Femtosecond Laser Direct Writing: Fabrication and Characterization of Waveguides and Gratings

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Acknowledgments

To Dr. Daniel Alexandre, for all the sweat and hard work in the lab, for all the frustrations, and the small leaps of joy with each success.

To Dr. Paulo Marques, for all the assistance provided, even when the time was short, and all the ingenious solutions given.

To Dr. António Pereira Leite, for the most generous help in the correction of this thesis, and all the wise advices given throughout the project.

To our physics workshop technitians, for the crucial help they gave us to upgrade our sample holder. To INESC, and all the investigators that belong to this institution that supported me in this project.

To the University of Porto, and particularly to the professors of the Department of Physics, for all the knowledge and wisdom that I absorbed from them.

To all my colleagues, that shared with me the struggle of these 5 years long years, in which many adventures were shared.

To my family, for being the ones that are always there for me.

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Abstract

Femtosecond direct writing is a revolutionizing technique that takes advantage of nonlinear absorption to achieve smaller than spot-size refractive index changes inside glasses and other optical materials, in a single step fabrication process. The present dissertation explores the basis of this technique, its implementation and results.

A review of the basic theoretical background on femtosecond direct writing is provided, with a brief analysis of the creation, propagation and interaction of high peak power femtosecond laser pulses with glasses.

The experimental setup for femtosecond direct writing created in this work, and the diverse char-acterization systems and techniques used, are presented and discussed in full detail.

The depth calibration of the damage pattern is presented and discussed, with an analysis of the eect of self focusing in the damage localization.

For a xed repetition rate of 500 kHz and 515 nm wavelength, the optimum parameters for writing waveguides were scanned in tems of average power P , waveguide depth and scan velocity.

Bragg grating waveguides were written by point-by-point femtosecond direct writing. The depen-dence on the duty cycle and writing laser polarization was studied, and the most stable gratings were found for 40% duty cycle, and parallel polarization relative to the scan direction, with grating strengths of ∼ 21 dB.

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List of Figures

1.1 [Left] Scheme of the material modication performed in the fused silica. [right] Wave-length shift observed in the interference pattern dependence on concentrations for

dif-ferent solutions. (from [20]) . . . 8

2.1 Mode-locking ultrashort pulse generation diagram. (from [23]) . . . 11

2.2 Diagram of the Chirped Pulse Amplication technique. . . 12

2.3 Autocorrelation measurement technique [28]. . . 13

2.4 Schematic of the focusing of a femtosecond gaussian beam inside a glass block with n2 refractive index. . . 14

2.5 Temporal broadening of dierent femtosecond pulses with various pulse durations ∆t, using propagation distance L inside BK7 (only GDD included in calculation). . . 16

2.6 Intensity prole of a gaussian pulse with 300 fs pulse width, and the respective wave-length shift due to self-phase modulation. . . 18

2.7 Scheme of the dierent photoionization regimes depending on the value of the Keldysh parameter. (from[40]) . . . 19

2.8 Avalanche ionization process: free carrier absorption followed by impact ionization. (from [40]) . . . 20

2.9 Schematic illustration of key steps of femtosecond-laser-induced structural change in bulk transparent materials. (a)(c) A hot electron-ion plasma is formed in the focal volume through nonlinear absorption of intense femtosecond laser pulses. (d) Depending on the amount of energy contained in the plasma, three dierent types of structural change can occur: isotropic refractive index change at low energy, birefringent refractive index change at intermediate energy, or void formation at high energy. (from [47]) . . 21

2.10 SEM images of self-organized periodic nanoplanes in the plane shown in Panel A. Panel B: E is parallel to S. Panel C: E is perpendicular to S. Nominal separation of the grating planes is 250nm. (from [50]) . . . 21

2.11 Waveguide structure of step-index optical ber. . . 23

2.12 b-v relation for modes of the step-index ber. (from [33]) . . . 24

2.13 Reectivity spectrum example. . . 25

2.14 Reectivity spectrum for two gratings with the same modulation amplitude, but rect-angular/sinusoidal shape. . . 26

3.1 Schematic of the experimental setup. . . 28

3.2 Schematic of the laser system. . . 29

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3.4 Sample 6 writing plan. . . 33 3.5 Example of damage pattern proles measured on the facet of written waveguides. The

laser was incident from the bottom . . . 34 3.6 Direct comparisson of the damage pattern observed in our system [right], compared with

the one's reported by Shane Eaton [70] [left]. Both were written with parallel polarization. 35 3.7 Experimental setup for waveguide characterization. . . 35 3.8 Calibration results. . . 36 3.9 Experimental setup for beam prole observation . . . 36 3.10 Fiber output beam image recorded on the ccd camera, using an objective lens with 60x

amplication. . . 36 3.11 Fiber output beam image recorded by the ccd camera, using an objective lens with 20x

amplication. . . 37 3.12 Experimental setup for grating characterization . . . 38 4.1 Waveguide depth (measured by the microscope observation technique) dependency on

the objective lens position, and expected values calculated by light refraction. . . 41 4.2 [Left] Waveguide depth (measured by the microscope technique) dependency on the

objective lens position for waveguides written at variable power and depth. [Right] Waveguide depth shift dependency on the average power for dierent depths, estimated by the objective lens displacement. . . 41 4.3 Experimental results for insertion loss measured for waveguides written at dierent

powers and depths. The set of dierent gures corresponds to dierent writing velocities [50, 100, 150, 200, 250, 300, 350] µm/s. . . 42 4.4 Insertion loss measured for waveguides written parallel and perpendicular to the scan

direction (piled and free). . . 43 4.5 Insertion loss measured for waveguides written parallel and perpendicular to the scan

direction (piled and free). . . 44 4.6 Mode eld diameter on x and y coordinates for waveguides written parallel and

perpen-dicular to the scan direction (piled and free). . . 44 4.7 Calculated values of Coupling Loss and Propagation Loss. . . 45 4.8 Inverted transmission spectra measured for the perpendicular polarization type of

writ-ten gratings, with an increasing duty cycle from left to right (40, 50 and 60%). . . 46 4.9 Inverted transmission spectra measured for the parallelly written gratings, with

increas-ing duty cycle from left to right (40, 50 and 60%). . . 46 4.10 Grating strength and peak localization dependance on duty cycle, for the gratings results

presented in gures 4.8 and 4.9. . . 47 4.11 Insertion loss measured for the gratings fabricated with parallel and perpendicular

po-larizations. The plotted lines correspond to the values of insertion loss measured for the simple waveguides written under same conditions. . . 48 4.12 Mode eld diameter on x and y coordinates for waveguides written parallel and

per-pendicular to the scan direction. The respective colored lines plotted correspond to the MFD for the waveguides written under same conditions. The black line corresponds to the MFD of the SMF-28 used in the measurements. . . 48

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4.13 Calculated values of Coupling Loss and Propagation Loss for BGW written with parallel and perpendicular polarization. The lines plotted correspond to the values of insertion loss measured for waveguides written under the same conditions. . . 49 B.1 Front panel and block diagram of the Labview program created for grating

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Chapter 1

Introduction

Since the early ages of the Humanity, light has been one the most important tools used over the centuries for protection and communication.

Nowadays, optical ber technology took control of most of the communication systems worldwide, as it oers lower power losses and larger bandwidth. Optical bers can also be used as sensors of temperature, pressure, and even gas detection, among other physical or chemical parameters.

