A laser machining method of a workpiece comprising: partially converting a first broadband unpolarized fiber laser beam at a fundamental wavelength into at least one second beam at a harmonic wavelength; guiding the first beam and one second beam along a path with the first and second beams being coaxially and temporally overlapped; impinging the first and one second beams upon a surface of the workpiece having different absorption coefficients at respective fundamental and harmonic wavelengths; controlling a fluence ratio between the first and one second beams to be at least equal to the inverse absorption coefficients ratio at which the second beam provides a material state change and has a focal plane closer to the surface than a focal plane of the first beam so as to increase an absorption coefficient of the workpiece for the first beam ; generating an axial chromatic aberration between the first and second beams such that the first beam has a focus within the workpiece at a distance from the surface, and the second beam has a second focus spaced upstream from the first focus wherein controlling the fluence ratio includes: displacing non-achromatic optics, which generates the achromatic aberration along the path, or replacing the non-achromatic optics with another, which is configured with different refractive curvatures or made from different optical material such as Fused Silica, CaF 2 , or MgF 2 , or others capable of altering respective focal distances of the first and second beams, the inverse absorption coefficient ratio being a ratio of absorption coefficients at respective fundamental and harmonic wavelength. partially converting a first broadband unpolarized fiber laser beam at a fundamental wavelength into at least one second beam at a harmonic wavelength; guiding the first beam and one second beam along a path with the first and second beams being coaxially and temporally overlapped; impinging the first and one second beams upon a surface of the workpiece having different absorption coefficients at respective fundamental and harmonic wavelengths; controlling a fluence ratio between the first and one second beams to be at least equal to the inverse absorption coefficients ratio at which the second beam provides a material state change and has a focal plane closer to the surface than a focal plane of the first beam so as to increase an absorption coefficient of the workpiece for the first beam ; generating an axial chromatic aberration between the first and second beams such that the first beam has a focus within the workpiece at a distance from the surface, and the second beam has a second focus spaced upstream from the first focus wherein controlling the fluence ratio includes: displacing non-achromatic optics, which generates the achromatic aberration along the path, or replacing the non-achromatic optics with another, which is configured with different refractive curvatures or made from different optical material such as Fused Silica, CaF 2 , or MgF 2 , or others capable of altering respective focal distances of the first and second beams, the inverse absorption coefficient ratio being a ratio of absorption coefficients at respective fundamental and harmonic wavelength. displacing non-achromatic optics, which generates the achromatic aberration along the path, or replacing the non-achromatic optics with another, which is configured with different refractive curvatures or made from different optical material such as Fused Silica, CaF 2 , or MgF 2 , or others capable of altering respective focal distances of the first and second beams, the inverse absorption coefficient ratio being a ratio of absorption coefficients at respective fundamental and harmonic wavelength. <EOS>