Transmission of a broadband light through a fiber optic loop: effect of nonlinear refractive index

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Transmission of a broadband light through a fiber optic loop: effect of nonlinear refractive index

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  Turk J Phys(2014) 38: 64 – 72c ⃝  T¨UB˙ITAKdoi:10.3906/fiz-1306-6 Turkish Journal of Physics http://journals.tubitak.gov.tr/physics/ Research Article Transmission of a broadband light through a fiber optic loop: effect of nonlinearrefractive index Erkin ZAKHIDOV ∗ , Abdumutallib KOKHKHAROV, Farrukh MIRTADJIEV,Sherzod NEMATOV, Ilkhom TADJIBOEV, Olga TRUNILINA Institute of Ion Plasma and Laser Technologies, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan Received:  10.06.2013  •  Accepted:  22.10.2013  •  Published Online:  17.01.2014  •  Printed:  14.02.2014 Abstract: The results of studies of broadband light transmission through a fiber loop and a double loop under the effectof nonlinear refractive index are presented in this paper. Fiber loop and double loop transmission/reflection vs. a couplersplitting ratio at various powers of the light with a spectral width of approximately 35 nm are studied and high efficientnonlinear light switching is demonstrated. It is shown that a double loop formed by consecutive connecting 2 fiber loopsallows us to exclude the strong spectral dependence of light transmission/reflection and to distribute input light equallybetween them. Such all-fiber devices can find a real application in broadband systems of optical communication anddata processing. Key words:  Fiber loop, double loop, directional coupler, optical Kerr effect, nonlinear optical switch 1. Introduction The unprecedented progress in optical communication and data processing systems during the last decades usingoptical fibers with signal transmission rates up to 1 Tb/s makes it important to develop a new generation of functional elements with essentially higher speeds [1]. One of the key decisions regarding this problem concernsall-fiber optical elements made of single-mode fibers [2]. Technologies for manufacturing fiber directional couplersat present allow the design of all-fiber elements with additional losses  ≤ 0 . 1dB / km [3,4].The specific feature of light propagation in an optical fiber favorable for nonlinear effects is extremely highintensities of a light to be reached in such a guiding medium even at moderate powers; at input power of 1W thelight intensity in a single mode fiber with core diameter of 5 µ m exceeds 1MW / cm 2 . Moreover, throughout allfiber length the light profile, phase, and polarization are preserved, which creates unique physical conditions forstudying nonlinear effects and developing principally new types of functional elements, using nonlinear processesin fibers [5–7].A fiber loop or fiber Sagnac interferometer, depending on its parameters, may be employed as a mirror,a spectral filter, or a switcher in a nonlinear regime [8–10]. The fiber loop has also shown a unique property toselect optical solitons from a nonsolitonic background in the light generated by nonlinear effects in fibers [11,12].However, the strong spectral dependence of a splitting ratio of a coupler, specific for devices based on coupledwaves [13], essentially limits the possibilities of employing of a fiber loop as a functional element in broadbandoptical communication and data processing systems. ∗ Correspondence: ezakhidov@hotmail.com 64  ZAKHIDOV et al./Turk J Phys In a double loop formed by consistently connecting 2 directional couplers [14] and having long ( ∼  1km)contours of a polarization maintaining fiber, the nonlinear switching of a narrow band CW light in the spectraldivision nearby 1 . 5 µ m has been observed and attributed to nonlinear walk-off in the phases of orthogonallypolarized waves. In that work it has been observed that transmission of the double loop studied, as in asingle loop, strongly depends on light wavelength. In [15] we have experimentally demonstrated that spectra of reflected and transmitted fractions of an ultra-broadband IR light (1 . 