Another important discovery was the invention of the laser in 1960 [1], in an accumulated eort after Albert Einstein's proposed theoretic foundation of light amplication by stimulated emission of radiation, in 1917. The laser technology oers sources with very high intensity and coherence which led to whole new areas of study, such as spectroscopy and interferometry, and also to the discovery of interesting phenomena, such as the Kerr eect [2] and frequency generation [3].

A new step was the development of short pulsed lasers, starting with DeMaria et al. demonstrating, in 1966, the rst picosecond mode-locked laser [4]. The short laser pulses unique characteristics, such as high peak intensity, short pulse duration and high repetition rate, made them nd a large set of applications, such as in molecular dynamics [5], high bit rate optical communications [6], optical coherence tomography (OCT) [7], supercontinuum generation [8], and micromachining [9].

The availability of ultra-short laser pulses opened up new possibilities in the eld of materials processing. In particular, the development of laser direct writing techniques useful for micro/nano fabrication of optical devices.

Refractive index modication

Hill et al. [10] demonstrated the rst permanent and controlled use of laser induced refractive index changes to fabricate Fiber Bragg Gratings (FBG) in a Germanium doped optical ber using 488 nm cw laser light. This rst technique had the disadvantage that the Bragg wavelength was directly imposed by the laser wavelength.

Later, Meltz et al. [11] demonstrated the fabrication of FBGs by exposing transversely the same type of germanium doped ber to an interference pattern, relying on a single UV photon absorption process. However, this method requires some sort of direct linear absorption of laser light and therefore, can only be applied to a restrict set of materials, with dopants or intrinsic defects needed for laser light absorption. Another issue is that this technique's spatial control is limited to the diraction limit of the laser beam.

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possible to achieve nonlinear multiphoton absorption in materials that would otherwise be transparent, due to their high energy band gap. Another advantage is that, due to the nonlinearity of the absorption, it can occur only in a fraction of the laser beam width, where the intensity is high enough [12]. This marks a new milestone towards 3D writing of integrated optical circuits with high resolution [13].

The region of damage created by this nonlinear interaction locally modies the chemical properties of the glass, so that it can be selectively removed by wet etching using a solution of etchants such as hydrouoric acid (HF) [14]. This nding opened the doors for hybrid applications such as lab-on-a-chip devices [20].

Most methods for creating optical circuits and devices use planar geometry, and so for creating 3D structures there is the need for multi-step fabrication schemes. With this ultrashort laser pulse direct-write technique, in-depth single-step fabrication of optic circuits can be achieved, and the same setup can write also microuidic channels, without any deposition process [15].

Another advantage of this technique is the possibility to use a wide range of glasses, such as fused silica, uoride phosphate, and Foturan (Schott). Fused silica, besides having low loss and being chemically inert, has the advantage, in comparison to the other glasses, of being the material used for low-loss optical ber fabrication. Therefore, good matching of physical parameters (such as refractive index) is garanteed.

However, planar lightwave circuits (PLC) technology [72] still show the lowest propagation loss 0.05 dB/cm and minimum bend radius of 2 mm. In fused silica the induced refractive-index change is relativelly low ∆n ∼ 0.01 which imposes limits to the minimum bend. The best bend radius of 15 mmwas found for a high NA = 1.25 oil-immersion objective [73], but at the cost of higher losses of 0.6 dB/cm. The lowest propagation losses reported are ∼ 0.1 dB/cm for a large variety of materials [74].

This technique had a rapid grougth in the past years, with several applications emerging such as waveguide retardes[19] and directional couplers[16] emerging.

The precision of this method enables direct writing of 1st order gratings by point-by-point inscrip-tion. Phase shifted [17] and Chirped [18] bragg gratings are among the recent applications.

In gure 1.1 we have an example of the potential applications from this technique. R. Osellame et. all [20] used a femtosecond laser do directly write a Mach-Zehnder interferometer in a fused silica sample. With the same laser, a microchannel was created by rstly damaging the material with the femtosecond laser, and then etching with HF acid.

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Figure 1.1: [Left] Scheme of the material modication performed in the fused silica. [right] Wavelength shift observed in the interference pattern dependence on concentrations for dierent solutions. (from [20])

One of the arms of the interferometer goes through the microchannel, changing the optical path. The spectrum observed will shift with the change of refractive index of the material that is owing inside the microchannel, and we can see in gure 1.1 that the fringes shifts linearly with the concentration of diferent solutions.

Objectives

The aim of this dissertation is to study the femtosecond direct writing technique, and its implemen-tation in fused silica samples. We will start by doing an optimization of parameters to nd the best fabrication conditions, and with this parameters take the advantage of this techniques precision to write rst order gratings.

Structure of thesis: description of chapter contents and their interconnection This thesis is divided in ve chapters, which are shortly presented here.

After this brief introduction, chapter 2 presents the background review necessary to introduce the reader to the area of femtosecond direct writing. In section 1, the major properties of ultrashort pulses are explored, and mode-locking and chirped pulse amplication techniques are analyzed. Finally we introduce the types of lasers mostly used in femtosecond direct writing systems, and discuss the possible methods used to characterize ultrashort pulses. In section 2 the propagation and focusing of gaussian pulses is analyzed, rst with basic linear propagation, but then analyzing the possible eects of pulse broadening and nonlinear propagation eects, such as self focusing and self phase modulation. Section 3 focuses on the interaction of femtosecond laser pulses with glass materials. The principles of photoionization and plasma formation are addressed, and the damage pattern and refractive index change origin discussed. Finally, section 4 introduces the principles of waveguide and gratings theory. Chapter 3 presents the femtosecond laser writing system created in this project (section 1), with full detail on the components chosen, system alignment and fabrication plan. Section 2 addresses the dierent systems used to analyze the waveguides and gratings written in this work. Microscope observation, insertion loss measurement, mode prole imaging and grating spectra measurement are analyzed.

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In Chapter 4 the results obtained for the dierent waveguides and gratings written are presented and discussed. Section 1 shows the results obtained for the waveguide depth control calibration and parameter optimization. Vertically piled waveguides are compared with single ones, for dierent writing polarizations. In section 2, spectra and losses of gratings written by point by point method with variable duty cycle and writing polarization are analyzed.

In chapter 5 a resume of the main results achieved is presented, and the proposal of future for new developments is advanced.

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Chapter 2

Background

This chapter introduces the background of physical concepts and techniques relevant to the ultrashort laser pulse technique employed in direct writing of optical devices. The presentation is necessarily synthetic, and addresses the most relevant aspects of short laser pulse production and propagation, as well as their interactions with dielectric materials. Throughout the chapter we try to drive the theoretical discussion close to the problematic of this work by calculating the inuence of the several phenomena under conditions close to the ones used, resulting from focusing on bulk fused silica.

2.1 Ultrashort laser pulses: Generation and Characterization

In this section the generation of ultrashort laser pulses, their most important properties and their characterization are addressed.

2.1.1 Pulse duration, spectral Bandwidth, Power and Energy

The pulse duration τp can be dened in various ways. For short pulses, gaussian and squared secant

are the most widely used ts to the envelope, and the duration of a pulse is generally dened by the full-width half-maximum (FWHM) of the intensity t. If we transform the pulse temporal shape to the frequency domain, we nd that the pulse width increases with the decrease of the pulse duration. In fact, a perfect pulse is spectrally limited by the relation τp∆f ≥ K, with K depending on the t

used (0.441 for gaussian and 0.315 for sech2_)[21].

