Chair of

OPTICAL INFORMATION TECHNOLOGY

(Lehrgebiet Optische Nachrichtentechnik)

Prof. Dr. Jurgen Jahns

Universitatsstraße 2758084 Hagen

Tel.: +49 2331 987-340Fax: +49 2331 987-352

E-Mail: jahns@fernuni-hagen.dewww.fernuni-hagen.de/ONT/LGONThome.html

Staff: Ext. E-Mail:

Dr. Qing Cao 1133 Qing.Cao@fernuni-hagen.deDr. Stuart Fancey (until 02/2002)Matthias Gruber 1131 Matthias.Gruber@fernuni-hagen.deManfred Jarczynski (since 05/2002) 1123 Manfred.Jarczynski@fernuni-hagen.deSusanne Kinne (until 08/2002) Susanne.Kinne@fernuni-hagen.deHans-W. Knuppertz (since 02/2002) 1128 Hans.Knuppertz@fernuni-hagen.deThomas Seiler (since 01/2002) 1122 Thomas.Seiler@fernuni-hagen.deDr. Stefan Sinzinger (until 3/2002)

Students:

Wael Abu Mari (until 06/2002)Andreas Borchmann (since 06/2002) 1125 Andreas.Borchmann@fernuni-hagen.deMounir El Youssoufi (since 06/2002) 1125 Mounir.ElYoussoufi@fernuni-hagen.de

Secretary:

Susanne Oetzel 1120 Susanne.Oetzel@fernuni-hagen.de

Photon sieve: paraxial theory

Qing Cao and Jurgen Jahns

Recently, a novel diffractive optical element named photon sieve, which consists of a greatnumber of pinholes properly distributed over the Fresnel zones, was proposed for thefocusing and imaging of soft x-rays and EUV radiations. In the initial work [1], the au-thors employed the traditional Fresnel zone plate theory and the numerical calculation ofFresnel-Kirchoff diffraction integral to analyse and design the photon sieve.

By use of a local Taylor expansion of the integrated function of the paraxial Fresnel diffrac-tion formula, the small-size property of the individual pinholes, we derive the paraxialexpression for the far-field of the individual pinholes. In terms of this expression and theliner superposition principle, we present the paraxially individual far-field model [2] forthose low-NA photon sieves. According to this model, the selection condition for thosepinholes are given by

k[Ln + r2n/(2q)] = 2mπ, Jinc(kanRn/q) > 0, (1)

k[Ln + r2n/(2q)] = 2(m + 1)π, Jinc(kanRn/q) < 0. (2)

where r2n = x2

n + y2n, Rn = [(xn + gnq)

2 + (yn + hnq)2]0.5; (xn,yn) and an are the central

position and the radius of the pinhole; k is the wavenumber, q is the distance between thephoton sieve and the focal point; Ln is the eikonal at (xn,yn); Jinc(.) is the traditional Jincfunction; gn and hn are the x- and the y-directional partial derivatives of the eikonal at(xn,yn). The first and the second conditions of Eq. (1) [or Eq. (2)] are used to determinethe central positions and the radii of those pinholes, respectively.

As an example, we derive the change of the field value Un(0,0) at the focal point from then-th pinhole with the ratio d/w, where d is diameter of the pinhole and w is the width ofthe local Fresnel zone. The expression is simple given by

Un(0, 0) ∝ (d/w)J1[π(d/w)/2]. (3)

The functional relation of Eq. (3) is drawn in the following figure, which is in excellentagreement with the calculated curve labeled “Total” in Fig. 2 of Reference [1].

0 1 2 3 4 5 6 7 8 9-2

-1

0

1

2

d/w

Am

plitu

de (

arbi

trar

y un

its)

[1] L. Kipp et al., “Sharper images by focusing soft X-rays with photon sieves”, Nature (London) 414(2001) 184-188

[2] Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model”, J.Opt. Soc. Am. A 19 (2002) 2387-2393.

Photon sieve: non-paraxial theory

Qing Cao and Jurgen Jahns

Photon sieves [1], which consist of a great number of pinholes whose positions and radii areproperly chosen, are a new class of diffractive optical elements. Recently, we developedthe paraxially individual far-field model [2] for the focusing analysis of low-numerical-aperture (low-NA) photon sieves. We now [3] extend this model to the non-paraxial caseof high-NA photon sieves working in the soft x-ray region, for which the paraxial diffrac-tion formula is invalid.

