## 1 Introduction
However, it is difficult to apply these to laser-generated acoustic waves due to the operation bandwidth and the requirement of the wave to be transmitted through or reflected from the meta-surface. Beamforming of acoustic waves through array sensors has been widely used to improve the contrast, spatial resolution, and signal-to-noise ratio of ultrasound images. Based on our understanding of previous research, two categories of techniques are conceptualized as the beamformer approaches, either at the excitation-side and the probing-side of acoustic waves. The traditional probe-side beamforming method achieves the purpose of signal enhancement by processing the received signal from the perspective of signal acquisition rather than directly generating stronger acoustic signals from the perspective of excitation. This is a fatal flaw in extremely absorbent biological tissues. Traditional probe-side beamformer methods include the delay and sum (DAS) method [22], the minimum variance (MV) method [23; 24], etc. The principle of these methods is to align the target beams according to the delay time and add them sequentially to enhance the signal. DAS is independent of echo data, which leads to the main lobe width being too wide and the side lobes intensity being too high [24]. The minimum variance (MV) method, e.g., adaptive beam synthesis, calculates a dynamic weight value based on the echo data, makes full use of the characteristics of the echo signal, reduces the side lobe signal, and improves the resolution of the image. The basic principle is to minimize the array output by keeping the gain in the desired direction constant. For traditional excitation-side forming, [PERSON] et al. achieved beam steering and enhancement by applying a time delay to each piezoelectric plate in an 8-element line array [25]. The distance between the line sources is about one wavelength. The delay time is controlled by the line source spacing and rotation angle. [PERSON] [26] proposed that a larger inter-element spacing can help improve the directivity of the steered wave, yet only to a certain extent; the grating lobes will be introduced (or the beam is not steerable) when the inter-element spacing exceeds its critical value, which is about half the wavelength of the sound wave and controlled by the desired maximum steering angle. The traditional excitation-side beamformer can achieve controllable superposition between different sources, thereby achieving high-degree-of-freedom beam direction control. In principle, it can also achieve the wavefront formation and control discussed in this article. However, a systematic study of the process of exciting, shaping, and steering photoacoustic waves using laser array sources is therefore still essential. The purpose of this article is to explore whether it is feasible to realize the formation and control of the wavefront in the process of photoacoustic excitation, as well as the mechanism of its formation and propagation. In this paper, the characteristics of surface and bulk waves excited by a laser array with partial time delay are numerically simulated using the finite element method (FEM). We verify whether, by applying a time delay between different elements of the laser array, the photoacoustic wave can be enhanced and whether this enhanced wave still propagates as a wavefront maintaining its complete shape.