Considering now a train of independent pulses equally spaced in time by ∆t (with repetition rate dened as R = 1

∆t), if the average power is given by ¯P, then the energy of each pulse is easily given by

Ep = ¯ P

R. If we consider a gaussian pulse, it can be shown that the peak power of a 2D gaussian pulse

is simply given by Pp = 2 ¯P [22]. Another interesting quantity is uence, which is dened as

F = Ep· R

π · v · w (2.1)

It is useful to calculate these properties for typical parameters used in this work. Using 300 fs as pulse duration, repetition rates on the order of 500 kHz and average power of 100 mW , we nd that the energy of each pulse is 0.2µJ and the peak power is around 1.3MW .

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2.1.2 Mode Locking

The mode locking technique allows the generation of ultrashort laser pulses, by periodically changing the gain/loss inside the laser cavity resonator [23]. We can classify mode-locking techniques as passive and active (see gure 2.1).

Figure 2.1: Mode-locking ultrashort pulse generation diagram. (from [23])

In active mode-locking, an external signal controls an optical loss modulator, often using the acousto-optic or the electro-optic eects, modulating the loss inside the cavity. The cavity parameters are chosen so the resonator overall gain is only positive when the modulator loss is at its minimum. The modulator frequency is matched with the cavity round-trip time tr, so that a single pulse resonate

inside the cavity, and a train of pulses with pulse frequency f = 1

tr is formed at the output.

In passive mode locking, the external modulation is replaced by a saturable absorber. Considering a uctuation peak (given by a noise spike or, if needed, some articial change in the cavity) in the continuous laser beam, if its peak power is sucient to saturate the absorber, the induced loss is lower than for the rest of the temporal strecht of the beam. If we target this loss to be around the threshold of the cavity gain, at each round trip this uctuation will gain energy, with the rest of the beam being absorbed. A train of light pulses rises from this interaction, with the same pulse rate of the active mode locking, and a pulse width that is inversely proportional to the pulse spectral width [24].

2.1.3 Chirped pulse amplication

With the mode locking based techniques we are able to create trains of very short pulses (down to f s) with very high repetition rates (up to several GHz with harmonic mode locking [25]). However,

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this comes at the cost of having low pulse energy. To tackle this problem, chirped pulse amplication (CPA) is widely used in order to amplify the ultrashort pulses (see gure 2.2).

Figure 2.2: Diagram of the Chirped Pulse Amplication technique.

The original laser pulse is temporally stretched through a highly dispersive medium, often by using a grating pair, that separates in time the dierent frequencies [26]. This translates into a high temporal widening of the pulse (∼ 100 ps) [27], which is required for decreasing the laser peak power by 3 orders of magnitude, so that it can be amplied while avoiding the nonlinearities and damage inside the amplication medium.

The laser beam passes (often several times) through an amplication medium, with the energy of the pulses increasing by 6 to 9 orders of magnitude. After amplication the laser pulse is recompressed, using a grating compressor, so that we get the original laser pulse temporal width, but with much greater peak power and pulse energy.

2.1.4 Types of lasers

Two types of lasers are most used in femtosecond writing setups: Ti-sapphire and Ytterbium amplied ber lasers. The Ti-sapphire oscillator can reach a repetition rate of 80 MHz, but this comes at the cost of having low pulse energy, so a regenerative amplifying system is often used. The CPA system gives higher power, but again this comes at a cost: the repetition rate is limited to ∼ 1−100 kHz. The pulse duration for these systems can be down to a few dozens of fs, and the fundamental wavelength is tunable (720 − 850 nm) due to the T i3+ _{ion large emission bandwidth.}

Fiber lasers oer an all ber approach alternative to the solid state lasers. The CPA system uses a ber stretcher (that can use, for example, a chirped Bragg grating), and the amplication is achieved by using an Ytterbium doped ber. Recent developments in the ber structure enabled these lasers to reach high output powers (∼ 10 W ). The pulse duration is around 300 fs, longer than the Ti-sapphire pulses, the center wavelength is 1030 nm, and the repetition rate can be up to 25 MHz.

2.1.5 Characterization of ultrashort pulses

With pulses on the femtosecond order of duration, normal optoelectronic methods to measure pulse parameters are not fast enough. The general approach is to use the autocorrelation technique

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Figure 2.3: Autocorrelation measurement technique [28].

As we can see in gure 2.3, the ultrashort pulse is split in half, and on one of the split pulses a time delay is produced, by forcing a greater propagation distance. The two pulses are combined in a second harmonic generation (SHG) crystal. The intensity of the generated beam, of frequency 2ω, is proportional to the product of the two signal intensities, I (t) I (t − τ). If we sweep now the time delay, and register the dierent intensity products we can get the intensity autocorrelation of the pulse, A (τ ) =´_−∞+∞I (t) I (t − τ ) dt. From A (τ), the I (t) can be recovered.

By using a spectrometer instead of a power meter, the spectrally resolved autocorrelation can be measured, and the beam electric eld retrieved. This technique is called Frequency-Resolved Optical Gating (FROG) [29]. More recently, the method of dispersion-scan [30] revolutionized the measurement of few cycle laser pulses, due to its simplicity compared to the FROG method: there is no need for beam splitting, and it takes advantage of the pulse compression stage to use it as a diagnostic tool.

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2.2 Propagation of Gaussian laser beams

In many applications, and in direct writing specically, the laser emission should display excellent spa-tial coherence. Proper design of the laser leads usually, or desirably, to the output being a fundamental spherical gaussian beam. The fundamentals of linear and nonlinear propagation of these beams are analyzed.

2.2.1 Linear propagation

In order to reach an intensity high enough to have optical breakdown inside a glass, femtosecond laser pulses are focused with an objective lens. If we neglect spherical aberration and nonlinear eects, we can approximate the beam amplitude prole by solving the paraxial wave equation, obtaining as solution the spherical beam [24]:

u (x, y, z) αe−jk x2+y2 2q , (2.2)

where q(z) is the complex beam parameter of the gaussian beam, dened as 1 q(z) = 1 R (z)− iλ0 πnω2_(z), (2.3)

where R (z) is the radius of curvature of the wave phase front, and ω (z) the beam radius (dened at e−2 of the axial intensity). One of the main advantages of this notation is that we can use the ABCD matrix from linear optics very simply, by applying the transformation

q (z) = Aq1+ B Cq1+ D

, (2.4)

to calculate q (z), where q1 is the complex beam parameter at the input of the ABCD matrix

system. The overall ABCD matrix of an optical system can be constructed by multiplying consecutive basic matrices, such as:

thin lens: " 1 0 −_f1 1 # ; propagation: " 1 L_n 0 1 # ; refraction: " 1 0 0 n1 n2 # .

Let us consider now the problem of focusing a femtosecond gaussian beam inside a glass block with planar interface (see gure 2.4).

Figure 2.4: Schematic of the focusing of a femtosecond gaussian beam inside a glass block with n2

refractive index.

By simple use of Snell's law, we see that the axial distance z0 _{inside the material is given by}

z0 = n2z n1 s 1 +n 2 2− n21 n2 2 R z 2 , (2.5)

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and thus depends on the numerical aperture R z.

