A Fiber Optic Phase Modulator with an Optical Frequency Shift of up to 20 GHz

Transcription

1 A Fiber Optic Phase Modulator with an Optical Frequency Shift of up to 0 GHz A.M.Maedov (1), A. L. Levin (), and V. T. Potapov (3) (1) Institute of Radio Engineering and Electronics, Russian Acadey of Sciences, Vvedenskogo sq. 1, Fryazino, Moscow Region, Russiae-ail: aedov@s.ire.rssi.ru () and (3) as (1) above ABSTRACT A fiber optic phase odulator is described in which the phase of a light wave traveling in an optical fiber is odulated by a coposite electroechanical resonator with Q The instantaneous frequency of the wave at the odulator output varies according to a haronic law. The interval of tuning of the instantaneous light wave frequency 6 achieved in the experient is 0 GHz, which corresponds to a odulation index of 10. It is deonstrated that a axiu value of the frequency tuning range is deterined by the elastic liit of the resonator aterial. INTRODUCTION Nuerous applications of the tunable lasers include the optical frequency doain reflectoetry (OFDR) [1] (which has inspired this study), integral optical device testing [], photodetector calibration [3], etc. The OFDR procedure involves a linear sweep of the light wave frequency, after which the beats between reference and scattered waves contain various spectral coponents uniquely corresponding to various parts of a tested line or a passive ultiplex network of fiber optic sensors. However, a iniu linewidth of the existing tunable seiconductor lasers aounts to several hundred kilohertz, thus restricting the range of tested wavelengths to several hundred eters [1]. An alternative to the direct odulation was represented by an electrooptical odulator [4] in which the source eitted a fixed frequency and the odulation was perfored behind the source. This approach requires using a highrate processing syste with a frequency band of a few gigahertz, since the optical wave frequency shift equals the frequency of the electric odulation signal. Another disadvantage of this schee was the presence of odulation haronics leading to nonlinear second-haronic distortions of the photocurrent beat signal. Previously [5], we proposed a schee of the fiber optic odulator in which the phase of a light wave propagating in the fiber was changed by extending a part of this fiber coiled around a piezoceraic cylinder. This solution is intrinsically copatible with single-ode fiber optic devices and is wavelength independent and can therefore be applied to any type of light source. In addition, this schee is free fro the proble of haronics and requires no wideband electronic processing syste because of a low resonance frequency of the piezoceraic cylinder ( 5 khz). A disadvantage of this odulator schee is a low resonator quality ( Q 5) for which the frequency tuning in a sufficiently wide range (4 GHz) is achieved at the expense of a considerable power (8 W) dissipated in the odulator. Below we describe a fiber optic phase odulator based on a coposite resonator (Fig.1a) around which about 300 of a single-ode optical fiber was wound. THEORY In order to study the light wave frequency odulation, we used a two-bea interferoeter schee (Fig.1b). In the case of a source with two longitudinal odes, the photocurrent i is deterined by the interference of four waves: i ra1 cosω t + ra + ω + a1t + ϕ) + at + ωt + ϕ) where r and t are the aplitude reflection and transission coefficients of the interferoeter; a 1 and a are the longitudinal ode aplitudes; ϕ is the phase increent; ω is the cyclic frequency of the light wave; and ω = π ν is the ode spacing (angle brackets denote tie average). Let the interferoeter to include a phase odulator such that ϕ =ϕ cos(. Under the condition ϕ >> 1, expression (1) reduces to, (1)

