In-Plane Optical Beam Collimation Using a Three-Dimensional Curved MEMS Mirror Yasser Sabry, Diaa Khalil, Bassam Saadany, Tarik Bourouina

Home , Collimated beam

To cite this version:

Yasser Sabry, Diaa Khalil, Bassam Saadany, Tarik Bourouina. In-Plane Optical Beam Collima- tion Using a Three-Dimensional Curved MEMS Mirror. Micromachines, MDPI, 2017, 8 (5), pp.134. 10.3390/mi8050134. hal-02437753

HAL Id: hal-02437753 https://hal.archives-ouvertes.fr/hal-02437753 Submitted on 24 Feb 2020

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés.

Distributed under a Creative Commons Attribution| 4.0 International License micromachines

Article In-Plane Optical Beam Collimation Using a Three-Dimensional Curved MEMS Mirror †

Yasser M. Sabry 1,2,*, Diaa Khalil 1,2, Bassam Saadany 2 and Tarik Bourouina 2,3

1 Department of Electronics and Communication Engineering, Faculty of Engineering, Ain-Shams University, 1 Elsarayat St., Abbassia 11517, Egypt; [email protected] 2 Si-Ware Systems, 3 Khaled Ibn El-Waleed Street, Heliopolis, Cairo 11361, Egypt; [email protected] (B.S.); [email protected] (T.B.) 3 Paris-Est, Laboratoire ESYCOM, ESIEE Paris, Cité Descartes, F-93162 Noisy-le-Grand CEDEX, France * Correspondence: [email protected]; Tel.: +20-100-183-4833 † This paper is an extended version of our paper published in the MOEMS and Miniaturized Systems XIII conference, 3–6 February 2014, San Francisco, CA, USA.

Academic Editor: Huikai Xie Received: 25 March 2017; Accepted: 18 April 2017; Published: 25 April 2017

Abstract: The collimation of free-space light propagating in-plane with respect to the substrate is an important performance factor in optical microelectromechanical systems (MEMS). This is usually carried out by integrating micro lenses into the system, which increases the cost of fabrication/assembly in addition to limiting the wavelength working range of the system imposed by the dispersion characteristic of the lenses. In this work we demonstrate optical fiber light collimation using a silicon micromachined three-dimensional curved mirror. Sensitivity to micromachining and fiber alignment tolerance is shown to be low enough by restricting the ratio between the mirror focal length and the optical beam Rayleigh range below 5. The three-dimensional curvature of the mirror is designed to be astigmatic and controlled by a process combining deep, reactive ion etching and isotropic etching of silicon. The effect of the micromachining surface roughness on the collimated beam profile is investigated using a Fourier optics approach for different values of root-mean-squared (RMS) roughness and correlation length. The isotropic etching step of the structure is characterized and optimized for the optical-grade surface requirement. The experimental optical results show a beam-waist ratio of about 4.25 and a corresponding 12-dB improvement in diffraction loss, in good agreement with theory. This type of micromirror can be monolithically integrated into lensless microoptoelectromechanical systems (MOEMS), improving their performance in many different applications.

Keywords: curved micromirrors; three-dimensional fabrication; Gaussian beams; surface roughness

1. Introduction Optical microelectromechanical systems (MEMS) technology has attracted great attention over the past couple of decades because of its reduced size, light weight and low cost [1]. There are two main architectures in the optical MEMS, namely in-plane architecture [2], where the light propagates from one component to another parallel to the substrate, and out-of-plane architecture [3], where the light hits the optical component either perpendicular to or with inclination on the substrate. For many applications, such as in optical telecommunication [1], optical coherence tomography [4] and on-chip sensing [5], the light source is connected to the optical MEMS device through a single-mode optical ﬁber, where the optical beam output from the ﬁber behaves as a Gaussian beam [2]. In this case, the propagation can be associated with beam size expansion before detection, leading to optical losses. This is even more serious in optical MEMS due to the size limit of the optical components [6,7]. Several

Micromachines 2017, 8, 134; doi:10.3390/mi8050134 www.mdpi.com/journal/micromachines Micromachines 2017, 8, 134 2 of 13 Micromachines 2017, 8, 134 2 of 13 solutions[6,7]. Several were solutions introduced were as introduced shown in Figure as shown1 to overcome in Figure this 1 to challenge, overcome such this challenge, as the use ofsuch a lensed as the fiberuse of [4 a] orlensed an external fiber [4] lens or an integrated external into lens the integr systemated ininto the the form system of a graded-index in the form of (GRIN) a graded-index lens or a ball(GRIN) lens lens [6–11 or]. a The ball lensed lens [6–11]. fiber solution The lensed is costly fiber duesolution to the is piece-by-piececostly due to the process piece-by-piece of lens formation process onof lens the fibers, formation in addition on the tofibers, the reliability in addition issue to tothe possible reliability fiber issue tip breakage. to possib Thele fiber external tip breakage. lens solution The suffersexternal from lens thesolution cost and suffers complexity from the of cost the assembly.and complexity In addition, of the refractiveassembly. lensesIn addition, have chromaticrefractive aberrationlenses have and chromatic requireanti-reflective aberration and coating require to eliminateanti-reflective the reflection. coating to The eliminate aberration theand reflection. the coating The bothaberration lead to and limited the coating working both wavelength lead to limited range. working wavelength range.

Figure 1. Optical beam propagation for the different architectures of (a) a cleaved fiber; (b) an Figure 1. Optical beam propagation for the different architectures of (a) a cleaved ﬁber; (b) an integrated integrated lens fiber; (c) an external lens; and (d) the proposed solution in this work. lens ﬁber; (c) an external lens; and (d) the proposed solution in this work.