If we use the paraxial approximation (R z) we have that z0 = n2z

n1

. (2.6)

Applying the matrices for this system we can calculate the beam spot size at the paraxial focal position z0_:

ωf ocus =

λf πω0

, (2.7)

where ω0 is the beam radius before focusing. In equation 2.7 we can see that the spot size inside the

material is the same as if it was focused in air. Calculation of the Rayleigh range (the position at which the beam radius is ωzR =

√

2ωf ocus), using the same method, shows that it scales by the index

of refraction: z_R0 = nπω 2 0 λ0 = nzR. (2.8)

For an objective lens, we can relate its numerical aperture with the focal length as N A = n0sin (θ) =

ω p

ω2_{+ f}2. (2.9)

Substituting in the beam spot size we get: ωf ocus= λ π √ 1 − N A2 N A (2.10) and z0_R= nλ π 1 − N A2 N A2 (2.11)

For a numerical aperture of NA = 0.55 and λ = 515 nm focusing in fused silica, we have ωf ocus=

0.25 µmand z_R0 = 0.55 µm

2.2.2 Temporal broadening of femtosecond pulses

The spectral phase of a laser pulse can be described by a Taylor expansion around the pulse center frequency ω0 [31]: φ (ω) = φ (ω0) + φ 0 (ω0) (ω − ω0) + 1 2φ 00 (ω0) (ω − ω0)2+ 1 6φ 000 (ω0) (ω − ω0)3+ · · · (2.12)

After propagation over a distance L inside a dispersive glass, this spectral phase is: φ (ω) = ω

cn (ω) L. (2.13)

We can now relate the group delay dispersion, GDD ≡ φ00₌ d2_φ

dω2, to the glass dispersion properties,

obtaining φ00= λ 3_L 2πc2 d2n dλ2. (2.14)

Using this relation, we can calculate the group delay dispersion by evaluating the derivative using the Sellmeier equation [32] for the given glass; for example, for silica [33] a1 = 0.6965325, a2 = 0.4083099,

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a3= 0.8968766, b1= 4.368309Ö10=3, b2 = 1.394999Ö10=2, b3 = 9.793399Ö101: n2 = 1 + a1λ 2 λ2_{− b} 1 + a2λ 2 λ2_{− b} 2 + a3λ 2 λ2_{− b} 3 . (2.15)

This dispersion in the frequency domain corresponds to a temporal broadening of the laser pulse. For a gaussian shape with initial pulse duration ∆t (dened by FWHM in intensity), and neglecting higher order dispersion terms, it can be proven [31] that the output pulse duration is

∆tout = s ∆t2₊ 4ln (2)φ 00 ∆t 2 . (2.16)

In gure 2.5 we have an example of the broadening in time for a 5 mm propagation distance inside Corning C0550 glass, which has a GDD value of 138 fs2_/mm_.

Figure 2.5: Temporal broadening of dierent femtosecond pulses with various pulse durations ∆t, using propagation distance L inside BK7 (only GDD included in calculation).

We can see that for pulses longer than 100 fs the broadening is below 1%, even after a propagation length of 5 mm. On the other hand, this broadening is critical for pulse lengths below 50 fs. For very short pulses, the eect of higher-order terms should be included.

In the case of the laser system used in this project, ∆t ∼ 350 fs. Consequently, the temporal broadening is negligible.

2.2.3 Nonlinear Propagation

When high peak power light pulses propagate in a dielectric material, its response needs to be described by expressing the dielectric polarization as a power series expansion on the electric eld:

˜ P (t) = 0 h χ(1)E (t) + χ˜ (2)E˜2(t) + χ(3)E˜3(t) + · · · i . (2.17)

For amorphous glasses, which present inversion symmetry, χ(2) _{= 0}_{. Leaving out higher orders in}

the expansion of equation 2.17, we have: ˜ P (t) = 0 χ(1)+3 4χ (3)_|E|2 ˜ E (t) = 0χeE (t) .˜ (2.18)

Equation 2.18 shows that the light intensity I = 1 20n0c E (t)˜ 2

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eective electric susceptibility χe .

The refractive index can then be calculated by computing n =√r=

p

1 + χe = n0+ n2I. (2.19)

We then nd the linear refractive index n0 =

p

1 + χ(1) as in linear propagation, and the nonlinear

refractive index:

n2 =

3χ(3) 40cn2₀

. (2.20)

This nonlinear refractive index has units of inverse of intensity. In most materials this coecient has a positive value, and for transparent crystals and glasses n2 varies from 10−16 to 10−14cm2/W.

For fused silica this value is about ∼ 3 × 10−16_cm2_/W_{, depending on both the wavelength and the}

pulse width [34, 35]. In air this refractive index is on the order of ∼ 3 × 10−19_cm2_/W _[36].

Self Focusing

If we think now of a high power gaussian beam transverse intensity distribution I (x, y), it will cor-respond to a spatial pattern of this refractive index, n (x, y) = n0 + n2I (x, y). Since the power at

the axis of the beam is greater than on its wings, and most materials have positive n2, we have a

distribution of refractive index that is equivalent to a positive lens. This results in self focusing of the beam. The strength of self-focusing depends only on the peak power [37]: if we change the beam radius to 2ω0, then the intensity will decrease to I₄0, and the refractive index changes to ∆n = n2₄I0; but the

equivalent self-focusing lens area increases by a factor of 4, so one eect compensates the other. The critical power for self-focusing is [21]:

Pc=

3.77λ2 8πn0n2

. (2.21)

If a pulse reaches this critical power then the collapse of the pulse is predicted. For fused silica, n0 = 1.45and n2= 3 × 10−20 m2/W. So, for λ = 515 nm, the critical power is ∼ 0.78 MW.

At high intensity, the laser beam electric eld can ionize the medium, thus creating a plasma in the high intensity region. When the intensity is sucient for nonlinear ionization to occur, the plasma created modies the refractive index according to

n = n0− N 2n0Nc , (2.22) where Nc= ω 2 0me

e2 is the plasma density.

This corresponds to the symmetric situation of self focusing: the plasma acts as a diverging lens [38]. When the two eects are in balance this leads to lamentary propagation, which is undesirable since it results in an elongated pattern of the refractive index. To avoid this eect, waveguide fabrication uses microscope objectives for achieving the necessary intensity for optical breakdown, but using powers P Pc.

Self-Phase Modulation

With high energy ultrashort pulses, we have the self focusing equivalent eect in time. The refractive index quickly changes over time, and so the beam experiences a time-dependent phase:

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φ (t) = k0[n0− n2I (t)] L.

By examining the instantaneous frequency ω (t) = dφ(t)

dt , we can see that at each point in time the

pulse will experience a frequency shift that will depend on the intensity derivative: ω (t) = ω0− n2

dI (t) dt k0L.

Considering now the extreme case of propagating a gaussian beam with parameters close to the ones used in this work, for a propagation of 1.5mm inside fused silica with the focus minimum obtained for a objective lens with 0.55 numerical aperture (∼ 0.3µm), self phase modulation accurs as shown in gure 2.6.

Figure 2.6: Intensity prole of a gaussian pulse with 300 fs pulse width, and the respective wavelength shift due to self-phase modulation.

As can be seen in gure 2.6, the pulse develops positive chirp, and new frequencies are created: in the front of the pulse, the intensity slope is positive and so we have red-shift; at the end of the pulse the intensity decreases and so there is a blue-shift. The wavelength shift is not linear, having two maxima, but if we consider the central lobe around these maxima [−150, 150] fs, we can approximate the change to a linear chirp.

The spectrum of the pulse is consequently broadened, and although this does not aect the pulse temporal envelope, the broader spectrum can be exploited to generate even shorter pulses.

The maximum wavelength shift obtained for this extreme case is around 2×10−7_pm_{, showing that}

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2.3 Interaction of femtosecond laser pulses with transparent materials

Lasers working in the visible or near-infrared spectral regions do not emit photons with sucient energy to be linearly absorbed by large band-gap dielectrics. In order to have valence electrons transferred to the conduction band of the material, non linear photoionization is necessary.

