1. Introduction

Nowadays, the introduction of ultra-intense laser systems has opened access to new applications, such as laser-driven plasma accelerators (LDPA) to produce high energy photons or particles [1–3], microfabrication laser [4,5], medical radioisotopes production [6,7], fusion energy [8–10], non-linear high harmonic generation [11,12], relativistic non-linear optics [13,14]. The success these laser applications depends on the ability to focus laser pulses into a small focal spot with a diameter of only a few microns, where the intensity can exceed 10$^{14}$ [W/cm$^2$]. In certain cases, particularly in applications where the goal is to maximize the intensity on the surface of a solid target, it is crucial to match the position of the target with that of the high-intensity region, which may be small when using a short focal length.

For lasers with moderate energy ($\sim$100 [$\mu$J]-10 [mJ]) and high repetition rates ($\sim$100 [Hz]-[MHz]), where the target needs to be refreshed for every shot, matching the position of the target to the position of the laser focus at the relevant repetition rates is a challenge which requires accurate, sensitive and fast positioning systems [1,2,15]. There are many positioner systems for targets with varying degrees of accuracy and response time [16–20], but maybe the most used is the confocal microscopy positioning system (CHIP) [21], with high accuracy and high speed response.

We have developed a novel target alignment system based on the CHIP system, which features various advantages, such as a simplified calibration method and improved accuracy. All these features of the introduced system significantly enhance its performance. Additionally, we have replaced the pair detector-aperture from the original design [21] with a non-linear detector that offers greater sensitivity and simplifies both the alignment and construction processes by eliminating the need for a conjugated focal plane selective aperture. Moreover, the implementation of this non-linear detector, which utilizes a Si-photodiode, for 1550 [nm] instead of an expensive specialized sensor for this spectral range, is highly advantageous. Overall, these improvements make our target alignment system a fast, more efficient, cost-effective, and user-friendly solution for a broad range of applications.

2. Nonlinear confocal positioner (NCP) design

The optical design of the Nonlinear Confocal Positioning system (NCPs) is an improvement of the confocal microscopy positioning system known as CHIP [21]. This upgrade of the original confocal setup (CHIP) consists of two stages. In the first stage, we replace the conjugated focal position detection with a nonlinear detector, with no need of a selective aperture as a pinhole or an optical fiber core. In the second stage, we introduce a simplified calibration method based on a previously proposed technique [22]. The NCP system consists in a collimated beam focused by a focal objective on a target surface. When the target is in the correct focal plane, the back-reflected light is collected by a simple lens in the conjugated plane where a nonlinear detector will measure the changes of the optical intensity as a function of the target position. The NCP system is designed to find the maximum intensity position. This means that even in the case of spatial aberrations [23] or change in the temporal [24] structure of the pulse, the system will locate the relative maximum intensity position, if the two-photon absorption condition is achieved.

The optical configuration of the NCP is shown in Fig. 1. A femtosecond Er-dopped fiber Amplifier (EDFA) delivers pulses of 100 [fs] at 1550 [nm] and with an average power up to 200 [mW]. The laser beam passes through a beam splitter (BS) to be focused by an aspherical lens (FL) of 25 [mm] of focal length and a diameter of 25 [mm]. The laser beam is focused on a Si-photodetector (reference detector) where a fraction of the light is reflected back to a second path. The Si-windowless detector is used to calibrate the instrument before replacing it with a target. Finally, a simple lens (L$_1$) is used to collect all the laser light reflected from the reference detector on a second Si-photodetector (BPW20RF) as is shown in Fig. 1. The pair of a lens L$_1$ and a second detector is called the conjugated or detection setup.

 

Fig. 1. Nonlinear Confocal Positioning (NCP) setup. A collimated beam is focused by an aspherical lens (FL) on the reference detector position. The back-reflected light goes to a detection setup consisting of a simple lens (L$_1$) and a Si-photodetector.

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The underlying premise of this technique (NCP) is that the Si-photodetector has a null linear response at wavelengths above 1100 [nm] [25], in our case, the signal that should be detected from our laser source (1550 [nm]) has to be from the Two-Photon Absorption (TPA). The light propagation intensity ($I$) on the photodetector should follow the absorption Eq. (1), where $\alpha$ is the linear absorption coefficient, $\beta$ is the non-linear absorption coefficient and $z$ is the position shift inside the photodiode [26].