1 − 1 . 6  µ m) of   ∼  100ps pulses enteredin a short contour double loop (1 − 2m) are practically identical, irrespective of light power.In the present work, spectral and power dependences of a broadband light reflection and transmissionthrough a fiber loop and a double loop are analyzed and experimentally studied. Perspectives for applicationof such fiber elements in broadband systems of optical communication and data processing are discussed. 2. Experimental set-up Fiber loops and double loops studied were made of ( SiO 2  + GeO 2 ) /SiO 2 type optical fiber with core/claddingdiameters of 6 µ m / 125 µ m and refractive indexes difference of 6 . 8 · 10 − 3 . Directional couplers were made byfusing and taping of a small site of 2 closely placed fiber pieces, where efficient energy transfer between coresof the fibers takes place due to the optical coupling between the evanescent tail of modes of one fiber in whichlight is launched and the guiding mode of another fiber [16]. At real technological parameters of such couplers,complete (100%) transfer of a light from one fiber to another occurs at a beat length of   L b  ≈  1 cm and ischaracterized by a periodic dependence on coupling length ( L co ) and operation wavelength ( λ ) [17]. In theloops studied  L co  was also maintained at  ∼  1cm.The length of a fiber contour ( L ) connecting 2 exit ports of a coupler to form a fiber loop may, in principle,vary from tens of centimeters to 1 kilometer and more, and so in all cases  L co  ≪  L . This circumstance allowssimplifying analysis of a nonlinear regime of light transmission through a fiber loop essentially, considering thatnonlinear interaction occurs only in a fiber contour, and interference only in a coupler [18].A fiber double loop was formed by connecting 2 single loops consistently. Here, the simplest case foranalysis is that when both couplers split a light intensity equally with ratio  α  = 0 . 5 and optical paths of 2 counter-propagating waves passing through 2 fiber pieces between 2 couplers should be absolutely equal.However, in reality, fiber coupler technologies (for example, splicing/taping) do not allow these conditionsto be maintained. In commercially available couplers, light splitting ratio and its spectral dependence mayslightly vary from sample to sample ( ∼  1%) and equality of lengths of 2 fiber pieces between couplers may becontrolled with accuracy of   ∼  1mm. In addition, there is another mechanism of optical paths’ inequality relatedto uncontrolled variations of a fiber core/cladding diameter having technological srcin [3]. Fiber core/claddingdiameter variations bring about relevant variations in guiding characteristics, particularly, light propagationconstant,  β  . If core diameters of the 2 fibers with length of   L  = 1m differ for 0 . 5% (∆ d co /d co  = 5  · 10 − 3 ),in assumption of linear dependence of   β  ( d co ) in the vicinity of   V   = 2 . 405 [13], the difference in their opticalpaths may be defined as:∆ L  = (∆ β/β  ) L  = ∆ n (∆ d co /d co ) L  = 6 . 8 ·  10 − 3 ×  5  · 10 − 3 ×  1m = 0 . 034mmSince the fiber loop and double loop studied were made of a fiber with weak birefringence (a fiber with stressesin the cladding area) [19] with  δn  ∼  (2 ÷ 5) · 10 − 8 (measured in straight fiber pieces), taking into account shortlengths of loops, 1 − 2m, walk off in the phases of 2 orthogonally polarized waves may be neglected.65  ZAKHIDOV et al./Turk J Phys The principal scheme of the experimental set-up is shown in Figure 1. A CW pumped Q-switched + mode-locked Nd 3+ : YAG laser ( λ  = 1 . 