Generation of ultra-low jitter radio frequency phase pulses by a phase-locked oscillator.

We demonstrate a novel, to the best of our knowledge, method for mode locking of an oscillator, which is based on the injection of a strong sinusoidal signal from an external source into the cavity. The oscillator generates a low phase noise carrier signal with a train of ultra-low jitter, short 2π phase pulses at a repetition period equal to the cavity round-trip time. Both the carrier signal and phase pulses are phase-locked to the external source. We demonstrate the effect in an optoelectronic oscillator that generates a train of short phase pulses at a high carrier frequency with the broadband spectrum of a dense RF frequency comb. The phase pulses can be converted to short, ultra-low jitter intensity RF pulses by beating the oscillator signal with the external source, used for locking.

Phase measurement by using a forced delay-line oscillator and its application for an acoustic fiber sensor.

We demonstrate, theoretically and experimentally, a new method to measure small changes in the cavity length of oscillators. The method is based on the high sensitivity of the phase of forced delay-line oscillators to changes in their cavity length. The oscillator phase is directly detected by mixing the oscillator output with the injected signal. We describe a comprehensive theoretical model for studying the signal and the noise at the output of a general forced delay-line oscillator with an instantaneous gain saturation and an amplitude-to-phase conversion. The results indicate that the magnitude and the bandwidth of the oscillator response to a small perturbation can be controlled by adjusting the injection ratio and the injected frequency. For signals with a frequency that is smaller than the device bandwidth, the oscillator noise is dominated by the noise of the injected signal. This noise is highly suppressed by mixing the oscillator output with the injected signal. Hence, the device sensitivity at frequencies below its bandwidth is limited only by the internal noise that is added in a single roundtrip in the oscillator cavity. We demonstrate the use of a forced oscillator as an acoustic fiber sensor in an optoelectronic oscillator. A good agreement is obtained between theory and experiments. The magnitude of the output signal can be controlled by adjusting the injection ratio while the noise power at low frequencies is not enhanced as in sensors that are based on a free-running oscillator.

Wideband tunable opto-electronic oscillator based on frequency translation.

We demonstrate a new method to obtain a widely tunable low phase-noise opto-electronic oscillator (OEO), based on translating the OEO signal into a lower intermediate frequency (IF) signal. The OEO signal is downconverted to IF by using a local oscillator (LO) signal, filtered by a high-Q filter; its frequency is then upconverted back into the high OEO frequency. The combination of a narrowband filter at a fixed central frequency with a tunable LO forms a tunable high-Q bandpass filter (BPF) that can be used to change the OEO frequency over a broad frequency region. The effect of the LO phase noise on the OEO is suppressed by the dual frequency conversions. Hence, a tunable LO with a high phase noise can be used to control the frequency of a very low phase-noise OEO. The use of a BPF with a lower center frequency than that of the OEO signal also enables increasing the effective Q-factor of the OEO filter.

Longitudinal mode selection in a delay-line homogeneously broadened oscillator with a fast saturable amplifier.

Homogeneously broadened delay-line oscillators such as lasers or optoelectronic oscillators (OEOs) can potentially oscillate in a large number of cavity modes that are supported by their amplifier bandwidth. In a continuous wave operating mode, the oscillating mode is selected between one or few cavity modes that experience the highest small-signal gain. In this manuscript, we show that the oscillation mode of a homogeneously broadened oscillator can be selected from a large number of modes in a frequency region that can be broader than the full width at half maximum of the effective cavity filter. The mode is selected by a short-time injection of an external signal into the oscillator. After the external signal is turned off, the oscillation is maintained in the selected mode even if this mode has a significantly lower small-signal gain than that of other cavity modes. The stability of the oscillation is obtained due to nonlinear saturation effect in the oscillator amplifier. We demonstrate, experimentally and theoretically, mode selection in a long cavity OEO. We could select any desired mode between 400 cavity modes while maintaining ultra-low phase noise in the selected mode and in the non-oscillating modes. No mode-hopping was observed during our maximum measurement duration of about 24 hours.

Wideband-frequency tunable optoelectronic oscillator based on injection locking to an electronic oscillator.