By use of a local Taylor expansion of the integrated function of the exact Rayleigh-Sommerfeld diffraction formula, the small-size property of the individual pinholes, wederive the non-paraxial expression for the far-field of the individual pinholes. In termsof this expression and the liner superposition principle, we present the non-paraxiallyindividual far-field model for those high-NA photon sieves. According to this model, thediffracted field Un(0,0) at the focal point from the n-th pinhole is given by

Un(0, 0) = kqAna2nexp[jk(Ln + Qn)]Jinc(kanRn/Qn)/Q2

n (1)

where Rn = [(xn+gnQn)2+(yn+hnQn)2]0.5; (xn,yn) and an are the central position and theradius of the pinhole; k is the wavenumber, q is the distance between the photon sieveand the focal point; Qn is the optical path length from the center of the pinhole to thefocal point; An and Ln are the real amplitude and the eikonal at (xn,yn); gn and hn arethe x- and the y-directional partial derivatives of the eikonal at (xn,yn).

The crucial idea of photon sieve is that all those individual diffracted fields have thesame argument at the desired focal point. By use of Eq. (1), we then briefly express theselection condition for those pinholes as

k(Ln + Qn) = 2mπ + constant, Jinc(kanRn/Qn) > 0, (2)

k(Ln + Qn) = 2(m + 1)π + constant, Jinc(kanRn/Qn) < 0, (3)

where the constant can be an arbitrary value. The first and the second conditions of Eq.(2) [or Eq. (3)] are used to determine the central positions and the radii of those pinholes,respectively.

We have showed that the model is highly accurate when the condition Nf ≤ 0.05 and(NA)2Nf � 1 are satisfied, where Nf is the Fresnel number of the individual pinhole andNA is the numerical aperture of the photon sieve. We also test the validity of this modelfor a typical high-NA photon sieve, whose spatial resolution is as high as 7 nm.

[1] L. Kipp et al., “Sharper images by focusing soft X-rays with photon sieves”, Nature (London) 414(2001) 184-188

[2] Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model”, J.Opt. Soc. Am. A 19 (2002) 2387-2393.

[3] Q. Cao and J. Jahns, “Nonparaxial model for the focusing of high-numerical-aperture photon sieves”,Submitted to J. Opt. Soc. Am. A.

Generalized Jinc functions

Qing Cao

The Fraunhofer diffraction of circular apertures has the Airy pattern distribution and isdescribed by the traditional Jinc function [1] [2]

Jinc(u) =J1(u)

u. (1)

Eq. (1) can also be expressed as the integral form

Jinc(u) =1

u2

∫ u

0vJ0(v)dv. (2)

We define a family of generalized Jinc functions as the following forms [3]

Jincn(u) =1

u2n+2

∫ u

0v2n+1J0(v)dv, (3)

where the order n is a non-negative integer, namely n=0,1,2,.... In particular, the zero-order one is just the traditional Jinc function. By use of the mathematical inductivemethod, we derive the following closed-form expression

Jincn(u) =n∑

m=0

(−2)m n!

(n − m)!

Jm+1(u)

um+1. (4)

This family of functions are very similar. To have an intuitive impression, we drawJinc0(u), Jinc1(u) and Jinc2(u) in the following figure.

In terms of these functions, we present [3] the series-form expressions for the Fresneldiffraction of circular apertures illuminated by converging spherical waves or plane waves.The leading term is nothing but the Airy formula for the Fraunhofer diffraction of circularapertures, and those high-order terms are related to those high-order Jinc functions,respectively. In particular, we show that, for the illumination of a converging sphericalwave, the first nineteen terms are sufficient for describing the three-dimensional fielddistribution in the whole focal region. We believe that this family of functions can alsofind applications in other areas, especially in those circularly symmetric systems.

[1] M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chapter 8.

[2] A. E. Siegman, Lasers, (Oxford University, Oxford, 1986), Section 18.4.

[3] Q. Cao, “Generalized Jinc functions and their application to the focusing and diffraction of circularapertures”, J. Opt. Soc. Am. A, In press.