Reflecting curved micromirrors are achromatic and can provide much a wider spectral response,Reflecting but curvedthey need micromirrors special attention are achromatic during andfabrication can provide to obtain much athe wider curved spectral surface. response, The butcommon they need non-planar special attention micro surfaces during fabricationfabrication to techniques obtain the curvedare gray-tone surface. mask The common [12], excimer non-planar laser micro[13], Reactive surfaces Ion fabrication Etching techniques (RIE) lag areeffect gray-tone [14] and mask photo [12 ],resist excimer (PR) laser reflow [13 ],[15,16]. Reactive On Ion one Etching hand, (RIE)non-silicon lag effect curved [14] andmicromirrors photo resist were (PR) reported reflow [15 using,16]. Ona polymer one hand, dispensing non-silicon and curved sucking micromirrors technique were[17], residual reported internal using a polymermaterial dispensingstress resulting and suckingfrom deposition technique of [ 17gold], residual on polysilicon internal for material the purpose stress resultingof light focusing from deposition [18], trapping of gold of gas on bubbles polysilicon during for themelting purpose a stack of lightof small focusing borosilicate [18], trapping glass tubes of gasunder bubbles a nitrogen during atmosphere melting a stack and offurther small grinding borosilicate and glass polishing tubes underfor atomic a nitrogen studies atmosphere [19] and deep and furthersilicon grindingetching and and PR polishing reflow fortargeting atomic optical studies in [19terconnects] and deep [20]. silicon On etching the other and hand, PR reflow silicon targeting curved opticalmicromirrors interconnects fabricated [20 ].on On the the wafer other top hand, surface silicon were curved reported micromirrors using isotropic fabricated chemical on etching the wafer for topthe surfacesake of wereoptical reported detection using of isotropicsingle atom chemical [21], selective etching forpolishing the sake method of optical on detectionthe top of of MEMS single atomtunable [21 ],vertical-cavity selective polishing surface-emitting method on laser the top [22] of and MEMS ion tunable beam irradiation vertical-cavity and surface-emitting electrochemical laseretching [22 ]for and atomic ion beam studies irradiation as well and as electrochemical optical interconnects etching for [23]. atomic The studies principal as well axis as opticalof the interconnectsaforementioned [23 micromirrors]. The principal is oriented axis of the out-of-pla aforementionedne with the micromirrors respect to the is orientedwafer substrate. out-of-plane This withrendered the respectthe micromirror to the wafer incompatible substrate. with This silico renderedn micro-optical the micromirror bench incompatiblesystems where with the light silicon is micro-opticalpropagating in-plane bench systems with respect where to the the light substr is propagatingate. Three-dimensional in-plane with (3-D) respect micro to optical the substrate. bench Three-dimensionalsystems requiring (3-D)further micro assembly optical or bench mounting systems steps requiring after furtherfabrication assembly were orintroduced mounting in steps the afterliterature. fabrication The most were common introduced is to in use the rotational literature. a Thessembly most to common create micro-optical is to use rotational subsystems assembly that toprocess create free-space micro-optical beams subsystems travelling that above process the surface free-space of the beams chip [24]. travelling Non-monolithically above the surface integrated of the chipmechanical [24]. Non-monolithically mounting systems integrated for connecting mechanical and aligning mounting optical systems componen for connectingts on a micro and aligning optical opticalbench (OB) components were also on areported micro optical[25,26]. bench This (OB)is, however, were also not reported compatible [25,26 with]. This the is, monolithic however, notintegration compatible efforts with for the the monolithic microoptoelec integrationtromechanical efforts systems for the microoptoelectromechanical (MOEMS) [27–30]. systems (MOEMS)In this [27 work,–30]. we demonstrate optical beam collimation and propagation loss reduction using a monolithicIn this micromachined work, we demonstrate curved mirror optical with beam an collimation in-plane principal and propagation axis, which loss is reductioncompatible using with asilicon monolithic micro-optical micromachined bench technology curved mirror [31]. withThe paper an in-plane is organized principal in axis,the following which is compatiblemanner. In withSection silicon 2, a micro-opticaltheoretical study bench is carried technology out for [31 the]. The possibility paper is of organized Gaussian in beam the following collimation manner. using Incurved Section surfaces2, a theoretical exhibiting study microscale is carried focal out forlength thes, possibility i.e., not so of large Gaussian compared beam collimationwith the incident using curvedGaussian surfaces beam exhibitingRayleigh range. microscale The focaldesign lengths, of astigmatic i.e., not micromirror so large compared curvatures with is the related incident to incidence angle of the incident Gaussian beam in order to generate a stigmatic collimated beam. The effect of the surface roughness of the micromirror is analyzed in Section 3. Then, the fabrication steps

Micromachines 2017, 8, 134 3 of 13

Gaussian beam Rayleigh range. The design of astigmatic micromirror curvatures is related to incidence angle of the incident Gaussian beam in order to generate a stigmatic collimated beam. The effect of the surface roughness of the micromirror is analyzed in Section3. Then, the fabrication steps of the micromirror and the resulting structure are presented in Section4. Finally, optical measurements are presented and discussed in Section5 using the introduced curved micromirror for single-mode ﬁber output collimation and propagation loss reduction where the ﬁber axis lies in-plane with the substrate.

2. Theoretical Analysis of Optical Beam Collimation Consider the incidence of a Gaussian beam on a curved micromirror as shown in Figure2.

TheMicromachines parameters 2017, of8, 134 the reﬂected beam are related to the incident beam by: 3 of 13

wout 1 of the micromirror and the Gresultingc = structure= q are presented in Section 4. Finally, optical(1) win 2 2 2 measurements are presented and discussed in (Se1 −ctiondin /5f using) + z othe/ f introduced curved micromirror for single-mode fiber output collimation and propagation loss reduction where the fiber axis lies d z2/ f 2 − d / f (1 − d / f ) in-plane with the substrate. out = o in in (2) f 2 2 2 (1 − din/ f ) + zo/ f 2. Theoretical Analysis of Optical Beam Collimation where win and wout are the min waist radii for the incident and reﬂected beams, respectively, din and dout areConsider the distances the incidence between of the a Gaussian beam waist beam location on a andcurved the micromirror mirror surface as atshown the point in Figure of incidence 2. The forparameters the incident of the and reflected reﬂected beam beams, are related respectively, to the incidentf is the beam focal by: length of the mirror and zo is the Rayleigh range of the incident beam. The beam-waist ratio wout/win is denoted by Gc and represents = wout = 1 Gc the collimation gain. The dependences ofw thein beam-waist− 2 + ratio2 2 and the ratio dout/f on the ratio d(1)in/ f (1 din / f ) zo / f for different ratios of f /zo are shown in Figure3. The beam-waist ratio has a maximum value occurring when the input distance and the focald lengthz 2 / aref 2 − equal.d / f The(1− d maximum/ f ) beam-waist ratio is given by: out = o in in − 2 + 2 2 (2) f (1 d in / ff) zo / f Gc = (3) zo where win and wout are the min waist radii for the incident and reflected beams, respectively, din and

dout areThe the variation distances of between the beam-waist the beam ratio waist around locationdin and/f = the 1 is mirror symmetric. surface The at the variation point of of incidence the ratio dforout /thef possess incident odd and symmetry reflected around beams, the respectively, point (din/f f= is 1, thedout focal/f = 1).length The outputof the beammirror waist and locationzo is the doesn’tRayleigh change range withof the the inciden input beamt beam. Rayleigh The beam-waist range when ratio the w inputout/win beamis denoted waist isby located Gc and at represents the focus ofthe the collimation mirror. Negative gain. The values dependences of dout/f ofare the obtained beam-waist when ratiodin/ andf < 1,the which ratio meansdout/f on the the output ratio d beamin/f for waistdifferent is located ratios of virtually f/zo are behindshown in the Figure mirror 3. and The the beam-waist beam is diverging ratio has aftera maximum reﬂection. value The occurring opposite casewhen occurs the input when distancedin/f >1 and and the the focal beam length is reﬂected are equal. in a convergingThe maximum state. beam-waist The output ratio beam is waistgiven mayby: have its waist located just at the mirror surface for a single value of din/f when zo/f = 2 and for two = f value of d /f when z /f = 0.5; one time for a veryGc small value of d /f and the second time for a d(3)/ f in o z in in that is slightly smaller than unity. o

Figure 2. Three-dimensional curved micromirror used in beam collimation. (a) In-plane cross section; Figure 2. Three-dimensional curved micromirror used in beam collimation. (a) In-plane cross section; ((b)) out-of-planeout-of-plane crosscross section.section.

Figure 3. Dependence of the beam-waist ratio Gc and the ratio dout/f on the ratio din/f in (a) and (b),

respectively, for different f/zo ratios.

Micromachines 2017, 8, 134 3 of 13 of the micromirror and the resulting structure are presented in Section 4. Finally, optical measurements are presented and discussed in Section 5 using the introduced curved micromirror for single-mode fiber output collimation and propagation loss reduction where the fiber axis lies in-plane with the substrate.

2. Theoretical Analysis of Optical Beam Collimation Consider the incidence of a Gaussian beam on a curved micromirror as shown in Figure 2. The parameters of the reflected beam are related to the incident beam by:

= wout = 1 Gc win − 2 + 2 2 (1) (1 din / f ) zo / f

d z 2 / f 2 − d / f (1− d / f ) out = o in in − 2 + 2 2 (2) f (1 d in / f ) zo / f where win and wout are the min waist radii for the incident and reflected beams, respectively, din and dout are the distances between the beam waist location and the mirror surface at the point of incidence for the incident and reflected beams, respectively, f is the focal length of the mirror and zo is the Rayleigh range of the incident beam. The beam-waist ratio wout/win is denoted by Gc and represents the collimation gain. The dependences of the beam-waist ratio and the ratio dout/f on the ratio din/f for different ratios of f/zo are shown in Figure 3. The beam-waist ratio has a maximum value occurring when the input distance and the focal length are equal. The maximum beam-waist ratio is given by:

= f Gc (3) zo

Figure 2. Three-dimensional curved micromirror used in beam collimation. (a) In-plane cross section; Micromachines 2017, 8, 134 4 of 13 (b) out-of-plane cross section.

