Why Is Flat Response Required?

In the all optical network (AON), the optical signals passed tens of nodes before reaching the destination node, as shown in Fig.1. The ROADM nodes are usually composed of wavelength selective switches (WSS), multiplexers/demultiplexers and optical switches. The wavelength multiplexers/demultiplexers are optical filters, including TFF-based WDM devices​, arrayed waveguide gratings (AWG) and optical interleavers.

Fig.1 Structure of all optical network

The spectral response of an optical filter without optimization is usually Gaussian-type, as shown in the left of Fig.2. The response of cascaded filters becomes narrower when the optical signal passes multiple nodes. As we know, wavelength jittering is inevitable for laser diode (LD). Loss increases rapidly when the wavelength of LD deviates from the ITU-grid, which is intolerable for the optical communication system. The spectral response of an optical filter after optimization is shown in the right of Fig.2. The response of cascaded filters is still flat. The wavelength jittering of LD doesn’t introduce much loss.

Fig.2 The spectral response of optical filter and wavelength jittering of laser diode

The spectral response of the TFF-based WDM devices is usually block-like due to the characteristics of TFF filters. However, the response of an AWG before optimization is usually Gaussian-type, which doesn’t meet the requirement by optical communication system.

Cause for Gaussian Passband

As we know, a standard AWG includes an input waveguide, an input star coupler, hundreds of arrayed waveguides, an output star coupler and tens of output waveguides. The wavelengths are dispersed in the output star coupler as shown in Fig.3. Different channels (λ₁, λ₂, λ₃, … ) are focused at the endface of different output waveguides, as shown in Fig.3(a). Then we enlarge one of the channels (λ₃) at the corresponding output, as shown in Fig.3(b). We can see that different wavelengths (λ₃₁, λ₃₂, λ₃₃) of the channel are focused at different positions. λ₃₂ is focused at the center of the output and the best coupling ratio is obtained. λ₃₁ and λ₃₃ are focused at the edge of the output and experience the highest power loss. That’s to say, when we enlarge one of the DWDM channels, the edge wavelengths experience more loss than the central wavelengths. Thus the spectral response of an AWG before optimization is usually Gaussian-type.

Fig.3 Wavelength dispersion in the output star coupler and refocusing of optical beams

Fig.4 shows the dispersed optical fields focused at the endface of one output. The optical field of edge wavelengths deviate from the waveguide center. The coupling coefficient and spectral transmission is given by Eq. (1) and (2) respectively, depending on the dispersed optical field and the eigen mode of the single mode waveguide ^[1].

                  (1)

                (2)

where λ_c is the central wavelength of the channel, D=dy/d λ is the dispersion of the focusing position, y is the position along the image plane (where the outputs are located).

Fig.4 Dispersed optical fields focused at the endface of one output

Eq. (1) means the correlation between the focused optical field and eigen mode . If the two functions and are identical, the correlation function will have a steep peak with highest maximum mathematically, which means a Gaussian-type narrow passband with minimal power loss at the central wavelength of a channel. Correlation between two different functions can flatten the peak of the function , while the height of the peak is cut down and power loss increases.

Passband Optimization

Different proposals are developed to obtain a flat response for AWGs. However, the passband optimization is accompanied with penalty of excess loss. The principles of different proposals are detailed as follow, the loss penalties are also discussed.

1)     Output with Multimode Waveguides

As shown in Fig.3(b), the central and edge wavelengths in the same channel are focused at different positions and experience different power loss, which results in the Gaussian-type spectral response. The circumstance is for a standard AWG with single mode waveguides as the outputs. In this proposal, multimode waveguides are employed to substitute the single mode waveguides at the outputs, as shown in Fig.5. The edge wavelengths are still focused at the positions deviating from the center, while the coupling loss will not increase rapidly as with single mode outputs. Thus the passband is broadened, as shown in Fig.6 ^[2].

Fig.5 Passband optimization with multimode waveguides employed as the outputs

Fig.6 Spectral response of the AWG with multimode waveguides as the outputs ^[2]

This proposal is characterized by simple solution and free of loss penalty. However, this AWG can’t be used as a wavelength multiplexer. What’s more, the demultiplexed wavelengths in the multimode waveguides can’t be coupled into single mode fibers for further transmission. Thus the applications of this proposal are limited. It can only be used as a demultiplexer and the demultiplexed wavelengths need to be received by photo detectors (PDs) directly.

A typical application of AWG with multimode outputs is in CWDM4 (four 20nm-spaced CWDM wavelengths 1270, 1290, 1310, 1330nm) transceiver module for data center. It is used as the demultiplexer and the demultiplexed wavelengths are immediately received by PDs.

2)     Input with Multimode Optical Field

A multimode interferometer (MMI) is added at the endface of the input waveguide. The fundamental mode of a single mode waveguide is converted into mltimodes with dual-peak in the MMI region, as shown in Fig.7. According to the principle of AWG, the optical field focused at the outputs is the image of the input optical field, with introduction of dispersion. Fig.8(b) shows the Gaussian-type eigen mode of the single mode waveguide output and the focused multimode optical field with dispersion . The correlation between this two optical fields according to Eq. (1) gives a flattened spectral response, which is shown in Fig.9 as the solid curve. For comparison with an AWG without optimization, Fig.8(a) gives the Gaussian-type eigen mode of the single mode waveguide output and the focused fundamental mode with dispersion . The correlation between the two identical optical fields gives a Gaussian-type response, which is also shown in Fig.9 as the dashed curve ^[1].

Fig.7 Optical field evolution in the MMI region ^[1]

Fig.8 Eigen mode of output waveguide and optical field focused at the image plane, (a) standard AWG, (b) AWG with MMI input

Fig.9 Broadened passband and loss penalty for an AWG with MMI input ^[3]

The comparison between the two spectral response curves in Fig.9 shows that the introduction of MMI at the input helps to broaden the passband, while the loss penalty is about 2dB.

3)     Tapering of Output Waveguides

When the output waveguide is tapered, the optical field keeps as fundamental mode, while the mode field diameter becomes narrower and the amplitude becomes higher, as shown in Fig.10. The taper is adiabatic, which means that the taper should be slow enough to avoid introduction of excess loss ^[4].

Fig.10 Optical field evolution in the taper region

At the left endface of the taper, the eigen mode of the waveguide and the focused optical field with dispersion are as shown in Fig.11(b). The correlation between this two optical fields according to Eq. (1) gives a flattened spectral response as shown in Fig.12. The correlation between two mismatched optical fields introduces excess loss. The reported loss penalty is less than the proposal employing MMI input. However, it is just a balance between passband width and excess loss theoretically.

Fig.11 Eigen mode of output waveguide and optical field focused at the output, (a) standard AWG, (b) AWG with tapered output ^[4]

Fig.12 Broadened passband and loss penalty for an AWG with tapered output ^[4]