In the first chapter (WDM Devices — AWG with Flat Response), the reasons for the Flat Response required, cause for Gaussian Passband, and three main passband optimization proposals are introduced in brief. This chapter is about two other passband optimization proposals.
4) Shaping of Phase Transfer Function
Let’s review the proposals of adding MMI at the input and taper at the output. The core feature is to flatten the focused optical field or the eigen mode of the output waveguide. Thus the correlation function between the two optical fields is flattened. Anyway, the correlation between two mismatched optical fields will introduce excess power loss. The more is the mismatch, the more is the power loss. The AWG designers need to balance the passband width and the loss penalty.
Mathematically, the correlation between a Gaussian field and a block-like field results in a well-flattened passband. Shaping of phase transfer function is such a proposal to obtain a focused optical field with block-like profile.
The shaping of phase transfer function is shown in Fig.13. The optical field from the input waveguide is diverged in the input star coupler and distributed into the arrayed waveguides. Fig.13(a) shows the optical field at the input and output aperture of the arrayed waveguides with dashed blue curve and solid red curve, respectively. The Gaussian-type optical field at the input aperture is split by the gaps between arrayed waveguides. Although, the profile of the segregated optical field at the output aperture is still Gaussian-type. Then the input aperture of each waveguide in the arrayed waveguides are adjusted by tapering. Those waveguides with input aperture tapered wider receive more optical power and thus the amplitudes of the optical fields they transfer are increased. Those waveguides with input aperture tapered narrower receive less optical power and thus the amplitudes of the optical fields they transfer are reduced. Thus the optical field at the output aperture of the arrayed waveguides is shaped as shown in Fig.13(b). For a standard AWG without optimization, the lengths of the arrayed waveguides are in arithmetic progression. In this proposal, the length of each waveguide is designed with minor adjustment. As shown in Fig.13(c), the waveguides numbered 33~67 and -33~-67 are superimposed with a phase shift π. Thus the optical field at the output aperture of the arrayed waveguides is obtained as shown in Fig.13(d), which is characterized by a sin(x)/x profile .
As we know, the optical fields are dispersed and focused in the output star coupler. The optical field at the image plane is the Fourier transformation of the optical field at the output aperture of the arrayed waveguides. The Fourier transformation is shown in Fig.14. The optical field at the output aperture of the arrayed waveguides has a sin(x)/x profile, whose Fourier transformation is block-like as shown in Fig.14(b).
Based on shaping of the phase transfer function, a block-like optical field with dispersion is focused at the image plane, as shown in Fig.15(b). The correlation between and the eigen mode of the output waveguide gives a well flattened spectral response, as shown in Fig.16.
The calculated 1-dB bandwidth is 57.2GHz (for 100GHz channel spacing), which is 3.3 times of the conventional AWG without optimization. However, the loss penalty is ~4dB, much more than above proposals.
5) Input with Dispersed Optical Fields
As we know, optical field at the output is the image of optical field at the input. For different wavelengths in the same channel, the image positions are dispersed as shown in Fig.4, which results in a Gaussian-type spectral response. On the contrary, the eigen mode of one output can be imaged to the input inversely. The image positions are also dispersed at the input. Thus, if we can input an optical field with dispersion, the images of different wavelengths (in the same channel) can be centered at the corresponding output simultaneously, which is expected to realize a flat spectral response.
Fig.17 is such an AWG with input of dispersed optical field. A Mach-Zehnder interferometer (MZI) is added at the input. The MZI is composed of a Y-branch, a pair of delay lines and an evanescent coupler, as shown in Fig.17(a). The MZI in Fig.17(b) includes one more evanescent coupler and delay line, just to facilitate the layout design of the device .
The two adjacent waveguides of the evanescent coupler serve as the input of the AWG. As shown in Fig.18, the MZI produces dispersed optical fields at the input of the first star coupler, where λis, λic and λil are the short, central and long wavelengths of the i-th channel. Considering wavelength λis, the optical field originating from point in Fig.17(a) reaches the input of the AWG and is split into the two adjacent waveguides of the evanescent coupler, as shown in Fig.18(a). According to the principle of the evanescent coupler, the parts of optical field in the two waveguides have a phase difference of 90º (90º vs 180º), while the optical field part between the waveguides has a medium phase of 135º. For the optical field originating from point , the phases of optical field parts in the two adjacent waveguides and between the waveguides are shown in Fig.18(b). The difference of phases in Fig.18(a) and (b) results from the delay lines. Then the optical fields at the AWG input as shown in Fig.18(a) and (b) are superimposed coherently. The parts of optical fields with synchronous phase are added constructively, while the parts with 180º phase difference are added destructively. The superimposition of the other parts with phase difference of 0~180º shows a medium effect. The superimposition of the optical fields in Fig.18(a) and (b) is shown in Fig.18(c) as the solid red curve. The optical field in the left waveguide is strengthened and that in the right waveguide is counteracted. The optical field between the waveguides shows as a side robe. For wavelength λis, the eigen mode of the i-th output is imaged at the input, which is shown in Fig.18(c) as the dashed blue curve .
