Optical-frequency-comb generation with collinear acousto-optic diffraction: Theory and simulations

Optical frequency combs (OFCs) are of extreme importance for modern photonics. A great number of OFC generation methods and practical application ideas have been suggested. In this paper we propose and theoretically analyze an OFC generation method based on frequency-shifting loop utilizing collinear acousto-optic (AO) diffraction. This method offers two OFC generation schemes. The first one applies the closed-loop optical system with collinear AO cell driven by external radio-frequency (rf) generator. The second scheme applies a principle of an optoelectronic oscillator. This system includes not only the optical feedback but also the optoelectronic feedback connecting the optical output of the system with the piezoelectric transducer of the AO cell and operates above the self-excitation threshold without external rf generator. In both cases OFCs may be obtained in several ways: two different types of single side band modulation and amplitude modulation. The switching between the methods is realized by mutual reorientation of a pair of polarizers placed in front of and behind the AO cell and achromatic half-wave plate included in the optical feedback loop. It is shown that the parameters OFCs obtained in the system with only optical feedback are determined by AO cell material, rf generator signal frequency and magnitude, optical loss and amplification. The system with both optic and electronic feedback gives the unique opportunity to obtain chirped OFCs even without using any rf generator. In this case the OFC parameters depend on the AO cell material, electric feedback gain, optical loss, and optical gain.

Figure 1

Collinear AO filter in ${\mathrm{LiNbO}}_3$ with arbitrary rotated input and output linear polarizers.

Figure 2

(a) Diffraction efficiency and (b) transmission functions for the $I_0, I_1$, and $I_2$ components of collinear AO diffraction.

Figure 3

Scheme of closed-loop optical system for OFC generation with a collinear AO filter.

Figure 4

Scheme of closed-loop optical system for OFC generation with a collinear AO filter and both optical and electronic feedback.

Figure 5

The process of OFC generation for (a) SSB modulation with $I_0$ or $I_1$ components and (b) amplitude modulation with $I_2$ component in closed-loop system.

Figure 6

The process of OFC generation in the system with two feedback loops for (a) SSB modulation with $I_0$ or $I_1$ components and (b) amplitude modulation with $I_2$ component.

Figure 7

The dependence of spectral interval between adjacent OFC components on optical wavelength.

Figure 8

Simulated OFC spectra and collinear AO cell transmission functions for varying mismatch generated with $I_0$ component: (a) $\alpha =0^{\circ }, \beta ={90}^{\circ }, \sigma =2.98, R=0,-1$ diffraction order; (b) $\alpha ={90}^{\circ }, \beta =0^{\circ }, \sigma =2.98, R=0, +1$ diffraction order; (c) $\alpha =0^{\circ }, \beta ={90}^{\circ }, \sigma =3.03, R=-2$; (d) $\alpha =0^{\circ }, \beta ={90}^{\circ }, \sigma =3.42, R=-3.5$

Figure 9

Simulated OFC spectra and collinear AO cell transmission functions for varying mismatch generated with $I_1$ component: (a) $\alpha =0^{\circ }, \beta ={45}^{\circ }, \sigma =5.52, R=0,-1$ diffraction order; (b) $\alpha ={90}^{\circ }, \beta ={45}^{\circ }, \sigma =4.18, R=0, +1$ diffraction order; (c) $\alpha =0^{\circ }, \beta ={45}^{\circ }, \sigma =5.43, R=-1.8$;

Figure 10

Simulated OFC spectra generated with $I_2$ component and collinear AO cell transmission functions for varying mismatch ($\alpha ={45}^{\circ }, \beta ={45}^{\circ }$): (a) $\sigma =4.8, R=0$; (b) $\sigma =4.04, R=0$, with optical phase compensation; (c) $\sigma =4.07, R=2.1$; (d) $\sigma =3.67, R=-2.1$

Figure 11

Simulated chirped OFC spectra obtained with SSB modulation for (a) $\sigma =5.59$ and (b) $\sigma =5.60$ and simulated dependence of number of OFC spectrum lines on the optical gain $\sigma$.