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Abstract
In this paper, high repetition rate flat coherent optical frequency comb generation based on the normal dispersion tantalum pentoxide (Ta2O5) optical waveguide is proposed and numerically investigated. The 1.2 meters long normal dispersion Ta2O5 integrated nonlinear waveguide through dispersion engineering is used to generate a flat optical frequency comb of about 50 nm span based on self-phase modulation and optical wave breaking near 1550 nm. The time-spectrum evolution during the pulse propagation process is analyzed by the X-Frog technique. The effects of various parameters on the broadening comb spectra bandwidth and flatness are considered, and the spectral coherence of the optical frequency comb is also studied. The simulation results show that the Ta2O5 integrated nonlinear waveguide has a great prospect in broadband high repetition rate flat coherent optical frequency comb generation.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
An optical frequency comb is an optical spectrum which consists of equidistant optical frequency components, while the intensity of the comb lines can vary substantially. Usually, such kind of optical spectrum is associated with a regular train of ultrashort pulses, having a fixed pulse repetition rate which determines the inverse line spacing in the spectrum. High repetition rate flat-top coherent optical frequency comb with wide bandwidth is suitable for wavelength division multiplexing [1], optical orthogonal frequency division multiplexing [2], arbitrary optical waveforms generation [3]. For optical communication and RF photonics, higher repetition rate, good spectral flatness, simplicity, robustness, and in some cases frequency tunability are needed [1]. Optical frequency comb generation solutions with high repetition rate between 10 GHz and 50 GHz mainly include four categories. The first type of comb is passive or active mode-locked laser comb generation scheme [4–7]. The mode lock conditions usually require good thermal and acoustic isolation for the fiber-based or quantum well/dash semiconductor-based mode-locked laser. Meanwhile, the frequency interval of the mode-locked laser is fixed by the cavity length. The flat spectral bandwidth of this kind comb (without the nonlinear broadening outside the cavity) is about 20 nm [4–7]. The second type of comb is electro-optic modulation comb generation scheme without the nonlinear broadening [8,9]. It can support flexible frequency spacing as it is driven by the RF signal, which overcomes the problem that the comb frequency interval is fixed by the cavity length of the mode-locked laser [10]. However, the flat spectral bandwidth of this kind comb is about 20 nm even with cascaded phase modulators [1]. The electro-optic modulator can also be installed in a cavity to boost the modulation efficiency for achieving the large bandwidth, but the generated combs have the triangle-shape spectra envelope [11,12]. The third type of comb is nonlinear microresonator Kerr comb generation scheme. The number of generated comb lines is large, but the comb flatness also needs to be improved for optical communication application. Meanwhile, a stable single soliton Kerr optical frequency comb operation for long time is difficult to achieve. It is necessary to precisely tuning the pump laser with the optical microcavity mode [13–18], which makes it difficult for the application outside the laboratory. The fourth type of comb is nonlinear supercontinuum generation broadening based comb generation scheme. Near the 2000 year, researchers used a mode-locked laser as a pulse source propagating in a near-zero flattened dispersion decreasing silica-based high nonlinear fiber (HNLF) for supercontinuum broadening to generate the optical frequency comb [19]. The flat wideband optical frequency comb generation based on the pulse compression, self-phase modulation (SPM) and optical wave breaking (OWB) in the normal dispersion silica-based HNLF has been deeply investigated [20–22]. The optical frequency comb generation efficiency is governed by the pumping pulse peak power P0, the effective interaction length Leff, and the nonlinear coefficient γ of optical fiber. Moreover, in order to make the spectrum flattened and broadened, the dispersion of the silica-based HNLF needs to be near zero in the normal-dispersion regime [23–25]. Furthermore, several hundred meters long silica-based HNLF are required to achieve the flat and broadband spectrum for their relatively low nonlinearity coefficient γ. However, the near zero normal dispersion sometimes deviates from the normal dispersion to the anomalous dispersion for a long length dispersion flattened silica-based HNLF, which is limited by the fiber fabrication process. To solve the dispersion fluctuations problem and preserve good spectral coherence of the optical frequency comb, it is necessary to add additional straining process to maintain the dispersion at near zero value in the normal dispersion region [26]. One solution for the above mentioned problems is to use short length fibers with large nonlinear coefficient γ such as fluorotellurite fibers [27]. Another solution is to use the integrated nonlinear chips with large nonlinear coefficient γ.
