have shown up in downstream. But the distance is different. For the larger site, the diffraction evolution is slower than the small one. Figure 5 shows the curve of on-axis intensity. The data is recorded by the beam profiling software. It demonstrates that the showing up process of Airy disk closely depends on the size factor.

Fig. 5 Evolution curves of on-axis intensity of two different size cases.

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In the other hand, the curves show that the on-axis intensity will finally converge to the average intensity of the undisturbed part of transmitted beam. And this process represents a recovery of beam quality. From the X-Y cross-sections in the last two profiles of Fig. 4 we can see, for a smaller damage size, the DIME-disturbed beam profile could recover to a relatively homogeneous distribution in a shorter range, but for the larger one, the recovery process becomes slower and more difficult. This effect indicates that larger damage site is more likely to be “dangerous” for laser line because the DIME-induced intensity fluctuation becomes more serious and even irrecoverable. DIME characterization provides a good way to evaluate the performance of fused silica optics.

4. Analytical modeling and simulation

In order to get a comprehensive description on DIME principle, theoretical study is carried out in this part. The modulation effect is derived from the wavefront interaction between transmitted beam and damage site. The process is illustrated in Fig. 6. The modeling of high-power laser system has been well investigated by [2]. Here, the beam propagation could be simplified by ignoring the interaction between laser and optical materials, because here we mainly concern the condition that damage site existing on the exit surface of fused silica optics. Comparing with the entrance side, damage on exit surface usually appears to be more serious and aggressive. Huygens-Fresnel diffraction integral is applied for modeling. The output wavefront could be expressed as:

U (x_{0}, y_{0}, Z = 0) = u_{0} h (x_{0}, y_{0}),

where

u_{0}

presents the upstream wavefront. Here we take uniformized planar wave

u_{0} = 1

into calculation.

h (x_{0}, y_{0})

presents the modulation term induced by damage region:

h (x_{0}, y_{0}) = {\begin{cases} 1 \notin s \\ t (x_{0}, y_{0}) \exp [j ϕ (x_{0}, y_{0})] \in s \end{cases},

where

t (x_{0}, y_{0})

could be named as amplitude factor and

ϕ (x_{0}, y_{0})

as phase factor. s indicates the size factor of damage region.

Fig. 6 Schematic diagram of transmitted beam modulation and propagation.

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Under paraxial approximation, the downstream wavefront $U (x, y, Z = z)$ could be briefly expressed as:

U (x, y, Z = z) = \frac{1}{j λ z} \exp (j k z) \iint_{\infty} U (x_{0}, y_{0}, Z = 0) \exp {j \frac{k}{2 z} [{(x - x_{0})}^{2} + {(y - y_{0})}^{2}]} d x_{0} d y_{0} .

Substituting Eqs. (1), (2), and (3):

\begin{array}{l} U (x, y, Z = z) = \frac{1}{j λ z} \exp (j k z) [\begin{array}{l} \iint_{(x_{0}, y_{0}) \in s} u_{0} h (x_{0}, y_{0}) \exp {j \frac{k}{2 z} [{(x - x_{0})}^{2} + {(y - y_{0})}^{2}]} d x_{0} d y_{0} \\ + \iint_{(x_{0}, y_{0}) \notin s} u_{0} h (x_{0}, y_{0}) \exp {j \frac{k}{2 z} [{(x - x_{0})}^{2} + {(y - y_{0})}^{2}]} d x_{0} d y_{0} \end{array}] . \\ = \frac{1}{j λ z} \exp (j k z) \iint_{(x_{0}, y_{0}) \in s} t (x_{0}, y_{0}) \exp {j \frac{k}{2 z} [{(x - x_{0})}^{2} + {(y - y_{0})}^{2}] + j ϕ (x_{0}, y_{0})} d x_{0} d y_{0} \\ + \frac{1}{j λ z} \exp (j k z) \iint_{(x_{0}, y_{0}) \notin s} \exp {j \frac{k}{2 z} [{(x - x_{0})}^{2} + {(y - y_{0})}^{2}]} d x_{0} d y_{0} \end{array}

And intensity distribution is:

I (x, y, Z = z) = {| U (x, y, Z = z) |}^{2} .

Based on Eqs. (4) and (5), numerical simulation could be implemented.

4.1 Analysis on diffraction factors

Equation (4) indicates that downstream propagation property is mainly determined by three factors: amplitude, phase, and size. Here we design a comparison program to check the effect of each factor individually. The simulations are shown in Figs. 7 and 8. Two intensity parameters, max intensity $I_{\max} = \max [I (x, y, Z = z)]$ and on-axis intensity $I_{axis} = I (0, 0, Z = z)$ , are adopted to describe the beam properties. Figure 9 shows their evolution curves along with the propagation distance.

