Two-tone Modulation Research Articles

Effect of fiber properties and dispersion management on distortions associated with two subcarriers modulation of laser diode in radio over fiber systems

We present numerical modeling and simulation on the effects of standard single-mode fiber (SSMF) properties and different dispersion management approaches on the distortions of laser diode. These distortions are associated with the two-tone modulation of laser diode for use in radio over fiber systems. The fiber properties include attenuation and dispersion. The dispersion management approaches include the use of nonzero dispersion-shifted fiber (NZ-DSF), fiber Brag grating (FBG), and dispersion-compensating fiber (DCF). The laser is directly modulated with two analog frequencies of 25 and 25.1 GHz at different modulation depths (m). The modulated laser signals are then propagated through SSMF at different lengths (L). The investigated laser signal distortions include the 2nd harmonic distortion (HD2), and the 2nd and 3rd intermodulation distortions (IMD2 and IMD3, respectively). The results reveal that all laser distortions are exacerbated as the fiber length increases, which is mainly due to the chromatic dispersion, while fiber attenuation has no effect. The use of dispersion management approaches gives almost similar effects on the reduction of IMD3 when L = 1 km, regardless of the value of m. Up to m = 0.3, DCF is the most effective approach for reducing all distortions over the entire fiber length range, while NZ-DSF is the least. When L = 2 km, FBG is the most effective approach for reducing both IMD2 and HD2 when m ≥ 0.4, whereas when L is increased to 6 km, DCF is the most effective approach up to m = 0.5.Graphical abstractSimulation setup of RoF system for two-tone direct modulation of laser diode using different dispersion management approaches

Self-Calibrated Measurement of Frequency Response for Broadband Photodetectors Based on Two-Tone Photonic Sampling

A self-calibrated method to measuring the frequency responses of broadband photodetectors (PDs) is proposed based on photonic pulse sampling of two-tone microwave signal, with the help of a mode-locked laser diode (MLLD) and a Mach-Zehnder modulator (MZM). Firstly, the repetition frequency of the optical comb from the MLLD divides the whole measuring frequency range into several segments. Then, a close-spaced two-tone signal modulates every comb tooth through the MZM and generates the sum- and difference-frequency products, working as the probing signal to extract the frequency response of the PD in every segment. Hyper-fine frequency response of the PD at any frequency point can be obtained in every segment by subtly varying the center frequency of the two-tone signal while keeping the difference frequency fixed. Finally, the whole frequency response of the PD in ultra-wide frequency range is obtained by seamlessly stitching the segmental frequency responses. In our experiment, measurement of a commercial PD is demonstrated up to 49.765 GHz with an optical comb at the repetition frequency of 9.953 GHz and a two-tone modulation up to 4.9765 GHz. The measured results are compared with those by using the traditional methods to check accuracy. Moreover, the uneven responses of the MLLD and the MZM are fully subtracted, verifying the ultra-wideband, hyperfine and self-calibrated measurement of PDs based on the two-tone photonic sampling.

Two-tone frequency modulation saturation spectroscopy for tunable frequency offset locking of a single laser

The two-tone frequency modulation spectroscopy (TTFMS) is widely used for gas trace detection with its low noise absorption signal. In this paper we propose and implement the TTFMS scheme for frequency offset locking a single diode laser to an atomic resonance line by using its dispersion signal. The TTFMS theory is first discussed under the assumption that the intermediate modulation frequency is comparable to the linewidth of the absorption feature, and the dependence of the TTFMS absorption and dispersion features on the intermediate modulation frequency and modulation index are investigated theoretically. Based on a fiber-coupled electro-optic modulator (EOM) with two-tone modulation, we experimentally demonstrated the performance of the frequency offset locking method. The result shows a short-term frequency stability of the frequency offset locked laser reached around 1.1 × 10−11, with an averaging time of 2 s. This method can find wide applications in fields requiring widely tunable frequency offset locking a single laser to the atomic resonance line, like precision spectroscopy and Raman optics for atom interferometers.

Harmonic and intermodulation distortions and noise associated with two-tone modulation of high-speed semiconductor lasers

We present results of modeling and simulation of the harmonic and intermodulation distortions as well as the intensity noise of high-speed semiconductor lasers under two-tone modulation. Multiple quantum-well lasers are considered, which are characterized by large differential gain and a modulation bandwidth of about 25GHz. The study is based on the rate equation model of semiconductor lasers excited by injection current with two sinusoidal tones separated by a radio frequency. The modulated laser signal is modeled in both the time and frequency domains. The time domain characteristics include the fluctuating waveform, while the frequency domain characteristics include the frequency spectrum of the relative intensity noise (RIN), carrier-to-noise ratio, modulation response, harmonic distortion, and the second- and third-order intermodulation distortions (IMD2 and IMD3). The analysis is performed for three frequencies of 5, 15, and 24 GHz, which are, respectively, lower, comparable, and higher than the laser relaxation frequency. The range of the modulation depth covers the regimes of small and large-signal modulation. We show that both RIN and IMD3 of two-modulated laser are minimum when the modulation frequency is 5GHz, and maximum when the modulation frequency is 24 GHz. The second-order harmonic distortion, IMD2, and IMD3 values are larger in the vicinity of relaxation oscillations and increase with the modulation index, especially under large-signal modulation.

