Femtosaniye lazerlerin metallerle etkileşimlerinde dalgakılavuzu davranışlarının incelenmesi
Investigation of waveguide behaviour in the interaction of femtosecond lasers with metals
Yazar: ABDULLAH KAMURAN TÜRKOĞLU
Danışman: DOÇ. DR. SELÇUK AKTÜRK
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Fizik Mühendisliği Ana Bilim Dalı
Derece: Doktora, 2012
Konu: Bilim ve Teknoloji = Science and Technology ; Fizik ve Fizik Mühendisliği = Physics and Physics Engineering ; Metalurji Mühendisliği = Metallurgical Engineering
Dizin: Dalga kılavuzları = Waveguides ; Gauss ışınları = Gaussian beam ; Lazerler = Lasers ; Malzeme işleme = Material processing ; Metaller = Metals

Özet:
Günümüzde metallerin işlenmesinde ultrahızlı lazer huzmeleri kullanılarak çok düşük boyut hassasiyetlerine erişilebilmektedir. Bu tip lazerlerde daha yüksek optik güç değerleri elde edildiğinden daha hızlı ve etkin dağlama işlemi yapılabilmektedir. Özellikle femtosaniye lazerlerin darbe süreleri, metallerin ısıl difüzyon sürelerinden çok daha kısa olduğundan, lazer-madde etkileşimi sırasındaki ısınma ve kayıplar azaltılabilmekte, yüksek kaliteli ve tekrarlanabilir mikro-işleme sağlanabilmektedir. Bu üstünlükler, femtosaniye lazerlerin mikroişlemede yaygın kullanımını sağlamış, uygulama alanı çeşitliliğini artırmıştır.Lazerle malzemelerin işlenmesi esnasında fiziksel olarak uzamsal ve zamansal çok fazla sayıda karmaşık olay meydana gelmektedir. Bu bağlamda yüksek enerjili lazer huzmelerinin metal malzemeler içerisindeki ilerleyişinin belirlenebilmesi, etkin ışık-madde etkileşimlerine yönelik, modelleme ve deneysel çalışmalarınının yapılmasını gerektirmektedir.Bu tez çalışmasında; lazer huzmeleriyle dağlama işleminde metalde ne geometride bir kovuk oluşturulduğunun önceden belirlenebilmesi için, femtosaniye lazer huzmeleri ile metallerin işlenmesi dinamiği, dalgakılavuzu davranışı etkileri hesaba katılarak, kuramsal ve deneysel olarak araştırılmıştır. Burada, literatürde mevcut çalışmaların ötesinde, metallerin lazerle dağlanması işlemiyle oluşturulan kovukların içi boş dar optik dalgakılavuzları gibi etkidikleri gösterilmektedir. Bunun için, birçok lazer darbesiyle dağlama işlem süreci bir pertürbasyon yaklaşımı ile modellenmiştir. Her gelen darbe, oluşturulan kovukta ilerlerken zayıflamakla birlikte, tabana ulaştığında hala eşik şiddeti değerini aşıyorsa kovuk derinliğinin ilerlemesine kendi katkısını yapacaktır. Dağlama işlemi ve derinliği, kovuk dibine ulaşan huzmelerin şiddeti, artık dağlama eşiği altına düşüyor olduğunda sonlanacaktır. Eşik değere inilinceye kadar etkiyen her lazer darbesinde, metal içerisinde oluşturulmakta olan kovuk, sanki bir dalgakılavuzu gibi davranarak katkısını sağlayacaktır.Bu bağlamdaki kuramsal çalışmalarda Gauss ve Bessel tipi lazer huzmelerinin, silindirik dalgakılavuzu içerisindeki karakteristik mod profili, eşleme ve zayıflama özellikleri modellenerek, metaller içerisindeki ilerleyişi sayısal olarak hesaplanmıştır. Bunun için silindirik boşluklu metal dalgakılavuzlarının