Optical Frequency Comb Spectrum Research Articles

Semiclassical theory of frequency combs generated by parametric modulation of optical microresonators

An optical microresonator, which parameters are periodically modulated in time, can generate optical frequency comb (OFC) spectral resonances equally spaced by the modulation frequency. Significant recent progress in realization of OFC generators based on the modulation of microresonator parameters boosted interest to their further experimental development and theoretical understanding of underlying phenomena. However, most of theoretical approaches developed to date were based on the lumped parameter models which unable to evaluate, analyse, and optimize the effect of spatial distribution of modulation inside microresonators. Here we develop the multi-quantum semiclassical theory of parametrically excited OFCs which solves these problems. As an application, we compare OFCs which are resonantly or adiabatically excited in a racetrack microresonator (RTM) and a Surface Nanoscale Axial Photonics (SNAP) bottle microresonator (SBM). The principal difference between these two types of microresonators consists in much slower propagation speed of whispering gallery modes along the SBM axis compared to the speed of modes propagating along the RTM waveguide axis. We show that, due to this difference, similar OFCs can be generated by an SBM with a much smaller size compared to that of the RTM. Based on the developed theory, we analytically express the OFC spectrum of microresonators through the spatial distribution of modulated parameters and optimize this distribution to arrive at the strongest OFCs generated with minimum power consumption.

Optical Frequency Comb Frequency-division Multiplexing Dispersive Interference Multichannel Distance Measurement

An optical frequency comb (OFC) frequency-division multiplexing dispersive interference multichannel distance measurement method is proposed. Based on the OFC dispersive interference, the wide OFC spectrum is divided into multiple channels using a wavelength-division multiplexer. Under the existing light source and spectrometer, a single interference system can realize six channels of the high-precision parallel absolute distance measurement. The influence of the spectrum width and shape on the performance of the distance measurement channel is analyzed. The ranging accuracy of six channels is higher than ± 4 μm under the optimization of a nonuniform discrete Fourier transform and Hanning window.

Reconfigurable microwave photonic filter based on a quantum dash mode-locked laser.

We demonstrate a reconfigurable microwave photonic (MWP) filter using a quantum dash (QDash) mode-locked laser (MLL) that can generate an optical frequency comb (OFC) with ∼50 comb lines and a free spectral range of 25 GHz. Thanks to the large number of comb lines, the MWP filter responses can be easily programmed by tailoring the OFC spectrum. We implement MWP filter responses with Gaussian, sinc, flat-top, and multiple peaks, as well as demonstrate that tuning of the central frequency. We achieve a minimum 3 dB bandwidth of ∼100 MHz for a sinc-shaped MWP filter, while the maximum out-of-band rejection can be up to ∼30 dB with Gaussian apodization. Our results show that the QDash-MLL is a promising OFC source for developing integrated and reconfigurable MWP filters.

Design of all-solid fluorotellurite fibers with near-zero-flattened dispersion profiles for mid-infrared optical frequency comb generation

All-solid fluorotellurite fibers with near-zero-flattened dispersion profiles in the wavelength range of 1840–2140 nm are designed for mid-infrared optical frequency comb (OFC) generation. The fiber core materials are TeO2-BaF2-Y2O3 (TBY) glasses. The fiber cladding materials are fluoroaluminate and TBY glasses. By controlling the core diameter and the thickness of the thin annular fluoroaluminate or TBY glass, the fiber with the chromatic dispersion value between −0.3 and 0.32 ps nm km−1 in the wavelength range of 1840–2140 nm is achieved. Furthermore, we perform numerical simulations on mid-infrared OFC generation via four-wave mixing in the designed fiber. By using a 1980 nm laser with a pulse width of 1.28 ps and a peak power of 60 W as the pump source, OFC spectrum expanding from 1127 to 4942 nm is obtained in a 2 m long fiber, and the pulse width of the generated OFC is about 25 fs. By varying the repetition rate of the pump source, mid-infrared OFC with tunable mode spacing is generated in the designed fiber.

Low-noise transfer of the spectral purity of an optical comb line using a feedforward scheme

We present a detailed frequency noise analysis of a feedforward scheme used to faithfully transfer the spectral properties of an individual line of an optical frequency comb spectrum to a single-mode laser and in this way indirectly amplify it, which is applicable to any arbitrary comb mode spacing. In contrast to previously reported implementation of the feedforward method for a similar purpose, we present a more thorough noise study, including the measurement of the additive noise of the setup. The reported experimental investigation was performed using two low-noise ultrafast mode-locked lasers with different repetition rates (~ 1 GHz and 250 MHz) and show a faithful transfer of the comb mode frequency noise to the auxiliary laser with a sub-radian additive phase noise integrated from 1 Hz to 1 MHz. We discuss the present limitations of the method that is able to transfer optical comb lines with sub-Hz linewidth and propose simple improvements.

Design of all-solid W-type index fluorotellurite fibers with near-zero-flattened chromatic dispersion for optical frequency comb generation.