2 (a) 1 а b (b) He-Ne C C U bias U cos t M O D P Fig. 1. Scheatic diagras showing : (a) the top view of a coposite electroechanical resonator, (1) bronze cylinder; () piezoelectric transducer and (b) the experiental setup: (D) photodiode, (C) fiber couplers, (M) fiber optic phase odulator, (O) oscilloscope, (P) aplifier. where t [ ( ] { Acos ( dt + B cos [ ( ± ] t i( = G ω dt}, () 0 0 ( = ϕ sin t is the instantaneous frequency; A = rt ( a1 + a ) and B = rt a1a are the beat G ( of the photodetector at the aplitudes. The coefficient of proportionality in () represents a spectral response [ ] instantaneous frequency. For siplicity, the constant coponent of the photocurrent is oitted, which is equivalent to assuing G(0) = 0. In the case of a single-ode laser operation ( a = 0 and B = 0 ), an aplitude-odulated wave is incident onto the photodetector. The odulation frequency of this wave exhibits periodic variations fro 0 to ax = ϕ. At the tie instants such that t << 1, the frequency is odulated according to a linear law and the photocurrent envelope is A i( G( ax, (3) This expression is of practical interest for deterining the aplitude frequency characteristics of photodetector structures: the photocurrent envelope displayed on the oscilloscope visualizes the frequency response of the photodetector. A convenient eans of calibrating the phase odulator is offered by a two-ode laser operation ( a = a, B 0). In this case, the photodetector easures the beats not only near the points of zero frequency, but at 1

3 the tie instants τ for which ( τ) = ω as well. Thus, we can readily deterine the light wave frequency deviation as ω ax =, (4) sin τ Let us analyze the factors deterining the range of frequency deviation. The phase odulation index ϕ and, hence, the range of instantaneous frequency deviation ax are proportional to the fiber strain aplitude. Denoting by l be the strain aplitude of the fiber halfturn, we obtain 4πn ax = N l, (5) λ where N is the nuber of turns, λ is the radiation wavelength, and n is the refractive index of the fiber core. Proceeding fro the general considerations, we expect that the resonator oscillation aplitude an, hence, the fiber strain l can be controlled by three paraeters: (i) elastic liit of the fiber; (ii) power transitted to the coposite resonator; and (iii) elastic liit of the resonator aterial. The elastic liit of the fiber is reached only for a relative fiber strain on the order of 1% [1]. This level of dynaic straining can be attained only in etallic glasses or in a specially treated berylliu bronze. An analysis of the latter two paraeters shows that, siilar to the case of a piezoceraic odulator [5], the ain factor liiting the strain aplitude in a low-q resonator is the transitted power. However, the situation will principally change for a resonator possessing very high Q, in which the strains corresponding to the elastic liit can readily be achieved. Let us consider this case in ore detail. For a cylindrical odulator operating on the principal bending ode, one can readily check that [6] 4 σ r0 l =, (6) 3 E d where σ is the elastic strain aplitude, E is the elastic odulus of the odulator aterial, r 0 is the cylinder radius, and d is the cylinder wall thickness. Forula (6) is derived under the assuption that the cylinder wall thickness d is sall as copared to the radius r 0. Therefore, all subsequent expressions will also refer to the case of a thin-wall cylinder. The principal bending ode frequency of a thinwall cylinder is given by the forula d E 0.48, (7) r0 ρ where ρ is the odulator aterial density. Using forulas (5) (7), we readily obtain an expression relating the instantaneous frequency deviation to the physicocheical paraeters of the odulator aterial: ax n σ = 1.8 N, (8) π λ Eρ The ter under square root sign in (8) has a physical eaning of the specific elastic energy stored per unit ass of the strained eleent. Therefore, this relationship iplies that the range of the instantaneous frequency deviation is deterined by the elastic odulus E, odulator aterial density ρ, and elastic stress σ. In practice, the axiu possible elastic stress σ is deterined by the elastic liit σ e1 of the odulator aterial. Exceeding this liit leads to violation of the Hooke law, whereby the oscillator becoes nonlinear and the syste escapes fro resonance. As is known [7], the σ e1 / ρe value is axiu for copper-based alloys. In addition, there is a specially developed coercial technology of theral treatent additionally increasing the σ σ e 1 value by ore than one order of agnitude. In order to deterine the transitter power, we have calculated echanical energy U stored in the strained resonator using the explicit for of the principal bending ode: 13 U = M S, (9) 16 Here, M is the cylinder ass, is the resonance frequency, and S is the axiu aplitude of the cylinder bending oscillations. At the sae tie, the oscillation aplitude S is related to the frequency tuning range