For wavelengths λic and λil, the optical fields at the input are shown in Fig.18(d-f) and (g-i), respectively. The superimposition of optical fields between waveguides is strengthened for wavelength λic and the superimposition of optical fields in the right waveguide is strengthened for wavelength λil. The eigen modes of the i-th output are also imaged at the input, which is shown in Fig.18(f) and (i) for wavelengths λic and λil as the dashed blue curves, respectively.
The details in Fig.18 are rather complicated, which are summarized in Fig.19. The MZI generates dispersed optical fields at the input of the AWG, as shown in Fig.19(a). The eigen mode of the i-th output is also imaged at the input, which is also dispersed as shown in Fig.19(b). For ease of view, the optical fields of wavelengths λis, λic and λil are presented with blue, green and red curves.
According to the principle of AWG, the eigen mode of the other outputs can also be imaged at the input. The dispersion of the images is the same as that of the randomly selected i-th output. The key point is to synchronize the dispersion of the input optical fields in Fig.19(a) with the dispersion of output images in Fig.19(b), as shown in Fig.18(c), (f) and (i). What’s more, the dispersed images of the other channels need to duplicate those of the randomly selected i-th channel. In order to synchronize the dispersions of MZI and AWG, the delay lines and the evanescent coupler need to be designed elaborately.
This proposal for passband optimization introduces no loss penalty inherently, except for power loss due to minor mismatch between the input optical fields and the images of output eigen mode as shown in Fig.18(c), (f) and (i).
C. R. Doerr, et. al., from Bell Laboratories reported this proposal. The spectral response of the AWG with input of dispersed optical fields is shown in Fig.20. The sample is designed for 40 channels with spacing of 100GHz. The measured 1-dB and 3-dB bandwidth are >56GHz and >72GHz. The transmittance of all channels is shown in Fig.21. The loss of all channels is <3.5dB.
There are other proposals to introduce input of dispersed optical fields, such as first-order mode assistance method [7-8], input with a three-arm interferometer . The methods are somewhat different, while the basic idea is similar.
Let’s review above proposals for passband optimization of AWGs. The 1-st proposal employs multimode waveguides as the outputs. The passband is broadened with no loss penalty, while the application is limited due to the multimode outputs.
The (2-4)-th proposals are based on Eq. (1). Mathematically, the spectral response of an AWG is regarded as the correlation function between the focused optical field and eigen mode of the output waveguide. Flattening one of the optical field helps to broaden the spectral response, while fundamental loss penalty is accompanied. The designer need to balance the passband width and the loss penalty. The 3-rd proposal changes the eigen mode of the outputs by tapering. The 2-th proposal changes the focused optical field by MMI input. The 4-th proposal also changes the focused optical field, while it is realized by elaborate design of the arrayed waveguides to construct a special phase transfer function.
The 5-th proposal pre-disperses the input optical field with a MZI. Thus for the different wavelengths in the same channel, the images are all focused at the center of the same output waveguide. The passband is broadened with no fundamental loss penalty.
 Okamoto, K，Yamada, H , Arrayed-waveguide grating multiplexer with flat spectral response, Optics Letters, 20(1): 43-45, 1995
 C.R. Doerr , L.W. Stulz , R. Pafchek, Compact and low-loss integrated box-like passband multiplexer, IEEE Photonics Technology Letters, 15(7): 918-920, 2003
 M. Kohtoku, H. Takahashi, and T. Kitoh, et. al., Low-loss flat-top passband arrayed waveguide gratings realized by first-order mode assistance method, Electronics Letters, 38(15): 792-794, 2002
 Tsutomu Kitoh, Progress on low-loss, wide and low-ripple passband arrayed-waveguide grating, OECC2010: 70-71
Written by Zhujun Wan, HYC Co., Ltd
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