desteklediği modlar bulunmuş, dalgaboyu ve kılavuz yarıçaplarına göre ilerleme sabitleri elde edilmiştir. Farklı huzme formları ve dalgakılavuzu modları için hesaplanılan eşlenme katsayılarından kılavuz içerisinde hareket edebilecekleri mesafeler hesaplanmıştır. Geliştirilen dalgakılavuzu modeli kullanılarak, metalde oluşturulacak silindirik kovukların üç boyutlu modellemesi analitik olarak gerçekleştirilmiştir.Geliştirilen modelin uygulanabilirliğini görmek üzere, hesaplamalara karşılık gelen deneyler gerçekleştirilmiştir. Deneysel çalışmalarda, merceklerle odaklanarak metal numuneler üzerine yönlendirilen darbeli femtosaniye lazer huzmelerinin deneysel ölçüm sonuçları elde edilerek, hesaplanan teorik bulgularla karşılaştırılmıştır. Bunun için, darbeli Yb-Cam femtosaniye lazer kullanılarak metal numuneler üzerinde kovuklar oluşturulmuştur. Lazerin dışarıdan tetiklenebilmesi, farklı sayıda darbelerin gönderilmesini sağlamıştır. Işık yoluna yerleştirilen polarizör ve dalga plakası optiği kullanılarak istenilen şiddette huzmeler elde edilmiştir. Lazer huzmesi, ince kenarlı ve konik merceklerle şekillendirilerek Gauss ve Bessel tipi huzme formları oluşturulmuştur. Saf bakır ve alaşım aluminyum numuneler, üç boyutta kontrole olanak tanıyan hareket istasyonuna monte edilerek, lazer huzmelerinin metalde istenilen noktalarda kovuklar oluşturması sağlanmıştır. Kovuklar, önce optik mikroskop, daha sonra taramalı elektron mikroskobu ile incelenerek dağlama eşik enerjisi değeri araştırılmıştır. Daha iyi tekrarlanabilir deneysel sonuçlar için, metal yüzeylerinde elmas zımpara ve pasta ile parlatılması ön-işlemi gerçekleştirilmiştir. Kovuk profiline ait derinlik ve çap değerleri, yüzey profilometresi ile alınan tekrarlı ölçümlerle elde edilmiştir.Ölçümler sonucunda erişilen deney sonuçlarının hesaplamalarla benzerliği, teorik dalgakılavuzu modelimizi doğrulamaktadır. Her lazer darbesinin derinlik oluşumuna katkısı ve farklı odaklama seçenekleriyle oluşan huzme şiddetlerinin etkileri kuramsal olarak modellenebilmiştir. Saydam ortamlarda çok düzgün ilerleyebilen Bessel lazer huzmesinin, metal içerisinde etrafındaki girişim halkalarının soğurulmasından dolayı kısa bir mesafe sonra zayıflaması beklenirken, metal içinde ilerleme mesafesinin önemli ölçüde arttığı belirlenmiştir. Soğurma nedeniyle oluşan zayıflama hesaplarına, saçılma ek kayıplarının da eklenmesi deneysel verilerle çok daha iyi uyumu sağlamıştır.Femtosaniye lazerle dağlama işlemiyle metallerde oluşturulan kovukların, geriden gelen lazer darbeleri için etkin bir dalgakılavuzu oluşturduğu gösterilmiştir. Farklı rejimlerdeki sonuçların karşılaştırılmasından, geliştirilen kuramsal dalgakılavuzu modeliyle dağlama eşiğine yakın enerjilerde lazerle mikroişleme sonucu elde edilen kovuk geometrilerinin etkin olarak hesaplanabildiği görülmüştür. Dalgakılavuzu etkilerine dayalı modelleme, dağlama işleminin detaylı anlaşılmasının ötesinde, işlem sonucu beklenen çıktıların tahmininde de kolay ve hızlı bir yol önermektedir.