2.3.1 Photoionization

There are two processes, multiphoton absorption and tunneling ionization, that compete with each other, and may dominate the photoionization process, under certain conditions of the incident beam.

Under multiphoton ionization, we have m photons such that they together possess an energy useful to bridge the material band gap:

mhν > Eg, (2.23)

where Eg is the band gap energy and ν is the laser frequency. In the region of high frequencies (but

lower than hν = Eg ) and low laser photon energy, this process dominates. But when we have a high

laser beam intensity, the electric eld distorts the band structure, so that tunneling photoionization occurs (see gure 2.7).

These two processes can be treated under the same theoretical framework as shown by Keldysh et al. [39]. The transition between these processes can be described by the Keldysh parameter

γ = ωp2m

∗_E g

eE , (2.24)

where m∗ _{and e are the eective mass and charge of the electron, and E is the amplitude of the}

laser electric eld. Depending on the Keldysh parameter, we will have photoionization by tunneling (γ < 1.5), by multiphoton (γ > 1.5), or an intermediate regime (γ ∼ 1.5).

Figure 2.7: Scheme of the dierent photoionization regimes depending on the value of the Keldysh parameter. (from[40])

2.3.2 Avalanche ionization

Electrons in the conduction band may absorb energy by free carrier absorption until they have enough energy to promote another electron from the valence band to the conduction band, by impact ionization; this process can occur again for the two resulting conduction band electrons, and so on, producing an electron avalanche (see gure 2.8).

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Figure 2.8: Avalanche ionization process: free carrier absorption followed by impact ionization. (from [40])

Under the avalanche ionization regime, the electron conduction band density N changes according to

dN

dt = αIN, (2.25)

where I is the laser beam intensity, and α is the avalanche ionization coecient [41]. For avalanche ionization to occur we need a minimum number of electrons in the conduction band, and the photoion-ization processes presented above can work as seeds for the avalanche ionphotoion-ization.

2.3.3 Plasma formation

Ultrafast pulses on the femtosecond timescale are shorter than the electron-phonon coupling time (∼ 1ps), and so the laser pulse will end before free electrons can transfer their energy to the lattice [42]. This enables the growth of the electron population in the conduction band, seeded initially by the photoionization processes, and its subsequent exponential growth through avalanche ionization. This creates a plasma inside the focal volume which oscillates at a frequency ωp given by

ωp =

s e2_N

0me

, (2.26)

where e and me are the charge and the mass of the electron, 0 is the vacuum permittivity, and N is

the density of free electrons.

As we can see by equation 2.26, as the density of free electrons increases, so does the plasma frequency. This will go on until the plasma frequency reaches the laser frequency @ N ∼ 1021_cm−3

, when the wave eld and the plasma enter in resonance with each other. This leads to absorption by the plasma of most of the light beam energy through free carrier absorption [40]. When the number of carriers reaches a critical value, we have optical breakdown of the material. The typical intensity threshold for optical breakdown of most materials, using femtosecond laser pulses, is around 1013

W/cm2 _[43].

2.3.4 Damage and Modication of dielectrics

The rst discovery of femtosecond laser induced refractive index modication in glass, by Davis et al. in 1996 [44], led to much research with a wide variety of glasses and laser exposure conditions.

The observed eects can be organized in three basic types of structural changes: isotropic refractive index change; formation of nanogratings and consequent birefringent refractive index change [45]; and void formation due to micro explosions [46].

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Each type of structural change is inuenced not only by the exposure parameters (energy, pulse duration, repetition rate, wavelength, beam polarization, focusing numerical aperture, and scan speed) but also by the material properties, such as band gap energy and thermal diusivity coecient. In fused silica, these three eects can be reached by changing the pulse energy and its duration [47, 48] (see gure 2.9).

Figure 2.9: Schematic illustration of key steps of femtosecond-laser-induced structural change in bulk transparent materials. (a)(c) A hot electron-ion plasma is formed in the focal volume through nonlin-ear absorption of intense femtosecond laser pulses. (d) Depending on the amount of energy contained in the plasma, three dierent types of structural change can occur: isotropic refractive index change at low energy, birefringent refractive index change at intermediate energy, or void formation at high energy. (from [47])

In the intermediate energy region, we have a birefringent modication with the formation of nanogratings (see gure 2.10). These sub-wavelength patterns can be observed by selective etching with hydrouoric acid [49]. The observed grating period is proportional to the laser wavelength, following roughly the trend Λ = λ

2n. The grating planes are oriented perpendicular to the laser polarization.

Figure 2.10: SEM images of self-organized periodic nanoplanes in the plane shown in Panel A. Panel B: E is parallel to S. Panel C: E is perpendicular to S. Nominal separation of the grating planes is 250nm. (from [50])

The mechanism for the formation of nanogratings is not yet fully understood. Shimotsuma et al. [51] based the explanation on an interference of the incident light eld with waves in the induced plasma. Since then, several models have been proposed [52, 53, 54], with none providing a full explanation of the dierent parameters changes.

At high pulse energies, with peak intensities of ∼ 1014_W/cm2_{, the pulse energy is well above the}

threshold for material modication, and the size and energy of the plasma increases. With sucient energy, resonant ion shielding can be reduced, leading to coulomb repulsion between ions, which forms localized voids [46]. By increasing the density around it, the hollow void is surrounded by a shell of higher refractive index.

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be attributed to laser-induced color centers. Saliminia et al.[55] observed photo-induced absorption peaks at 213 and 260 cm-1_{. However, both centers were completely erased after annealing at 400} ◦_C,

although waveguiding behavior was still observed up to 900 ◦_{C. More recent observations of Raman}

spectra sustains the view that the refractive index modication is due to densication [56]. This is attributed to localized melting and rapid resolidication of the glass, freezing the high temperature state [57].

This is the useful regime for typical writing procedures employed to produce integrated optical devices by direct writing.

2.3.5 Wavelength Optimization

In early experiments, when femtosecond laser writing was tried in fused silica using infra-red wavelength ∼ 1045 nm, only weak and irregular damage tracks were observed for the wide range of exposure conditions equivalent to the ones commonly used successfully with other glasses. By employing the laser second harmonic this problem was tackled, with smooth and low loss waveguides created.

The second harmonic, at 515 nm, provides a 4-fold smaller spot-size, and so even considering 50% loss in the conversion, we have twice the uence (see eq. 2.1). This represents a considerable advantage for delivering sucient energy for refractive index modication. More recently, waveguides were written in fused silica with 1045 nm infra-red light, but still showed weak refractive index contrast and irregular morphology [87].

2.3.6 Repetition Rate

Comparing the interaction of ultrashort laser pulses with dierent pulse repetition rates, two basic regimes arise. For low repetition rate lasers, the energy deposited by each pulse is thermally diused in the material before the next pulse arrives. For high repetition rates (above 200 kHz [80]), there is accumulation of energy from one pulse to the next one, with an accumulation of heat in the focal volume. In this regime the size of the melted volume depends on the number of pulses delivered. However, this cumulative heating eect was much more dicult to nd in fused silica. By comparing with borosilicate glass (Corning 1737F), for which heat accumulation is well reported in the literature [77, 80], we see that the 9.1 eV band gap of fused silica is more than twice that of borosilicate glass. In fact, a twofold higher absorption was observed for borosilicate glass under the same uence [78, 73]. Also, the melting point of fused silica is 1800 ºC, 1.5 fold higher than that of borosilicate, making it more dicult to achieve melting temperatures through heat accumulation. With a combination of tightly focusing and 26 MHz repetition rate, heat accumulation was possible [88], but only nonuniform damage was observed.

