以微分近場光學顯微術重建光波導折射率分布

Reconstruction of Optical Waveguide Index Profiles by Differential Near-Field Scanning Optical Microscopy

蔡宛卲(Wan-Shao Tsai)

指導教授 ： 王維新

國立臺灣大學/電機資訊學院/電子工程學研究所/博士(2008年)

https://doi.org/10.6342/NTU.2008.01517

摘要

本論文提出以微分近場光學顯微術，來反推光波導中的折射率分布。微分近場光學顯微術係以量測微分場取代數值微分場。在反推計算中，大幅降低使用數值微分場造成的折射率分布的誤差，忠實呈現
光波導中的折射率分布，而不需使用額外的雜訊處理。
文中首先簡介近場光學顯微術，以及所改善的微分近場光學顯微術；接著介紹重建折射率的量測方法，包括稜鏡耦合量測系統、直接激發耦合量測系統等。接著介紹傳統式近場量測重建折射率的演算法，包含逆WKB 法、遞迴計算與直接反推計算，並詳述微分近場的直接反推計算。在模擬的部分，代入理論雜訊模擬量測的光場，比較重建折射率不同演算法之間的差異；模擬結果顯示，在雜訊為30dB 的情形，遞迴計算所重建出的折射率分布比直接反推計算準確。此外也以加入雜訊的方式，模擬以近場光學顯微術量測的場形，比較在重建折射率時有無微分場對於重建折射率的影響；模擬結果顯示，微分場大幅提高了所重建折射率的準確性，其折射率分布的均方根誤差為0.3150，與無微分場的結果1.2247 相比，誤差值較小。
在實驗結果方面，將所提出以微分近場光學顯微術反推光波導折射分布的技術，分別應用在一維的平面金屬擴散式波導和二維的單模光纖上面。一維的鈦金屬擴散式鈮酸鋰平面光波導在深度方向的折射率分布為漸變式，重建的折射率分布與已知的鈦擴散模型相吻合；比較有無微分場時所重建的折射率均方根誤差，分別為0.2440 與1.9143，也與模擬的誤差範圍一致。二維的單模光纖其折射率分布屬於步階式，利用其圓對稱性結構，可以用微分近場光學顯微術的技術直接重
建二維的折射率分布；同時也與在無微分場的情況下，各種對場形處
理的其他方法作比較。由重建的折射率分布看來，微分近場光學顯微
術展現了在反推計算上重建折射布分布的優勢。

關鍵字

積體光學 ； 鈮酸鋰 ； 光學波導 ； 折射率分布 ； 近場光學顯微術 ； 光纖

並列摘要

In this dissertation, differential near-field scanning microscopy (DNSOM) is proposed to improve near-field scanning microscopy (NSOM) in the reconstruction of the refractive index profiles of optical waveguides.
Differential fields are measured in the DNSOM system, which avoid numerical differentiation in the inverse calculation algorithm and lower the noises of the reconstructed refractive index profile by the numerical differential fields. The refractive index profiles of optical waveguides are truly reconstructed with measured differential fields, and no other smoothing techniques are required.
The measuring systems for the reconstruction of refractive index profiles are first introduced, which include prism coupler, end-fire coupling, NSOM, and the proposed DNSOM system. Then the algorithms for reconstructing the refractive index profile of the conventional methods are
derived, which are inverse WKB, iterative calculation, and inverse calculation. The inverse calculation algorithm with differential fields is further derived. In the simulation, noises are added in the calculated fields to simulate measured fields and to compare the reconstructed index profile with different calculating algorithm. Simulated results show that at signal-to-noise level of 30 dB, iterative calculation algorithm is more accurate then inverse calculation algorithm in the reconstruction of
refractive index profile. Furthermore, calculated fields with noises are also simulated to compare the reconstruction of refractive index profile with and
without differential fields. Simulated results show that the DNSOM system provides more accurate index profile than the NSOM system. The root-mean-square errors of the reconstructed refractive index profile with and without differential fields are 0.3150 and 1.2247, respectively.
The proposed DNSOM system is applied in both the one-dimensional planar metal-diffused optical waveguide and the two-dimensional single-mode optical fiber. The refractive index profile of the one-dimensional titanium diffused lithium niobate (Ti:LiNbO3) optical waveguide is graded-index distribution. And the reconstructed index profile is well-matched with the known Ti diffusion model. Moreover, the root-mean-square errors of the reconstructed refractive index profile with the DNSOM and the NSOM system are 0.2440 and 1.9143, respectively, which are in the same order with the simulated results. The refractive index
profile of the single-mode optical fiber is step-index distribution. For its symmetrical structured, two-dimensional refractive index profile is reconstructed by the DNSOM system. The reconstructed index profile is
also compared with other field-smoothing techniques by the NSOM system. The DNSOM system shows great advantages in the reconstruction of the refractive index profile with the inverse calculation algorithm.

並列關鍵字

Integrated optics ； optical waveguides ； lithium niobate (LiNbO3) ； refractive index profiles ； near-field scanning optical microscopy (NSOM) ； optical fiber.

參考文獻

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