Bose-Einstein condensation of photons in a long fiber cavity.

We demonstrate photon Bose-Einstein condensation (photon-BEC) at a broad temperature range that is valid also in the long 1D fiber cavity limit. It is done with an erbium-ytterbium co-doped fiber (EYDF) cavity by overcoming the challenging requirement of sublinear light dispersion for BEC in 1D using a chirped-gratings Fabry-Perot. We experimentally show with a square-root mode-dispersion, a quadratic temperature dependence of the critical power for condensation (compared to a linear dependence in finite regular fiber-cavities) between 90 K and 382 K, as the theory predicts.

Nonlinear light mode dispersion and nonuniform mode comb by a Fabry-Perot with chirped fiber gratings.

We demonstrate a nonlinear light mode dispersion and a nonuniform frequency mode comb by a chirped fiber Bragg gratings (CFBG) Fabry-Perot (FP) at the 1550 nm wavelength regime. We give analytical expressions for the general chirp case, and an experimental demonstration with a linear chirp, showing a square-root dependence of the dispersion as a function of the FP mode number. Such sublinear dispersion is required, for example, for photon Bose-Einstein condensation (BEC) in a one-dimensional (1D) system like fiber cavities.

Bose-Einstein condensation of photons in an erbium-ytterbium co-doped fiber cavity.

Bose-Einstein condensation (BEC) is a special many-boson phenomenon that was observed in atomic particles at ultra-low temperatures. Later, BEC was also shown for non-atomic bosons, such as photons. Those experiments were usually done in micron-size cavities, where the power (particle number) was varied, and not the temperature, until condensation was reached. Here we demonstrate BEC of photons in a few-meters-long one-dimensional (1D) erbium-ytterbium co-doped fiber cavity at, below and above room temperature, between 100 K and 415 K. The experiments were done at about the 1550 nm wavelength regime having a few to tens of µW intra-cavity light power (107-108 photons). By varying the power and also the temperature, we found linear dependence of the condensation on power for various temperatures and of the critical power (for condensation) on temperature. These findings agree, functionally and quantitatively, with the theoretical BEC prediction without any adjustable parameter.

Thermalization of one-dimensional photon gas and thermal lasers in erbium-doped fibers.

We demonstrate thermalization and Bose-Einstein (BE) distribution of photons in standard erbium-doped fibers (edf) in a broad spectral range up to ~200nm at the 1550nm wavelength regime. Our measurements were done at a room temperature ~300K and 77K. It is a special demonstration of thermalization of photons in fiber cavities and even in open fibers. They are one-dimensional (1D), meters-long, with low finesse, high loss and small capture fraction of the spontaneous emission. Moreover, we find in the edf cavities coexistence of thermal-equilibrium (TE) and thermal lasing without an overall inversion (T-LWI). The experimental results are supported by a theoretical analysis based on the rate equations.

CW laser light condensation.

We present a first experimental demonstration of classical CW laser light condensation (LC) in the frequency (mode) domain that verifies its prediction (Fischer and Weill, Opt. Express20, 26704 (2012)). LC is based on weighting the modes in a noisy environment in a loss-gain measure compared to an energy (frequency) scale in Bose-Einstein condensation (BEC). It is characterized by a sharp transition from multi- to single-mode oscillation, occurring when the spectral-filtering (loss-trap) has near the lowest-loss mode ("ground-state") a power-law dependence with an exponent smaller than 1. An important meaning of the many-mode LC system stems from its relation to lasing and photon-BEC.

Experimental observation of critical phenomena in a laser light system.

We experimentally demonstrate critical behavior of a passively mode-locked laser with properties that are similar to those of gas-liquid and magnetic spin systems. The laser light modes provide a special nonthermodynamic many-body system where noise takes the role of temperature. It is also a rare opportunity of an experimental pure one-dimensional system. As theoretically predicted, we identified in the laser light-mode system two thermodynamiclike phases, one characterized by spontaneous pulses and the second by field-induced parapulses, separated by a first order phase transition boundary that is terminated by the critical point. We also measured the critical exponents, ß≈0.52, γ≈1, and δ≈3.1, which are close to the mean field values that are exact in the laser system.

Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser.

We have recently predicted (R. Weill, B. Fischer and O. Gat, Phys. Rev. Lett.104, 173901, 2010) condensation of light in actively mode locked lasers when the laser power increases, or the noise, that takes the role of temperature, decreases. The condensate is characterized by strong light pulses due to the dominance of the lowest eigenmode ("ground state") power. Here, we experimentally demonstrate, for the first time, light mode condensation transition in an actively mode-locked fiber laser. Following the theoretical prediction, the condensation is obtained for modulations that have a power law dependence on time with exponents smaller than 2. The laser light system is strictly one dimensional, a special opportunity in experimental physics. We also discuss experimental schemes for condensation in two- and three-dimensional laser systems.

Picosecond flat-top pulse generation by low-bandwidth electro-optic sinusoidal phase modulation.