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2.4 Waveguide theory

Two basic types of waveguides were used in the project: optical bers and three dimensional written waveguides. The optical bers used were standard single-mode bers and polarization maintaining bers. Gratings, written by the point-by-point technique, were also produced with the ultrashort laser pulses.

The text below summarizes the fundamentals of these optical waveguides. 2.4.1 Cylindrical Optical Waveguides

Let us consider a cylindrical optical waveguide, with core radius a and n0 refractive index, and cladding

radius b and n1refractive index (see gure 2.11). Most bers have some refractive index prole function

more complex than the single step case, but this simple analysis is useful to give light to the basic propagation aspects.

Figure 2.11: Waveguide structure of step-index optical ber.

In general, b a and we can assume the cladding to be innite. Since this problem has cylindrical symmetry, it is useful to express the wave equation in cylindrical coordinates (with r as radial distance, φ as azimuthal angle and z as the axial position). If we suppose that the index contrast is small

n1

n0 ∼ 1 then the Maxwell equations can be simplied, and a scalar Helmholtz equation is applicable:

∂2U ∂r2 + 1 r ∂U ∂r + 1 r2 ∂2U ∂φ2 + ∂2U ∂z2 + n (r) 2_k2 0U = 0. (2.27)

We are looking for guided wave solutions with a propagation constant β in the z direction,

U (r, φ, z) = u (r) e−jlφe−jβz, l = 0, ±1, ±2. (2.28) If we compute the solutions that converge to 0 when r → ∞ in the cladding, and do not diverge at r = 0in the core, we nd that they are given by

u (r) α    Jl(kyr) , r < a Kl k0yr , r > a , (2.29)

where Jl(u) are Bessel function of the rst kind, and Kl(u) are modied Bessel functions of the

second kind. And the dimensionless parameters u = kyr = rpn21k02− k2z and w = k0yr = rpk2z− n22k20.

For the fundamental mode (l = 0), the Gaussian distribution is widely used as an approximation to the Bessel function solution. The mode propagates along the ber with k0n1 < kz < k0n0, and so

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it propagates with an eective index that is limited between the core and cladding indices, given by ne= k_kz₀. Two important normalized parameters are the propagation constant b = a

r n2 ef f−n 2 0 n2 1−n20 and the normalized frequency ν = ak0pn21− n20.

Applying the appropriate boundary conditions to the problem (continuity of the tangential compo-nents of the−→E ,−→H elds), it represents that u (r) must be continuous and have a continuous derivative at r = a; we get the eigenvalue equation [33]:

Jm(u)

uJm−1(u)

= Km(w) wKm−1(w)

. (2.30)

Using this equation we can calculate the possible w and u values for each LPml mode. Using

the relations υ2 _{= u}2_{+ w}2 _{and b =} w2

w2_+u2 we can calculate the dispersion relation for the dierent

modes. We can see in gure 2.12 that the propagation constant b is only positive above a minimum ν value (except for the fundamental mode). Indeed, given the waveguide parameters (refractive indices, working wavelength, and core radius) the υ parameter is xed, and the propagated modes are the ones that have non-zero propagation constant value. From this simple analysis we can see that for υ < 2.405 we have single mode guiding. There is polarization degeneracy, i.e., each mode actually corresponds to weakly linearly polarized modes in the two orthogonal transverse directions (thus LPml notation).

Figure 2.12: b-v relation for modes of the step-index ber. (from [33]) If we consider an elliptical core, with ellipticity = ax−ay

ax , a suitable analysis is necessary. In this

case there is no polarization degeneracy, and two orthogonally polarized eigen modes can be found which propagate with dierent eective indices. Using perturbation method analysis, the geometrical birefringence (dened by B = nef f,1− nef f,2= kz,1

−kz,2

k0 ) is given by:

Bg = n1∆2G (υ) , (2.31)

where G (υ) is the normalized geometrical birefringence, that depends on the propagation param-eters u and w [33].

2.4.2 Gratings

Let us consider a sinusoidal index modulation of the core refractive index: n (z) = n0+ δn 1 + cos 2πz Λ , (2.32)

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where n0 is the unmodulated core refractive index, δn is the refractive index modulation amplitude,

and Λ is the modulation period. The propagation in the perturbed waveguide is usually discussed under the coupled-mode theory formalism. For a grating with certain parameters (n0, δn, r) and length L,

the amplitudes of the reected and transmitted guided waves can be related to the amplitude of the incident wave, and transmission and reection values obtained. The maximum reection is localized at the Bragg grating wavelength, which is given by

λB = 2nef fΛ, (2.33)

where nef f is the eective refractive index of the waveguide [58].

The reectivity spectrum can be shown to be [33]: R = sin 2_(ρL) ρ κG 2 + sin2_(ρL) (2.34) where ∆k = kz− π_Λ is the wave vector detuning, ρ =

q

∆k2_{− κ}2

G, and κG = π

λ.ν.∆n.g (z) is the

coupling coecient, in which ν is the fringe visibility usually estimated at 1, and for a uniform grating g (z) = 1. The reectivity spectra of a grating with modulation amplitude of ∆n = 10−4, and center wavelength of λB = 1550nmis shown in gure 2.13.

Figure 2.13: Reectivity spectrum example.

To access the dierence between the responses of rectangular and sinusoidal grating proles, the reectivity spectra were calculated using Rsoft CAD software, for a step index ber with 0.01 index contrast and 0.001 grating modulation. The results are shown in gure 2.14.

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Figure 2.14: Reectivity spectrum for two gratings with the same modulation amplitude, but rectan-gular/sinusoidal shape.

The peak reectivity is slightly higher for rectangular gratings, but the FWHM reectivity and side lobes peak reectivity are higher.

If we consider now the same modulated refractive index inside a birefringent waveguide, then the two waveguide polarization modes will have dierent eective refractive indices. We can see that the dierent eective refractive indices of the two modes with orthogonal polarization state will translate into a shift of the Bragg grating wavelength:

B = ∆nef f =

∆λB

2Λ . (2.35)

Therefore, a measurement of the shift ∆λB of the response peaks allows the evaluation of the

waveguide birefringence, as long as the written gratings do not alter too much the average refractive index prole of the waveguide. So, weak modulation should be used.

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Chapter 3

Laser Writing and Characterization:

Experimental Systems and Techniques

This chapter provides the essential information on the implementation of the ultrashort laser pulse writing system and its operation. It also contains a description of the experimental setups used for the characterization of the guided optic devices produced, and the corresponding measurement techniques applied.

3.1 Femtosecond Laser Writing System

The femtosecond laser writing system comprises dierent blocks: Femtosecond laser with repetition rate and power control. Beam delivery system including spot monitoring.

High accuracy sample positioning and displacement sub-system.

The schematic of the nal laser writing system used to produce the experimental results in chapter4 is presented in gure 3.1.

Figure 3.1: Schematic of the experimental setup.

During the tests, the setup was upgraded and modied several times, depending on the results and problems faced when testing the setup. The beam expander block was not present in the initial tests. Although we managed to write waveguides and gratings without the beam expander, their quality,

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namely the grating strength and waveguide losses were not as good as expected. The beam expander, together with the pin-hole lets the laser beam ll the objective lens aperture so that we can lower the eective numerical aperture to the lens numerical aperture.