Generalized confocal imaging system

Qing Cao, Matthias Gruber, and Jurgen Jahns

The classical 4-f imaging setup is widely used in optical interconnects because it offerstelecentricity and good imaging performance for extended fields. As shown in Fig. 1, oneimportant feature of this setup is that all the object distance d1, the image distance d2 andthe focal length f are the same. However, design restrictions in practical setups often donot allow one to choose the parameters d1, d2 and f in this way. This is particularly the casefor planar-integrated free-space optical interconnects [1]. To overcome this disadvantageand to provide additional design freedom, we propose here a generalized confocal imagingsystem, shown in Fig. 2.

f f

f fd1=f d2=f

f f

f f

F

d1 d2

φ1 φ2 φ1 φ2

Fig. 1 Fig. 2

According to matrix optics, the total matrix M between the object plane and the imagingplane in Fig. 2 can be determined to be

M =

⌊−1 2f −d1 −d2 −f2

F

0 −1

⌋. (1)

On the other hand, according to the Collins’ diffraction integral [2], one knows thatthe complex amplitude distribution φ2(x2,y2) at the imaging plane has a simple rela-tion φ2(x2,y2)=φ1(x1,y1) with the complex amplitude distribution φ1(x1,y1) at the objectplane, when A=D=-1 and B=C=0, where A, B, C, D are the four matrix elements of theABCD matrix. From Eq. (1) one can find that the three conditions A=-1, D=-1 andC=0 is always satisfied for the structure of Fig. 2. The fourth relation B=0 holds when

d1 + d2 +f 2

F= 2f (2)

Eq. (2) is the imaging condition for the setup of Fig. 2. In particuar, the classical 4-fsetup corresponds to the case of F=∞ and d1=d2=f. Because the two f lenses still havea common focal plane and the added F lens is just located at this plane, we name thissetup the generalized confocal imaging system.

Compared with the conventional 4-f setup, the main advantage of this setup is that theobject distance d1 and the image distance d2 can be almost artitrarily chosen. Thisadvantage is especially suitable for planar-integrated micro-optical system [1], for whichthe object distance d1 are often different from the imaging distance d2.

[1] J. Jahns, “Planar packaging of free-space optical interconnects”, Proc. IEEE 82 (1994) 1623-1631.

[2] S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics”, J. Opt. Soc. Am.60 (1970) 1168-1177.

Highly reflective and robust Ag-Al compound mirrors on fused silica wafers

M. Gruber, R. Kerssenfischer, Th. Seiler

In planar-integrated free-space optics signals may have to bounce up and down a consid-erable number of times inside the planar substrate to reach their destinations. To obtaina high coupling efficiency it is therefore mandatory to cover the optical elements with ahighly reflective coating. Thin metal films are often used because they can convenientlybe applied at low cost by means of physical vapor deposition.

Aluminum is well-suited for its chemical passivity and its good adherence to fused silica,however, it reflects less than 90 % of the light in the 850 nm wavelength region. Silver, bycontrast, has a high reflectivity of more than 99 % but lacks the other two properties. Sothe idea is to use a compound coating that combines the advantages of both metals.

First the optical elements are fabricated on a fused silica wafer using lithography and dryetching. They are all surrounded by ditches of typically 1µm width and depth. Thena thin layer of about 100 nm of silver is deposited first, followed by a layer of aluminumwith a thickness of about 200 nm (Fig. 1). In this way the aluminum can mechanicallyanchor the mirrors in the ditches and shield the silver from aggressive chemicals in theenvironment. From the glass side the coating has the high reflectivity of silver.

fused silica wafer

Ag Al

etched ditch

Fig. 1: Idea of a Ag-Al compound mirror.

sample mirror

S

D

Fig. 2: Measurement setup.

For experimental characterization a sample mirror of this type was fabricated. In thissample the aluminum patch was made larger to be able to compare the performance ofthe two metals. The difference in reflectivity can already be perceived clearly with thenaked eye or a CCD camera (Fig. 3). For a quantitative evaluation the setup of Fig. 2was used. During the measurement the sample was shifted along the measurement pathshown in Fig. 3.

fused silica

Ag

Al

measurement path

Fig. 3: Experimental mirror sample.

reflectivity [%]

20

40

60

80

100

Fig. 4: Measured reflectivity.