Taking into account that each TPA event generates a pair of electron-hole with an efficiency $\eta$ in the photodiode [27] and by solving the light propagation equation (Eq. (1)), where the linear response is assumed to be negligible at 1550 [nm], the photocurrent ($I_{PD}$) in the Si-photodetector by the TPA can be approximated to

We measure the photocurrent of the Si-photodetector (BPW20RF) as a function of the peak power from the femtosecond pulses delivered from the EDFA (Fig. 2). The laser pulses are focused with a lens $F$ on the detector surface, in order to stimulate the TPA signal. From these data, a quadratic function can be fitted (Eq. (2)). We introduce the full non-linear absorption coefficient $\beta _{Full} \equiv \eta \delta \beta$, where the product of $\beta _{Full}I_0$ is the relative fraction of light absorbed by the photodiode due to TPA. A quadratic function (red line) of the form $I_{PD}=aP^2+b$ fits well to the experimental data ( blue circles), where $b=$ 7.664$\times 10^{-7}$ [A] is the background noise on the photodiode, and $a=1.3809 \times 10^{-11}$ [A/W$^2$], where $a=k \beta _{Full}$ with $k=e\lambda$/2$\pi h c w_0^2$. For a focal spot size (radius) of $w_0=$ 4.38 [$\mu$m], we obtain $\beta _{Full}=$ 1.3315$\times 10^{-17}$ [cm$^2$/W]. In conclusion, this quadratic dependence of the photocurrent with the intensity allows us to substitute the pinhole-photodiode pair of the confocal setup in [21] with a simple non-linear detector such as a Si-photodiode for 1550 [nm].

 

Fig. 2. The Figure shows the Two-Photon Absorption response of the Si photodetector.

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3. High accurate calibration step

As the NCP is a relative positioning system, it needs to be calibrated in order to ensure a reliable instrument. The accuracy of the NCP system will depend directly on the calibration procedure, so we propose a high accuracy calibration method based on our previous work [22]. In this paper, we use a Si-photodetector (BPW20RF), instead of a pair pinhole-photodiode as was proposed in Ref. [22], to measure directly the focal position. The nature of the nonlinear detection scheme where the photodiode acts simultaneously as a nonlinear media and a detector, allows us to do this change. This improvement in the calibration method will let us simplify the alignment procedure of the detector because the sensing area is much larger than the beam size. Also, by removing the protective window from the photodiode, the reflected light comes directly from the sensing surface. This gives the real focal position of the reference without introducing an offset in the measurement. A measurement of the TPA signal, generated with the focused beam on the Si detector, is obtained as a function of the detector position along the optical axis (z-scan measurement). In Fig. 3, the TPA peak intensity (red line) defines the reference focal plane position. Once this position is located, the reference (windowless) detector is kept fixed. After this procedure, we calibrate the position of the conjugated focal detector, so a maximum is detected by the sensor itself. This calibration is performed with a linear stage and a micrometer attached to it to accurately locate the detector at the conjugated focal plane. In Fig. 3, the blue line shows the z-scan measurement at the conjugate focal plane. Both TPA signals have a maximum intensity at position 6.685 [mm] with an error of 1 [$\mu$m] between both signals.

 

Fig. 3. z-scan calibration method of the NCP system. The red line shows the TPA response at the direct focal plane, with a maximum peak at 6.685 [mm] $\pm$ 5 [$\mu$m]. The blue line shows the TPA response at the conjugated focal plane, with a maximum peak at 6.686 [mm] $\pm$ 5 [$\mu$m].

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4. Experimental results

Once the NCP system has been calibrated as described in Section 3, we can replace the reference detector by a target. In our case, we used a copper (Cu) plate, as used in laser-driven X-ray sources [2,15]. We tested the reliability of the system by recovering the focal position, defined as the location of the maximum intensity, for two different initial positions. The target is mounted over a second translation stage, so we can introduce an initial offset position along the optical axis. We locate the absolute maximum for several measurements. The mean value is calculated and reported as the focus position, and the error is given by the standard deviation. Figure 4(a) shows the z-scan measurements to find the relative focal position on the target surface at 7.237 [mm] $\pm$ 3 [$\mu$m] for an initial position of 1.2 [mm], and Fig. 4(b) shows the z-scan measurements to find the relative focal position on the target surface at 6.935 [mm] $\pm$ 5 [$\mu$m] for an initial position of 1.5 [mm]. The offset between the two initial positions is 300 $\pm$ 5 [$\mu$m], which is close to the difference between the two focal positions measured (302 [$\mu$m]) by the NCP system.

 

Fig. 4. z-scans measurements at two different initial positions. (a) shows the results for a home position of 1.2 [mm] ($\mu =$ 7.237 [mm] $\pm$ 3 [$\mu$m]) and (b) for a home position of 1.5 [mm] ($\mu =$ 6.935 [mm] $\pm$ 5 [$\mu$m]).