The full system works as follows: the beam from the fs laser is attenuated by the power control unit, and then guided through a beam expander that expands the beam until it barely overlaps the objective lens, with the pin-hole blocking the residual light to precisely ll the objective lens. The polarization is controlled by rotating a λ

2 waveplate. The sample is placed in a xy motor stage that

controls the focus positioning. A CCD camera is used to form an image with the light reected by the sample that passes through the mirror M3. This is useful during alignment and to nd when the beam

focus is at the sample surface. 3.1.1 Femtosecond Laser

The laser used in this project was the ber-amplied laser Satsuma, from Amplitude Systèmes. It provides pulses with duration ∼ 350 fs (FWHM of Lorentzian), and the repetition rate ranges from single shot to up to 2 MHz. The maximum average power is 10 W in the fundamental wavelength, corresponding to 20 µJ of maximum energy per pulse. The laser system comprises several sub-units, organized as shown in gure 3.2. The laser main specications are represented in table 3.1

Parameters Specication Operation Wavelength 1030 nm Bandwidth <10 nm Beam diameter 1.5 mm Polarization contrast >>100:1 Pulse duration 350 fs Maximum Average power 10 W Maximum Pulse Energy 20µJ

Table 3.1: Satsuma ber laser main specications.

Figure 3.2: Schematic of the laser system.

Satsuma uses two optical modulators to change the pulse repetition rate. A pulse picker selects pulses from the main oscillator before the amplication stage. By reducing the repetition rate before amplication, the energy per pulse can be changed independently of the average power. The pulse picker frequency is limited to the range fpp [0.5 M Hz, 2 M Hz]. We can choose also to turn o the

pulse picker and use the original oscillator frequency(25 MHz).

When we change fpp, in order to have minimum pulse width, compression adjustment is required.

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enables further control of the repetition rate and pulse energy. In this unit the repetition rate can be reduced to a submultiple of the fpp frequency, down to single shot. The MOD transmission eciency

can be changed independently, so we can have full control on the pulse energy. 3.1.2 Power Control of the laser beam

To control the laser power quickly when writing, it is not recommended to use the laser external modulator (MOD), so we decided to use an external Watt Pilot unit from Altechna (see gure 3.3).

Figure 3.3: Schematic of the power control unit from Altechna. The power control unit assumes a linearly polarized incident beam. It uses a λ

2 waveplate that

inverts the beam polarization relative to the waveplate fast axis. So if the waveplate axis makes an angle θ with the laser beam polarization direction, then after the waveplate the polarization direction will make a 2θ angle with its initial polarization direction. By rotating this waveplate we can choose how much power is transmitted in each linear polarization state. Then a couple of thin lm polarizers, positioned at the Brewster angle, separate the s polarization from the p polarization. The s polarization is recommended because, at the Brewster angle, the reected beam is completely polarized, and the transmitted beam is only partially polarized [59].

3.1.3 Beam Delivery System

Some of the optical components of the beam delivery system were already available when the project started, but others were specied and purchased in its initial phase. Since we are dealing with a femtosecond high peak power laser, there are some concerns in choosing the right optics:

The damage threshold of all the optics must be considered. This damage threshold is established for a given pulse duration, because not only the peak power changes, but also the laser light interaction and absorption in materials changes with the timescale of the pulse duration.

For a rough approach we can still estimate the equivalent threshold power for dierent pulse dura-tions by considering the at top pulse average intensity: I = Ep

A∆t.

The other concern is with dispersion, since the laser spectrum is wide (10 nm) in comparison with typical continuous laser sources, and so dierent wavelengths will travel at dierent velocities in dispersive media, which can split up in time the dierent spectral components, thus destroying the pulse shape. Having this in mind, whenever possible low GDD optics were chosen.

The specied mirrors are low GDD ultrafast mirrors from Altechna (1-OS-2-0254-5-[1P45-GDD]), with less than 10 fs2 _{GDD value at the operation wavelength and 100mJ/cm}2 _{@50f s} _{laser damage}

threshold.

For polarization control, λ/2 waveplates, with laser damage threshold of 10J/cm2 _@10ns_{, were}

chosen, covering the possibility of rotating the writing polarization to test the eects of dierent writing polarizations.

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The objective lens is a Newport aspheric lens #5722-B with numerical aperture NA = 0.55, 2.9 mm working distance, and clear aperture of 5 mm. Aspheric lenses are important to minimize spherical aberrations, which will aect the beam waist shape and thus the refractive index pattern inscribed inside the fused silica. As seen in subsection 2.2.2, temporal broadening due to dispersion is negligible for this lens glass (Corning C-0550), even for the 2.9 mm lens thickness. The objective lens z position is read by using a digital dial indicator from Mitutoyo, with the probe set against a plate that holds the objective lens.

The beam expansion is made through two planar-convex lenses with 35 mm and 80 mm focal lengths, from Melles Griot. The lenses are placed at a distance given by f1+f2 = 115 mm, constituting

a simple telescope [60]. Theoretically this system has a magnication m = f2

f1 = 2.3, maintaining the

beam collimated. Without the beam expansion the beam diameter was measured to be 2.5 mm. Using this combination of lens we can barely overll the objective lens aperture. The pin-hole placed after the beam expander selects the beam so that it exactly lls the objective lens.

The XY motor stage consists of two Aerotech ABL10100-BL linear stages mounted orthogonally. These air-bearing stages are suspended by air pressure, which gives the high precision (20 nm position reading precision, and 50 nm positioning precision) and stability needed for the right alignment when writing micrometer sized patterns. The xy stages are controlled by a C program written by Daniel Alexandre [61], which has a graphic interface that permits full control of the (x,y) position, and translation with a constant velocity in the x or y directions. Scripts for writing waveguides and gratings were adapted to our needs, minimizing the time necessary for each writing session.

Alignment

The alignment is achieved generally by taking advantage of the orthogonality between the two opti-cal tables. The components are aligned progressively from the laser until the sample, making sure orthogonality is maintained at each step. The step by step alignment procedure is the following:

Aligning the laser beam with the three mirrors M1−M3progressively, aligning rst M1, certifying

that the beam is parallel to the optical table, and just then aligning the mirror M2, and then

M3. The perpendicularity is important so that the angle of reection on the mirrors is close to

the working angle (45º ).

With a mirror placed face up on the XY motor stage, a check on the reected beam is performed, following its path. By tuning the mirrors' angles slightly (the coarse alignment is made in the rst step through the perpendicularity of the mirrors placement), the system will be aligned when just after the power control the reected and transmitted beam coincide.

For the beam expander, the rst lens to be put in place is L1 because it has a planar interface

with the incoming beam and so we can again use the reection on L1 for alignment. Another

important concern is to align the laser beam with the center of the lens. To check this, we can verify again the reections in the path between the alignment mirror and L1. After aligning L2,

we need to tune the distance L1− L2 to guarantee that the beam is collimated. This can be done

by using a mirror after L2 to withdraw the laser beam out of the system, checking if the beam

spot size does not change after a long propagation distance (∼ 2 m).

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For aligning the λ

2 waveplate the procedure is the same. Then the waveplate angle is adjusted

until minimizing the transmitted power measured after a polarizer, placed on top of the objective lens L4 with the axis symmetric to the polarization we want.

When aligning the objective lens, we start by placing the alignment mirror on top of the objec-tive support, merging together again the incident and reected beams. When this is done, the objective lens angle is corrected, so we need only to merge its center with the beam.