The nonlinear integrated chips have attracted much attention for optical frequency comb generation in photonic-chip waveguides via supercontinuum generation and in microresonators via Kerr-comb generation [28]. Chip-based platforms offer several key features compared with fiber-based platforms, which include high effective nonlinearities and the ability to perform strong dispersion engineering over extremely broad bandwidths. The quest for high-performance platforms for integrated nonlinear optics has naturally focused on the materials with high nonlinearity, low loss characteristics, low two-photon absorption (TPA) effect such as Hydex(SiOxNy) [29], stoichiometric silicon nitride(Si3N4) [30,31], silicon-rich nitride(SixNy) [32], chalcogenide glasses [33,34], aluminum nitride (AlN) [35], gallium nitride (GaN) [36], gallium phosphide (GaP) [37], aluminum gallium arsenide (Al0.17Ga0.83As) [38], lithium-niobate(LiNbO3) [39], tantalum pentoxide (Ta2O5) [40] and so on. The optical frequency comb can be generated either in the normal dispersion regime or in the anomalous dispersion regime. For the microresonators Kerr-comb generation, the optical frequency comb generation in the normal dispersion microcavities has been proposed for higher conversation efficiency, but the comb line power difference is still more than 10 dB in the middle of the comb spectrum [17]. Coherent supercontinuum generation has been demonstrated in Si3N4-core/SiO2-clad integrated nonlinear waveguide with either normal dispersion or anomalous dispersion [41,42]. But the repetition rate of the optical frequency combs is very low (∼100 MHz). Hao Hu et al. generated the 10-GHz optical frequency comb by seeding the picosecond pulse laser to the AlGaAsOI chip with low pump power [38]. However, the comb spectral smoothness is poor for the pump is in the anomalous dispersion regime. Thus, the anomalous dispersion condition is not suitable for flat-top supercontinuum based comb generation. Since the pulse repetition rate is equal to the frequency spacing of the comb lines, for the pump pulses with high repetition rate between 10 GHz and 50 GHz, the peak power of such pulses (tens W order) is much lower than that of femtosecond pulses at low repetition rate (thousands W order), making it very challenging to realize efficient on-chip frequency comb broadening at high repetition rate except a highly-nonlinear waveguide can be used.
Recently, CMOS-compatible Ta2O5 waveguide has been utilized for the nonlinear applications due to its huge optical nonlinearity [40,43,44]. The refractive index of Ta2O5 at 1550 nm is roughly the same as Si3N4, which allows a small bending radius and high optical confinement in the Ta2O5-core/SiO2-clad waveguide. The nonlinear refractive index of Ta2O5 is higher than Si3N4 as shown in Table 1, and the low stress in Ta2O5 waveguide enables crack-free high confinement thick waveguide. It also has been widely used in optical coating for a high destroyed threshold than Si3N4, which is better for high power nonlinear application [43,45]. A record low propagation loss of 3 ± 1 dB/m across the entire telecommunications C-band Ta2O5-core/SiO2-clad planar waveguide has been demonstrated for the application requiring long length spiral waveguide (10 m long spiral) [46]. Similar low loss high confinement thick waveguides have also been achieved in Ta2O5 (6 dB/m, 24 cm long) [47], Si3N4 (1 dB/m, 50 cm long spiral) [30,31] and LiNbO3 (2.7 dB/m, 11 cm long) [39,48] multimode optical waveguide through reducing the scattering loss from the interaction of light with the roughness of all the surfaces. The maximum achievable nonlinear phase formula is shown as follows [32]:
where γ represents the nonlinear coefficient, P0 represents the peak power of the pulse, Leff, max = 1/α represents the maximum effective length of the waveguide, and α represents the coefficient of the waveguide propagation loss. The SPM based spectrum broadening factor is approximated by the value of ϕ NL, max. The larger the ϕ NL, max, the wider the spectrum will be [49]. Table 1 summarizes four relatively mature low loss integrated photonics platforms with the material and waveguide propagation loss parameters. Since the nonlinear refractive index n2 of Ta2O5 is larger than the other three materials, Ta2O5 integrated waveguide with shorter physical length can be used to generate optical frequency comb for achieving the approximate spectral bandwidth and comb flatness. Combining these characteristics and recent remarkable progress on reducing the waveguide propagation loss, it is very promising to design a high confinement thick Ta2O5 waveguide to generate the supercontinuum based optical frequency comb. Therefore, we propose a flat and broadband highly coherent optical frequency comb with high repetition rate based on the normal dispersion Ta2O5 integrated optical waveguide.