We report the first experimental demonstration to our knowledge of a microwave frequency upshifting system based on phase modulation. A sequence of flat-top optical and RF pulses at a repetition rate of 18.22 GHz, each with a FWHM time width of approximately 25 ps, is generated from a sinusoidal RF tone of only 3.680 GHz, in good agreement with our analytical and numerical calculations. A simple explanation of this technique based on Talbot effect theory is provided. The practical limitations and capabilities of the phase-modulation-based frequency upshifting approach for ultrabroadband RF waveform generation are also discussed.

Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating.

We propose and experimentally demonstrate an all-optical (all-fiber) temporal differentiator based on a simple pi-phase-shifted fiber Bragg grating operated in reflection. The proposed device can calculate the first time derivative of the complex field of an arbitrary narrowband optical waveform with a very high accuracy and efficiency. Specifically, the experimental fiber grating differentiator reported here offers an operation bandwidth of approximately 12 GHz. We demonstrate the high performance of this device by processing gigahertz-bandwidth phase and intensity optical temporal variations.

Reconfigurable generation of high-repetition-rate optical pulse sequences based on time-domain phase-only filtering.

We propose and demonstrate a fiber-based phase-only filtering technique for programmable optical pulse shaping, in which the filtering operation is implemented in the time domain by means of an electro-optical (EO) phase modulator. The technique has been applied for generating customized ultrahigh-repetition-rate optical pulse sequences (>40 GHz) from single input pulses by driving the EO phase modulator with a periodic electronic waveform (RF tone). The generated output pulses are replicas of the input pulse and both the repetition rate and the envelope profile of the generated sequences can be controlled and tuned electronically using this approach.

Complete characterization of optical pulses by real-time spectral interferometry.

We demonstrate a simple method for complete characterization (of amplitudes and phases) of short optical pulses, using only a dispersive delay line and an oscilloscope. The technique is based on using a dispersive delay line to stretch the pulses and recording the temporal interference of two delayed replicas of the pulse train. Then, by transforming the time domain interference measurements to spectral interferometry, the spectral intensity and phase of the input pulses are reconstructed, using a Fourier-transform algorithm. In the experimental demonstration, mode-locked fiber laser pulses with durations of approximately 1 ps were characterized with a conventional fast photodetector and an oscilloscope.

Spectral Fraunhofer regime: time-to-frequency conversion by the action of a single time lens on an optical pulse.

We analyze a new regime in the interaction between an optical pulse and a time lens (spectral Fraunhofer regime), where the input pulse amplitude is mapped from the time domain into the frequency domain (time-to-frequency conversion). Here we derive in detail the conditions for achieving time-to-frequency conversion with a single time lens (i.e., for entering the spectral Fraunhofer regime) as well as the expressions governing this operation. Our theoretical findings are demonstrated both numerically and experimentally. A comparative study between the proposed single-time-lens configuration and the conventional dispersion + time-lens configuration for time-to-frequency conversion is also conducted. Time-to-frequency conversion with a single time lens can be used for applications similar to those previously proposed for the conventional time-to-frequency converters, e.g., high-resolution measurement of fast optical temporal waveforms. Moreover, our results also indicate that the spectral Fraunhofer regime provides additional capabilities for controlling and processing optical pulses.

Frequency shifting of microwave signals by use of a general temporal self-imaging (Talbot) effect in optical fibers.

A simple and practical microwave frequency-shifting technique based on a general temporal self-imaging (GTSI) effect in optical fiber is proposed, formulated, and experimentally demonstrated. The proposed technique can be applied to an arbitrary periodic microwave signal (e.g., a microwave tone) and provides unparalleled design flexibility to increase the frequency of the input microwave signal up to the desired value (limited only by the photodetector's bandwidth). For instance, we demonstrate frequency upshifting of microwave tones from approximately 10 to approximately 50 GHz and from approximately 40 to approximately 354 GHz. These results also represent what is to the authors' knowledge the first experimental observation of GTSI phenomena.

Measuring temperature profiles in high-power optical fiber components.

We demonstrate a new method for measuring changes in temperature distribution caused by coupling a high-power laser beam into an optical fiber and by splicing two fibers. The measurement technique is based on interrogating a fiber Bragg grating by using low-coherence spectral interferometry. A large temperature change is found owing to coupling of a high-power laser into a multimode fiber and to splicing of two multimode fibers. Measurement of the temperature profile rather than the average temperature along the grating allows study of the cause of fiber heating. The new measurement technique enables us to monitor in real time the temperature profile in a fiber without the affecting system operation, and it might be important for developing and improving the reliability of high-power fiber components.

Data storage in optical fibers and reconstruction by use of low-coherence spectral interferometry.

We demonstrate optical data storage in optical fibers and reconstruction by use of low-coherence spectral interferometry. The information was stored by means of writing fiber Bragg gratings with different central wavelengths at different locations of the fiber. We need only a single short pulse is needed to read all the stored data. The maximum theoretical reconstruction rate that can be obtained with our technique is 10 Tbits/s. Our storage technique can be useful for identifying users in optical communication networks.