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.