All-solid W-type index fluorotellurite fibers (AWFTFs) with near-zero-flattened dispersion profiles are designed for optical frequency comb (OFC) generation. The fiber core and cladding materials are ${{\rm TeO}_2} {\text - } {{\rm BaF}_2} {\text - } {{\rm Y}_2}{{\rm O}_3}$TeO2-BaF2-Y2O3 (TBY) and fluoroaluminate glasses. Those two glasses have large refractive index contrast as well as similar thermal expansion coefficients and softening temperatures. The zero-dispersion wavelength of the TBY glass is about 2517 nm. By introducing fluoroaluminate glasses with relatively low refractive index as the cladding material and controlling the core diameter, the zero-dispersion wavelength of the fiber is shifted from 2517 nm to the wavelength region of 1500-1600 nm. Furthermore, two layers of thin annular glasses including a fluoroaluminate-glass-based inter-layer and a TBY-glass-based outer layer are added around the fiber core, which makes the fiber have a flat dispersion profile in the wavelength range of 1500-1600 nm. By optimizing the parameters (the core diameter, the thickness of the thin annular glass, etc.) of AWFTFs, the fiber with the chromatic dispersion value between $ - {0.2}$-0.2 and 0.35 ps/nm/km in the wavelength range of 1500-1600 nm is achieved. To investigate the application of the AWFTFs for OFC generation via cascaded four-wave mixing, we perform numerical simulations. The simulated results show that flat-top OFC spectrum expanding from 1450 to 1700 nm with tunable mode spacing from 25 to 100 GHz can be generated in 2 m long fiber by using a 1550 nm laser with a pulse width of 0.825 ps and a peak power of 60 W as the pump source.

Novel programmable microwave photonic filter with arbitrary filtering shape and linear phase.

We propose and demonstrate a novel optical frequency comb (OFC) based microwave photonic filter which is able to realize arbitrary filtering shape with linear phase response. The shape of filter response is software programmable using finite impulse response (FIR) filter design method. By shaping the OFC spectrum using a programmable waveshaper, we can realize designed amplitude of FIR taps. Positive and negative sign of FIR taps are achieved by balanced photo-detection. The double sideband (DSB) modulation and symmetric distribution of filter taps are used to maintain the linear phase condition. In the experiment, we realize a fully programmable filter in the range from DC to 13.88 GHz. Four basic types of filters (lowpass, highpass, bandpass and bandstop) with different bandwidths, cut-off frequencies and central frequencies are generated. Also a triple-passband filter is realized in our experiment. To the best of our knowledge, it is the first demonstration of a programmable multiple passband MPF with linear phase response. The experiment shows good agreement with the theoretical result.

Frequency noise performances of a Ti:sapphire optical frequency comb stabilized to an optical reference

We report on a detailed analysis of frequency noise and intensity dynamics of a free-running femtosecond Ti:sapphire optical frequency comb (OFC) pumped by a multi-mode 532nm laser. We have used these results for phase locking the OFC to a Hz-wide, cavity stabilized, 698nm semiconductor laser. An analysis of the in-loop error signals and an estimation of Allan deviation indicates a lower limit for the frequency stability of the OFC at the level of ∼5.3×10−14 for 125ms integration time comparable with the clock laser frequency stability over the entire OFC spectrum. The noise transfer processes between the pump laser and the Ti:sapphire laser have been studied in detail, comparing the resulting frequency noise of the OFC output spectrum with both a single-mode and a multi-mode pump lasers. In the latter case, we employed a pump beam steering control to maintain an OFC regime with a minimum impact of pump laser amplitude noise on the carrier-envelope offset frequency.

Flat optical frequency comb generation and its application for optical waveform generation

We demonstrate the generation of a flat optical frequency comb (OFC) using an electro absorption modulator (EAM) and two cascaded phase modulators (PM). Compared with previous flat OFC generation schemes using a Mach–Zehnder modulator (MZM) for amplitude gating of the phase modulated light, an EAM creates much shorter time window for amplitude gating, and more flattened OFC spectrum is obtained using EAM as an amplitude gate. In our experiment, a very flat OFC having 11 lines within 3-dB bandwidth (3.8nm), and 40GHz comb line spacing is generated. Besides the excellent spectral flatness, the strong time-domain linear-chirp of the generated OFC can be simply compensated by a dispersion compensation fiber (DCF) link, which is preferred for optical waveform generation based on spectral manipulation. In this paper, we also demonstrate the OFC application for generation of several optical waveforms by manipulating the amplitude and phase of the comb lines. High repetition-rate optical cosine pulse, optical pulse burst, optical square and triangle pulses are successfully generated.

Generation of regular femtosecond pulses in AlGaInP semiconductor laser

It is shown experimentally that stable ~ 200 fs regular pulses and optical frequency comb spectrum containing ~ 70 discrete frequencies can be achieved using semiconductor injection laser working in the conditions of superfluorescence under dc pumping current, which is lower than the threshold of laser action.

Characterization of an optical frequency comb using modified direct frequency comb spectroscopy

We introduce a method for determination of the absolute frequencies of comb lines within an optical frequency comb spectrum. The method utilizes the experimental and theoretical approach of the velocity-selective optical pumping of the atomic ground state hyperfine levels induced by resonant pulse-train excitation. The information on the laser pulse repetition frequency and carrier–envelope offset are physically mapped onto the 87Rb ground state hyperfine level population velocity distributions. Theoretical spectra are calculated using an iterative analytic solution of the optical Bloch equations describing the resonant pulse-train excitation of four-level 87Rb atoms. They are employed to fit the measured spectra and obtain the parameters of the frequency comb, thus providing a practical algorithm which can be used in real-time measurements.

Limit of optical-frequency comb generation due to material dispersion

The limit of optical frequency comb (OFC) generation (i.e., the limit of frequency difference measurement) due to the material dispersion in the EO crystal is experimentally studied. By using a modified monolithic OFC generator, we observed the OFC spectrum, and confirmed that the envelope of the OFC around 780 nm extended to a span as wide as 16 nm (or 7.6 THz) reaching the limit of the OFC generation. We also proposed a method of stabilizing the Fabry-Perot cavity for the monolithic OFC generator.