Several recorded intenity values are plotted in Fig. 4. One can see three distinct levelsas expected. About 7 % of the incoming intensity was reflected at positions without anycoating due to Fresnel reflections from the two glass surfaces. The silver part showeda reflectivity of about 98 %, the aluminum part of just below 80 % which is somewhatworse than expected. The mechanical stability was good and so far no degradation of theperfomance due to chemical reactions was observed.

Cascadable fan-out module for short-haul parallel optical interconnects

M. Gruber, R. Kerssenfischer, J. Jahns

The ever growing demand for bandwidth in communication and computing systems makesit increasingly necessary to use optical technology not just for long-haul but also for short-haul interconnects which are usually highly parallel. Fiber ribbon-based systems with MTconnectors have emerged as a de-facto standard in this domain in recent years. To be ableto meet future interconnection demand highly compact and scale-proof switching fabricsare needed for these systems.

We propose a solution based on planar-integrated free-space optics because it supports atruely 3-dimensional parallel system architecture and provides VLSI compatibility. Fordemonstration a key component of a switching fabric, an optical fan-out module, wasconstructed. With a cascaded design approach we can conveniently tailor an opticalsystem that is perfectly adjusted to any required fan-out. Our demonstrator (Fig. 1)implements a 1 × 4 fan-out of 12 optical signals that are coupled into the free-spaceoptical system via MT-mounted single-mode fibers; for the out-coupling MT-mountedmulti-mode fibers are used. The MT connectors are linked to the free-space system via amicro-machined metal fixing plate [1]. Fig. 2 shows the schematic structure of the 1 × 2fan-out stage that was basically repeated four times in our demonstrator.

fixing plate

MT connectors

DOEs

dielectricmirror

Fig. 1: MT-based 1×4 fan-out demonstator.

BS

L1 L2 L3

D

Fig. 2: Schematic of a single 1×2 fan-out stage.

The optical components were designed as surface-relief diffractive phase elements andthe optical system was fabricated using iterated binary lithographic copying and reactiveion etching techniques. Reflective coatings were realized as Ag-Al compound mirrors [2].In experimental tests the optical fan-out could be successfully verified and a couplingefficiency of −11.4 dB (for each of the four output channels) was measured. Although thisis not yet good enough for real-world applications it still marks an improvement of aboutan order of magnitude compared to previous experimental studies [1].

mechanical mount

DOEs

Fig. 3: Planar-integrated optical system.

fixing plate

MT connectors

DOEs

Fig. 4: System with plate and MT connectors.

[1] M. Gruber, E. ElJoudi, J. Jahns, S. Sinzinger, Appl. Opt. 40 (2001) 2902-2908.

[2] M. Gruber, R. Kerssenfischer, J. Jahns, “Highly reflective and robust . . .”, see this Annual Report.

Concept and approaches of planar integrated free-space opticsin the HOLMS-project

Manfred Jarczynski, Matthias Gruber, Jurgen Jahns

In the last Annual Report [1] the tasks ofONT in and the aims of the EU-fundedHOLMS-project (High-Speed Opto-ElectronicMemory Systems) were outlined. One yearlater we want to give an overview of theendeavours for concept, layout and design.Two different kinds of PIFSO-systems arenecessary, one for the interconnections betweenmemory-multi-chip-module (MEM-MCM) andPCB-embedded waveguides as far as fibre con-nectors and the other one for similar tasks onthe processor-multi-chip-module (CPU-MCM)[2]. A first design approach for the intercon-nection between opto-electronic elements onthe MEM-MCM and waveguides was realisedand can be viewed in figure 1.

Fig. 1: The realisation of the MEM-OUT-PIFSO-system (bottom) and ascaled view of the diffractive opticalelements.

The objectives of this design, which is called the MEM-OUT-PIFSO, are a fan-out offour and a fan-in of two as well as interface elements for laser-diodes and waveguides.The design concept is based on a multi-channel imaging system, with an interface andbeam splitting element in the centre of the symmetrical setup. The optical input elementconsists of a combined lens and grating. The lens collimates the beam from the sourceand the grating generates a four-times beam splitting. To both sides diffractive opticalelements (DOE) for a re-deflection follow the input DOE. The fan-in is generated by theoutput DOEs. These DOEs deflect and focus the beam on the destination area.

