Optik 127 (2016) 973–980 Contents lists available at ScienceDirect Optik jo ur nal homepage: www.elsevier.de/ijleo Harmonic distortion and power relations in a single loop optoelectronic oscillator A. Mukherjee a,∗ , D. Ghosh b , N.R. Das c , B.N. Biswas d a Department of Electronics & Communication Engg., Central Institute of Technology, Kokrajhar, Assam, India b Department of Electronics & Communication Engg., Siliguri Institute of Technology, Siliguri, West Bengal, India c Institute of Radio Physics & Electronics, Calcutta University, West Bengal, India d Education Division, SKF Group of Institutions, Mankundu, West Bengal, India a r t i c l e i n f o Article history: Received 12 January 2015 Accepted 26 October 2015 Keywords: Injection locked oscillator Mach–Zehnder modulator Optoelectronic oscillator Modulation index Distortion a b s t r a c t This paper begins with a review of the work in the field of single loop optoelectronic oscillator. Detailed theoretical investigation of the system incorporating an injection locked oscillator in place of the con- ventional bandpass filter is presented. Power relations and harmonic distortions of the oscillator are calculated. Experimental results showing in good agreement with theoretical predictions are given. © 2015 Elsevier GmbH. All rights reserved. 1. Introduction Recently, a good deal of work on a single loop optoelectronic oscillator (OEO) has been reported (Mukherjee [3,5], Chatterjee [6], Biswas [4], Zhou and Blasche [12], Yao and Maleki [8–11]) and very little effort has been directed towards the development of a systematic analytical approach for studying the output power rela- tionship and harmonic distortions of an OEO. Biswas [13] presented a derivation for AM to PM conversion in an injection synchronised oscillator. In the last fifteen years or so, generation of spectrally pure microwave and mm-wave has been achieved using optical schemes. The most widespread approach is based on the opto- electronic oscillator where high Q optical cavities with extremely low loss are used with optoelectronic feedback loops. The generic OEO consists of a light source (usually a laser), light modulator, optical cavity and a photodetector; the output of which is fed back to the modulator to achieve a closed-loop configuration (Fig. 15). This feedback loop can generate self-sustained oscillation if its overall gain is greater than the loss, and the circulating waves add up in phase. The former requirement can be met with insertion of gain in the loop and, the latter, by controlling the phase. Since the loop can support waves circulating many times, the oscillator is ∗ Corresponding author. Tel.: +91 9475178324. E-mail address: a.mukherjee@cit.ac.in (A. Mukherjee). fundamentally multi-mode, with the mode spacing determined by the free spectral range of the cavity. By adding a filter in the loop with a prescribed centre frequency, the output of the oscillator can be obtained at that frequency. In this way, any frequency supported by the bandwidth of the components can be generated. Now, this multi-mode oscillation can be suppressed if the band- width of the filter in the loop is narrow enough so that only a single mode of oscillation survives in the loop. Such a narrow-band filter, however, is not practical, especially when the length of the fibre is long and the operating frequency is in the microwave and mm-wave range. One approach to mitigate this problem is to replace the RF band-pass filter by an injection locked oscillator in the loop. The synchronised oscillator ignores any signal that lies outside the locking range. So the trick is to synchronise the centre frequency of the injection locked oscillator with that of the free running frequency of the OEO. In this paper we present a conventional oscillator and its amplitude governing equation along with the steady state value is derived. The phase plane portrait of the oscillator reveals that the oscillator output voltage is convergent implying the stability of the system. Now, the RF band-pass filter is replaced by this oscillator with injection synchronisation. It is worthwhile to mention that the net input to RF adder in the OEO consists of three signal components: (i) output voltage from the Mach–Zehnder modu- lator (MZM), (ii) output voltage from the injection synchronised oscillator and (iii) synchronising signal. The steady state amplitude and the free-running frequency are derived theoretically and http://dx.doi.org/10.1016/j.ijleo.2015.10.126 0030-4026/© 2015 Elsevier GmbH. All rights reserved.