682 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 15, NO. 5, MAY 2003 Measurement of Chirp Parameters and Halfwave Voltages of Mach–Zehnder-Type Optical Modulators by Using a Small Signal Operation Satoshi Oikawa, Tetsuya Kawanishi, and Masayuki Izutsu, Senior Member, IEEE Abstract—A method is described for measuring the chirp pa- rameters and the halfwave voltages of Mach–Zehnder-type optical modulators. These parameters can be obtained from the optical spectrum components by using a small signal operation, while the conventional method needs large voltages. We demonstrated the measurement of the frequency responses up to 40 GHz. Index Terms—Chirp parameter, halfwave voltage, Mach–Zehnder (MZ) structure, optical harmonics, optical modulator. I. INTRODUCTION L iNbO (LN) OPTICAL modulators, using Mach–Zehnder (MZ) waveguide structures, are essential for optical and wireless telecommunication networks, such as broad-band optical networks up to 40 Gb/s for trunk lines [1], and narrow-band optical networks for fiber-radio systems [2]. For such optical modulators, the estimation of the halfwave voltage and the chirping at high frequency is required. The halfwave voltage, which is the voltage to switch an optical output power from the maximum to the minimum, is required to drive an optical modulator. In addition, -cut LN optical modulators have small chirping because the radio frequency (RF) electric fields applied to the optical paths of the MZ structures are asymmetric. The chirp parameter of an optical modulator can be easily measured by using dispersive media such as optical fibers [3]. However, by the conventional method, we can not measure a chirp parameter at a specific frequency. We reported a method to measure simultaneously chirp parameters and halfwave voltages of LN optical modulators by using a large signal operation [4]. We calculated these parameters from the high-order optical harmonics. Chirp parameters, halfwave voltages, and even bias points were accurately measured at specific frequencies by this method. But it was difficult to measure these parameters over a wide frequency range because of a narrow-band operation of a high power amplifier. In this letter, we propose a method to measure chirp parameters and halfwave voltages of an MZ-type optical modulator by using a Manuscript received August 23, 2002; revised January 14, 2003. S. Oikawa is with New Technology Research Laboratories, Sum- itomo Osaka Cement Company, Ltd., Chiba 274-8601, Japan (e-mail: soikawa@sits.soc.co.jp). T. Kawanishi and M. Izutsu are with Communications Research Laboratory, Tokyo 184-8745, Japan. Digital Object Identifier 10.1109/LPT.2003.809944 small signal operation. These parameters are calculated from two optical spectrum components, the carrier and the first harmonic. Thus, the frequency response of these parameters over a wide frequency range can be evaluated without using higher order optical components. II. PRINCIPLE Consider an output lightwave from an MZ-type optical mod- ulator whose electric field is described by (1) (2) where is the electric field of the incident light. and are the phase delays due to the difference in optical length between paths. ( ) is the angular frequency of the electric signal fed to the optical modulator. is the first kind Bessel function of the order . and are the magnitude of the optical phases induced by the RF electric field applied to each optical path of the MZ waveguides. As shown in (2), the modulated output lightwave from an op- tical modulator has many frequency components. Now we at- tend to two frequency components. One is the frequency com- ponent of the carrier (carrier component, henceforth) and the other is that of the first-order harmonic (first component). The optical power of the carrier component, in (2), is ex- pressed by (3) The optical power of the first component, in (2), is ex- pressed by (4) 1041-1135/03$17.00 © 2003 IEEE