Optical attenuation from moving lenses settled between fiber-optic collimators

Sarun Sumriddetchkajorn Intelligent Devices and Systems Research Unit

National Electronics and Computer Technology Center Pathumthani, Thailand

sarun.sumriddetchkajorn@nectec.or.th

Abstract— This paper proposes and theoretically shows how movable lenses inside an imaging system situated between two fiber-optic collimators alter the optical beam waist tremendously and thereby induce high optical attenuation. Under the condition that the maximum movement of the lens is comparable to the focal length of the lens, a higher maximum optical attenuation (e.g., >30 dB) can be accomplished under a shorter focal-length (e.g., <100 �m) lens. This result implies that a very-compact in-line high-dynamic-range variable fiber-optic attenuator can be easily implemented.

Keywords— Variable optic attenuators, Fiber-optic collimators, Fiber-optic communications, Moving lenses, Tunable lenses, Optical MEMS.

I. INTRODUCTION Apart from optical switches, a variable fiber-optic

attenuator (VFOA) is one of the basic fiber-optic components for several applications ranging from optical communications to photonic signal processing. Most VFOAs deployed in today fiber-optic networks are simply based on mechanical movement of a reflective surface in the optical path. In addition, several movements of the objects such as tilting mirrors, translating mirrors, translating optical filters, and moving membranes were proposed and experimentally demonstrated [1-6] in order to block some part of the optical beam or to misalign the optical beam at the output fiber-optic collimator.

Based on the understanding that optical attenuation can be generally achieved via longitudinal, lateral, and angular misalignment between fiber-optic collimators [7], the latter two mechanisms are typically chosen as they offer higher dynamic range (e.g., 30 dB) under small movements of 500 µm and 0.4°, respectively. For the longitudinal movement, a very long moving distance of > 50 cm or a tunable long-focal-length lens [8] is required because the two fiber-optic collimators are already positioned in a straight line and their output optical beams slightly diverge. In this paper, we show for the first time that very high optical attenuation can actually be accomplished under a very-short longitudinal distance leading to a very-compact in-line high-dynamic-range VFOA.

II. PROPOSED STRUCTURE Our VFOA structure composes of only two fiber-optic

collimators arranged in a straight line as shown in Fig.1. Note that each fiber-optic collimator is fabricated by positioning a graded index (GRIN) lens in front of a single mode optical fiber (SMF) with a desired spacing. The key idea in achieving high optical attenuation for this longitudinal configuration is to greatly alter the optical beam waist at the receiving fiber-optic collimator. This can be done by inserting a 1:N imaging system between these two fiber-optic collimators. If the optical beam goes from left to right, N is equal to F2/F1. Otherwise, it is equal to F1/F2. The distance between the two lenses is equal to F1+F2. Similarly, the spacing between the lens i (i = 1 and 2) and its adjacent GRIN lens is Fi. This arrangement is also known as a 4F optical system.

Fig. 1. Proposed movable lens-based VFOA architecture.

From Fig.1, the optical beam emerging from the input fiber-optic collimator is a Gaussian-like optical beam with an optical beam waist of wT. After it passes through the 1:N imaging system, it changes to wR. In addition, the two lenses inside the 1:N imaging system can be electronically or magnetically controlled to longitudinally move with offsets of Δf1 and Δf2, altering the optical beam waist wR and the radius

of curvature of the optical beam (RR). Because the changed wR does not match wR for the receiving fiber-optic collimator, optical attenuation is obtained.

III. THEORETICAL ANALYSIS For the longitudinal misalignment between two fiber-optic

collimators, optical loss in dB can be expressed as [7].

( )( )[ ] ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−= 22

2

1/

/4log10)(

TR

TR

ww

wwdBLoss . (1)

Because wR and RR can be manipulated via moving the two lenses inside the 1:N imaging system, wR and RR at the receiving fiber-optic collimator can be related to the optical beam waist (wT) and the radius of curvature (RT) of the optical beam at the transmitting fiber-optic collimator as.

)/1()/1(11

2T

T

RRR qBAqDC

wj

Rq ++=−=

πλ . (2)

Here, λπ /2

TT wjq = , λ is the wavelength of the optical beam, and RT is equal to infinity for the plane wave. A, B, C, and D are elements of ABCD matrix of the 1:N imaging system. They can be determined as follows.

