First-order loss-less differentiators using long period gratings made in Er-doped fibers David Krčmařík1,2,3, Radan Slavík1,*, Yongwoo Park2, Mykola Kulishov4, and José Azaña2 1 Institute of Photonics and Electronics AS CR, Chaberská 57, Prague, 18251, Czech Republic Institut National de la Recherche Scientifique (INRS) Centre Energie, Matériaux et Télécommunications, Varennes, Quebec, J3X 1S2, Canada 3 Faculty of Electrical Engineering CTU, Technická 2, Prague, 16627, Czech Republic 4 HTA Photomask Inc., 1605 Remuda Lane, San Jose, California 95112, USA * Corresponding author:
[email protected]
2
Abstract: An active-fiber-based all-optical first-order temporal differentiator with power efficiency surpassing 100% is demonstrated experimentally. It is based on a long-period fiber grating (LPFG) inscribed into a piece of highly-doped Erbium-doped fiber (EDF). The performed theoretical analysis considers effects like relative position of the LPFG with respect to the input end of the EDF and influence of the input signal power. In the design, parameters like noise characteristics and level of non-linear interaction are taken into account. The advantages of such an implementation over the setup using concatenation of a passive LPFG with an amplifier lies in reducing the unwanted nonlinearities and reducing the amplified spontaneous emission (ASE). 2009 Optical Society of America OCIS codes: (050.2770) Gratings; (060.2410) Fibers, erbium; (060.2340) Fiber optics components; (200.4740) Optical processing
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Received 10 Nov 2008; revised 11 Nov 2008; accepted 11 Nov 2008; published 6 Jan 2009
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1. Introduction Recently, there appeared several reports on design [Error! Reference source not found.,2] and experimental implementation [3-7] of all-optical temporal differentiation, which has been found to be useful for various signal processing tasks like advanced waveform generation (e.g., Hermite-Gaussian pulses [3] or monocycle pulses [4]), optical signal analysis and characterization [8], and ultrafast pulse shaping (e.g., flat-top pulse synthesis [9]). The temporal differentiation has been realized using two main approaches. The first is based on various schemes incorporating nonlinear interaction in semiconductor optical amplifiers (SOA) [4,6,7]. This method provides the differentiation of the optical intensity profile of the input waveform. The other approach, of our interest here, provides the differentiation of the optical signal’s complex field envelope (including its amplitude and phase) and it is based on a linear optical filter that has a quadratic spectral transfer function in intensity with zero transmission at the optical signal carrier frequency [1-3,5]. Such differentiator strongly attenuates all the close-to-carrier frequency spectral components and thus is inherently very lossy, especially when considering passive optical filters reported so far (e.g., [1-3,5]). Hence, the energetic efficiency (EE), defined as the ratio between the signal power after and before the differentiator, is a key performance parameter of the differentiation process. The EE of a temporal differentiator is typically increased when processing a spectrally broader input signal but always at the expense of an increased processing error. A promising implementation of the optical differentiation is based on the use of a uniform long-period fiber grating (LPFG) operating in full-coupling condition around its resonance (zero-transmission) frequency [3]. This all-fiber solution was demonstrated to enable obtaining processing bandwidths well within the THz range. It has been theoretically estimated that the EE of the LPFG-based optical differentiator is necessarily lower than 10% to ensure a reasonably low relative processing error (< 5%) [3]. This low EE issue becomes even more critical when considering higher-order temporal differentiators [10] or simple signal processors that require cascading of several such components. In previous experiments with optical differentiation, the significant intrinsic processing loss was counterbalanced by pre- or post- (or both) amplification of the signal. Amplification of a too weak signal at the differentiator output may be very noisy, i.e. the differentiated signal power can be so low that the resulting power has a level comparable to that of the amplified spontaneous emission (ASE) of the used optical fiber amplifier, while pre-amplification may give rise to significant nonlinearities. The best possible implementation would be a simultaneous amplification and filtering which may be implemented, e.g., by making the differentiator directly into an active medium (e.g., erbium-doped fiber, EDF). LPFGs made in EDF potentially suitable for all-optical differentiation were demonstrated recently [11] and theoretical tools for their rigorous analysis were subsequently developed [12]. Here, we use the theoretical tools presented in [12] to design all-optical differentiators made in EDF that provide an EE surpassing 100%. This improvement (increase of EE from 100%) is the next logical and critical step to enable an efficient cascading of several differentiators for implementing higher-order temporal differentiations, as required for a range of applications. For instance, the higher-order derivatives of an input Gaussian-like signal can be applied for synthesis of different pulse shapes [3,9] or for advanced optical coding since differentiators of different orders can be used to generate waveforms that are temporally orthogonal among them (e.g, Hermite-Gaussian waveforms, computed as the successive time #103947 - $15.00 USD
(C) 2009 OSA
Received 10 Nov 2008; revised 11 Nov 2008; accepted 11 Nov 2008; published 6 Jan 2009
19 January 2009 / Vol. 17, No. 2 / OPTICS EXPRESS 462
derivatives of an input Gaussian) [13]. We investigate the noise characteristics of the hereproposed differentiators that originate in the ASE and perform their design. Another phenomenon that we study is the unwanted non-linear distortion that can be minimized by controlling the power level along the propagation. After analyzing all these phenomena, we fabricated optimized active differentiator samples and demonstrated accurate optical differentiation of ultrashort pulses reaching an EE over 100% with expected noise level suppression above 40 dB and low non-linear distortion (