Abstract:
Ultrashort-pulsed lasers allow very high processing quality and repeatability in precision material processing. Sub-picosecond pulse durations of these lasers are much shorter than the heat diffusion time in metals; which brings about advantages such as minimal collateral damage and high precision in ablation. Moreover, efficient and rapid ablations are easily obtained by their high peak powers of femtosecond lasers due to their low pulse periods. Those features have made a great impact on the popularity of femtosecond laser usage recently while increasing the number and variety of the applications.However, light-matter interactions during laser material processing involve complicated dynamics and therefore require detailed modelling. In this thesis, dynamics of femtosecond-laser drilling of metals is investigated both theoretically and experimentally, by taking the waveguide-like behaviors into account which has not considered in this field previously. Apart from the available literature, the drilling of metals by consecutive femtosecond pulses is modelled by an iterative waveguide approach to reveal the ablated hole geometry. The hole evolution is handled theoretically within the framework where each pulse propagated to the bottom whose energy exceeding the ablation threshold must contribute to the final hole depth. The subsequent pulses with lower energies shall have no effect on the hole shape, thereby finalizing the ablation. The ablation scheme can be improved by including absorption and scattering effects to our waveguide model. Corresponding experiments are performed to check and strengthen the validity of prescribed theory.Waveguide properties can be exploited to understand and simulate the processes in action during femtosecond-laser drilling of metals. In order to model the optical properties of laser beam in cavities, the theory of light propagation in cylindrical metallic waveguides need to be reviewed first, while including modal analysis and calculation of propagation constants. The analysis of hybrid modes becomes simpler for the case of waveguide radii which is much larger than the laser wavelength. In general, the components of the electric field inside a cylindrical waveguide is expressed in terms of different orders of the Bessel function of the first kind. This is beacuse, when a linearly polarized Gaussian beam is incident to the cavity, only hybrid modes are excited.The propagation of a laser beam through a cylindrical waveguide mainly depends on the incoming beam properties, its coupling to the guide and the guiding material itself. The relevant attenuation and phase constants were formulated. Losses in metallic waveguides occur mainly due to the partially absorbed electric fields at the sidewalls. The power coupling efficiency for each mode was calculated. Intensity variation of the wave through the hole was estimated by calculating the total loss contributed by all available excited modes inside.Effect of the laser ablation was considered from the waveguide point of view. When a laser beam is incident on a metal surface, it generates a hole with radius determined by the region in which intensity is above the threshold. High surface quality cylindrical structures generated in metals during femtosecond laser ablation also calls for taking into account the waveguide-like behaviors. Due to their high reflectivities, metallic cavities can guide light, with attenuation determined by absorptions. In particular, it was shown that cylindrical holes generated during laser ablation of metals act like hollow optical waveguides.A theoretical perturbation approach was presented to estimate ablation profiles, depths and aspect ratios. Since laser drilling of metals is generally achieved by a large number of consecutive pulses, we consider that each pulse is first guided within the cavity formed thus far, attenuated in the tapered cavity formed by the previous ones and finally, makes its own contribution to ablation at the cavity end. The pulse attenuates as it propagates while reduced intensity generates a hole with smaller radius. Since the attenuation constant is proportional to the inverse cube of the hole radius, it becomes stronger as the hole gets deeper. When the pulse fluence inside the cavity falls down to the threshold value, it is completely absorbed, hence the ablation process stops while the maximum depth is reached. After that, increasing the number of pulses further will have no effect on the hole depth.An advanced waveguide theory was used to calculate attenuation constants and to perform iterative MatLab calculations in order to model pulse-by-pulse ablation. This beaviour was investigated for both Gaussian and Bessel type beam waveforms. Aluminum and copper were used as sample media both in our theoretical calculations and in experiments in order to understand the effect of losses in the waveguides.The effect of the number of pulses and input intensity on hole depth was analyzed first. Due to the attenuation in the waveguide, when the intensity falls below to the threshold, the hole depth reaches its maximum value and