First experimental results show the functionality of the input DOE. This can be viewedin figure 2, which presents the light distribution generated by the input-DOE at the rearplane of the planar substrate. It can be seen, that the zero order (in the middle of thefour desired spots) is not suppressed well. Therefore, the efficiency of the DOE is not welland further investigations have to be spent on the design on such components.

Fig. 2: First experimental result of the input-DOE, which combines a collimating lens and a beamsplitter.

[1] S. J. Fancey et al., “Low Latency OPTO-Electronic Processor Memory Interconnection Demonstra-tor”, FernUniversitat, Fachbereich Annual Report 2001, p. 89

[2] M. Jarczynski, M. Gruber, J. Jahns, “Planar integrated free-space optics for coupling and fanin/-outin a low latency processor memory interconnection”, Proc. SPIE Photonics Fabrication Europe 2002

Talbot and Montgomery interferometers as tapped delay-line filters

Jurgen Jahns, Adolf Lohmann* and Hans Knuppertz* Lehrstuhl f. Nachrichtentechnik, Univ. of Erlangen-Nuremberg

With the advent of practical ps/fs-laser systems on the one hand and the continuous in-crease of the data rates in communications and computing systems, the need for temporaloptical filtering devices arises that operate at very large frequencies. This need stemsfrom the fact that systems applications often require operations such as beam shaping,signal regeneration, encoding and decoding, etc.. Here, we are interested in grating in-terferometers based on self-imaging since they can be realized in a compact form usingfree-space or waveguide optics and since gratings offer a good amount of design flexibility.

Let us briefly review the self-imaging phenomenon, here, only for the one-dimensionalcase. Generalization to two dimensions (in either cartesian or cylindrical coordinates) isstraightforward. The “grating” is described as:

G1(x) =∫

G1(ν)exp(2πiνx)dν (1)

withG1(ν) =

∑m

Amδ(ν − νm) (2)

Propagation from the G1-location over a finite distance ∆z is described by

G1(ν) → G1(ν)exp⌊2π∆z

λ

√1 − λ2ν2

⌋(3)

In the paraxial case, one may approximate this as

G1(ν) → G1(ν)exp[−iπλ∆zν2

](4)

For this case, a grating with νm=mν1 (m:integer) yields the Talbot effect [1], i.e., self-images appear at locations ∆z=kzT =k(2/ν2

1λ) with k=1,2,3.... In an earlier paper [2],a temporal filter was described based on the Talbot self-imaging effect. The underlyingidea was to use specially designed phase gratings separated by a distance ∆z. The secondgrating is used to combine the diffraction orders coherently into a single output beam sothat the light can be collected by a point detector. Hence, the ideal grating pair wouldsatisfy G1(x)G2(x)=1. As can be seen from eq. (4), however, the time delays for theTalbot interferometer increase quadratically with m which makes it unsuitable for theimplementation of general tapped delay-line filters.

Here we consider a different case of self-imaging as described in the theory of W. D.Montgomery [3]. We specify ν2

m=(1/λ)2-(m/zM)2 with m=1,2,3,... For the 2-D case,we replace ν2 → ν2

x + ν2y . Inserting this into eq. (3) and using ∆z = M · zM we now

obtain a linear time delay τm. For the m-th diffraction order we obtain τm = mMλ/c. AMontgomery interferometer can thus be described by a temporal impulse response:

h(t) =N∑

m=0

hmδ(t − mτ) (5)

where the coefficients hm and the time delays can be chosen by design.

[1] H.F. Talbot, Phil. Mag. 9 (1836) 401-407.

[2] J. Jahns, E. ElJoudi, D. Hagedorn, S. Kinne, Optik 112 (2001) 295-298.

[3] W. D. Montgomery, J. Opt. Soc. Am. 57 (1967) 772-778.

