36 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 1, JANUARY 1, 2008 Ultraflat Optical Comb Generation by Phase-Only Modulation of Continuous-Wave Light S. Ozharar, F. Quinlan, I. Ozdur, S. Gee, and P. J. Delfyett, Fellow, IEEE Abstract—We propose a theory and experimentally verify ultra- flat comb generation by dual-sine-wave phase-only modulation. This novel approach requires a single optical element and is very practical and efficient in terms of both power budget and bandwidth. Using this approach, we have generated two optical spectra, one with 11 comb lines and 1.9-dB flatness and the other with 9 comb lines and 0.8-dB flatness. Index Terms—Continuous-wave (CW) modulation, optical fre- quency comb, phase modulation. I. INTRODUCTION E QUALLY spaced, stable optical frequency combs have many applications such as arbitrary waveform generation [1], and spectral-phase-encoded optical code-division multiple access [2]. Mode-locked lasers referenced to an external or internal optical reference can generate optical frequency combs with large bandwidth and high stability. However, these lasers are very demanding and expensive due to the requirements of good thermal and acoustic isolation, a stable optical ref- erence [3], or a carrier envelope offset stabilization scheme [4] according to the type of laser. An alternative method of generating optical frequency combs is by external modulation of continuous-wave (CW) light. This method is based on sideband generation and is relatively simple and cost-effective [5]. Ho and Kahn proposed to integrate an optical loop with CW modulation in order to broaden the resulting spectrum [6]. Bennett et al. experimentally realized this optical comb gener- ator and generated very broad spectra up to 1.8 THz; however, the amplitude variation among the comb lines of the spectra was 40 dB which limits the use of these comb lines [7]. Other approaches involve using more than one modulator in series or in parallel. Gheorma et al. used an integrated dual-parallel modulator in order to realize a flat optical spectrum [8]. Since this special modulator requires controlling three DC bias inputs in addition to two RF inputs, it needs extra care to avoid bias Manuscript received July 19, 2007; revised October 4, 2007. This work was supported by Alcatel-Lucent Bell Laboratories and by National Science Foun- dation ITR & STC CMDITR Programs. S. Ozharar, F. Quinlan, I. Ozdur, and P. J. Delfyett are with the College of Optics and Photonics, Center for Research and Education in Optics and Lasers, University of Central Florida, Orlando, FL 32816 USA (e-mail: sozharar@creol.ucf.edu; delfyett@creol.ucf.edu). S. Gee was with the College of Optics and Photonics, Center for Research and Education in Optics and Lasers, University of Central Florida, Orlando, FL 32816 USA. He is now with Gwangju Institute of Science and Technology, Gwangju 500-712, Republic of Korea. Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2007.910755 drift. Also, as the number of modulators involved in the system increases, so does the loss and the complexity of the system. Another important thing to note is that any kind of amplitude modulation will reduce the efficiency of the system, since it is based on modulating the loss rather than frequency of the input light. Sakamoto et al. uses a dual-drive intensity modulator to generate a flat spectrum, and the resulting optical power efficiency is only 1% including insertion loss of the modulator [9]. In this letter, we demonstrate, both theoretically and ex- perimentally, a novel method to generate an ultraflat optical comb with the use of a single phase modulator driven with two sine waves at different amplitudes and frequencies. Using our method, we have realized an optical frequency comb with 11 comb lines spaced by 3 GHz and better than 2-dB amplitude variation, and also an optical comb consisting of 9 comb lines spaced by 3 GHz and with better than 1-dB flatness. Since the setup has only one optical element (phase modulator) other than the seed laser, our method is extremely simple and inexpensive. The optical power efficiency is also very high due to the nature of phase modulation. The power efficiency of both cases are calculated theoretically and experimentally. II. THEORY OF DUAL-SINE-WAVE PHASE MODULATION The phase modulated electric field can be rewritten as a sum of its harmonics where the amplitudes are given by the Bessel functions of the first kind of the corresponding order evaluated at the depth of modulation as shown in the equation below [10]: (1) In (1), is the sinusoidal modulation waveform at frequency with a depth of modulation . is the scalar input electric field, is the Bessel function of the first kind and on the order of . Equation (1) tells us that the ampli- tude of the th harmonic is given by . The absolute values of amplitudes of the first three harmonics as a function of are plotted in Fig. 1 in logarithmic scale. There are several features to note in Fig. 1. First, when there is no phase modulation (i.e., ), all harmonics other than the zeroth harmonic (i.e., the input signal) are zero as expected. Second, the amplitude of the th harmonic is equal to the am- plitude of the th harmonic since the property holds. As a result, the spectrum is always symmetric. However, the key point to note is that there is no value where the neighboring harmonics will satisfy a flatness better than 1041-1135/$25.00 © 2007 IEEE