Micromachines 2017, 8, 134 4 of 13

The variation of the beam-waist ratio around din/f = 1 is symmetric. The variation of the ratio dout/f possess odd symmetry around the point (din/f = 1, dout/f = 1). The output beam waist location doesn’t change with the input beam Rayleigh range when the input beam waist is located at the focus of the mirror. Negative values of dout/f are obtained when din/f < 1, which means the output beam waist is located virtually behind the mirror and the beam is diverging after reflection. The opposite case occurs when din/f >1 and the beam is reflected in a converging state. The output beam waist may have its waist located just at the mirror surface for a single value of din/f when zo/f = 2 and Figure 3. Dependence of the beam-waist ratio Gc and the ratio dout/f on the ratio din/f in (a) and (b), for twoFigure value 3. Dependence of din/f when of z theo/f = beam-waist 0.5; one time ratio forGc aand very the small ratio d valueout/f on of thedin/ ratiof andd inthe/f secondin (a) and time (b), for a respectively, for different f/zo ratios. din/f thatrespectively, is slightly for smaller different thanf/zo ratios. unity. The microfabrication process tolerance may result in a variation of the curved micromirror radiusThe of microfabrication curvature, which process affects tolerance the obtainable may result beam’s in a beam-waist variation of theratio. curved The impact micromirror depends radius on ofthe curvature, gain sensitivity which to affects the curved the obtainable surface focal beam’s length. beam-waist The corresponding ratio. The impact change depends is determined on the gainby: sensitivity to the curved surface focal length.Δ f d / Thef (1 corresponding− d / f ) + ( z change/ f ) 2 is determined by: Δ G = in in o c − 2 + 2 3 / 2 f [(1 d in / f ) ( z o / f )2 ] ∆ f din/ f (1−din/ f )+(zo/ f ) ∆Gc = 3/2 f −1 2 2 (4) Δ [(1−din/ f ) +(zo/ f ) ] (4) f  z o  −1 =  ∆ f z, d / f ≈ 1 =  o in ≈ f  f f  f , din/ f 1

For a givengiven percentagepercentage changechange inin thethe focalfocal length,length, thethe gaingain sensitivitysensitivity becomesbecomes veryvery highhigh whenwhen thethe ratio zoo//f fisis very very small. small. AsAs depicted depicted in Figure in Figure 4a,4 thea, the beam-waist beam-waist ratio ratio is less is lesssensitive sensitive to the to focal the focallength length variation variation when when zo/f ziso /largerf is larger than than 0.2. 0.2.The The output output be beamam waist waist location location is, is, however, however, very sensitivesensitive toto thethe variationsvariations asas shownshown inin FigureFigure4 b.4b. In In the the case case of ofz oz/o/ff > 0.2, thethe fabricationfabrication tolerancetolerance impactimpact onon thethe outputoutput beambeam waistwaist locationlocation cancan bebe compensatedcompensated byby activeactive axialaxial alignment.alignment.

Figure 4. Dependence of the beam-waist ratio Gc and the ratio din/f on the ratio zo/f in (a) and (b), Figure 4. Dependence of the beam-waist ratio Gc and the ratio din/f on the ratio zo/f in (a) and (b), respectively, for different din/f ratios. respectively, for different din/f ratios. The inclined incidence of the beam on the mirror in a tangential plane, while being normal to The inclined incidence of the beam on the mirror in a tangential plane, while being normal to the the sagittal plane, has the effect of splitting the focal length as well as the input ratio din/f of the d f sagittalmirror each plane, into has two the different effect of values: splitting the focal length as well as the input ratio in/ of the mirror each into two different values: f = 0.5R cos(θ ) fip =ip 0.5Ripip cos(θincinc) (5)(5)

fop = =0.5Rop/ cosθ(θinc ) (6) fop 0.5Rop /cos( inc ) (6) d 2d in = in  d  2d (7) f  inip = Rip cosin (θinc )   θ (7)  f ip Rip cos( inc )

 d  2d cos(θ ) in = in inc   (8)  f op Rop where the subscripts “ip” and “op” are used for the in-plane and out-of-plane directions, respectively, and R is the radius of curvature of the mirror in the indicated plane. The inclined

Micromachines 2017, 8, 134 5 of 13

d 2d cos(θ ) in = in inc (8) f op Rop where the subscripts “ip” and “op” are used for the in-plane and out-of-plane directions, respectively, and R is the radius of curvature of the mirror in the indicated plane. The inclined incidence has the effect of effectively increasing the out-of-plane focal length of the curved surface while at the same time decreasing its in-plane focal length, and therefore, a stigmatic inclined curved surface should have non-equal radii of curvature in the two orthogonal planes. As will be shown in the fabrication section, the out-of-plane plane radius of curvature can be limited to 100 µm. Fortunately, increasing angle of incidence compensates for this limit. For instance, focal length matching occurs ◦ ◦ ◦ at incidence angles θinc = 0 , 45 and 60 for Rop/Rip = 1, 0.5 and 0.25 respectively. Away from the stigmatic beam generation angle, the reﬂected beam exhibits an elliptical cross section as well different beam waist location in the two orthogonal planes. This can be of particular interest in beam shaping/matching applications.

3. Effect of Surface Roughness The effect of the surface roughness expected from the micromachining of the 3-D curved surface on the collimated optical beam proﬁle is investigated in this section. For this purpose, the overall phase transformation of the 3-D mirror is divided into the phase curvature responsible for the collimation of the beam, which is already considered in Section2, and a random phase due to the surface roughness. The phase curvature corresponding to the curvature of the mirror surface is given by:

2π x2 + y2 φ = (9) λ 2 f where f is the equivalent focal length of the mirror. The random phase is given by:

2π φ = z (10) n λ n where zn = f(x,y) is the random height variation of the surface due to the surface roughness. In our analysis, f(x,y) is assumed a random rough surface that has a Gaussian height distribution function and Gaussian autocovariance functions (in both x- and y-direction). The surface is assumed to have an RMS height σrms and assumed to be isotropic in the sense that the correlation length Lc in the x- and y-direction are assumed equal. The simulation procedure is carried out using the Fourier optics approach as follows [32]. The ﬁeld at the mirror surface, denoted by Ein(x,y,din), is multiplied by the phase transformation function and the new output ﬁeld is denoted by Eo(x,y,din):

Eo(x, y, din) = Ei(x, y, din) exp(−jφn − jφ) (11)

A fast Fourier transform (FFT) is applied to get this output ﬁeld in the spatial frequency domain:

Go( fx, fy, din) = FFT{Eo(x, y, din)} (12)

The ﬁeld is propagated a distance dout by phase multiplication in the spatial frequency domain:

Go( fx, fy, dout) = Go( fx, fy, din) exp(−jkzdout) (13) where kz is the axial components of the wave vector. Finally, the output ﬁeld proﬁle after propagating the distance dout is obtained by inverse Fourier transform: Eo(x, y, dout) = IFFT Go( fx, fy, dout) (14) Micromachines 2017, 8, 134 6 of 13

