IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 15, NO. 4, APRIL 2003 545 Response Characteristics of Thin-Film-Heated Tunable Fiber Bragg Gratings Lin Li, Jianxing Geng, Ling Zhao, Gang Chen, Gaoting Chen, Zujie Fang, and Cedric Fung Lam, Member, IEEE Abstract—We investigate the thermal response of a tunable fiber Bragg grating (FBG) with a metal coating on bare fiber surface as a heater both theoretically and experimentally. By solving a dif- ferential equation of temperature as a function of time, together with some reasonable approximation, we obtained an explicit de- scription of the thermal response characteristics with the struc- ture’s heat capacity and a time constant as its parameters. Using a squared wave modulation current and a tunable laser, we mea- sured the temporal response of the tunable FBG. The obtained re- sponse curves match our solution. A time constant in the range of subseconds was deduced. Discussions on the tuned FBG spectra are also given at the end to explain the linewidth broadening effect at higher temperature. Index Terms—Fiber Bragg grating (FBG), thermal response. I. INTRODUCTION T UNABLE FIBER devices have great importance in lightwave communication systems and optical sensing systems. Fiber Bragg grating (FBG) tuning using temperature [1]–[3] and stress [4], [5] are attractive to people who are developing enabling techniques. Among the variety of tun- able filters, an FBG filter coated with a thin-film heater on the surface is a practical and prospect device because of its compactness, fast response, and good efficiency [1]–[3]. The temperature distribution in a thin-film heated chirped FBG for dispersion compensation has been investigated in [6] and [7]. This letter focuses on the temporal response of a thin-film heated FBG with uniform metal coating. A differential equation is used to describe the thermal flow in the metal-coated fiber. In order to obtain analytical solutions, some approximations have been taken to simplify the temperature distribution inside the fiber, the thermal diffusion, and radiation dissipation. An ex- plicit temporal solution of wavelength tuning has been obtained in terms of the thermal capacity and a time decay constant. We measured temporal responses of the wavelength shift using a squared waved current applied on the metal heater and a tunable laser. The responses in both the rising phase and falling phase were measured at different current amplitudes. From those re- sponse curves, the time constant was deduced to be in the range of a subsecond. II. THEORETICAL ANALYSIS To understand the temporal response characteristics of the thin-film heated fiber grating, a differential equation describing Manuscript received July 23, 2002; revised December 19, 2002. L. Li, J. Geng, L. Zhao, G. Chen, G. Chen, and Z. Fang are with the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China (e-mail: lilingkate@hotmail.com). C. F. Lam is with the Opvista Inc., Irvine, CA 92618 USA. Digital Object Identifier 10.1109/LPT.2003.809284 temperature distribution and thermal flow should be established. For uniform metal coating and the length of coating much larger than the grating length, temperature distribution is supposed not to be a function of the position along the grating. In this case, only radial distribution and thermal flow needs to be in- vestigated. Under the above assumption, a tunable FBG with a metallic heater can be modeled as a silica cylinder with thin-film thermal source on its surface and surrounded by air. Thus, the heat generated in the thin-film metal heater will diffuse and ra- diate into the fiber core as well as to the surrounding air. Thermal energy conservation requires (1) where are the thermal diffusivities of the fiber and air, re- spectively, is specific heat of the metal film, is the coeffi- cient of thermal radiation dissipation, is the ambient temper- ature, and is the temperature of the thin-film metal heater. The electric power is given by where is the resistivity of the thin-film metal, is its thickness, is the radius of the fiber, and is the length between two electrodes. Inside the FBG and in the surrounding air, thermal flow should obey Fourier thermal diffusion law. Since the diameter of the fiber is so small and its thermal conductivity (about 14 mW/cm C) is much larger than that of the surrounding air (about 0.26 mW/cm C), the temperature gradient inside the grating will be very small and one can neglect its thermal diffusion and take the temperature of the grating as . As a result, the third term on the right-hand side of (1) denoting the contribution of the fiber, can be included in the thermal capacity . In the surrounding air, the temperature at some distance apart from the fiber can be considered as the ambient temperature because of convection. Here, is a parameter that will be greatly affected by the surrounding condition and is to be decided by experiment. The thermal flow inside the viscose layer of thickness has to be solved from a diffusion equation. The solution shows that it is proportional to to the first order. Second, since the temperature is roughly in the range below 473.15 K, the second term describing radiation dissipation can be approximated as . 1041-1135/03$17.00 © 2003 IEEE