4 ν = / π by the following expression: ax ax S = ν λ ax, (10) 4 N n Using (9) and (10) together with a forula for the transitted power, P = U / Q, we obtain an expression for the frequency deviation range: 16Nn PQ ν ax =, (11) λ M As can be seen fro this expression, the frequency tuning range can be increased by reducing the resonance frequency and increasing the Q value and the power transitted to the resonator. EXPERIMENT The radiation source in our experients was a He Ne laser of the LGN-07 type ( λ= 0.63µ ). In coparison with the coercial device, our setup allowed the resonator frequency to be changed relative to the aplification circuit, thus switching the source fro double- to single-ode lasing. The interferoeter schee assued a two-bea configuration (Fig.1b) with a phase odulator in the signal ar. The fiber optic phase odulator represented a 300--long single-ode optical fiber tightly coiled in seven layers ( 1000 turns) on a coposite electroechanical resonator. The resonator coprised a pair of elastic cylindrical eleents ade of bronze, touching one another along the cylinder generatrix. The principal bending ode of the cylindrical eleents ( 4.9 khz) was excited with the aid of piezoceraic transducers. In an unloaded state (~10 turns), the odulator had Q ~1000. The piezoceraic transducers were driven by a unipolar ac voltage with an aplitude of about 150 V applied to the electrodes. Fig.. Oscillogras of the photodetector signal observed in a double-ode lasing regie. When the laser operated in a double-ode regie, the oscillogra contained syetric spikes (Fig. ) described by the second ter in (). The spikes correspond to an interode beat frequency of v = 650 MHz. The instantaneous frequency deviation produced by the phase odulator was calculated as described in [5]. Forula (4) yields 10 GHz, which corresponds to the total frequency tuning range of 0 GHz As deonstrated above, the frequency deviation in our syste was deterined by the interval of a linear relationship between the elastic strain aplitude and the external force agnitude. Calculation of the value for a odulator with ρ = 8000 kg/ 3, σ 100 MPa, E = 10 GPa, ax λ = 0.63 µ, n = 1.45, and N =1000 yields / π 9.4 GHz, in agreeent with the experiental value. If the ax oscillation aplitude increases so that σ σ e 1, the anharonicity of the restoring force becoes an iportant factor e1

5 leading to a nonlinear relationship between the resonance frequency ad the external force aplitude. ν ax, (GHz) 10 5 Fig. 3. The plot of instantaneous frequency deviation versus frequency of the applied voltage (U = 150 V). As a result, the resonance curve exhibits bending typical of the nonlinear oscillator. Fig.3 shows a resonance curve characteristic of the oscillations with a finite aplitude. The frequency detuning in our case was 150 HZ. The transitted power estiated by forula (11) for the instantaneous frequency deviation ν = 10 GHz aounts to P 1W. However, no heating of the resonator was observed in experient. A thorough analysis of the energy losses showed that the resonator quality is ostly deterined by a response to the acoustic eission fro the oscillating syste to the environent. In our opinion, the use of a specially heat-treated berylliu bronze eleent will allow the instantaneous frequency deviation range up to 100 GHz (with a total frequency tuning range of 00 GHz) for a odulator coil containing 1000 turns. This is coparable to the frequency tuning range of a single-frequency dynaic seiconductor laser. REFERENCES ν, (khz) 1. P. Oberson, B. Huttner, and N. Gisin, Opt. Lett. vol.4, pp (1999).. H. Barfuss and E. Brinkayer, J. Lightwave Technol. vol.7, pp.3-10 (1989). 3. Miguel V. Andres, Meas. Sci. Technol. vol. 3, pp.17-1 (199). 4. K. Tsuji, K. Shiizu, T. Horiguchi, and Y. Koyaada, IEEE Photonics Technol. Lett. vol.7, pp.804- (1995). 5. V. T. Potapov, A. M. Maedov, D. A. Sedykh, and S. V. Shatalin, Pis a Zh. Tekh. Fiz. vol.17 (16), pp (1991) Sov. Tech. Phys. Lett. vol.17, pp.575 (1991). 6. N. M. Belyaev, Resistance of Materials (Gostekhizdat, Moscow, 196). 7. Zh. P. Pastukhova and A. G. Rakhshtadt, Spring Alloys of Non-ferrous Metals (Metallurgiya, Moscow, 1983).