A simulation study was carried out to analyze the effect of the surface roughness of the etched mirror on the collimated beam. The effect is evaluated by calculating the coupling efficiency (overlap integral) between the resulting and the ideal beam. The radius of curvature of the mirror in the in-plane direction is assumed 300 µm, while the out-of-plane radius of curvature is 150 µm, similar to the value obtained practically as will be shown in the next section. The incident beam has a minimum waist radius of 5 µm, a wavelength of 1550 nm and located at the focal plane of the mirror in a 45-degree Micromachines 2017, 8, 134 6 of 13 incidence orientation. The RMS roughness σrms is assumed in the range of 0 to λ/10. Three values of the correlationin a 45-degree were incidence assumed: orientation. 5λ, 10λ andThe 20RMSλ. roughness σrms is assumed in the range of 0 to λ/10. TheThree resulting values of couplingthe correlation efficiency were assumed: is depicted 5λ, 10 inλ Figure and 205λa.. Since the roughness generation is a stochasticThe process, resulting the coupling simulation efficiency was repeatedis depicted 20 in times Figure for 5a. each Since point the ro andughness the averagegeneration was is a taken. The couplingstochastic efficiencyprocess, the decreases simulation with was therepeated increase 20 times of the for RMS each value point ofand the the roughness, average was as taken. expected. The coupling efficiency decreases with the increase of the RMS value of the roughness, as expected. It reaches about 75% for the case of Lc = 10λ and σrms = λ/10. If we would like to maintain at least It reaches about 75% for the case of Lc = 10λ and σrms = λ/10. If we would like to maintain at least 95% 95% of the coupling efficiency, then σrms should be less than 0.04λ, 0.06λ and 0.1λ for Lc = 5λ, 10λ of the coupling efficiency, then σrms should be less than 0.04λ, 0.06λ and 0.1λ for Lc = 5λ, 10λ and Lc = and Lc = 20λ, respectively. Example resulting beam profiles for the case of σrms = 0.1λ are shown 20λ, respectively. Example resulting beam profiles for the case of σrms = 0.1λ are shown in Figure 5b. x in FigureThe x5-axisb. The is normalized-axis is normalized to the waist of to the the resulting waist of beam the resultingprofile in case beam of profileThe loss inin caseefficiency of The is loss in efficiencyresulting is from resulting the asymmetry from the in asymmetry the beam profile in the in beam addition profile to the in widening addition of to the the profiles widening out of of the profilesthe out±4w oflimit the due±4 wto limitthe surface due to roughness. the surface roughness.

(a) (b)

Figure 5. Effect of surface roughness on coupling efficiency and collimated beam profile. Figure 5. Effect of surface roughness on coupling efficiency and collimated beam profile. (a) Coupling (a) Coupling efficiency versus RMS roughness normalized to the wavelength at different roughness efficiencycorrelation versus lengths; RMS roughness(b) collimated normalized beam profile to versus the wavelength the transverse at differentdimension roughness normalized correlationto the lengths;ideal (b beam) collimated waist radius. beam profile versus the transverse dimension normalized to the ideal beam waist radius. 4. Silicon Micromirror Fabrication 4. SiliconThe Micromirror optical axis Fabrication of the target 3-D curved micromirror lies in-plane with respect to the wafer Thesubstrate optical to axiscollimate of the the target optical 3-D beam curved genera micromirrorted from liessingle-mode in-plane withoptical respect fibers tolocated the wafer substratehorizontally to collimate on the the wafer optical substrate beam or generated any other fromlight source single-mode integrated optical in the fibers system. located It enables horizontally the use of the fiber-mirror configuration to replace the lensed fiber as previously shown in Figure 1d. on the wafer substrate or any other light source integrated in the system. It enables the use of the The fabrication of the micromirror was carried out into six main steps [33]. First the definition of the fiber-mirror configuration to replace the lensed fiber as previously shown in Figure1d. The fabrication in-plane profile of the micromirror with a 300-μm radius of curvature was performed using of thestandard micromirror photolithography was carried out(see into top sixview main in stepsFigure [33 6a).]. First The thelithographic definition process of the in-planeends with profile a of the micromirrorpatterned SiO with2 mask a 300- layerµ mforradius the following of curvature etching. was Second, performed anisotropic using deep standard reactive photolithographyion etching of (see topthe viewsilicon in was Figure carried6a). out, The ending lithographic with a deeply process etched ends cylindrical with a patterned surface as SiO shown2 mask in Figure layer 6b for the following[34]. By etching. this anisotropic Second, anisotropicetching step, deepthe central reactive line ion of the etching out-of-plane of the siliconcurvature was (principal carried out,axis) endingis withdefined. a deeply The etched axis cylindricaldepth with respect surface to as the shown wafer intop Figure surface6b was [ 34 ].chosen By this to anisotropicbe large enough etching that step, the centraloptical line fiber of can the be out-of-plane inserted and curvature aligned with (principal micromirror. axis) isThen, defined. side wall The protection axis depth was with carried respect to the waferout using top surfacea Teflon-like was chosenlayer to toprevent be large sidewall enough etching that from optical top fiber and canensure be the inserted following and isotropic aligned with etching starts at the mirror principal axis as shown in Figure 6c. The protection step was followed by micromirror. Then, side wall protection was carried out using a Teflon-like layer to prevent sidewall a long isotropic etching step using SF6 plasma to achieve the desired out-of-plane profile of the etching from top and ensure the following isotropic etching starts at the mirror principal axis as shown micromirror as shown in Figure 6d, in a similar way to that used to fabricate micro fluidic channels in Figurereported6c. The in [35]. protection The out-of-plane step was radius followed of cu byrvature a long of isotropicthe micromirror etching surface step usingis about SF 1506 plasma μm. to Achieving larger radii of curvatures requires deeper etching, which may result in a fragile wafer. The protective layer was removed in the fifth step as shown in Figure 6e using a high-temperature oxygen plasma ashing process. As will be shown below, the resulting surface roughness was about 22 nm RMS. Therefore, the surface was post-processed for optical quality requirement by smoothing

Micromachines 2017, 8, 134 7 of 13 achieve the desired out-of-plane profile of the micromirror as shown in Figure6d, in a similar way to that used to fabricate micro fluidic channels reported in [35]. The out-of-plane radius of curvature of the micromirror surface is about 150 µm. Achieving larger radii of curvatures requires deeper etching, which may result in a fragile wafer. The protective layer was removed in the fifth step as shown in Figure6e using a high-temperature oxygen plasma ashing process. As will be shown below, the resulting surface roughness was about 22 nm RMS. Therefore, the surface was post-processed for Micromachines 2017, 8, 134 7 of 13 opticalMicromachines quality 2017 requirement, 8, 134 by smoothing and Aluminum metallization as shown in Figure67 f.of Top13 andand tilted Aluminum views ofmetallization the fabricated as shown micromirror in Figure after 6f. To stepp and 5 are tilted shown views in of Figure the fabricated7a,b, recorded micromirror using a scanningafterand Aluminum step electron 5 are shown metallization microscope in Figure (SEM).as shown7a,b, recorded in Figure using 6f. To ap scanning and tilted electron views of microscope the fabricated (SEM). micromirror after step 5 are shown in Figure 7a,b, recorded using a scanning electron microscope (SEM).

Figure 6. The fabrication steps of the collimating 3-D curved micromirror. (a) Photolithography, Figure 6. The fabrication steps of the collimating 3-D curved micromirror. (a) Photolithography, (Figureb) deep 6. reactive The fabrication ion etching, steps (c) ofsidewall the collimating passivation, 3-D (d curved) isotropic micromirror. etching, (e )( apassivation) Photolithography, removal, (b) deep reactive ion etching, (c) sidewall passivation, (d) isotropic etching, (e) passivation removal, and(b) deep (f) metallization. reactive ion etching, (c) sidewall passivation, (d) isotropic etching, (e) passivation removal, andand (f) ( metallization.f) metallization.

Figure 7. Scanning electron microscope (SEM) images of the fabricated micromirror. (a) Top view FigurewhereFigure 7. theScanning7. Scanning in-plane electron electroncurvature microscope microscope is emphasized; (SEM) (SEM) images (bim) agestilted of theof view the fabricated fabricatedwhere micromirror.the micromirror. out-of-plane (a) Top (curvaturea) Top view view where is theemphasized.where in-plane the curvaturein-plane curvature is emphasized; is emphasized; (b) tilted view(b) tilted where view the where out-of-plane the out-of-plane curvature iscurvature emphasized. is emphasized.