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The nonlinear detection principle can also be used with a CMOS camera if spatial resolution is needed. We use the speckle, generated by TPA, to measure the position of the focal point [2], to achieve this, we replaced the NCP detector by a Si-CMOS camera (CS126CU), this camera is also blind at 1550 [nm]. We repeated the calibration procedure described before (Section 3) for the CMOS camera (Fig. 5(a)), where the real focal position (reference detector) is located at 3.238 [mm] and the CMOS camera (conjugated detector) is at 3.262 [mm]. A calibration error of 24 [$\mu$m] is perceptible from the data exposed. This calibration error is due to the noise from the CMOS sensor and its high sensitivity with respect to a single-pixel detector, so we were not capable to improve the calibration for the CMOS sensor.

 

Fig. 5. (a) shows the calibration of the NCP system with a CMOS camera as the conjugated detector. The reference detector (red line) shows a maximum peak at 3.238 [mm] $\pm$ 3 [$\mu$m], when the conjugated CMOS detector (blue line) shows a maximum peak at 3.262 [mm] $\pm$ 3 [$\mu$m]. (b) shows the comparison between the TPA-photocurrent and the processed data of the TPA-speckle detected of a Cu-target. A peak in the TPA-photocurrent is located at 10.315 [mm] and a maximum of the TPA-speckle distribution is located at 10.340 [mm]. The image of the TPA-speckle reflected at the peak of the photocurrent is shown in (c), and for the TPA-speckle signal is shown in (d).

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A z-scan focusing measurement of a Cu-target has been done with the NCP system and the CMOS sensor. An image of the speckle generated at the target surface is registered as a function of the $z$-position. Each speckle image was processed by a Fourier analysis to get the low frequencies response of the speckle [2,19]. Figure 5(c) shows the TPA-photocurrent response of the CMOS camera (blue line) and the TPA-speckle processed signal (red line), both in terms of the target position. A difference of 25 [$\mu$m] between the two peaks is visible from the results, this variation corresponds to the calibration error reported before. Nevertheless, the results are consistent with each other. The speckle decreases when the target is closer to the focal plane, which means that the beam size is comparable to the target surface roughness.

Finally, we tested the system for tilt tolerance of the target with respect to their normal. A z-scan measurement was performed for a small angle of incidence on the surface target. We located the Cu-target plate so the normal is at an angle of 7.8 degrees with respect to the beam path (Fig. 6(b)). These results are shown in Fig. 6(a) for six measurements of the same Cu-target target, locating the focal position at 6.607 [mm] $\pm$ 2 [$\mu$m]. The speckle reflected by the target limits the detection of the TPA on the photodetector, because the intensity drops, proportional to the angle of incidence. Nevertheless, the system was capable to detect some TPA signal for small angles of incidence ($\theta _i$< 8$^{\circ }$) with high accuracy.

 

Fig. 6. A series of measurements of the target position for an incidence angle $\theta$ are shown in (a) with a focal position at $\mu =$ 6.607 [mm]. (b) shows a picture of the copper plate located in front of the focusing lens with an incidence angle of $\theta =$ 7.8$^{\circ }$.

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The double peak found in Fig. 4, 5(c) and 6(a), appears only in the case of rough surfaces, as these copper targets. As it can be observed, this feature does not affect the position of the main peak.

5. Conclusions

The NCP (Nonlinear Confocal Positioner) shows to be a reliable and highly accurate micron-scale target positioner. The novelty of our system is that the Si-photodiode and the Si-CMOS act as a nonlinear media and detector at once, providing the system a high sensitivity and ease of alignment. A main advantage of our system is that even in the case of spatial aberrations or change in the temporal structure of the pulse, the system will locate the relative maximum intensity position, if the two-photon absorption condition is achieved. The TPA detection by the Si-photodetectors represents a good alternative light sensor at the NIR range, where linear detectors can be more expensive. Also, the large active area of the Si-detector allows us to simplify the alignment of the system in comparison to the CHIP setup [21], where a collection aperture (optical fiber core) has to be carefully aligned. Our confocal setup is simple to align with no need of a conjugated focal plane selective aperture. The results shown in this work demonstrate good capabilities to retrieve the focal plane position on a rough target surface with errors below 5 [$\mu$m] (z-stage step resolution). The z-scan focusing measurements done with the Si-CMOS sensor allowed us to compare the TPA with the TPA-speckle signal, with an error between focus detections comparable with the calibration error, which validates the NCP reliability. Moreover, incorporating a camera as a detector gives the opportunity to derive spatial information from the target, instead of a photodiode which increases the acquisition rate. Also, their tolerance for tilt targets within a small angle (<8$^{\circ }$) has been proved. Finally, the TPA signal can be detected with a Si-detector and a few of [mW] average power, delivered from a femtosecond laser source. Also, the NCP system can be extrapolated to other spectral regions, as an example for Ti-sapphire systems, a GaP-photodiode could cover the TPA detection at 800 [nm] range. The characteristics of the NCP make it an ideal option to improve the high intensity, high average power, laser-driven plasma accelerators and microfabrication applications.