064 µ m,  P   pulse  = 200kW,  τ   pulse  = 100ps,  f   = 1kHz) was used as source of apump light (1) and a low intensity He–Ne laser (1.15  µ m) for control of the polarization properties of the fiberloop (2). The pumping light generated a light continuum in low-mode fiber (3) with  L  = 20m,  d co  = 10 µ munder simultaneous action of several nonlinear effects of third order nonlinearity [16]. The light continuum wasan ultra-broadband radiation with pulse duration of   <  100ps extended in the spectral range of 1 . 1 − 1 . 6 µ m [20].The presence of higher order guided modes and the possibility of 4-wave mixing of different spectral componentsof the light continuum [21] in the fiber generator exclude distinguished formation of stimulated Raman scattering(SRS) solitons, simplifying the analysis of nonlinear light transmission in a fiber loop neglecting soliton effects[18]. The fiber generator of the light continuum is a convenient source of an ultra-broadband light operating atmoderate laser powers, and at higher powers a light continuum may be generated in other types of nonlinearmedia [22]. A narrower band (approx. ∆ λ  = 35nm) light of relevant intensity was formed by cutting off thelight continuum using wavelength-selective multilayer dielectric (4) and broadband dielectric (5) mirrors. This light entered and exited the fiber loop (or double loop) (6) by means of microlenses (7). Parameters of the light waves reflected and transmitted through a fiber loop (double loop) were measured with avalanche photo diodes(8) and oscilloscope (9), and light pulse energy with a powermeter (10). Light spectra were measured with a monochromator (11), high sensitive germanium photodetector (12), and boxcar integrator (13), and registeredby “ X  − Y   ” recorder (14). Nd:YAG 1e –e 4 5 5 5 5 5 5 7 7 7 7 1 111 1 14 Figure 1.  Schematic diagram of the experimental set-up (explanations in the text). 3. Light transmission through a fiber loop Let us consider light passage through a fiber loop. The light with amplitude of   A 0  ( A 0  =  I  1 / 2 0  , where  I  0  - lightintensity) entering a fiber loop through one of its input ports is split at the coupler into 2 counter-propagatingwaves. If the coupler’s splitting ratio is  α  (in terms of intensity), the amplitudes of 2 counter-propagating wavesin the clockwise and counterclockwise directions are defined, accordingly: A cw  =  I  1 / 2 cw  = ( αI  0 ) 1 / 2 =  α 1 / 2 A 0  (1)66  ZAKHIDOV et al./Turk J Phys and A ccw  = ( − I  ccw ) 1 / 2 = [ − (1 − α ) I  0 ] 1 / 2 =  i (1  −  α ) 1 / 2 A 0  (2)Note that the wave  A ccw  obtains an additional phase of 90 ◦ in the coupler when it crosses from one fiber toanother [13]. These 2 waves passing along the fiber contour in 2 opposite directions obtain the same phase shifts(in the case of lack of Sagnac effect and/or nonlinear effects their optical paths are identical) [23,24] and onceagain interfere in the coupler. Thus, the amplitudes of waves leaving the fiber loop through the port via lightthat enters (reflected wave) and through another one (transmitted wave) are, accordingly: A rf   =  α 1 / 2 A ccw  +  i (1  −  α ) 1 / 2 A cw  =  i [ α (1  −  α )] 1 / 2 A 0  +  i [ α (1  −  α )] 1 / 2 A 0  = 2 i [ α (1  −  α )] 1 / 2 A 0  (3)and A tr  =  α 1 / 2 A cw  +  i (1  −  α ) 1 / 2 A ccw  =  α 1 / 2 α 1 / 2 A 0  +  i 2 (1  −  α ) 1 / 2 (1  −  α ) 1 / 2 A 0  ==  αA 0  −  (1  −  α ) A 0  = (2 α  −  1) A 0 .  (4)Note that the transmitted wave retains the same phase as the input wave, and the reflected one is shifted by90 ◦ .At high intensities of entering light one should consider the effect of nonlinear refractive index inducedby self-phase modulation (SPM) and cross-phase modulation (XPM) [21]. In the conditions of our experimentdue to ultrashort light pulses ( τ   p  <  100ps) were used counter-propagating waves that interact in a very smalldistance ( <  1 . 5cm), and thus the nonlinear phase induced by a counter-propagating wave, XPM, is much lessthan that in the own field of a wave, SPM. The nonlinear phase induced by SPM is [25]:∆ ϕ  = (2 πn 2 | A | 2 L ) /λA eff  ,  (5)where  n 2  = 3 . 