Table 1. Four low loss integrated platforms with the material and waveguide propagation loss parameters
2. Numerical simulation model
The refractive index of Ta2O5 at 1550 nm is roughly the same as Si3N4. Therefore, the 1550 nm light can be better limited in smaller waveguide sizes. The dispersion and nonlinear coefficients γ of the integrated Ta2O5 optical waveguide are numerically analyzed. Fig. 1(a) shows the Ta2O5-core/SiO2-clad planar optical waveguide structure designed in the simulation. The investigation of the dispersion characteristics of the waveguides is performed numerically using the finite element method (FEM) mode solver that takes both the dispersion of the materials and, as well, the dispersion induced by the geometry of the waveguide core into account. We use the group velocity dispersion (GVD) coefficient D to describe the second order dispersion, with the expression shown as follows:
Fig. 1. Dispersion engineering of the Ta2O5 waveguide: (a)Ta2O5 waveguide structure; (b) The all guided mode field distribution of the waveguide with 690 nm × 2300 nm at 1550 nm; (c) TE0 mode field of the integrated waveguide with 690 nm × 2300 nm cross-section dimensions (Ta2O5-core/SiO2-clad); (d) Simulated GVD with a fixed height of 690 nm while the width changes; (e) Simulated GVD with a fixed width of 2300 nm while the height changes; (f) The effective mode field area Aeff and the nonlinear coefficient γ of the TE0 mode with the 690 nm × 2300 nm Ta2O5 waveguide structure.
Here, λ is wavelength in micrometers. And for silica, the Sellmeier equation is [51]:
The mode simulation results in the Fig. 1(b) show that designed waveguide with 690 nm × 2300 nm cross-section dimension is a multimode waveguide in 1550 nm band. It should be noted that the multimode waveguide can reduce the scattering loss caused by the sidewall roughness of the optical waveguide. Fig. 1(c) shows the quasi-TE fundamental mode (TE0 mode) field of Ta2O5 integrated waveguide, which is chosen for the optical frequency comb generation. Fig. 1(d) and (e) show the simulated TE0 mode GVD versus wavelength for 690-nm-height Ta2O5 waveguides with different waveguide widths, and 2300-nm-width Ta2O5 waveguides with different waveguide heights, respectively. The GVD can be engineered from the anomalous dispersion to the normal dispersion through the different waveguide geometry. The dispersion parameters (β2, β3, β4) of the TE0 mode with the 690 nm × 2300 nm waveguide structure are also calculated. Fig. 1(f) shows the variation of the effective mode field area Aeff and the nonlinear coefficient γ of the TE0 mode with the 690 nm × 2300 nm waveguide structure in the wavelength range from 1300 nm to 1800nm. The nonlinear coefficient γ=2πn2/λAeff is highly dependent on the effective mode field area Aeff of the waveguide [52], the calculated γ is about 3.1625 W-1m-1 at 1550 nm with the nonlinear refractive index n2 as shown in Table 1.
The simulated dispersion and nonlinear coefficient of the TE0 mode are used to study the broadband high repetition rate flat optical frequency comb generation. The schematic diagram of the optical frequency comb generation is shown in Fig. 2, including the optical pulse source with high repetition rate, the high power Erbium-doped fiber amplifier (EDFA) and the normal dispersion Ta2O5 spiral waveguide with a relatively long length. The TE0 mode can be excited by the inverse taper. The inverse taper design for TE0 mode coupling and the optimized spiral multimode waveguide design for prohibiting the high-order mode excitation are still under investigation. We want to note that studying the spectral envelope of single-shot pulse and spectral envelope of optical frequency comb has certain commonality. The envelope evolution of the single shot pulse and spectrum in the Ta2O5 waveguide is analyzed by the generalized nonlinear Schrödinger equation (GNLSE) as the following [47]:
3. Numerical simulation results and discussion
Table 2 gives the detailed parameters in the simulation. The Ta2O5 waveguide cross section is chosen to be 690 nm × 2300 nm with a flattened normal dispersion of the TE0 mode near 1550 nm as shown in Fig. 1. In addition, refer to the current commercial 1550 nm electro-optic comb which provides high repetition rate tunable optical pulse source between 10 GHz and 50 GHz [9] and the high power EDFA, the optical pulse peak power P0 injected into the waveguide is assumed to be 30 W [24,27], the input pulse half width T0 is assumed to be 1 ps. The Ta2O5 spiral waveguide length is assumed to be 1.2 meters long. The propagation loss α of the TE0 mode in the waveguide is assumed to be 3 dB/m according to the reported literature [46]. Using the parameters as shown in Table 2, an initial unchirped hyperbolic secant pulse is fed into the waveguide, and the simulation results are shown in Fig. 3. Fig. 3(a) and (b) show the envelope evolution of the optical frequency comb spectrum and pulse during the propagation. It can be seen that due to the effects of SPM and OWB in the normal dispersion Ta2O5 waveguide, both the pulse and the spectrum are broadened as the propagation distance increases. Fig. 3(c) shows the broadening pulse and spectrum envelope when the propagation distance reaches 1.2 meters. A relatively flat wavelength range of about 50 nm with about 4 dB power fluctuation appears in the middle of the spectrum, which is better for the practical application of the optical frequency comb in the optical communication. One can see that the normal dispersion value of β2 is far away from the near-zero dispersion, which is better for solving the dispersion fluctuations problem in silica-based HNLF comb scheme as claimed in the introduction.
