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Frequency comb representations and detection of the offset frequency. a Time and frequency domain representation of an optical frequency comb. The optical output of a mode-locked laser is a periodic train of optical pulses with pulse period, T r , and pulse envelope A(t). In the frequency domain, this pulse train can be expressed as a Fourier series of equidistant optical frequencies, with mode spacing, f r = 1/T r . It is the regular frequency spacing of the modes in the optical spectrum that inspired the analogy to a comb, although the analogy of a frequency ruler better describes the OFCs measurement capability. The frequency of any optical mode, ν N , is characterized by only two degrees of freedom, f r and f 0 , such that ν N = N ⋅ f r + f 0 . The mode spacing, f r , is accessed by directly detecting the amplitude modulation of the optical pulse train using an optical photodetector. This detection results in an electronic pulse train composed of coherently related microwave Fourier harmonics, n ⋅ f r . Note that the optical spectrum contains information about the offset of the harmonic comb from 0 Hz, f 0 , whereas the microwave spectrum only yields harmonics of f r because direct photodetection is not sensitive to the optical carrier. In the yellow shaded inset, we show the relationship between f 0 and the carrier-envelope offset phase, ϕ CEO (t). The evolution in the pulse-to-pulse change in the carrier-envelope phase is given by Δϕ CEO = 2πf 0 /f r . Notably, when f 0 = 0, every optical pulse has an identical carrier-envelope phase. The pulse envelope, A (t), depicted by a blue dashed line is related by the periodic Fourier transform to the spectral envelope. b Offset frequency detection via self-referencing. Frequency depiction of how nonlinear self-comparison can be used to detect f 0 .
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Optical frequency combs were developed nearly two decades ago to support the world’s most precise atomic clocks. Acting as precision optical synthesizers, frequency combs enable the precise transfer of phase and frequency information from a high-stability reference to hundreds of thousands of tones in the optical domain. This versatility, coupled w...
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... comb equation. The deterministic behavior of the OFC spectrum described above is most succinctly described by the comb equation. To understand the comb equation, we will begin by exploring the relatively simple mathematics that describe the optical field output from a MLL (see Fig. 1). The optical field of the laser pulse train can be described by a carrier frequency, ν c = ω c /(2π), that is modulated by a periodic pulse envelope, A(t). Typically, the time between optical pulses range between 1 and 10 ns. Due to the pulse periodicity, the optical field can also be described as a periodic Fourier series of optical ...
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... frequencies are easily measured as long as they fall within the bandwidth limit of precision frequency counters (<10 GHz). As a simple example, consider two optical carriers close in frequency, ν 1 and ν 2 , that can be interfered to produce an optical carrier with an amplitude modulation at the difference frequency, Δf = ν 1 − ν 2 , (see Fig. 1a). When this signal is incident on a photodetector, the detector produces a voltage proportional to the amplitude modulation. This signal is often referred to in the literature as a heterodyne optical beat frequency. This technique of difference frequency measurement is at the heart of nearly all measurement techniques with optical ...
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... modulation. Because MLLs used as OFCs typically have optical cavity lengths that vary between 30 cm and 3 m, f r is an easily accessible microwave frequency between 1 GHz and 100 MHz, respectively. Direct photodetection of the optical pulses results in an electronic signal that only follows the amplitude modulation of the pulse train. As seen in Fig. 1a, the frequency decomposition, or Fourier Transform, of the resulting electronic pulses yield harmonics of f r , but yield no information about f 0 . Said otherwise, direct optical heterodyne between two optical modes of the comb only yields information about f r because f 0 is common to each mode, ...
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... of f 0 . As explained previously, the fact that f 0 is related to the phase of the optical carrier makes it extremely difficult to access directly. In 1999 a method was proposed to produce a heterodyne beat at f 0 21 by nonlinear self-referencing between the extremes of the optical comb spectrum (see Fig. 1b). The simplest manifestation of this technique is obtained by frequency doubling light from a comb mode on the low end of the optical comb spectrum and interfering it with fundamental light at twice the frequency such ...
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... to high-stability optical references can enable the derivation of microwave signals with stabilities better than 10 −15 , yielding greater than a 100 times improvement over what can be achieved with the best room-temperature electronic oscillators 35 . In principle, the generation of low-noise microwave is relatively straight forward. As shown in Fig. 1, the phasestabilized optical pulses from an OFC can be converted to a stable electronic pulse train via direct detection with high-speed photodetectors. Subsequent electronic filtering isolates a single harmonic of f r within the bandwidth of the photodetector producing a sinusoidal signal. Signals derived in this manner can be ...
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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...