We experimentally demonstrate a wideband-frequency tunable optoelectronic oscillator (OEO) based on injection locking of the OEO to a tunable electronic oscillator. The OEO cavity does not contain a narrowband filter and its frequency can be tuned over a broad bandwidth of 1 GHz. The injection locking is based on minimizing the injected power by adjusting the frequency of one of the OEO cavity modes to be approximately equal to the frequency of the injected signal. The phase noise that is obtained in the injection-locked OEO is similar to that obtained in a long-cavity self-sustained OEO. Although the cavity length of the OEO was long, the spurious modes were suppressed due to the injection locking without the need to use a narrowband filter. The spurious level was significantly below that obtained in a self-sustained OEO after inserting a narrowband electronic filter with a Q-factor of 720 into the cavity.

Noise induced in optical fibers by double Rayleigh scattering of a laser with a 1/fν frequency noise.

We study, theoretically and experimentally, intensity noise induced by double Rayleigh scattering in long optical fibers. The results of the theoretical model are compared to experimental results performed with a high-coherence-length laser with a frequency noise spectrum that is dominated by 1/fν noise. Excellent quantitative agreement between theoretical and experimental RF spectra were obtained for frequencies as low as 10 Hz and for fiber lengths between 4 and 45 km. Strong low-frequency intensity noise that is induced by 1/fν frequency noise of the laser may limit the performance of interferometric fiber optic sensors that require high-coherence-length lasers. The intensity noise due to double Rayleigh backscattering can be suppressed by reducing the coherence length of the laser. Therefore, the intensity noise has a complex and non-monotonic dependence on the 1/fν frequency noise amplitude of the laser. Stimulated Brillouin scattering will add a significant noise for input powers greater than about 7 mW for a 30 km length fiber.

Comprehensive model for studying noise induced by self-homodyne detection of backward Rayleigh scattering in optical fibers.

Backward Rayleigh scattering in optical fibers due to the fluctuations that are "frozen-in" to the fiber during the manufacturing process may limit the performance of optical sensors and bidirectional coherent optical communication systems. In this manuscript we describe a comprehensive model for studying intensity noise induced by spontaneous Rayleigh backscattering in optical systems that are based on self-homodyne detection. Our model includes amplitude and frequency noise of the laser source, random distribution of the scatterers along the fiber, and phase noise induced in fibers due to thermal and mechanical fluctuations. The model shows that at frequencies above about 10 kHz the noise spectrum is determined by the laser white frequency noise. The laser flicker frequency noise becomes the dominant effect at lower frequencies. The noise amplitude depends on the laser polarization. A very good agreement between theory and experiment is obtained for fibers with a length between 500 m to 100 km and for a laser with a linewidth below 5 kHz.

Optical under-sampling by using a broadband optical comb with a high average power.

We demonstrate a new method to improve the performance of photonic assisted analog to digital converters (ADCs) that are based on frequency down-conversion obtained by optical under-sampling. The under-sampling is performed by multiplying the radio frequency signal by ultra-low jitter broadband phase-locked optical comb. The comb wave intensity has a smooth periodic function in the time domain rather than a train of short pulses that is currently used in most photonic assisted ADCs. Hence, the signal energy at the photo-detector output can be increased and the signal to noise ratio of the system might be improved without decreasing its bandwidth. We have experimentally demonstrated a system for electro-optical under-sampling with a 6-dB bandwidth of 38.5 GHz and a spur free dynamic range of 99 dB/Hz(2/3) for a signal with a carrier frequency of 35.8 GHz, compared with 94 dB/Hz(2/3) for a signal at 6.2 GHz that was obtained in the same system when a pulsed optical source was used. The optical comb was generated by mixing signals from two dielectric resonator oscillators in a Mach-Zehnder modulator. The comb spacing is equal to 4 GHz and its bandwidth was greater than 48 GHz. The temporal jitter of the comb measured by integrating the phase noise in a frequency region of 10 kHz to 10 MHz around comb frequencies of 16 and 20 GHz was only about 15 and 11 fs, respectively.

Self-similar amplification in fiber Bragg gratings written in fiber amplifiers.

We show, by using numerical simulations, that self-similar pulses with a duration on the order of few nanoseconds and an energy on the order of 10 µJ can be obtained at the output of a fiber Bragg grating (FBG) written in a fiber amplifier. The evolution of the amplified pulses is determined by the combined effect of Kerr nonlinearity, normal-dispersion, gain, and gain saturation, which limit the pulse energy. The output pulse mainly depends on the initial pulse energy rather than on the initial pulse profile. The reduced group velocity in FBGs can significantly increase the total gain for a given amplifier length. Hence we find that the proposed amplification scheme can be highly advantageous for amplification of nanosecond-scale pulses in fiber amplifiers.

