A high power single mode, SM, fiber laser configured to operate in a Green spectral range in a continuous-wave, CW, mode and comprising: a single frequency, SF, single mode, SM, polarized seed source configured to operate to emit the SM pump light with linewidth narrower than 0.2 nm at a fundamental wavelength in one micrometer spectral range; at least one ytterbium, Yb, doped fiber amplifier configured to receive and amplify the SF SM polarized pump light at the fundamental wavelength while maintaining the linewidth narrower than 0.2 nm; the high power, SM, fiber laser further comprising: a SM input passive fiber, LP, configured to guide the SM pump light from the seed source, and coupled to the input core region of the Yb fiber amplifier, and an output SM passive fiber coupled to the Yb fiber amplifier configured to guide the amplified SM pump light, the Yb fiber amplifier provided with a monolithic multimode, MM, core surrounded by at least one cladding, the MM core being configured to support the single mode at the fundamental wavelength and including: opposite input and output uniformly dimensioned core regions (56, 57) coupled to respective input and output SM passive fibers (62, 59), a uniformly dimensioned central core region having a diameter larger than that of the input and output core regions (56, 57), and a pair of mode transforming regions bridging the input and output core regions (56, 57) with respective ends of the central core region, wherein the SM input and output passive fiber (62, 59) and the input and output core regions (56, 57) of the Yb doped amplifier are configured with respective mode field diameters matching one another; and a nonlinear optical frequency converter configured to convert the amplified SF SM polarized pump light at the fundamental wavelength in a single-pass second-harmonic generation, SHG, scheme to output SF SM Green light in a 510 - 540 nm wavelength range with an average power in a range from over 350 W to kW-levels, wherein the SM fiber laser operates with a wall plug efficiency between 15 % and 35%. a single frequency, SF, single mode, SM, polarized seed source configured to operate to emit the SM pump light with linewidth narrower than 0.2 nm at a fundamental wavelength in one micrometer spectral range; at least one ytterbium, Yb, doped fiber amplifier configured to receive and amplify the SF SM polarized pump light at the fundamental wavelength while maintaining the linewidth narrower than 0.2 nm; the high power, SM, fiber laser further comprising: a SM input passive fiber, LP, configured to guide the SM pump light from the seed source, and coupled to the input core region of the Yb fiber amplifier, and an output SM passive fiber coupled to the Yb fiber amplifier configured to guide the amplified SM pump light, the Yb fiber amplifier provided with a monolithic multimode, MM, core surrounded by at least one cladding, the MM core being configured to support the single mode at the fundamental wavelength and including: opposite input and output uniformly dimensioned core regions (56, 57) coupled to respective input and output SM passive fibers (62, 59), a uniformly dimensioned central core region having a diameter larger than that of the input and output core regions (56, 57), and a pair of mode transforming regions bridging the input and output core regions (56, 57) with respective ends of the central core region, wherein the SM input and output passive fiber (62, 59) and the input and output core regions (56, 57) of the Yb doped amplifier are configured with respective mode field diameters matching one another; and a nonlinear optical frequency converter configured to convert the amplified SF SM polarized pump light at the fundamental wavelength in a single-pass second-harmonic generation, SHG, scheme to output SF SM Green light in a 510 - 540 nm wavelength range with an average power in a range from over 350 W to kW-levels, wherein the SM fiber laser operates with a wall plug efficiency between 15 % and 35%. opposite input and output uniformly dimensioned core regions (56, 57) coupled to respective input and output SM passive fibers (62, 59), a uniformly dimensioned central core region having a diameter larger than that of the input and output core regions (56, 57), and a pair of mode transforming regions bridging the input and output core regions (56, 57) with respective ends of the central core region, wherein the SM input and output passive fiber (62, 59) and the input and output core regions (56, 57) of the Yb doped amplifier are configured with respective mode field diameters matching one another; and a nonlinear optical frequency converter configured to convert the amplified SF SM polarized pump light at the fundamental wavelength in a single-pass second-harmonic generation, SHG, scheme to output SF SM Green light in a 510 - 540 nm wavelength range with an average power in a range from over 350 W to kW-levels, wherein the SM fiber laser operates with a wall plug efficiency between 15 % and 35%.