More than one effect was encountered regarding the isotropic etching of silicon using SF6. First, a significantMore than dependence one effect ofwas the encountered etch rate on regard the trenching the width isotropic was etchingobserved, of siliconas shown using in SFFigure6. First, 8. Thea significant etch rate dependenceis normalized of with the respectetch rate to on the the etch trench rate of width the largest was observed, trench width. as shown The data in Figure markers 8. representThe etch rate the ismeasured normalized normalized with respect data to whilethe etch the rate solid of theline largest is a logarithmic trench width. fitting. The dataThis markerskind of logarithmicrepresent the behavior measured is well-known normalized for data a diffusion-limited while the solid etchingline is a process logarithmic [14]. Thefitting. etch This rate forkind a 10of μlogarithmicm trench width behavior is about is well-known one fifth the for rate a diffusion-limited for a 500 μm trench etching width. process The [14].second The observation etch rate for is a the 10 μm trench width is about one fifth the rate for a 500 μm trench width. The second observation is the

Micromachines 2017, 8, 134 8 of 13

More than one effect was encountered regarding the isotropic etching of silicon using SF6. First, a significant dependence of the etch rate on the trench width was observed, as shown in Figure8. The etch rate is normalized with respect to the etch rate of the largest trench width. The data markers represent the measured normalized data while the solid line is a logarithmic fitting. This kind of logarithmicMicromachines behavior 2017, 8, 134 is well-known for a diffusion-limited etching process [14]. The etch rate8 of for13 a 10 µMicromachinesm trench width2017, 8, is134 about one fifth the rate for a 500 µm trench width. The second observation8 of is 13 the correlationcorrelation between between the the mask mask opening opening width width and and the the isotropicisotropic etchingetching roughness as shown shown in in Figure Figure 9. 9.correlation The smaller between the maskthe mask opening opening is, widththe higher and th thee isotropic roughness. etching Considerable roughness asroughness shown in can Figure be The9. smallerThe smaller the mask the openingmask opening is, the is, higher the higher the roughness. the roughness. Considerable Considerable roughness roughness can be observedcan be inobserved the smallest in openingthe smallest by inspectingopening by the inspecting SEM images the withSEM theimages naked with eye, the while naked the eye, roughness while inthe the roughnessobserved inin thethe smallestlargest openingopening isby much inspecting less, but the still SEM observable. images with The theatomic naked force eye, microscope while the largest opening is much less, but still observable. The atomic force microscope (AFM) was used in (AFM)roughness was inused the in largest order toopening get a quantitative is much less, meas buturement still observable. for the roughness The atomic of the force largest microscope opening. order to get a quantitative measurement for the roughness of the largest opening. The top and 3-D The(AFM) top was and used 3-D tilted in order views to get of thea quantitative surface topology, measurement obtained for using the roughness the AFM on of anthe area largest of 10 opening. μm by tilted views of the surface topology, obtained using the AFM on an area of 10 µm by 10 µm, are shown 10The μ m,top are and shown 3-D tilted in Figure views 10a,bof the respectively.surface topology, The measuredobtained using roughness the AFM has on a peakan area of of319 10 nm, μm anby in Figure 10a,b respectively. The measured roughness has a peak of 319 nm, an average of 16 nm and average10 μm, areof 16 shown nm and in Figurean RMS 10a,b 22 nm. respectively. The lag effect The as measured well as the roughness surface roughness has a peak of of the 319 isotropic nm, an an RMS 22 nm. The lag effect as well as the surface roughness of the isotropic etching roughness can etchingaverage roughness of 16 nm and can an be RMSinterpreted 22 nm. knowingThe lag effect that aas diffusion well as the process surface governs roughness the transport of the isotropic of the beetchingetching interpreted roughnessradicals knowing from can thebe that interpretedplasma, a diffusion where knowing process it is thatcr governseated, a diffusion to the the transport processsubstrate, governs of where the etchingthe chemical transport radicals etching of the from theoccurs.etching plasma, Due radicals where to this itfrom diffusion is created, the plasma, proces to thes, where substrate,a lower it amount is wherecreated, of chemical etchants to the etchingissubstrate, received occurs. wherein thinner Due chemical totrenches. this etching diffusion This process,directlyoccurs. a Duerelates lower to this amountto the diffusion lag of effect. etchants proces Ats, the isa lower received same amount time, in thinnerwhen of etchants the trenches. amount is received Thisof etchants directlyin thinner is relatesnot trenches. enough, to theThis a lag effect.roughdirectly At surface the relates same resultsto time, the lagfrom when effect. the the etchingAt amount the sameprocess of etchants time, because when is not the enough, amountsurface a roughisof notetchants surfaceoverwhelmed is not results enough, by from the a the etchingetchants.rough process surface because results thefrom surface the etching is not overwhelmedprocess because by the the surface etchants. is not overwhelmed by the etchants.

FigureFigure 8. Normalized8. Normalized isotropic isotropic etching etchin rateg rate versus versus the the etched etched trench trench opening opening width width while. while. The trenchThe trenchFigure length 8. Normalized is 300 μm. isotropic The measured etchin datag rate (in versus markers) the is etched fitted totrench a logarithmic opening function width while. (in line). The lengthtrench is 300lengthµm. is The300 μ measuredm. The measured data (in data markers) (in markers) is ﬁtted is to fitted a logarithmic to a logarithmic function function (in line). (in line).

Figure 9. SEM images showing the roughness of the isotropically-etched trenches. The opening FigurewidthsFigure 9. SEMare9. SEM75 images μ mimages in ( showinga); 150showing μm the in roughnessthe(b) roughnessand 500 of μ them of in isotropically-etched the(c). isotropically-etched trenches. trenches. The openingThe opening widths arewidths 75 µm are in (75a); μ 150m inµ m(a); in 150 (b )μ andm in 500 (b) µandm in500 (c μ).m in (c).

Micromachines 2017, 8, 134 9 of 13 Micromachines 2017, 8, 134 9 of 13

Micromachines 2017, 8, 134 9 of 13

FigureFigure 10. 10.The The isotropic isotropic etchingetching roughnessroughness measured in in aa 500 500 μµmm trench trench using using the the atomic atomic force force microscope (AFM). A top view of the measured surface is shown in (a) while a tilted 3-D view is microscope (AFM). A top view of the measured surface is shown in (a) while a tilted 3-D view is shown Figureshown in10. ( bThe). isotropic etching roughness measured in a 500 μm trench using the atomic force in (b). microscope (AFM). A top view of the measured surface is shown in (a) while a tilted 3-D view is 5. Measurementshown in (b). Results and Discussion 5. Measurement Results and Discussion 5. MeasurementIn this section, Results the manufactured and Discussion 3-D curved micromirror is utilized for collimating the output beamIn thisof single-mode section, the manufacturedfibers and propagation 3-D curved loss micromirror reduction thereof. is utilized Consider for collimating the arrangement the output beamshown ofIn single-mode inthis Figure section, 11. ﬁbersthe manufactured and propagation 3-D curved loss reduction micromirror thereof. is utilized Consider for collimating the arrangement the output shown inbeam Figure of 11 single-mode. fibers and propagation loss reduction thereof. Consider the arrangement shown in Figure 11.

Figure 11. Measurement setup of the reflected beam from the fabricated mirror.