Synchronization between two weakly coupled delay-line oscillators.

We study theoretically the generation of a continuous-wave signal by two weakly coupled delay-line oscillators. In such oscillators, the cavity length is longer than the wavelength of the signal. We show by using an analytical solution and comprehensive numerical simulations that in delay-line oscillators, the dynamics of the amplitude response cannot be neglected even when the coupling between the oscillators is weak. Therefore, weakly coupled delay-line oscillators cannot be accurately modeled by using coupled phase-oscillator models. In particular, we show that synchronization between the oscillators can be obtained in cases that are not allowed by coupled phase-oscillator models. We study the stability of the continuous-wave solutions. In delay-line oscillators, several cavity modes can potentially oscillate. To ensure stability, the bandwidth of the delay-line oscillator should be limited. We show that the weakly coupled delay-line oscillator model that is described in this paper can be used to accurately model the synchronization between two weakly coupled optoelectronic oscillators. A very good quantitative agreement is obtained between a comprehensive numerical model to study optoelectronic oscillators and the model results given in this paper.

Single-cycle radio-frequency pulse generation by an optoelectronic oscillator.

We demonstrate experimentally passive mode-locking of an optoelectronic oscillator which generates a single-cycle radio-frequency pulse train. The measured pulse to pulse jitter was less than 5 ppm of the round-trip duration. The pulse waveform was repeated each round-trip. This result indicates that the relative phase between the pulse envelope and the carrier wave is autonomously locked. The results demonstrate, for the first time, that single-cycle pulses can be directly generated by a passive mode-locked oscillator. The passive mode-locked optoelectronic oscillator is important for developing novel radars and radio-frequency pulsed sources and it enables studying directly the physics of single-cycle pulse generation.

Low-frequency transmitted intensity noise induced by stimulated Brillouin scattering in optical fibers.

We study theoretically and experimentally the spectral properties of low-frequency transmitted intensity noise induced by stimulated Brillouin scattering in optical fibers. In fibers with a length of 25 km the Brillouin scattering induces transmitted intensity noise with a bandwidth on the order of tens of kHz. The power spectral density of the noise can be stronger than the shot noise in the photo-detector even when the optical power is significantly lower than the Brillouin threshold. The low-frequency transmitted intensity noise is caused due to depletion of the pump wave by the stochastic Brillouin wave. Since pump depletion occurs over a long distance, noise with a narrow bandwidth is generated in the transmitted wave. When the pump power is high enough, the spectrum of the induced noise contains features such as hole at low frequencies and ripples. Good quantitative agreement between theory and experiments is obtained. Low-frequency intensity noise induced by Brillouin scattering may limit the generation of ultra-low noise signals in optoelectronic oscillators and may limit the transfer of ultra-low noise signals in fibers.

Comprehensive computational model of single- and dual-loop optoelectronic oscillators with experimental verification.

We describe a comprehensive computational model for singleloop and dual-loop optoelectronic oscillators (OEOs). The model takes into account the dynamical effects and noise sources that are required to accurately model OEOs. By comparing the computational and experimental results in a single-loop OEO, we determined the amplitudes of the white noise and flicker noise sources. We found that the flicker noise source contains a strong component that linearly depends on the loop length. Therefore, the flicker noise limits the performance of long-cavity OEOs (≧5 km) at low frequencies (f<500 Hz). The model for a single-loop OEO was extended to model the dual-loop injection-locked OEO (DIL-OEO). The model gives the phase-noise, the spur level, and the locking range of each of the coupled loops in the OEO. An excellent agreement between theory and experiment is obtained for the DIL-OEO. Due to its generality and accuracy, the model is important for both designing OEOs and studying the physical effects that limit their performance. We demonstrate theoretically that it is possible to reduce the first spur in the DIL-OEO by more than 20 dB relative to its original performance by changing its parameters. This theoretical result has been experimentally verified.

Pulse propagation in a fiber Bragg grating written in a slow saturable fiber amplifier.