Citations
... Optical frequency combs (OFCs) offer broadband optical spectra comprised of many discrete frequencies that are equally spaced, corresponding to coherent train of pulses with a stable repetition rate. 1 These precision light sources have become ubiquitous in various photonic technological applications. 1,2 Ultra-stable OFC-based spectroscopy, in particular, has seen significant growth in recent years due to the ability of these lasers to enhance the performance of existing spectrometers, such as virtual imaging phase array etalons, or Michelson-based Fourier transform interferometers. ...
This paper presents a novel approach to dual-frequency comb generation utilizing a single fiber Fabry–Perot resonator, advancing the implementation of these sources in fiber-based systems. Dual-comb applications such as spectroscopy, ranging, and imaging, known for their high-resolution and rapid data acquisition capabilities, benefit significantly from the stability and coherence of optical frequency comb sources. Our method leverages the birefringent property of the resonator induced by the optical fiber to generate two orthogonally polarized optical frequency combs in a monolithic resonator. This approach allows for the generation of two different frequency combs with slightly different repetition rates, exhibiting excellent mutual coherence, making it highly relevant for dual-comb applications. The 40 nm bandwidth generated combs are induced by switching-waves in a normal dispersion fiber Fabry-Perot resonator. These comb types have the advantage of being easily generated by a pulse pumping scheme, which is employed in this study. Finally, the potential of the source is demonstrated by a proof-of-concept spectroscopy measurement.
... Another less explored application of OMOs is the generation of optical frequency combs (OFCs). Nowadays, extensive research is being conducted on OFCs due to their crucial role in various applications such as optical metrology, precision spectroscopy, optical clocks, and rf photonics [34][35][36]. So far, researchers have successfully utilized electro-optic (EO) modulation or intrinsic parametric nonlinearities of materials (such as Kerr media), commonly exhibiting high repetition rates, to demonstrate the integrated optical microcombs [36][37][38][39][40]. On the other hand, OFCs with low repetition rates (typically below 1 GHz) are better suited for other applications, such as high-resolution spectroscopy [41,42], mode-locked lasers with ultranarrow spectral widths [43], integrated pulse sources for quantum optics [44], and lownoise microwave frequency comb generations [45,46]. ...
Cavity optomechanical oscillations (OMOs) have been extensively studied for their rich physics and various practical applications. However, due to the highly nonlinear nature of the dynamical process, the exact sideband structure of an optomechanically oscillating optical cavity field remains unknown, although it is essential to a comprehensive understanding and accurate manipulation of such systems. Here, we establish a correspondence between the Bloch-band structure and the coupled sideband dynamics of OMOs, thus providing a theoretical framework for unveiling the detailed structure of cavity optical modes in terms of their resemblance to the well-known Wannier-Stark states and ladders. Surprisingly, the locations of these ladders are irrelevant to pump frequency or power but only depend on the resonant frequency of the optical mode and mechanical-mode frequency. By an energy transfer picture, we build up a connection between the highly nonlinear OMOs and a Bloch-band structure that can be solved linearly. Quantitatively, this picture uncovers the underlying mechanism of the optimization of the pump detuning and optical decay rate, as well as the determination of the minimum input pump power, for sustaining a cavity OMO.
Published by the American Physical Society 2025
... Frequency combs can be generated using various methods, including four-wave mixing in nonlinear media, periodic modulation of a continuous-wave laser, or stabilizing the pulse train generated by a mode-locked laser (Fortier and Baumann 2019). One advantage of utilizing four-wave mixing (FWM) for frequency comb generation is its transparent handling of data formats and bit rates. ...
This study introduces a waveguide design capable of generating supercontinuum spectrum and frequency combs within the mid-infrared range. The proposed structure consists of an As2Se3 core and cladding layers of MgF2 and SiO2, exhibiting two zero-dispersion wavelengths at 2100 nm and 2850 nm. Theoretical modeling and numerical simulations demonstrate the generation of a supercontinuum spanning a wavelength range of 4500 nm, from 1000 to 5500 nm, at a − 30 dB level, as well as frequency combs featuring up to 44 comb lines with a flatness of 15 dBm. The supercontinuum was generated in the maximum range of 30 dB using a 1 kW input pulse and 1 and 4 mm long waveguides. The generated frequency combs cover the wavelength range of 2073.1–2159.8 nm, making them suitable for applications such as gas sensing, industrial process monitoring, and medical diagnostics. The proposed waveguide design offers advantages over existing methods in terms of the number of comb lines, flatness, and effective area while operating in the mid-infrared region.
... Optical frequency combs and their discrete spectra enable phase-coherent links across the electromagnetic spectrum and underpin some of the most advanced measurements in physics [1,2]. Usually, they are derived from femtosecond pulsed lasers and their frequency components are described by ν m = mf rep + f ceo , where f rep and f ceo are the laser's pulse repetition rate and carrier-envelope-offset frequency, and m ∈ N 0 is the comb line index. ...
