Octave Spanning Tunable Frequency Comb from a Microresonator

Abstract

Optical frequency combs [1,2,3] have revolutionized the field of frequency metrology within the last decade and have become enabling tools for atomic clocks [4], gas sensing [5,6] and astrophysical spectrometer calibration [7,8]. The rapidly increasing number of applications has heightened interest in more compact comb generators. Optical microresonator based comb generators bear promise in this regard. allow deriving an optical frequency comb directly from a continuous wave laser source and have been demonstrated in a number of optical microresonator geometries [9,10,11,12,13,14,15]. Critical to their future use as 'frequency markers', is however the absolute frequency stabilization of the optical comb spectrum [16]. A powerful technique for this stabilization is self-referencing [16,17], which requires a spectrum that spans a full octave, i.e. a factor of two in frequency. In the case of mode locked lasers, overcoming the limited bandwidth has become possible only with the advent of photonic crystal fibres for supercontinuum generation [18,19]. Here, we report for the first time the generation of an octave-spanning frequency comb directly from a toroidal microresonator on a silicon chip. The comb spectrum covers the wavelength range from 990 nm to 2170 nm and is retrieved from a continuous wave laser interacting with the modes of an ultra high Q microresonator, without relying on external broadening. Full tunability of the generated frequency comb over a bandwidth exceeding an entire free spectral range is demonstrated. This allows positioning of a frequency comb mode to any desired frequency within the comb bandwidth. The ability to derive octave spanning spectra from microresonator comb generators represents a key step towards achieving a radio-frequency to optical link on a chip, which could unify the fields of metrology with micro-and nano-photonics and enable entirely new devices that bring frequency metrology into a chip scale setting for compact applications such as space based optical clocks.In addition to the advantage of compact integration, microresonator based frequency combs have high power per comb line, which is a result of the smaller resonator size and the correspondingly higher repetition rate. This high power per comb line enables direct comb spectroscopy [20] and is advantageous for many applications, and critical for high capacity telecommunication. On the other hand, the high repetition rate of micro-combs results in a smaller peak power of the optical pulses that are underlying the generated frequency comb. This renders spectral broadening using nonlinear fibres [1,18] inefficient. Spectral broadening is a method which allowed for the first broadening of mode locked lasers to octave spanning combs ten years ago [19], leading to a breakthrough of the optical frequency comb technology.Here we show that the high power enhancement in a microresonator itself is sufficient for direct octave spanning frequency comb synthesis without the need for any additional spectral broadening. Optical freq...

Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator

“…The magnitude, phase, and real part of χ (3) are plotted vs δωT 2 for three different ratios T 1 /T 2 = 40,10,5. The parametric gain seen by the sidebands is determined by Re[χ (3) ]. Low-frequency PPs lead to a parametric suppression of the gain.…”

“…To better elucidate the nature of the PPs, the magnitude, phase, and real part of χ (3) are plotted in Fig. 7 as a function of the sideband detuning, for three different values of T 1 /T 2 .…”

“…Low-frequency PPs lead to a parametric suppression of the gain. For the gain to be parametrically enhanced, δω must be large enough that the inversion can no longer follow the intensity in antiphase; in other words, the phase of χ (3) must be between −π/2 and π/2.…”

“…We will later calculate the instability threshold in the limit of small primary mode intensity, and are therefore interested in the lowest-order nonlinearity. We obtain χ (3) , the dimensionless frequency-dependent portion of the third-order PP nonlinear susceptibility, by evaluating at |Ẽ 0 | 2 = 0:…”

“…A monochromatic external pump beam is coupled to a mode of the microresonator, and at sufficient pump power the third-order χ (3) Kerr nonlinearity, responsible for the intensitydependent refractive index, couples the pumped mode to fluctuations at other frequencies, which leads to interesting physics. Starting from an initial demonstration of third-order optical parametric oscillation (OPO) [1,2], in which the pump beam provides sufficient parametric gain to allow a few pairs of sidebands to oscillate, this technique has been extended to generate wide-spanning frequency combs [3,4], and most recently temporal solitons [5,6]. The many degrees of freedom one can manipulate in these systems, such as the group velocity dispersion (GVD), the free spectral range of the resonator, the detuning of the pump frequency relative to the cold-cavity to lase and as the current is increased the population inversion remains clamped to its threshold value.…”