Mykola Kulishov

Ultrafast all-optical differentiators

We report the experimental realization of an ultrafast all-optical temporal differentiator. Differentiation is obtained via all-fiber filtering based on a simple diffraction grating-assisted mode coupler (uniform long-period fiber grating) that performs full energy conversion at the optical carrier frequency. Due to its high bandwidth, this device allows processing of arbitrary optical signals with sub-picosecond temporal features (down to 180-fs with the specific realizations reported here). Functionality of this device was tested by differentiating a 700-fs Gaussian optical pulse generated from a fiber laser (@ 1535nm). The derivative of this pulse is an odd-symmetry Hermite-Gaussian waveform, consisting of two linked 500-fs-long, pi-phase-shifted temporal lobes. This waveform is noteworthy for its application in advanced ultrahigh-speed optical communication systems.

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.

Long-period fiber gratings as ultrafast optical differentiators.

It is demonstrated that a single, uniform long-period fiber grating (LPFG) working in the linear regime inherently behaves as an ultrafast optical temporal differentiator. Specifically, we show that the output temporal waveform in the core mode of a LPFG providing full energy coupling into the cladding mode is proportional to the first derivative of the optical temporal signal (e.g., optical pulse) launched at the input of the LPFG. Moreover, a LPFG providing full energy recoupling back from the cladding mode into the core mode inherently implements second-order temporal differentiation. Our numerical results have confirmed the feasibility of this simple, all-fiber approach to processing optical signals with temporal features in the picosecond and subpicosecond ranges.

Nonreciprocal waveguide Bragg gratings.

The use of a complex short-period (Bragg) grating which combines matched periodic modulations of refractive index and loss/gain allows asymmetrical mode coupling within a contra-directional waveguide coupler. Such a complex Bragg grating exhibits a different behavior (e.g. in terms of the reflection and transmission spectra) when probed from opposite ends. More specifically, the grating has a single reflection peak when used from one end, but it is transparent (zero reflection) when used from the opposite end. In this paper, we conduct a systematic analytical and numerical analysis of this new class of Bragg gratings. The spectral performance of these, so-called nonreciprocal gratings, is first investigated in detail and the influence of device parameters on the transmission spectra of these devices is also analyzed. Our studies reveal that in addition to the nonreciprocal behavior, a nonreciprocal Bragg grating exhibits a strong amplification at the resonance wavelength (even with zero net-gain level in the waveguide) while simultaneously providing higher wavelength selectivity than the equivalent index Bragg grating. However, it is also shown that in order to achieve non-reciprocity in the device, a very careful adjustment of the parameters corresponding to the index and gain/loss gratings is required.

Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings

We propose a novel linear filtering scheme based on ultrafast all-optical differentiation for re-shaping of ultrashort pulses generated from a mode-locked laser into flat-top pulses. The technique is demonstrated using simple all-fiber optical filters, more specifically uniform long period fiber gratings (LPGs) operated in transmission. The large bandwidth typical for these fiber filters allows scaling the technique to the sub-picosecond regime. In the experiments reported here, 600-fs and 1.8-ps Gaussian-like optical pulses (@ 1535 nm) have been re-shaped into 1-ps and 3.2-ps flat-top pulses, respectively, using a single 9-cm long uniform LPG.

Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings

A simple and general approach for designing practical all-optical (all-fiber) arbitrary-order time differentiators is introduced here for the first time. Specifically, we demonstrate that the Nth time derivative of an input optical waveform can be obtained by reflection of this waveform in a single uniform fiber Bragg grating (FBG) incorporating N &pi-phase shifts properly located along its grating profile. The general design procedure of an arbitrary-order optical time differentiator based on a multiple-phase-shifted FBG is described and numerically demonstrated for up to fourth-order time differentiation. Our simulations show that the proposed approach can provide optical operation bandwidths in the tens-of-GHz regime using readily feasible FBG structures.

Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings

We report the fabrication of a pi-phase-shifted long-period fiber grating (LPFG) capable of operating as a terahertz-bandwidth second-order temporal differentiator. We demonstrate its operation experimentally by differentiating subpicosecond long optical pulses. A new scheme for achieving high-order photonic temporal differentiation based on LPFG filters is also proposed and demonstrated. In particular, we prepared a LPFG-based first-order differentiator that was frequency and bandwidth matched to the second-order device and demonstrated the cascadability of these devices leading to the implementation of a third-order differentiator. By also employing these devices in reflection, up to the fifth-order differentiation is demonstrated experimentally.

Trapping light in a ring resonator using a grating-assisted coupler with asymmetric transmission

A recently proposed concept suggests that a matched periodic modulation of both the refractive index and the gain/loss of the media breaks the coupling symmetry of the two co-propagating modes and allows only a unidirectional coupling from the i-th mode to j-the mode but not the opposite. This concept has been used to design a ring resonator coupled through a complex grating composed of both real (index) and imaginary (loss/gain) parts according to Euler relation: n = n0 exp(-jkx) = n0 (cos(kx) - j sin(kx)). Such asymmetrical coupling allows light to be coupled into the ring without letting it out. We present a detailed theoretical analysis of the ring resonator in the linear regime, and we investigate its linear temporal dynamics. Three possible states of the complex grating leads to the possibility of developing a dynamic optical memory cell where, for example, a data modulated train of optical pulses can be stored. This data can be accessed without destroying it, and can also be erased thus permitting the storage of a new bit. Finally, the ring can be used for pulse retiming.

Theory and practice of long-period gratings: when a loss becomes a gain.

Losses of cladding modes are part of the mechanism of operation of a long-period grating (LPG) when it is used as an optical filter. We present a LPG computer simulation that accounts for these losses. On the basis of this simulation, we show that losses result in qualitatively different LPG spectral behavior. There is an optimal loss value that provides sidelobe-free, 100% power transfer from the core to the cladding mode for a uniform LPG. We obtained a simple equation that relates this optimum lose value to the LPG length and the cross-coupling coefficient. Based on the results, we propose new approaches to LPG design in a fiber as well as in waveguide platforms for fiber-optic communication and sensor applications. A design of a LPG reconfigurable filter is suggested.

Design of terahertz-bandwidth arbitrary-order temporal differentiators based on long-period fiber gratings

We show that long-period fiber grating (LPG) incorporating N-1pi-phase shifts can serve as an Nth order temporal differentiator that operates in transmission. Due to the inherent large bandwidth provided by LPGs, subpicosecond (terahertz-bandwidth) optical signals may be processed with centimeters-length devices. Design parameters for up to fifth-order differentiators are given.