Optical frequency combs and their spectra of evenly spaced discrete laser lines are essential to modern time and frequency metrology. Recent advances in integrated photonic waveguides enable efficient nonlinear broadening of an initially narrowband frequency comb to multi-octave bandwidth. Here, we study the nonlinear dynamics in the generation of such ultra-broadband spectra where different harmonics of the comb can overlap. We show that a set of interleaved combs with different offset frequencies extending across the entire spectrum can emerge, which transform into a single evenly spaced ultra-broadband frequency comb when the initial comb is offset-free.
... Optical frequency combs have been utilized for over twenty years as a means of efficiently extracting information across a wide spectral bandwidth from optical systems [1]. The equidistant modes or 'teeth' for a comb allow it to perform single shot measurements of spectral features in the optical domain, which includes application to molecular absorption spectroscopy [2][3][4] and trace gas sensing [5][6][7]. ...
We present an acousto-optic frequency comb readout scheme synthesized from multiple intra-comb beat measurements using digitally enhanced heterodyne interferometry. The readout scheme enables a single acousto-optic frequency comb to achieve a compression factor, which normally requires a dual comb measurement scheme. We demonstrate an absorption measurement of the 2ν3 P10 line obtaining a noise equivalent absorption sensitivity of 1.75 × 10⁻⁸cm⁻¹Hz−1/2. Additionally we demonstrate the ability of the system to software-adjust the compression factor to access a wider optical bandwidth.
... In the optical realm, optical parametric coupling has played a major role in quantum engineering endeavors. [11][12][13][14][15][16][17] Optical frequency combs (FCs), 18,19 squeezed laser, 20 and squeezed optical frequency combs 13 have gained recognition as formidable tools for precision metrology and spectroscopy, positioning themselves as strong contenders for quantum processing. [21][22][23][24] The landscape of frequency comb (FC) research has seen a rich tapestry of studies delving into nonlinear processes, unveiling techniques for generating bosonic FCs. ...
We present a theoretical framework for generating squeezed microwave and magnonic frequency combs achieved through the parametric coupling of magnon modes to a cavity. This coupling exploits the intrinsic non-linear magnon modes of a ferromagnetic sphere. When subjected to a strong, coherent microwave field, we show that the system exhibits spontaneous generation of squeezed frequency combs. Our exploration crosses various regimes of comb generation, prominently highlighting phenomena such as squeezing and squeezed lasing. This study paves the way for a pioneering room-temperature, multi-frequency maser characterized by both its magnonic and microwave squeezing properties. The implications of our findings hold promise for advancements in spintronics, quantum sensing, information processing, and quantum networking.
... Since their groundbreaking realization in 2000 [1], optical frequency combs (OFCs) have demonstrated significant potential in various applications [2], including precision frequency measurement [3,4], time-frequency transfer [5][6][7][8], and optical frequency conversion [9,10]. These applications exploit the distinctive comb-like spectral properties of OFC, where each radio frequency (RF) or optical spectral line follows the formula f n = f ceo ± nf r ± f beat (with n being the comb tooth order, f ceo the carrier-envelope offset frequency, f r the repetition frequency, and f beat the beat frequency) [11,12]. ...
This paper presents a combined theoretical and experimental method for noise suppression in the repetition frequency (fr) locking of erbium-doped fiber optical frequency combs (OFCs). This study proposed a novel mathematical model to bridge the noise relationship of fr between the free-running and locked modes, and analyzed this relationship from two perspectives: the additional phase noise and the frequency stability. In addition, to integrate theoretical modeling with experimental validation, this study designed fr locking strategy that uses a phase-locked loop (PLL) with PFD + PIID (a phase frequency detector and a proportional, first-order integer, second-order integer, first-order differential controller). Under synchronization of the fr with a microwave reference (REF), this study achieved OFC additional frequency stabilities of 2.81 × 10−15@1 s and 8.08 × 10−19@10,000 s at 200 MHz fundamental frequency locking and 4.25 × 10−16@1 s and 1.91 × 10−19@10,000 s at 1200 MHz harmonic locking. The simulated and experimental results are in good agreement, confirming the consistency of the theoretical model and experiment. This work provides a reliable theoretical model that can be used to predict stability for OFC locking and significantly improves the additional frequency stability of OFCs.
... 7 Additionally, optical frequency comb technology continuously evolves for more than two decades and gains great interest for use in laser ranging, calibration of astronomical spectrographs, and comb-based spectroscopy. 8,9 For many of the above applications, the synchronized operation between different sources is essential, 10,11 and for this reason, much research effort has been devoted to the generation and control of synchronized pulse trains from different sources as well as to the phase locking of frequency combs using active and passive techniques or their combination. 11 Furthermore, coherent combining of phase locked lasers has been established as a method to address the limitations of the low optical power levels of single sources. ...
