Comparison of Integrated Optical Phase Shifters Designed in Different Regime

. A comparative study, in aspects of both wavelength dependence and fabrication tolerance, is carried out between silica-based phase shifters designed in two different regime, namely length difference regime and refractive index difference regime. Results show that in the wavelength range of 1500-1600 nm, phase shifter designed in refractive index difference regime has a working wavelength range 2.8~3.1 times wide as that designed in length difference regime; while in the aspect of fabrication tolerance, phase designed in length difference regime is advantageous, with respect to waveguide core dimension error, and waveguide core refractive index error as well.


INTRODUCTION
Since the concept of integrated optics was proposed at the end of 1960s, integrated optics theory and technology have been developing rapidly. Up to recent years, integrated optical technologies have been brought out from laboratory and into the realm of practical application. A variety of integrated optical elements, couplers, modulators and wavelength division multiplexers for instance, are widely applied in the fields of optical communication, optical interconnects, and optical sensing as well.
Phase shifter, which is applied to introduce phase difference between optical waveguide branches, has been widely used in the integrated optical devices based on interference principle, e.g. Mach-Zehnder interferometer [1,2], optical isolator [3,4], arrayed waveguide grating(AWG) [5,6], and optical mixer [7,8]. The structure selection of phase shifter plays a key role in optimizing the performance of integrated optical devices. There exists two common regimes for generating phase shifts between different optical waveguide branches: one regime is to generate phase difference by introducing waveguide length difference between waveguides (named length difference regime, or LDR, in this paper), as widely applied in design of arrayed waveguides in AWG; the other regime is to generate phase difference by introducing the effective refractive index difference between different waveguides (named refractive index difference regime, or RIDR in this paper), which can be implemented by changing the geometric dimension of the waveguide cross section. These two phase shift design regimes will produce integrated optical devices of different performance, For example, Pierre Labeye and his team show that the phase shifter based on refractive index difference regime has better performance in terms of the range of working wavelength [9]. But up to now, there is few reports on the comprehensive performance of the two phase shifters, for example, there is a lack of comparison fabrication tolerance between the two phase shifting regimes.
In the current article, a comprehensive comparison of SiO 2 based waveguide have been presented between phase shifters designed by the two phase shifting regimes, LDR and RIDR, based on calculation of the wavelength dependence and fabrication tolerance behavior.

THEORY AND METHOD
The two phase shifting regimes are shown in Fig.1. Fig.1 (A) represents LDR, in which phase difference is generated by increasing length of the waveguide 2 (WG2) with respect to waveguide 1 (WG1) by L  ; Fig. 1 (B) represents the RIDR, in which phase difference is generated by locally increasing WG2 width to 1 W . For phase shifter designed in LDR, considering wavelength dependence of waveguide effective refractive index, phase difference generated between the two waveguides, WG1 and WG2 shown in Fig.1 difference between the two waveguides. Correspondingly, for phase shifter designed in RIDR, phase difference between WG1 and WG2 can be expressed as where 1 W is width of the waveguide in the phase shift section; L is length of phase shifter, as shown in Fig.1 (B).
Silica-based optical waveguides with refractive index contrast of 0.45% are adopted, height of waveguide core is assumed to be 6. times as that of phase shifter in LDR.  Due to inevitability of waveguide core dimension error, as well as refractive index error, induced in the process of waveguide fabrication, it is of importance to take these errors into consideration while designing a phase shifter. Phase shift of the two 90 degree phase shifter designed at the wavelength of 1550 nm in different regimes and presented in Fig.3, with width, height, waveguide core refractive index taken into consideration. Tab. 1 gives phase shift change slope with respect error of waveguide width, waveguide height, and waveguide core refractive index as well. It can be seen clearly that phase shifter designed in RIDR is more sensitive to fabrication errors, compared with that designed in RIDR. Difference between is ascribed to the length of phase shifter. For a 90 degree phase shifter in LDR, the length difference, as denoted above as L  , is only 268nm;

Fabrication Tolerance
while for the phase shifter designed in RIDR, the shifter length is several mm, a much larger value than that in LDR. Since waveguide fabrication error exist over the waveguide part that are different between WG1 and WG2, device of large length suffer much seriously from fabrication error.

CONCLUSIONS
In this paper, a comparative study, in aspects of wavelength dependence and fabrication tolerance, is carried out between integrated optical phase shifters designed in two different regimes, namely LDR and RIDR. The results show that in the wavelength range of 1500-1600 nm, the phase shifter designed in LDR are more sensitive to wavelength, but possesses much higher fabrication tolerance; while the phase shifter designed in RIDR have an operating wavelength range 2.8~3.1 times wide as that in LDR, but it suffers much seriously from waveguide fabrication error.