A single-modeFigureFigure 11. 11.opticalMeasurement Measurement fiber is setupinserted of the on reflecte reflected the silicond beam beam fromsubstrate from the the fabricated fabricatedsuch that mirror. mirror. its optical axis is parallel to the silicon substrate and tilted with respect to the mirror principal axis. For the sake of opticalA single-modespot characterization, optical fiber the reflectedis inserted beam on isthe captured silicon insubstrate the far fieldsuch on that a scanning-slitits optical axis beam is A single-mode optical fiber is inserted on the silicon substrate such that its optical axis is parallel parallelprofiler. toThe the observed silicon substrate beam ellipticity, and tilted defined with respby theect ratio to the of mirrorthe spot principal size in the axis. in-plane For the direction sake of to the silicon substrate and tilted with respect to the mirror principal axis. For the sake of optical opticalto the out-of-planespot characterization, direction, theis adjustedreflected tobeam be closeis captured to unity in (aboutthe far 1.05)field byon aletting scanning-slit the incidence beam spot characterization, the reflected beam is captured in the far field on a scanning-slit beam profiler. profiler.angle of Thethe beamobserved on thebeam mirror ellipticity, be about defined 45°. Thbye the axial ratio distance of the spotbetween size thein the optical in-plane fiber direction and the The observed beam ellipticity, defined by the ratio of the spot size in the in-plane direction to the tomirror the out-of-planewas adjusted direction, such that is the adjusted fiber tip to is be loca closeted toat theunity micromirror (about 1.05) focal by planeletting by the minimizing incidence out-of-planeangle of the direction, beam on the is adjusted mirror be to about be close 45°. to Th unitye axial (about distance 1.05) between by letting the optical the incidence fiber and angle the of the observed output beam diameter◦ at the far field. The collimated output beam spot diameter was themirrormeasured beam was on at theadjusted different mirror such belocations about that the 45away fiber. The from tip axial isthe loca distancemicromirrorted at betweenthe micromirrorand compared the optical focal to fiber planethe andmeasurements by the minimizing mirror of was adjustedthethe observedoptical such fiberthat output output the beam fiber beam tipdiameter without is located at using the at far the the field.micromirror micromirror. The collimated focal plane output by beam minimizing spot diameter the observed was outputmeasuredIn beam the at case diameter different of using atlocations a the standard far away field. single-mode from The collimatedthe micromirror fiber with output a andcore beam comparedradius spot of diameter4.5 to μthem fedmeasurements was from measured 1550 nm of at differentthelaser optical source, locations fiber a reduction output away frombeam in thethe without divergence micromirror using anglethe and micromirror. of compared the beam to by the a measurementsfactor of 2 was ofachieved the optical by the fiber outputmicromirror.In beam the case without The of outputusing using a beam standard the micromirror.has asingle-mode minimum waist fiber radiwithus a ofcore about radius 10 μofm, 4.5 which μm fed is afrom typical 1550 value nm laserforIn many thesource, caseoptical a ofreduction usingMEMS a applications. standardin the divergence single-mode A typical angle captured fiber of the with beam beam a core by profile a radius factor at oneofof 4.52 location wasµm achieved fed d fromis shown by 1550 the in nm lasermicromirror.Figure source, 12a. aThe The reduction profile output was inbeam thefitted has divergence to a a minimum Gaussian angle waistprofile of radi the withus beam averageof about by a root 10 factor μ meanm, ofwhich 2square was is a achievederrors typical smaller value by the micromirror.forthan many 1% andoptical The 1.5% output MEMS in the beamapplications. x- and has ay- minimum directionsA typical waist capturedrespectively radius beam ofas aboutprofile shown 10at in µone m,Figure location which 12b,c. is da is typicalThis shown is value anin forFigureindication many 12a. optical ofThe the MEMSprofile good was applications.performance fitted to a Gaussian Aoffered typical by profile captured the fabricatedwith beam average profilemicromirror, root atmean one squareusing location theerrorsd presentedis smaller shown in Figurethanmethod, 121%a. inand The terms 1.5% profile of in its wasthe phase fittedx- and front to y a -transformation Gaussiandirections profilerespectively function. with average asThis shown experiment root in meanFigure was square 12b,c. repeated errors This with is smaller an a indication of the good performance offered by the fabricated micromirror, using the presented thanspecial 1% and single-mode 1.5% in the fiberx- and withy -a directions core radius respectively of 2 μm working as shown at a in 675 Figure nm 12wavelength.b,c. This is The an indicationspecial method, in terms of its phase front transformation function. This experiment was repeated with a of the good performance offered by the fabricated micromirror, using the presented method, in terms special single-mode fiber with a core radius of 2 μm working at a 675 nm wavelength. The special

Micromachines 2017, 8, 134 10 of 13

MicromachinesMicromachines 2017 2017, 8, ,8 134, 134 1010 of of 13 13 of its phase front transformation function. This experiment was repeated with a special single-mode µ fiberﬁberfiber is with is positioned positioned a core radius at at the the of same same 2 m location location working used used at a for 675for the nmthe standard standard wavelength. one one because The because special of of th ﬁberthee constant constant is positioned focal focal length length at the ofsameof the the locationmirror mirror independent usedindependent for the standardof of the the wavelength wavelength one because value. value. of the A A constantreduction reduction focal in in the lengththe divergence divergence of the mirror angle angle independentof of the the beam beam byofby thea a factor factor wavelength of of 4.25 4.25 was was value. achieved. achieved. A reduction The The resulting resulting in the divergenceoutput output beam beam angle has has a ofa minimum minimum the beam waist bywaist a radius factor radius ofof of 4.25about about was 10 10 µ μachieved.μmm as as well. well. The This This resulting visible visible outputbeam beam will beamwill be be has used used a minimumhereinafter hereinafter waist for for evaluating radiusevaluating of about the the propagation propagation 10 m as well. loss loss This reduction reduction visible offeredbeamoffered will by by bethe the used micromirror. micromirror. hereinafter for evaluating the propagation loss reduction offered by the micromirror.

FigureFigure 12.12. Measured MeasuredMeasured spot spotspot profile: profile:profile: ( (a(aa)) )contour contourcontour plot; plot;plot; ( (b(bb)) )in-plane in-planein-plane beam beambeam profile profileprofile (markers) (markers)(markers) fitted fittedfitted to toto a a GaussianGaussian profile profile profile (line), (line), and and ( c()c ) out-of-plane out-of-plane beam beam profileprofile profile (markers)(markers) (markers) fittedfitted fitted toto to aa a GaussianGaussian Gaussian profileprofile profile (line).(line). (line).

TheThe collimation collimation of of the the beam beam by by the the micromirrormicromirro micromirror r was was also also evaluated evaluated by by measuring measuring the the detected detected powerpower in in free free space space with with a a limited-aperture limited-aperture detectordetector detector asas as shownshown shown inin in FigureFigure Figure 1313. 13..

FigureFigureFigure 13. 13. MeasurementMeasurement Measurement setup setup of of the the power power on on a a detector detector with with aperture aperture radius radius a.a .a.