We have developed a model to study nonlinear pulse propagation in a fiber Bragg grating written in an erbium-doped fiber amplifier. The saturation effect in such amplifiers depends on the accumulated energy along the pulse rather than on the pulse instantaneous power. We have shown that the gain saturation effect cannot be neglected when Bragg solitons are amplified by erbium-doped fiber amplifiers. The slow saturation of the amplifier limits the output pulse power, and it tends to split the amplified pulse into several pulses. We have shown that when the propagation velocity of the amplified pulses decreases, the amplifier gain per unit length increases.

Feasibility and safety of multiple daily insulin injections in general medicine wards.

AIM: Intravenous insulin improves clinical outcome in patients hospitalized in intensive care units. Whether glucose control with multiple daily subcutaneous insulin injections (MDI) is beneficial in patients hospitalized in general medical wards is unknown. We tested the feasibility, safety and efficacy of glucose control with MDI in diabetic patients hospitalized in a general medicine ward. METHODS: Eighty-eight adults with diabetes mellitus were studied in an internal medicine department. All patients were treated with subcutaneous pre-meal insulin analogue and Glargin insulin. A conservative and an intensified protocol was tested. RESULTS: Mean daily glucose levels decreased in the conservatively treated patients from 275+/-71 mg/dl at day 1 to 197.0+/-60 mg/dl at day 4 of hospitalization p=0.0001 and in the intensified protocol to 191+/-38 mg/dl already on day 1 remaining stable throughout the hospitalization. A mean daily glucose <180 mg% was reached by day 2 in 48% of patients in the intensified and in 32% in the conservative groups. Only one serious event of hypoglycemia was noted in the intensified group. CONCLUSION: Intensive insulin treatment with MDI is feasible, safe and efficacious in general medicine wards.

Noise distribution in the radio frequency spectrum of optoelectronic oscillators.

We analyze the distribution of the rf spectrum in optoelectronic oscillators due to the finite duration of the spectrum measurement. The distribution of the periodogram or the rf spectrum at a given frequency is calculated using a reduced model and is compared to a comprehensive numerical simulation. The model shows that the rf spectrum at a given frequency fluctuates from measurement to measurement with an exponential distribution.

Multirate asynchronous sampling of sparse multiband signals.

Because optical systems have a huge bandwidth and are capable of generating low-noise short pulses, they are ideal for undersampling multiband signals that are located within a very broad frequency range. We propose a new scheme for reconstructing multiband signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels. The scheme, which we call multirate sampling (MRS), entails gathering samples at several different rates whose sum is significantly lower than the Nyquist sampling rate. The number of channels does not depend on any characteristics of a signal. In order to be implemented with simplified hardware, the reconstruction method does not rely on the synchronization between different sampling channels. Also, because the method does not solve a system of linear equations, it avoids one source of lack of robustness of previously published undersampling schemes. Our simulations indicate that our MRS scheme is robust both to different signal types and to relatively high noise levels. The scheme can be implemented easily with optical sampling systems.

Two-soliton interaction in the vicinity of a defect inside a fiber Bragg grating and its application for obtaining an all-optical memory.

We study the interaction between two Bragg solitons in the vicinity of a defect inside a fiber Bragg grating. A soliton that is trapped in the defect can be released by launching a second soliton. The effect can be used to obtain an all-optical memory that is not strongly sensitive to the phase and the timing arrival of the solitons.

Efficient method for launching in-gap solitons in fiber Bragg gratings using a two-segment apodization profile.

We theoretically demonstrate what is a new method for efficient launching of in-gap solitons in fiber Bragg gratings. The method is based on generating a soliton outside the grating bandgap. Then, the soliton is adiabatically coupled into the bandgap by using its particlelike behavior. We compare our method to a previously published launching scheme that is based on generating the soliton directly within the grating bandgap. When using low-intensity incident pulses, the transmission efficiency of our method is three times higher than that of the previously published scheme.

Experimental reconstruction of a highly reflecting fiber Bragg grating by using spectral regularization and inverse scattering.

We demonstrate experimentally, for the first time to our knowledge, a reconstruction of a highly reflecting fiber Bragg grating from its complex reflection spectrum by using a regularization algorithm. The regularization method is based on correcting the measured reflection spectrum at the Bragg zone frequencies and enables the reconstruction of the grating profile using the integral-layer-peeling algorithm. A grating with an approximately uniform profile and with a maximum reflectivity of 99.98% was accurately reconstructed by measuring only its complex reflection spectrum.