Fig. 7 Simulation results of small size case (100μm). Beam profiles under amplitude (upper-line) and phase (lower-line) factors are exhibited and ranged according to the propagation distance. Left panels exhibit the initial parameters.

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Fig. 8 Simulation results of large size case (500μm). Beam profiles under amplitude (upper-line) and phase (lower-line) factors are exhibited and ranged according to the propagation distance. Left panels exhibit the initial parameters.

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Fig. 9 Evolution curves of the intensity parameters along with propagation distance.

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Comparing the results from simulation and experiment, we can conclude that:

■ Amplitude factor: Amplitude factor attributes to AM in damage site. Downstream intensification is not very prominent according to the beam profiles (upper line in Figs. 7 and 8) and intensity curves (dash curves in Fig. 9). Ariy disk shows up in center after a propagation distance.
■ Phase factor: Phase factor attributes to PM in damage site. It won’t weaken the beam intensity but cause a re-distribution effect, as what a lens does. Hot spot with even 9x intensity zoom will show up in near range, according to the profiles (lower line in Figs. 7 and 8) and intensity curves (solid curves in Fig. 9).
■ Size factor: the size factor performs an aperture effect in diffraction. Smaller aperture results in a faster diffraction, and that means the Ariy disk and hot spot will show up in a shorter distance. Consequently, for small site, the intensity distribution in far-field would be smoother than the large one.

4.2 Simplified polygon crater model

As what we’ve noticed in experiment, AM and PM characters usually present together, so the modulation effect of actual damage site is always multiform. As the appearance of damage morphology is highly random, it’s complex to build a comprehensive simulation model. Therefore, for analytical description of DIME, we use a polygon model to approximately represent the irregular explosion shape and crater-like morphological feature. Here we take the pattern shown in Fig. 10 as an example. It’s pentagon-shaped with typical crater features: opaque AM region locals in center (S₀) and the partial transparent PM regions (S₁~S₅) circle around, spreading along with the crack fringe.

Fig. 10 Pentagon DIME model with crater-like morphological features.

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In modeling, the modulation term in Eq. (2) are set as following:

h (x_{0}, y_{0}) = {\begin{cases} 0 \in s_{0} \\ a_{i} \exp (j ϕ_{i}) \in s_{i} (i = 1, 2, ..., 5) \\ 1 \in e l s e \end{cases} .

It’s a combination status with both amplitude and phase factors. Transmitted beam propagation is simulated based on Eqs. (4) and (5). Considering the variety in actual damage event, in calculation, phase value

ϕ_{i}

is randomly generated in

[- π, π]

range, and amplitude value

a_{i}

in [0, 1] range. Simulation results are shown in Fig. 11

Fig. 11 Numerical simulation of the simplified DIME model with crater-like pentagon pattern.

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Comparing with the experimental results shown in Fig. 4, we can see that simulation matches well with reality. The polygon crater model with opaque center and lens-like transparent round is representative and provides a good description of actual DIME phenomenon. Hot spot in near-field and Airy disk in far-field reveal the effects from PM and AM, and these are the phenomena that would probably take place on the exit surface of fused silica optics in high power laser system.

Conclusion

This paper focuses on the DIME phenomenon in high power laser system. The topic has been widely noticed but rarely investigated in deep. Both experimental and analytical works are presented. First, UV laser damage experiment is implemented on fused silica optics. A series of instruments, including beam profiler, interferometer, OCT, and microscope, has been set in a standard LIDT testing bench and applied for DIME characterization. Typical carter-like damage site is studied synthetically. Morphological features of damage site are classified into AM and PM according to their particular characters in modulation effect. After that, for theoretical description, modeling and simulation are performed. Different modulation effects from the amplitude, phase, and size factors are checked respectively, and then a general principle of DIME is concluded: phase factor could induce downstream intensification and generate hot spot in near range, while amplitude factor could induce intensity block and generate Ariy disk in far-field. Size factor influences diffraction speed and determines the showing up positions of Ariy disk and hot spot. Furthermore, simplified polygon model is designed to simulate actual damage site. Pentagon pattern with crater features, in other words, AM in center and PM around, is adopted. The simulation beam profiles match well with experimental results, and that demonstrates the polygon crater model is usable and representative. Generally, the research is an expansion of current fused-silica-LID issue. DIME characterization provides a good way to evaluate the performance of fused silica optics. And the analytical method is helpful for understanding the beam quality of high power laser system.

Reference and links

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Studies on transmitted beam modulation effect from laser induced damage on fused silica optics

Abstract

1. Introduction

2. Experimental setup

3. Experiments and results

3.1 DIME characterization

3.2 Discussion

4. Analytical modeling and simulation

4.1 Analysis on diffraction factors

4.2 Simplified polygon crater model

Conclusion

Reference and links

Cited By

Figures (11)

Equations (6)

Optics Express