Theoretically,Theoretically, the the transmitted transmitted power power in in terms terms of of the the system system aperture aperture radius radius a a and and the the beam beam spot spot Theoretically, the transmitted power in terms of the system aperture radius a and the beam spot radiusradius at at the the detector detector is is given given by by [36]: [36]: radius at the detector is given by [36]:  a 2 2 P = 1 − exp − 2 a  P = 1 − exp − 2 2  2 (15)  w 2  a (15) P = 1 −exp w−2 (15) w2 TheThe power power collected collected by by a a detector detector with with 3.5 3.5 mm mm aperture aperture radius radius is is shown shown in in Figure Figure 14a. 14a. The The powerpowerThe waswas power measuredmeasured collected atat by differentdifferent a detector distancedistance with 3.5 d mmd inin aperture thethe farfar radiusfieldfield awayaway is shown fromfrom in the Figurethe beambeam 14a. waist. Thewaist. power TheThe measurementswasmeasurements measured were at were different carried carried distance out out one one dtime timein the for for farthe the field collimated collimated away from beam beam the by by beamthe the micromirror, micromirror, waist. The measurementsdenoted denoted by by P Pc,c , andwereand another carriedanother out timetime one forfor time beambeam for theoriginallyoriginally collimated emiemitted beamtted byby the thethe micromirror,single-modesingle-mode denotedfiber,fiber, denoteddenoted by Pc, and byby anotherPPo.o . TheThe experimentaltimeexperimental for beam data originallydata are are depicted depicted emitted using byusing the markers markers single-mode whil while fiber,e the the theoretical denotedtheoretical by data Pdatao. Theare are experimentaldepicted depicted using using data lines. lines. are ThedepictedThe power power using is is normalized normalized markers while with with therespect respect theoretical to to the the init datainitiallyially are maximum depictedmaximum using power. power. lines. The TheThe measured measured power power is power normalized clearly clearly startswithstarts respect to to fall fall when towhen the the initially the beam beam maximum diameter diameter power.starts starts to Theto ex exceed measuredceed the the detector detector power clearlyaperture aperture starts as as given given to fall by by when Equation Equation the beam (9). (9). ThediameterThe micromirrormicromirror starts to exceed significantlysignificantly the detector reducesreduces aperture thethe propagationpropagation as given by Equation losseslosses withwith (9). respect Therespect micromirror toto thethe originaloriginal significantly fiberfiber output.reducesoutput. theTheThe propagation detecteddetected powerpower losses from withfrom respect thethe micromirrormicromirror to the original hashas fiber aa slowerslower output. roll-offroll-off The detected andand dropsdrops power toto from halfhalf the itsits maximummicromirrormaximum value value has a25 slower25 cm cm far roll-offfar from from and the the drops micromirror micromirror to half its co co maximummparedmpared to to value less less 25than than cm 8 far8 cm cm from without without the micromirror using using the the micromirror.comparedmicromirror. to less TheThe than ratioratio 8 cm betweenbetween without thethe using twotwo the detecteddetected micromirror. powerspowers The is ratiois depicteddepicted between inin the FigureFigure two detected 14b,14b, wherewhere powers thethe improvementisimprovement depicted in Figurereaches reaches 14 about b,about where 11–12 11–12 the dB. dB. improvement Indeed, Indeed, in in the reachesthe far far field, field, about the the 11–12 ratio ratiodB. between between Indeed, the the in detected thedetected far field, powers powers the isratiois given given between by: by: the detected powers is given by:

Micromachines 2017, 8, 134 11 of 13

a2 1 − exp −2 2 2 Pc θdiv−cd Gp = = (16) Po a2 Micromachines 2017, 8, 134 1 − exp −2 2 2 11 of 13 θdiv−od where the beam spot radius in the far field was replaced by wd/z = d/θ . The maximum improvement  a 2  o div 1− exp− 2  is achieved when the spot radius becomes much larger θ than2 d 2 the detector aperture. In this case, Taylor = Pc =  div−c  G p (16) expansion of the exponential terms can be appliedPo to seconda 2  order and Equation (16) becomes: 1− exp− 2   θ 2 2   div−od  2 θdiv−c 2 where the beam spot radius in the Gfarp−max field= was replaced= G by wd/zo = d/θdiv. The maximum(17) θ2 c improvement is achieved when the spot radius bedivcomes−o much larger than the detector aperture. In this case,Themaximum Taylor expansion power gain of the due exponential to the usage te ofrms the can collimating be applied mirror to second is given order by the and beam-waist Equation ratio(16) becomes: squared. For the fabricated micromirror and using the single-mode fiber at 675 nm, the power 2 gain is Gp = (4.25) = 18 that is about 12.5 dB, in goodθ 2 agreement with the measured data. This value G = div−c = G 2 is independent of the specific sizes of the beamp−max spot2 and thec detector aperture, as long as significant(17) θ − truncation loss is encountered. div o

Figure 14.14. (a) The normalized power collected by the detector;detector; (b) diffraction loss reduction in dBdB using thethe collimatingcollimating micromirror.micromirror. TheThe measured measured data data is is given given in in markers markers when when the the theoretical theoretical one one is givenis given in in lines. lines.

The maximum power gain due to the usage of the collimating mirror is given by the beam-waist 6. Conclusions ratio squared. For the fabricated micromirror and using the single-mode fiber at 675 nm, the power gain Opticalis Gp = (4.25) beam2 = collimation 18 that is about was analyzed12.5 dB, in and good successfully agreement carried with the out measured using a micro-reflector data. This value with is aindependent three-dimensional of the specific curved sizes surface. of the The beam surface spot wasand etchedthe detector in silicon aperture, by a techniqueas long as combiningsignificant deeptruncation reactive loss ion is etchingencountered. and isotropic etching technologies. The produced surface is astigmatic with an out-of-plane radius of curvature that is about half the in-plane radius of curvature. Having the incident6. Conclusions beam in-plane and inclined by 45◦ with respect to the principal axis, the reflected beam is kept stigmatic with about a 4.25-fold reduction in the beam expansion angle in free space and about 12-dB Optical beam collimation was analyzed and successfully carried out using a micro-reflector reduction in propagation losses. The fibre–mirror configuration may serve as a potential replacement with a three-dimensional curved surface. The surface was etched in silicon by a technique combining for the lensed fibers widely used in the MOEMS system. This replacement has the advantage of deep reactive ion etching and isotropic etching technologies. The produced surface is astigmatic producing monolithically integrated systems with a wider-band spectral response. with an out-of-plane radius of curvature that is about half the in-plane radius of curvature. Having Authorthe incident Contributions: beam in-planeY.M.S. and carried inclined out the by theoretical 45° with analysis,respect to studied the principal the roughness axis, the effect reflected usingoptical beam simulations,is kept stigmatic fabricated with the about structure, a 4.25-fold performed reduction the experiments in the andbeam wrote expansion the manuscript. angle D.A.in free participated space and in theabout design 12-dB of thereduction optical setup in propagation and the method losses. of roughnessThe fibre–mirror simulation. configuration B.S. participated may in serve the idea as a and potential design of the fabrication steps. T.B. participated in the idea, revised the paper and supervised the overall work. replacement for the lensed fibers widely used in the MOEMS system. This replacement has the Conflicts of Interest: The authors declare no conflict of interest. advantage of producing monolithically integrated systems with a wider-band spectral response.

Author Contributions: Y.M.S. carried out the theoretical analysis, studied the roughness effect using optical simulations, fabricated the structure, performed the experiments and wrote the manuscript. D.A. participated in the design of the optical setup and the method of roughness simulation. B.S. participated in the idea and design of the fabrication steps. T.B. participated in the idea, revised the paper and supervised the overall work.

Conflicts of Interest: The authors declare no conflict of interest.

Micromachines 2017, 8, 134 12 of 13

Abbreviations The following abbreviations are used in this manuscript:

RMS Root mean square MOEMS Micro-opto-electro-mechanical systems RIE Reactive ion etching PR Photo resist 3-D Three-dimensional OB Optical bench SEM Scanning electron microscope AFM Atomic force microscope

