We propose a new type of broadband and low repetition rate (RR) frequency comb generator that has the shape of an elongated and nanoscale-shallow optical bottle microresonator created at the surface of an optical fiber. The free spectral range (FSR) of the broadband azimuthal eigenfrequency series of this resonator is the exact multiple of the FSR of the dense and narrowband axial series. The effective radius variation of the microresonator is close to a parabola with a nanoscale height that is greater or equal to λ/2πn0. (Here λ is the characteristic radiation wavelength and n0 is the refractive index of the microresonator material.) Overall, the microresonator possesses a broadband, small FSR and accurately equidistant spectrum convenient for the generation of a broadband and low RR optical frequency comb. It is shown that this comb can be generated by pumping with a cw laser, with a radiation frequency that matches a single axial eigenfrequency of the microresonator or, alternatively, by pumping with a mode-locked laser, which generates a narrowband low RR comb matching a series of equidistant axial eigenfrequencies situated between adjacent azimuthal eigenfrequencies.
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