The xy platform needs to be calibrated before usage, and so a homing function provided by the manufacturer needs to be called. The program interface has an icon to call the function. Since in this step the xy stage moves to the extreme points, caution must be taken with the objective z level so that it does not hit the plate borders. Our platform was machined to prevent this happening for typical objective lens height levels.

To calibrate the z position, we nd the objective lens position that focuses the beam on the sample surface. For this we use the ccd camera, that forms an image of a plane at the innity with the aid of the camera lens L3: when the beam is focused at the surface of the sample a

bright spot will appear in the image, because the reected beam comes collimated. This also happens when the beam propagates through the entire sample and is focused on the other side, so the two spots are normally observed; the rst one is chosen (the second one is also less brighter because of attenuation from the propagation inside the sample).

When the beam spot is slightly outside or inside the surface, interference rings appear. We can use them to ne tilt the sample in order to guarantee that we write at the same height for all xy positions over the sample area. For this ne tilting the minimum laser power possible is used, so that we guarantee that no damage occurs on the sample and/or on the ccd camera. The sample is aligned when we see exactly the same interference pattern in all four corners, using only translations of the xy stage.

Power Calibration

To quickly know the average power that reaches the sample, it is useful to just measure the average power after the attenuator. So, a conversion table was created by measuring the power after the attenuator and the power just before reaching the sample. This way we could know the required value after the attenuator to ensure that a certain power reaches the sample. For the second measurement only an approximation of the true value was possible, because we need to bring the objective lens near the power meter, but still avoiding that the focus is too close to the power meter surface, to avoid the risk of damage. The power conversion table (table 3.2) measured for the nal setup shows that the percentage of power loss in our system is relativelly constant at 47%.

Attenuator Power (%) Power After Attenuator (mW) Power After Lens (mW) Loss (%)

0 0 0

-25 99 53 46

50 198 105 47

75 295 157 47

100 391 209 47

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3.1.4 Fabrication

The samples used in this work were of fused silica, with 2.5 × 7.6 mm planar dimensions, and 1 mm thickness. The samples were polished using the procedure described in Annex A. Whenever possible the polishing was made after writing, to avoid the edge where the beam is focused asymmetrically, although this eect is negligible in fused silica [62].

After nding the zero position for the objective lens stage, the objective lens was moved to the position calculated for the wanted focus location inside the fused silica sample. Waveguides were written by simply translating the sample using the xy stage, at a constant velocity.

For writing waveguide gratings, the laser gate was externally controlled by a periodic square time function generated by the synthesized function generator DS345, from Stanford Research Systems. The amplitude of this signal function was in turn externally controlled by the main program, by connecting one of the output bits from the xy stage drivers. This simple arrangement permitted the automated writing of gratings by simply translating the sample at constant velocity with the signal modulation turned on. The Bragg wavelength can easily be tuned by simply tuning the modulation frequency fmod. Using the Bragg relation, we can easily see that the Bragg wavelength is given by

λB= 2nef f

υ fmod

,

where υ is the velocity of the sample and nef f the eective index of refraction. We chose to x the

Bragg wavelength to 1550 nm, because it corresponds to the optical communications typical region and is also within the range of the characterization system used.

A single sample can be used to write hundreds of waveguides or gratings, even without any of them piled. To facilitate the searching of specic devices and avoid mistakes when analyzing the dierent devices, we created an easy to read sample ling schemes that show the exact location of each device written, with the most relevant writing parameters identied, and several points of reference to help track the wanted device. In gure 3.4 we can see the scheme of sample 6, which contains most of the devices analyzed whose results are reported in this thesis.

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3.2 Characterization of Guided Wave Devices

In parallel with the assembly of the laser writing system, the characterization setups needed to eval-uate the guided wave devices fabricated were studied and implemented. Indeed, these setups were tested initially with samples produced and supplied by Luis Fernandes (from his PhD research at the University of Toronto), such as linear channel waveguides and Bragg gratings with stress tracks [63].

The characterization setups were then employed to test the rst devices produced with the local writing system, in order to optimize the writing conditions.

3.2.1 Microscope Observation

Before further characterization of waveguide losses, samples were observed to check the damage proles and measure the depth at which they were written. An example of the measurement results is shown in gure 3.5.

Figure 3.5: Example of damage pattern proles measured on the facet of written waveguides. The laser was incident from the bottom

The edge of the sample was included in the image whenever possible, so that we could measure orthogonally to an edge line. The absence of circular symmetry in the damage pattern shows that, for these conditions, we are in the non-cumulative heating regime. This elongated shape is due to the combination of self focusing and plasma defocusing, since we have peak powers of ∼ 1.3 MW (see subsection 2.1.1 ) which are on the order of magnitude of the 0.8 MW critical power for fused silica of (see subsection 2.2.3 ). These damage patterns are in reasonable agreement with both the experimental results and the theoretical expectation from models reported by Couairon et al. [64] and Burakov et al. [65]. The damage pattern is quite long (about ∼ 25µm), so we needed to choose one point of reference in order to have coherent measurements. As can be seen in gure 3.6, we compared our damage patterns to ones reported by Shane Eaton, and linked the similar zones reported to have higher and lower refractive index with ours.

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Figure 3.6: Direct comparisson of the damage pattern observed in our system [right], compared with the one's reported by Shane Eaton [70] [left]. Both were written with parallel polarization.

For reference of the waveguide localization we decided to chose the bright spot at the bottom of the damage pattern, since this region is associated with an higher refractive index, and therefore the waveguide is written in that zone.

3.2.2 Insertion Loss

Figure 3.7: Experimental setup for waveguide characterization.

Figure 3.7 shows the setup implemented for characterization of the insertion loss of the waveguides. A Santec TLS-120 tunable laser is used as source. The laser light is butt coupled by aligning each of the bers ends, mounted on precision stages (Elliot Scientic E2100) with the respective waveguide facet. The precision stage piezo controls permit easy, precise, and stable alignment.

The transmitted light is then guided to the Exfo IQ-1640 power meter. By measuring the power P1

transmitted by the sample, and the power P0 transmitted by feeding the tunable laser beam directly

into the power meter, we can evaluate the insertion loss: IL = 10 log₁₀ P1

P0

. (3.1)

Since we typically tested several waveguides in a row, the measurements could take a long time, and to check if there were any laser power changes we extracted 10% of the laser power by using a 90-10 coupler (JDS Uniphase FFC-CA22PB110) to be used as reference level. The 90-10 coupler response was tested to guarantee linearity. The results are shown below.

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Figure 3.8: Calibration results.

For the linear regression we obtained an R2 _{of 0.9999994. This linearity is useful because a change}

in the 10% output is then equivalent to a proportional change in the 90% output. So, even if the laser power changes during measurements, we can keep the results equivalent.

3.2.3 Mode Prole Measurements

Figure 3.9: Experimental setup for beam prole observation

To measure the proles of the modes that propagate in the waveguides, the setup represented in gure 3.9 was employed. The diverging beam that emerges from the end facet of the sample is imaged by aligning an objective lens until focusing on the CCD camera (Applied Scintilation Technologies -Chameleon CMLN-13S2M) is achieved, at a large distance from the lens.

Theoretically we should try to use an objective lens with high magnication in order to ll most of the camera area, in order to have better resolution. But the camera used introduces a lot of noise, nonlinear response and displays regions with greater response than others. These eects can be seen in gure 3.10.

Figure 3.10: Fiber output beam image recorded on the ccd camera, using an objective lens with 60x amplication.