Calibration-free and bias-drift-free microwave characterization of dual-drive Mach–Zehnder modulators using heterodyne mixing

An electrical method is proposed for the microwave characterization of dual-drive Mach–Zehnder modulators based on heterodyne mixing. The proposed method utilizes the heterodyne products between the two-tone modulated optical sidebands and frequency-shifted optical carrier, and achieves calibration-free and bias-drift-free microwave measurement of dual-drive Mach–Zehnder modulators with high resolution electrical-domain techniques. Our method avoids the extra calibration for the photodetector and reduces half the bandwidth requirement for the photodetector and the electrical spectrum analyzer through carefully choosing a half frequency relationship of the two-tone modulation. Moreover, our measurement avoids the bias drifting problem due to the insensitivity to the bias phase of the modulator under test. The frequency-dependent modulation depths and half-wave voltages are measured for a commercial dual-drive Mach–Zehnder modulator with our method, which agree well with the results obtained by the conventional optical spectrum analysis method.

Two-tone intensity-modulated optical stimulus for self-referencing microwave characterization of high-speed photodetectors

The two-tone intensity modulated optical stimulus is proposed and demonstrated for measuring the high-frequency response of photodetectors. The method provides a narrow linewidth and wide bandwidth optical stimulus based on the two-tone modulation of a Mach–Zehnder electro-optical intensity modulator, and achieves the self-referenced measurement of photodetectors without the need for correcting the power variation of optical stimulus. Moreover, the two-tone intensity modulation method allows bias-independent measurement with doubled measuring frequency range. In the experiment, the consistency between our method and the conventional methods verifies the simple but accurate measurement.

Self-calibrating measurement of high-speed electro-optic phase modulators based on two-tone modulation.

We propose a self-calibrating method for high-frequency response measurement of electro-optic phase modulators based on two-tone modulation. The method utilizes the electrical domain measurement of heterodyning spectrum between the two-tone modulation optical signal and the frequency-shifted optical carrier, and eliminates the need to correct the responsivity fluctuation in the photodetection. High-frequency modulation depth and half-wave voltages are measured and compared to those with the traditional optical spectrum analysis method in the experimental demonstration. The proposed method enables calibration-free and accurate frequency response measurement of electro-optic phase modulators by using high-resolution electrical spectrum analysis.

Two-tone frequency-modulation spectroscopy in off-axis cavity

As opposed to a conventional optical resonator, an off-axis-aligned cavity is able to transmit without distortion radiation modulated at a frequency even far above the cavity bandpass. This allows us to implement a simple spectroscopic technique that combines the cavity path-length enhancement of integrated cavity output spectroscopy (ICOS) and the noise reduction associated with radio-frequency modulation (FM). An FM-ICOS spectrometer is demonstrated for the first time using a two-tone modulation technique. The performance is compared to the traditional ICOS by examining the acetylene absorption at 1543.77 nm. A signal-to-noise ratio improvement by a factor 3.5 is found with our proof-of-concept setup. Larger improvements are expected in a more optimized setup.

Multiplexing of Millimeter-Wave Signals for Fiber-Radio Links by Direct Modulation of a Two-Mode Locked Fabry–PÉrot Laser

In this paper, we introduce generation of multiplexed signals on the millimeter-wave bands for fiber-radio systems where an optical millimeter-wave generator is based on a two-mode locked Fabry-Pe/spl acute/rot (FP) slave laser, whose injection current is directly modulated by a signal source. We qualitatively consider the distortion of the millimeter-wave signals from the FP slave laser. The distortion components on the millimeter-wave bands are induced from the simultaneous modulation of the locked modes and the nonlinear modulation response of the FP laser. Two-tone modulation of the locked FP laser is examined to evaluate the dynamic range of the millimeter-wave signals against the second- and third-order distortion components. We also perform fiber transmission of three 156-Mb/s-BPSK signals on the 60-GHz band to demonstrate fiber-radio down-link systems. The total capacity of the down-link system is discussed. In addition, two methods for multicarrier generation on the millimeter-wave bands are proposed. Multicarrier generators supported by these methods can be used as local signals for up-link millimeter-wave signals. The first method is based on multitone modulation of the FP slave laser. We attempt the down-conversion of a 52-Mb/s ASK signal on the 60-GHz band by using the millimeter-wave local signals. The second method depends on the distorted modulation of the FP slave laser by using a single continuous wave signal where the DC-bias level of the FP laser's injection current is partly under the threshold value. We confirm that five carriers on the 60-GHz band are effectively generated by using the second method. Furthermore, the influences of the chromatic dispersion effects on the millimeter-wave local signals are investigated for both methods.