stays the same regardless of the number of later-coming pulses. In addition, increasing input intensity also increases the maximum depth, as expected. It is because, threshold value will be reached deeper in the cavity at higher intensity, also as the input intensity increases, the initial hole diameter also increases and hence losses decrease.Achievable depths for different intensities were calculated for aluminum and copper. The results show that near the ablation threshold, the increase in the hole radius dominates the rise of hole depth, while for higher intensities, the depth dependence tends to be linear. It was also noted that lower ohmic losses for copper yields significantly deeper structures.The effect of the input beam size was also studied. Propagation distance through the metals were calculated for different radii of the incoming beam. As expected, beam size has a very strong effect on cavity length, due to inverse-cubic dependence of losses on cavity radius.Corresponding experiments were performed to compare the results with the theoretical findings of the model. A Yb:Glass femtosecond laser, operating at 1030 nm central wavelength was employed as the source. External triggering of the laser enabled us to apply series of pulses with adjustable numbers. The laser power level impinging on the sample was changed by means of external optics. As sample media, pure copper and industrial grade aluminum alloys were used. Surface of samples were initially polished with diamond powder. The threshold levels were initially checked by optical microscope and then by scanning electron microscopy. More accurate threshold values were determined by means of an asymptotic approach in various depth vs intensity studies.Surface profilometer was used to measure the cavity depths and profiles after ablation. Upon analyzing the effect of number of pulses on the hole depth for a fixed intensity value, the results were found to be consistent with the main result of the waveguide approach; ablation depth does not increase after a certain level, due to attenuation.Next, experiments were performed to analyze the effect of the beam intensity on the maximum depth. The dependence of the maximum hole depth on the input beam size was investigated. Lenses of different focal lengths were employed in the beam line in order to ablate different holes in aluminum. In changing lenses, laser power was adjusted to get same fluence value on the target sample.On the analysis of former theoretical calculations and the initial results by experimental approach, qualitatively similar ablation behaviors are observed. The discrepancies between can be attributed to several factors. First, attenuation is obviously further increased due to the scattering by the generated nanostructures in the cavity walls, as it was revealed in microscopy studies. So, although the initial theoretical model with only absorption losses predicted significantly deeper structures at the beginning, a better agreement was achieved upon also including the scattering losses caused by nanostructures formed on the cavity walls. Also, in most of the calculations, dielectric constant of the aluminum was taken as the pure material by using the Lorentz-Drude model, whereas the experimental sample was a commercial alloy.Calculated cross sectional profile of the ablated hole was seen to be confirmed by the experimental profiler results. Hole depths calculations for different number of pulses indicated that ablation stops after a certain distance of propagation. Experimental findings validate this result that ablation stops at a fixed depth regardless of the exceeding number of pulses. Similar qualitative agreements between theory and experiments can also be noted for beam size dependence. Verified results show that, waveguide behavior in metals is essential to consider in femtosecond-laser drilling of these materials.In conclusion, theoretical and experimental results on the analysis of waveguide behaviors during femtosecond laser ablation of metals were presented in this study. It was shown that the waveguide behavior can explain many of the ablation characteristics, including the effects of number of pulses, ablated material, incident intensity and focused beam width. Mechanisms such as evolution of the depth per pulse and the propagation of incoming pulse energy in different focusing configurations can be modelled to the practical applications.Theoretical results that are based on mode analysis of cylindrical hollow metal waveguides and iterative approach for modelling the ablation; yielded a good qualitative matching with experiments, thus supported our model. Quantitative agreements were further improved by taking the scattering losses into account. The waveguide behaviour was seen to be particularly effective at fluences close to the ablation threshold. Results show that the presented waveguide behavior in metals is not only essential for complete understanding of the interaction of femtosecond laser pulses with metals during laser ablation, but they also provide a simplified and fast way for estimation of process outcomes.