References

1. Wu, M.; Solgaard, O.; Ford, J. Optical MEMS for Lightwave Communication. J. Lightwave Technol. 2006, 24, 4433–4454. [CrossRef] 2. Sabry, Y.M.; Khalil, D.; Bourouina, T. Monolithic silicon micromachined free-space optical interferometers on chip. Laser Photonics Rev. 2015, 9, 1–24. [CrossRef] 3. Holmstrom, S.T.; Baran, U.; Urey, H. MEMS laser scanners: A review. J. Microelectromech. Syst. 2014, 23, 259–275. [CrossRef] 4. Elhady, A.; Sabry, Y.M.; Yehia, M.; Khalil, D. Dual-fiber OCT measurements. In Proceedings of the SPIE 8934, Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XVIII, San Francisco, CA, USA, 1 February 2014; p. 89343J. 5. Gaber, N.; Sabry, Y.M.; Marty, F.; Bourouina, T. Optofluidic Fabry-Pérot micro-cavities comprising curved surfaces for homogeneous liquid refractometry—Design, simulation, and experimental performance assessment. Micromachines 2016, 7, 62. [CrossRef] 6. Sabry, Y.M.; Omran, H.; Khalil, D. Intrinsic improvement of diffraction-limited resolution in optical MEMS fourier-transform spectrometers. In Proceedings of the 31st Radio Science Conference (NRSC), Cairo, Egypt, 28–30 April 2014; pp. 326–333. 7. Erfan, M.; Sabry, Y.M; Sakr, M.; Mortada, B.; Medhat, M.; Khalil, D. On-Chip Micro–Electro–Mechanical System Fourier Transform Infrared (MEMS FT-IR) Spectrometer-Based Gas Sensing. Appl. Spectrosc. 2016, 70, 897–904. [CrossRef][PubMed] 8. Syms, R. Principles of free-space optical microelectromechanical systems. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2008, 222, 1–18. [CrossRef] 9. Nussbaum, P.; Völkel, R.; Herzig, H.P.; Eisner, M.; Haselback, S. Design, fabrication and testing of microlens arrays for sensors and microsystem. Pure Appl. Opt. 1997, 6, 617–636. [CrossRef] 10. Zickar, M.; Noell, W.; Marxer, C.; de Rooij, N. MEMS compatible micro-GRIN lenses for fiber to chip coupling of light. Opt. Express 2006, 14, 4237–4249. [CrossRef][PubMed] 11. Lee, S.; Huang, L.; Kim, C.; Wu, M.C. Free-space fiber-optic switches based on MEMS vertical torsion mirrors. J. Lightwave Technol. 1999, 17, 7–13. 12. Oppliger, Y.; Sixt, P.; Stauffer, J.M.; Mayor, J.M.; Regnault, P.; Voirin, G. One-step 3D shaping using a gray-tone mask for optical and microelectronic applications. Microelectron. Eng. 1994, 23, 449–454. [CrossRef] 13. Mihailov, S.; Lazare, S. Fabrication of refractive microlens arrays by excimer laser ablation of amorphous Teflon. Appl. Opt. 1993, 32, 6211–6218. [CrossRef][PubMed] 14. Bourouina, T.; Masuzawa, T.; Fujita, H. The MEMSNAS Process: Microloading Effect for Micromachining 3D structures of Nearly All Shapes. IEEE/ASME J. Microelectromech. Syst. 2004, 13, 190–199. [CrossRef] 15. Kogel, B.; Debernardi, P.; Westbergh, P.; Gustavsson, J.S.; Haglund, A.; Haglund, E.; Bengtsson, J.; Larsson, A. Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process. IEEE J. Quantum Electron. 2012, 48, 144–152. [CrossRef] 16. Park, S.; Jeon, H.; Sung, Y.; Yeom, G. Refractive Sapphire Microlenses Fabricated by Chlorine-Based Inductively Coupled Plasma Etching. Appl. Opt. 2001, 40, 3698–3702. [CrossRef][PubMed] 17. Hsiao, S.; Lee, C.; Fang, W. The implementation of concave micro optical devices using a polymer dispensing technique. J. Micromech. Microeng. 2008, 18, 085009. [CrossRef] Micromachines 2017, 8, 134 13 of 13

18. Burns, D.M.; Bright, V.M. Micro-electro-mechanical focusing mirrors. In Proceedings of the Eleventh Annual International Workshop on Micro Electro Mechanical Systems, Heidelberg, Germany, 25–29 January 1998; pp. 460–465. 19. Cui, G.; Hannigan, J.M.; Loeckenhoff, R.; Matinaga, F.M.; Raymer, M.G. A hemispherical, high-solid-angle optical micro-cavity for cavity-QED studies. Opt. Express 2006, 14, 2289–2299. [CrossRef][PubMed] 20. Lee, M.; Choi, C.; Lim, K.; Beom-Hoan, O.; Lee, S.G.; Park, S.; Lee, E. Novel fabrication of a curved micro-mirror for optical interconnection. Microelectron. Eng. 2006, 83, 1343–1346. [CrossRef] 21. Moktadir, Z.; Koukharenka, E.; Kraft, M.; Bagnall, D.M.; Powell, H.; Jones, M.; Hinds, E.A. Etching techniques for realizing optical micro-cavity atom traps on silicon. J. Micromech. Microeng. 2004, 14, S82–S85. [CrossRef] 22. Kanbara, N.; Tezuka, S.-I.; Watanabe, T. MEMS tunable VCSEL with concave mirror using the selective polishing method. In Proceedings of the IEEE/LEOS International Conference on Optical MEMS and Their Applications Conference, Big Sky, MT,USA, 21–24 August 2006; pp. 9–10. 23. Ow, Y.; Breese, M.B.H.; Azimi, S. Fabrication of concave silicon micro-mirrors. Opt. Express 2010, 14, 14511–14518. [CrossRef][PubMed] 24. Wu, M.C.; Lin, L.-Y.; Lee, S.-S.; Pister, K.S.J. Micromachined freespace integrated micro-optics. Sens. Actuators A Phys. 1995, 50, 27–134. [CrossRef] 25. Flanders, D.; Whitney, P.; Masghati, M.; Racz, L. Mounting and Alignment Structures for Optical Components. U.S. Patent US006625372B1, 23 September 2003. 26. Do, K.; Sell, J.; Kono, R.; Jones, D.; Torro, R.; Kozlovsky, W.; Gupta, B.; Pace, D.; Chapman, W.; Sawyer, K. Micro Optical Bench for Mounting Precision Alighned Optics, Optical Assembly and Method of Mounting Optics. U.S. Patent US006775076B2, 10 August 2004. 27. Sabry, Y.M.; Khalil, D.; Saadany, B.; Bourouina, T. Integrated Wide-Angle Scanner Based on Translating a Curved Mirror of Acylindrical Shape. Opt. Express 2013, 21, 13906. [CrossRef][PubMed] 28. Sabry, Y.M.; Bourouina, T.E.; Saadany, B.A.; Khalil, D.A.M. Integrated Monolithic Optical Bench Containing 3-D Curved Optical Elements and Methods of its Fabrication. U.S. Patent Application 20130100424, 25 April 2013. 29. Omran, H.; Medhat, M.; Mortada, B.; Saadany, B.; Khalil, D. Fully integrated Mach-Zhender MEMS interferometer with two complementary outputs. IEEE J. Quantum Electron. 2012, 48, 244–251. [CrossRef] 30. Omran, H.; Sabry, Y.M.; Sadek, M.; Hassan, K.; Shalaby, Y.M.; Khalil, D. Deeply-etched optical MEMS tunable ﬁlter for swept laser source applications. Photonic Technol. Lett. 2013, 26, 37–39. [CrossRef] 31. Sabry, Y.M.; Khalil, D.; Saadany, B.; Bourouina, T. Three-dimensional collimation of in-plane-propagating light using silicon micromachined mirror. In Proceedings of the SPIE 8977, MOEMS and Miniaturized Systems XIII, San Francisco, CA, USA, 1 February 2014; p. 89770J. 32. Goodman, J.W. Introduction to Fourier Optics; Roberts and Company Publishers: Englewood, CO, USA, 2005. 33. Sabry, Y.M.; Saadany, B.; Khalil, D.; Bourouina, T. Silicon micromirrors with three-dimensional curvature enabling lens-less efﬁcient coupling of free-space light. Light Sci. Appl. 2013, 2, e94. [CrossRef] 34. Marty, F.; Rousseau, L.; Saadany, B.; Mercier, B.; Français, O.; Mita, Y.; Bourouina, T. Advanced etching of silicon based on deep reactive ion etching for silicon high aspect ratio microstructures and three-dimensional micro- and nanostructures. Microelectron. J. 2005, 36, 673–677. [CrossRef] 35. Boer, M.; Tjerkstra, R.; Berenschot, J.; Jansen, H.; Burger, G.; Gardeniers, J.; Elwenspoek, M.; Berg, A. Micromachining of Buried Micro Channels in Silicon. IEEE/ASME J. Microelectromech. Syst. 2000, 9, 94–103. [CrossRef] 36. Goldsmith, P. Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications; Wiley-IEEE Press: Hoboken, NJ, USA, 1997.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).