If the \(Y\) and \(R\) is the primly decided then the \(\theta_{i}\) can be automatically decided by generalize equation 5 and with \(\theta_{i}\) can be calculated the actual field propagation length \(L^{actual}_{mmi}\) for 3dB power splitting ratio. An example Y=1.545 and R=5 then by the equation 5, resonance parameter theta will be \(\theta_{i}\)=9 degree and propagation length is approximately \(L^{actual}_{mmi}\)=9.87 \(\mu m\), it will always less then the MMI length \(L_{mmi}\)=2R shown in graph 4. Other parameters used in the designs of 3dB MMI coupler are as follows; Width of the polymer waveguide is \(W_{g}\)=1 \(\mu m\) which is inter connected to the adiabatic tapered access waveguide. The tapers are required to adapt the waveguide width \(W_{g}\) used in the rest of the system to the MMI section optimum access waveguide width \(W_{a}\) for minimum imbalance performance. It is desirable to make \(L_{tp}=5\) as small as possible, given requirements and tolerance for the minimize reflection properties. This tapered access waveguide width \(W_{a}=W_{g}+2{dw}=1.5\;\mu\)m that ensure the complete input power is carried by first limited modes and also prevent the reflection properties in the MMI region, where end of the access waveguide angled place at the arc of the MMI section about the center to center of waveguide distance Y for the restricted interference mechanism or general interference mechanism. The refractive index of the SU-8 core is \(\approx n_{f}\)=1.578 and cladding refractive index assumed as \(\approx n_{c}\)=1 air. MMI region width is \(W_{mmi}=4\;\mu\)m and length is \(L_{mmi}=2R\) or 10 \(\mu\)m. All corner of the MMI segment is curved that restrict the Fresnel reflection within region and walls reflections are restricted due to angled placed ports, it is useful in the interferometric measurement. Now, After the deciding all geometrical parameter of the 3dB MMI coupler through out the novel designing parameter equation. It is assumed that the designs are for the transverse electric (TE) polarization at wide-band wavelength (or wavelength independence structure). It has been simulated with FEM computational tool as COMSOL MultiPhysics. Geometry of 3dB MMI couple is shown in figure 5 (in middle) and cross section of waveguide structure used in our design with required parameters (inside right). The propagating field (electric field component Ex) is coupled into input Port \(P_{in}\#1\) with the wavelength span 800 nm to 1600 nm. Simulated field propagation in the optimized MMI 3dB coupler is shown figure 5 (in middle) for input signal at port \(P_{in}\#1\), port \(P_{out}\#3\) and port \(P_{out}\#4\). As expected, the propagating field patterns is more or less unchanged with input wavelength span along the MMI region. 3dB normalized output powers at \(P_{out}\#3\) and port \(P_{out}\#4\) are almost equal splitting power ratio of input signal for the 3dB coupler with optimized Angled ports. It can be clearly seen by output normalize power graph of this \(2\times 2\) 3dB MMI coupler in figure 5 (inside left). The simulated transmission responses of the optimized 3dB MMI coupler, given in Figure 6, show that the device has much smaller wavelength dependence and more robust 3dB coupling over a wide spectral range, as compared to conventional, directional couplers. The average normalized splitting ratio, for the highly wideband wavelength range, was 51% ot 49%.