Fig. 3. Simulation results of an initial unchirped hyperbolic secant pulse propagates in a 1.2 m long Ta2O5 waveguide: (a) Evolution of the spectrum and the pulse during the propagation; (b) The three-dimensional evolution of the spectrum and pulse during the propagation; (c) The spectrum and pulse envelope when the pulse propagates to 1.2 m.
Table 2. The parameters used in the simulation.
The X-FROG technology is utilized to study the evolution of the time domain and frequency domain of the pulse. The specific expression for the cross correlation of the reference pulse and the output pulse is [54]:
Figure 4 shows the simulated spectrograms of the initial unchirped hyperbolic secant pulse at the propagation distance of 0 m, 0.4 m, 1.2 m, and 2.0 m by using the X-FROG technique. It links the frequency and time domain images of the pulse in a clear manner, which reflects the dispersion and nonlinear effects on the time domain and frequency domain of the pulse during the propagation. Fig. 4(a) shows the spectrogram of the pulse when the pulse is just fed into the waveguide without the propagation. Fig. 4(b) shows the spectrogram of the pulse in the early stage of propagation, where the SPM effect dominates the spectrum broadening and introduces a chirp (or instantaneous frequency shift). The shape of the spectrogram appears “S” shape, and the spectrum broadens with multi-peak oscillation structure (i.e. its flatness is not good). With further propagation, the dispersion profile becomes the governing factor of the nonlinear dynamics. Because the dispersion is in the normal GVD regime, the group velocity monotonically increases with wavelength. Hence, the red-shifted wavelength component (where the instantaneous frequency attains the maximum value) of the leading edge of the pulse propagate faster. At certain time as shown Fig. 4(c), the red-shifted wavelength component and the unshifted central wavelength component will create new frequencies through the four wave mixing (FWM) in the frequency domain (OWB in the time domain) at the leading edge of the pulse; the FWM also occurs between the blue-shifted wavelength component and the unshifted central wavelength component at the trailing edge of the pulse [21,49]. The spectrum amplitude of the multi-peak oscillation near the center wavelength in Fig. 4(c) is flattened owing to the FWM (or OWB) effect and the spectrum bandwidth near the center wavelength becomes wider. Corresponding to the spectrogram, it can be seen that the energy at the center wavelength of the leading edge of the pulse is continuously transferred to the long wavelength, and the energy at the center wavelength of the trailing edge of the pulse is continuously transferred to the short wavelength. As shown in Fig. 4(d), when the pulse propagates at the distance of 2.0 m, the central part of the spectrum does not broaden anymore as the propagation distance grows larger. To the contrary, the pulse has undergone a broadening in the temporal domain. Moreover, the central section of the pulse is progressively flattened in both the temporal and frequency domains. Owing to the normal GVD, the newly generated frequencies in the wings of the spectrum have completely overtaken (or have left behind) the leading (trailing) edges of the initial pulse. Therefore, the overlap among pulse components with different instantaneous frequencies and the associated FWM no longer occurs. In addition, the pulse becomes nearly rectangular with relatively sharp leading and trailing edges and is accompanied by a nearly linear chirp across its entire bandwidth [49]. It is this linear chirp that can be used to compress the pulse to nearly Fourier-transform limit by passing it through a dispersive delay line. Considering comprehensively, a propagation waveguide length of 1.2 m is preferable to achieve the better results.