Millimeter-wave signal properties resulting from electrooptical upconversion

This paper describes the combined effects of laser chirp, electrooptical mixing, dispersive fiber transmission, and photodetection on the nonlinear signal properties of the electrooptically generated millimeter-wave signal (60 GHz). Analytical expressions describing the complex currents of fundamental and higher order products are provided for the case of single-tone modulation as well as for two-tone modulation, respectively. Examples will be considered including the nonlinear amplitude response (output power at millimeter-wave range versus input power at IF), the nonlinear phase response (relative output phase at millimeter-wave range versus input power at IF), the input related 1-dB gain compression condition, the amplitude response of third- and fifth-order intermodulation products, as well as the input related intercept points for the latter signals. The model developed performed well, even under moderate to large signal conditions, and very good agreement has been achieved between theory and experiment.

Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes

A theoretical and experimental analysis of the nonlinear dynamics of Fabry-Perot (FP) and distributed feedback (DFB) multiple-quantum-well (MQW) laser diodes is presented. The analysis is performed under single-tone and two-tone direct modulation. In the FP laser, we observe period doubling and in the DFB laser both period doubling and period tripling are identified. Period doubling is found over a wide range of modulation frequencies in both lasers. The reason for this wide modulation frequency range is attributed to the large relaxation frequencies found in MQW laser diodes. The spontaneous emission factor is measured for both FP and DFB lasers. The dependencies of period doubling on output power and RF input power level are also analyzed. The nonlinear dynamics of the laser are found to be enhanced when modulated under two-tone modulation. Numerical simulations carried out show good agreement with the measured results.

Interferometric conversion of laser chirp to IM: effect of the interferometer free spectral range on the output nonlinear distortion

The two-tone modulation behavior of a semiconductor laser followed by a Mach-Zehnder interferometer is theoretically analyzed under the small-signal assumption. Illustrations are given of the signal at the Mach-Zehnder output, showing the influence of the interferometer free spectral range on the second-order harmonic (2HD) as well as the third-order intermodulation distortion (IMD). The direct intensity modulation (IM) distortions are also reported together with those of frequency modulation (FM) to facilitate direct comparison. The results show that a Mach-Zehnder with low free spectral range is required to achieve low FM distortion levels over those of the direct IM.

Intermodulation and harmonic distortions of laser diodes with optical feedback

Analytical expressions for the second-order harmonic and the third-order intermodulation distortions of laser diodes with optical feedback are derived. It is shown theoretically and experimentally that optical feedback from the transmission fiber considerably enhances intermodulation and harmonic distortions of laser diodes. Third-order intermodulation distortions up to -15 dBc must be expected for two-tone modulation and low-intensity modulation indexes m approximately=7% per carrier, which affects the performance of subcarrier multiplexed (SCM) communication systems. To avoid additional distortions the external feedback level must be two orders of magnitudes lower than the critical external feedback level of the laser diode.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two-tone optical heterodyne spectroscopy using buried double heterostructure lead–salt diode lasers

Two-tone optical heterodyne detection using single mode buried double heterostructure lead-salt diode lasers is studied. Residual amplitude modulation with these lasers is found to be substantially smaller than has been noted in previous work with mesa stripe lasers, permitting improved sensitivity for measurement of small optical absorption. Minimum detectable absorption well below 10(-5) is measured at a laser power of 3 microW, in good agreement with signal-to-noise calculations using the experimental values of the FM and AM modulation indices. Optical heterodyne detection with two-tone modulation at 145 and 155 MHz is found to be nearly an order of magnitude more sensitive than conventional second harmonic detection at kilohertz frequencies. In addition to improved detection sensitivity, the double heterostructure lasers offer the important advantages of single mode operation above liquid nitrogen temperature.

Single-tone and two-tone AM–FM spectral calculations for tunable diode laser absorption spectroscopy

A generalized theory for optical heterodyne spectroscopy with phase modulated laser radiation is used which allows the calculation of signal line shapes for frequency modulation spectroscopy of Lorentzian gas absorption lines. In particular, synthetic spectral line shapes for both single-tone and two-tone modulation of leadsalt diode lasers are presented in which the contributions from both amplitude and frequency modulations are included.

Harmonic detection with tunable diode lasers ?two-tone modulation

The minimum absorption detectable by a tunable diode laser spectrometer utilising harmonic techniques is often limited by interference fringes generated by scattered light. The sensitivity of the spectrometer to absorption can be increased by applying a jitter modulation. In this paper, the theory of harmonic response for single- and two-tone modulation over optical fringes and Lorentzian absorption lines is developed and compared to experimental measurements. A simple analytic expression for the two-tone harmonic line shape is derived. This expression provides a physical understanding of the effects of the second modulation, and a means to unravel the effects of the second modulation on the linewidth and line shape. For a specific choice of the jitter frequency and phase, it is possible to simultaneously minimise the fringe signal and increase the harmonic absorption signal. The results of this investigation are applicable to trace gas detection using tunable diode lasers, and to other areas of spectroscopy and magnetic resonance where harmonic techniques are used.