Two monolithic edge-emitting passively mode-locked InAs/InGaAs semiconductor quantum dot lasers generating ps optical pulses at repetition rates of 10 GHz and optical frequency combs centered at 1260 nm are mutually coupled in an all-optical passive synchronization experiment. The two lasers, with different free-running repetition rates, are coupled through a long delay fiber path, they synchronize, and generate optical pulse trains with identical repetition rates in a wide range of experimental conditions (optical frequency, optical delay, and coupling strength). The common repetition rate can be easily fine-tuned with the control of the external coupling path length. In synchronized state, both lasers operate with significantly reduced timing jitter with respect to their free-running values. Finally, under specific conditions, the repetition rate locking is accompanied by partial mutual coherence between the lasers, as indicated by the formation of interferometric fringes.
... An optical frequency comb, characterized by a series of equally spaced discrete lines, finds broad application in various fields [1][2][3]. The ability to accurately control the photonic sideband emission and process frequencyencoded quantum entanglement via one channel is at the heart of numerous quantum information applications, including universal one-way quantum computing [4,5], scalable generation of entangled cluster states [6,7] and high-dimensional entanglement protocols [8][9][10] in optical frequency comb. ...
... The radiative loss is characterized by the radiative decay rate γ 1D of an individual coupled emitter. To give rise to a frequency comb equally spaced by Ω in the scattered light spectrum, we impose a dynamical modulation on the resonance frequency of n th qubit with a general form ω n (t) = ω 0 + ∆ n (t) = ω 0 + R r=1 A n r cos(rΩt + α n r ), (1) where ω 0 is the equilibrium qubit resonance frequency; A n r and α n r are n-dependent amplitude and phase for r th modulation tone, respectively. Here, n enumerates the qubits that are spaced periodically, and the total number of the considered modulation tones is assumed to be R. ...
The capability to design spectrally controlled photon emission is not only fundamentally interesting for understanding frequency-encoded light-matter interactions, but also is essential for realizing the preparation and manipulation of quantum states. Here we consider a dynamically modulated qubit array, and realize frequency-controlled single-photon emission focusing on the generation of a frequency comb constituted solely of even-parity or anti-Stokes sidebands. Our system also offers parity-dependent bunching and antibunching in frequency-filtered quantum correlations. In particular, the waveguide quantum electrodynamics (QED) setup is extended to include chiral and non-local coupling architectures, thereby enhancing its versatility in Floquet engineering. Our proposal also supports the predictable generation of high-dimensional entangled quantum states, where the corresponding effective Hilbert space dimension is well controlled by energy modulation. Moreover, the utilisation of sophisticated numerical tools, such as the matrix product states (MPSs) and the discretization approach, enables the efficient simulation of multi-photon dynamics, in which the non-Markovian Floquet steady states emerge. This work fundamentally broadens the fields of collective emission, and has wide applications in implementing frequency-encoded quantum information processing and many-body quantum simulation.
... Both benefited each other with their respective technological advancements. In a parallel scientific universe, from 2000, the development of femtosecond lasers or optical frequency comb [4][5][6] has revolutionized the impact of RF-photonics in the field of high precision spectroscopy [7], arbitrary waveform generation [8], highly precise atomic clocks [9], arbitrary RF waveform generation [10] and massively parallel optical communication system [11][12][13][14][15][16][17][18][19][20][21]. An optical frequency comb is an optical range spectrum of multiple evenly spaced optical frequencies. ...
... A widely spaced and flat optical frequency comb with other required parameters discussed in section 2 can be exploited as a multichannel source for future flexible optical networks. To date, multiple approaches have been proposed to realize a comb-based WDM transmission system [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The basic block diagram corresponding to the comb-based WDM transmission system is shown in figure 17. ...
A flexible optical communication network is needed to realize a backbone transport network for 6G communication and further higher generation communication technologies. However, the practical implementation of the higher generation network experiences some serious challenges due to the existing multicarrier generation technology i.e. an array of multiple discrete laser sources (less spectrally efficient, complex, bulkier and costlier). Recently, a multicarrier generation technique using the optical frequency comb has been extensively researched. It can reduce the complexity, cost, and size compared to the existing multicarrier generator. Moreover, it increases the utilization of available spectral efficiency due to its capability to tune the operating frequency and carrier spacing. So, considering these advantages, we reviewed the multiple optical frequency comb generation techniques, categorized as mode-locked laser, microresonator and electro-optic modulator based frequency combs. We identify the salient features of different frequency comb generation techniques by keeping the requirements of a flexible optical network in mind. We also reviewed the drawbacks and possible solutions proposed to improve the characteristics of the optical frequency comb. Further, we reviewed the optical frequency comb expansion techniques to broaden the spectrum of the optical frequency comb, which is the requirement in optical frequency comb suitable for communication applications. At last, we summarize the progress in the practical implementation of the optical frequency comb as a multichannel source in a flexible optical network.