Fig. 4. Spectrograms of the initial unchirped hyperbolic secant pulse at various propagation lengths: (a) 0 m; (b) 0.4 m; (c) 1.2 m; (d) 2.0 m.
The broadening spectra bandwidth (ωSPM) and flatness of the generated optical frequency comb are not only related to the propagation waveguide length, but also other parameters need to be considered. The empirical formula is [22]:
Fig. 5. The final broadening spectra under the condition that only one parameter is changed while the other parameters are constant: (a) only change β2; (b) only change P0; (c) only change T0; (d) only change β3; (e) only change chirp parameters C; (f) only change loss α; (g) only change input pulse waveform.
Figure 5(g) shows the final broadening spectra by injecting different pulse waveforms into the waveguide without changing the other conditions. It can be seen that the final broadening spectra from different input pulses are significantly different. The generated comb spectral flatness of the Gaussian pulse (<2dB power fluctuation in the middle of the spectrum of about 50nm) is better than the hyperbolic secant pulse (about 4dB power fluctuation in the middle of the spectrum of about 50nm). For the super Gaussian pulse (m = 3, or m = 5), the comb spectrum has been greatly broadened and flattened with 3dB bandwidth about 100nm. Maybe one can obtain the super Gaussian input pulse through the line by line pulse shaping for a better flat-top comb generation, which still need to be investigated in the near future [55]. We can also see that higher conversation efficiency can be achieved just the same as normal dispersion microresonator kerr-comb [17], but with good comb flatness. It can be concluded from the Fig. 5 that when the appropriate parameters and a reasonable waveguide structure are selected, a broadband flat optical frequency comb can be generated. And the detailed simulations give us a guideline for the comb generation experiment in the future.
The high repetition rate optical frequency comb can provide multi-wavelength single frequency laser source for wavelength division multiplexing or ultra-short pulse light source (through the pulse compression [23]) for time division multiplexing. Therefore, it is extremely important to study the spectral coherence of the optical frequency comb. The spectral coherence of the optical frequency comb generated by the picosecond pulse pumping in the normal dispersion region can be analyzed using the first-order mutual coherence function [54]:
Fig. 6. Spectral coherence of the optical frequency comb generated by a hyperbolic secant pulse propagating in 1.2 m long integrated waveguide.
We want to note that our proposal and assumed simulation parameters are based on other researchers’ experiment work on the Ta2O5 waveguide [44,46,47] and meters-long low loss high confinement waveguide [31,46]. We hope our numerical investigations on the novel optical frequency comb schemes based on Ta2O5 optical waveguide will be helpful for opening up new opportunities and potential benefits for optical frequency comb technology in the ps regime which have good comb flatness within 4 dB in a nearly 50 nm bandwidth or more (3 dB bandwidth of nearly 100 nm for super Gaussian pulse condition).
4. Conclusion
We proposed and investigated a high repetition rate flat coherent optical frequency comb generation based on the normal dispersion Ta2O5 optical waveguide. The normal dispersion near the 1550 nm band is achieved through the dispersion engineering by changing the Ta2O5 waveguide structure. By seeding a 1550 nm high repetition rate 1ps hyperbolic secant pulse with a peak power of 30 W into 1.2 meter long Ta2O5 waveguide, flat optical frequency comb with flatness of about 4 dB in 1525nm-1575 nm is obtained through the numerical simulation. The simulation results indicate that the on chip integrated Ta2O5 nonlinear spiral waveguide with much shorter length is comparable with the hundreds of meters silica HNLF for the optical frequency comb generation [23]. In order to analyze the evolution of the time and frequency domain of the pulse and study the dispersion and nonlinear effect on the optical comb generation, we use X-Frog technology to analyze the spectrogram of the pulse during the propagation. The analysis indicates that the SPM plays a leading role in the initial stage of the propagation, and the OWB plays a leading role in the later stage of the propagation. The two combined effect make the spectrum envelop of optical frequency comb flattened. The effects of various parameters on the optical frequency comb generation are analyzed, such as the input pulse shape, second order dispersion, third order dispersion, input pulse width, input pulse peak power, input pulse chirp parameter C and propagation loss. We also find that the frequency comb has good spectral coherence across the entire spectrum.
Funding
Fundamental Research Funds for the Central Universities (2017JBM002); National Natural Science Foundation of China (61827818).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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