2  ·  10 − 16 cm 2 / W denotes the nonlinear refractive index coefficient of fused quarts,  A eff   = π ( d eff  / 2) 2 is the effective area, and  d eff   -diameter of a light spot in a single mode fiber ( d eff   increases approx.1 . 5 times when wavelength increases from 1 . 1 to 1 . 6 µ m [5]).When  A cw  =  A ccw  nonlinear phases of 2 counter-propagating waves are equal to each other and ampli-tudes of reflected and transmitted waves according to formulae (3) and (4) are:  A rf   = 2 i [ α (1  −  α )] 1 / 2 A 0  =2 i [0 . 5 × (1  −  0 . 5)] 1 / 2 A 0  =  iA 0  and  A tr  = (2 α  −  1) A 0  = (2 × 0 . 5  −  1) A 0  = 0, i.e. the fiber loop completelyreflects a light irrespective of its power.Nonlinear phases of the 2 counter-propagating waves may be different only when  α  ̸ = 0 . 5( A cw  ̸ =  A ccw ).In a nonlinear regime the amplitudes of these 2 waves taking into account formula (5) may be defined as: A ′ cw  =  A cw  exp ( iϕ 0  +  iγ  | A cw | 2 L ) (6)and A ′ ccw  =  A ccw  exp ( iϕ 0  +  iγ  | A ccw | 2 L ) .  (7)Here  ϕ 0  denotes a linear phase and  γ   = 2 πn 2 /λA eff   is a nonlinearity coefficient. Then the amplitudes of reflected and transmitted waves are, respectively: A rf   =  α 1 / 2 A ′ ccw  +  i (1  −  α ) 1 / 2 A ′ cw  (8)67  ZAKHIDOV et al./Turk J Phys and A tr  =  α 1 / 2 A ′ cw  +  i (1  −  α ) 1 / 2 A ′ ccw .  (9)Finally, nonlinear transmission of a fiber loop is: β   ≡  P  tr /P  0  = | A tr | 2 / | A 0 | 2 = 1  −  4 α (1  −  α ) { cos 2 [( α  −  1 / 2) γ  | A 0 | 2 L ] } .  (10)According to formula (10) at  α  = 0 . 5 transmission of a fiber loop is equal to 0 in a nonlinear regime, as discussedabove. However, now, even when  α  ̸ = 0 . 5, if (1 − 2 α ) γ  | A 0 | 2 L  = (2 k − 1) π  the fiber loop completely transmitsa light. In this case, at low intensities, when (1  −  2 α ) γ  | A 0 | 2 L ≪ π  formula (10) becomes sufficiently simpler: β   = 1  −  4 α (1  −  α ) = (2 α  − 1) 2 =  β  0 . In this way, initially low linear transmittance of a fiber loop maybe increased dramatically (up to 100%) under the light of a definite power. Such a phenomenon, named lightswitching, has interesting prospects to be employed in functional elements in optical communication and dataprocessing systems [1].In Figure 2 the fiber loop transmission vs. light wavelength,  β  ( λ ) =  P  tr /P  0 , at different input powersis shown. The solid line corresponds to the function  cos 2 x  adjusted to experimentally measured values of transmission at low powers,  β  0 ( λ ) ( A 0  <  10 W   , closed circles). With increasing of light power the  β  ( λ ) plotbecomes different from  β  0 ( λ ) (open circles,  A 0  = 220W), but in the vicinity of   α  = 0 . 5 β  ( λ ) is still near to 0.Further increasing of   A 0  brings about much stronger changes in  β  ( λ ), and the ratio  β  ( λ ) /β  0 ( λ ), the switchingcoefficient, conventionally used for quantitative estimation of transmission changes, reaches values up to 10(triangles and squares, at  A 0  = 505W and 950W, respectively). Thus, under the effect of nonlinear refractiveindex the spectrum of linear transmission of a fiber loop  β  0 ( λ )  ∼  cos 2 ( λ ) is dramatically transformed, stillbeing near to zero in the vicinity of   α  = 0 . 5. 1.1 1.2 1.3 1.4 1.5 1.60.00.20.40.60.81.0    T  r  a  n  s  m     s  s     o  n    (  a .  u .    ) Wavelength, (µm) Figure 2.  Fiber loop transmission ( β  ) vs. a light wavelength. Solid line is the calculated dependence (function  cos 2 x );closed circles, open circles, triangles, and squares are  β   values measured at light powers of 10W ,  220W ,  505W, and950W, respectively. P  tr ( A 0 ) dependences in a fiber loop calculated using formula (10) at various  α  are shown in Figure3. The solid line corresponds to complete transmission of a fiber loop ( β   = 1 , α  = 0 or 1). At strongasymmetric splitting,  α  = 0 . 96, the  P  tr ( A 0 ) function (dashed line) has a small periodic fraction (nonlinear68
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