Montgomery Interferometer with complementary phase gratings

H. Knuppertz, J. Jahns and Th. Seiler

As a continuation of earlier research [1] we investigate the self-imaging effect in a generalform, based on Montgomery’s theory for periodic wave fields. The objective is to constructan interferometer, that may serve as a tapped delay line filter for the shaping of very shorttime signals in the range of femtoseconds. The advantage of the new design, comparedwith the Talbot interferometer, is the linear time-behaviour of the interferometer. Onepossible application is an equalizer in long distance optical transmission lines.

The result of the Montgomery theory [2] is that any optical element can create periodicwave fields in the propagating direction, if only the far field shows the characteristic Mont-gomery ring pattern on the whole or partial; see also [3]. An example for this pattern isshown in fig.2 left. This pattern serves as input for an iterativ Fourier transform algorithm(IFTA), that yields pixel patterns for complementary phase gratings, consisting of 5132

pixels each sized 8·8 (µm)2. The four-level gratings then are fabricated with the help ofour clean-room facilities.

For Montgomery phase gratings, one observes a complex amplitude identical to thatof theobject at distances ∆z=MzM behind the element where zM is the Montgomery distance.The idea for our experimental setup was, to illuminate two complementary phase grat-ings separated by ∆z=zM with a plane wave. If both gratings are properly aligned, a plane

wave should again emerge behind the secondgrating.

Our first experiment verifies this prediction.Fig.1 shows the setup for the test of twocomplementary phase gratings. Behind thesecond element the plane wave is collimated bya lens. In the focus we observe the predictedspot (Fig.2 right). The calculated Montgomerydistance for our design was zM=9.105 mm,confirmed by the measurement with the value9.1 mm.

Fig. 1: Interferometer setup for the self-imaging experiment consisting of com-plementary phase gratings at the Mont-gomery distance.

Fig. 2: Far field diffraction pattern of a single grat-ing (left) and of a pair of two complementary phasegratings (right).

[1] J. Jahns, E. ElJoudi, D. Hagedorn,S. Kinne, “Talbot interferometer as atime filter”, Optik 112 (2001) 295-298

[2] W. D. Montgomery,“Self-imaging ob-jects of infinite apertur”, J. Opt. Soc.Am. 57 (1967) 772-778.

[3] A. W. Lohmann, Optical InformationProcessing, Uttenreuth (1979), see:“Yet another look at Talbot-images”,pp. 108-111.

Virtual laboratory experiments for an internet-based photonics course

M. Gruber, M. El Joussoufi, A. Borchmann, J. Jahns

In connection with the bachelor study program at FernUniversitat Hagen the ONT groupstarted to develop a virtual lab course on photonics in 2001 [1, 2]. It is intended to exploitthe various new possibilities for distance-teaching provided by the internet. Students candownload Java applets that invite them to explore the working principles of importantoptical and photonic setups, and to test and observe the influence of basic experimentalparameters so that they can acquire a feeling for the underlying physical phenomena. Thusthe course prepares students for real laboratory work in a rather realistic environment.

The virtual lab course has recently been expanded by two new applets dealing with thecharacterization of a communication system by means of an eye diagram and the couplingof optical signals into fibers.

Fig. 1 shows the control windowof the first applet. Pressingthe start button sets off threeprocesses: A random signal isgenerated and displayed in thecenter window; its transmis-sion through a communicationchannel is simulated and theemerging eye diagram shown inthe top window; the transmit-ted and AD-converted signal isdepicted in the bottom win-dow. By means of control barssystem parameters like signallevel, noise level, or detectionthreshold can be modified.

Fig. 2 shows the control win-dow of the second applet. Itsimulates the coupling of lightfrom a LED or a LD into afiber on the basis of ray tracing.Control buttons allow one tochange various geometrical andoptical parameters such as thedistance between light sourceand fiber, its core diameter, orN.A.; in addition, a lens withvariable focussing power andsize can be added to the basicsetup. The coupling efficiencyis continuously monitored.

threshold for�AD-conversion

high

low

additive �noise

start

reset

detected signal

random binary input signal

output signal after AD conversion

Fig. 1: Graphical interface of the eye diagram simulation applet.

Fig. 2: Graphical interface of the LD/LED-fiber coupling applet.

[1] See http://www.ice-bachelor.fernuni-hagen.de/kursbe/kurs-20038.html.de

[2] See the Annual Report 2001, p. 84.