,1/1

11/101

101

101

1/101

101

1

11

1

1122

2

22

⎥⎦

⎤⎢⎣

⎡−

Δ+⎥⎦

⎤⎢⎣

⎡−

⎥⎦

⎤⎢⎣

⎡ Δ−⎥⎦

⎤⎢⎣

⎡ Δ+⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡ Δ−=⎥

⎦

⎤⎢⎣

⎡

FfF

F

fFfFF

fFDCBA

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

ΔΔ+Δ−−Δ−Δ

ΔΔ+ΔΔ−Δ−ΔΔΔ+Δ−−=⎥

⎦

⎤⎢⎣

⎡

21

21

21

21

2

1

21

12

21

212

21

221

11

22

1

2

21

21

21

22

1

2

FFff

FFf

FF

FFff

FFff

FFfff

FFf

FF

FFff

FFf

FF

DCBA

. (3)

Taking into consideration that fiber-optic collimators used

in one fiber-optic component such as an optical switch and a VFOA are the same, the 1:1 imaging system (F1=F2=F) is preferred. In addition, for simplicity in design and implementation, only one active component is needed. Hence, in this work, Δf1 is set to 0 and Δf2 is changed to Δf. Under these conditions and by substituting Eq(3) in Eq(2), RR and wR can be written, respectively, as.

( )

( ) ( )42222422

4222

////1

TT

TR wFfwfFf

wfR

πλπλπλ

Δ+Δ+ΔΔ+

= , (4)

and

( )( )2

4222

//1/1

FfFfwf

ww TTR Δ+Δ−

Δ+=

πλ . (5)

IV. SIMULATION RESULT From Eqs(4) and (5), it can be clearly observed that RR and

wR can be controlled by altering the longitudinal position of the lens inside the 1:1 imaging system, thus affecting the optical loss value in Eq(1). In addition, Δf=0 makes RR=∞ and wR=wT. This implies that a zero optical loss value is theoretically obtained.

As we would like to have a compact VFOA, the 4F distance should not be too long. In this work, we consider three imaging systems. The first one has two 1-cm focal length lenses. Each lens can be programmed to axially move at a longest distance of 1 cm (i.e., Δfmax/F=1). The 2nd imaging system composes of two 1-mm focal length lenses. Again, each lens can be set to move at a 1-mm longest distance. For the 3rd imaging system, each lens has a focal length of only 100 µm and it can be longitudinally translated with a maximum distance of 100 µm.

Fig. 2. Relationship between the normalized change of lens position Δf/F and the radius of curvature RR. Dash, solid, and dash-dot lines represent three imaging systems where 1-cm, 1-mm, and 100-µm focal-length lenses are employed, respectively.

Fig. 3. Changes in the optical beam waist ratio versus the normalized change of lens position Δf/F. Dash, solid, and dash-dot lines represent three imaging systems where 1-cm, 1-mm, and 100-µm focal-length lenses are employed, respectively.

In all three cases, RR equally reduces from infinity to less than one during the change in Δf from 0 to its maximum normalized value as shown in Fig.2. This result implies that the wavefront of the optical beam at the receiving fiber-optic collimator is transformed from its original plane wave to a diverging spherical wave.

For the optical beam waist wR, it tremendously reduces more than 10 times from its original beam waist of wT when Δf reaches its normalized maximum value as shown in Fig.3. In addition, a shorter focal-length lens shows a stronger rapid change in the optical beam waist.

Fig. 4. Simulated optical loss in dB versus the normalized change of lens position Δf/F. Dash, solid, and dash-dot lines represent three imaging systems where 1-cm, 1-mm, and 100-µm focal-length lenses are employed, respectively.

As the optical beam waist wR is altered via Δf, high optical attenuation levels are expected. From Fig.4, when Δf is equal to the focal length of the lens, an imaging system having 100-µm focal length lenses give the highest maximum optical attenuation of 33.98 dB. In this case, the GRIN-GRIN distance is only 4F = 400 µm, implying a very compact VFOA module. Lower maximum optical attenuation levels of 23.99 dB and 14.06 dB are obtained by utilizing 1-mm and 1-cm focal length lenses in the imaging system, respectively. Similarly, 4-mm and 4-cm GRIN-GRIN distances are expected. These results also indicate that shorter focal-length lenses used in the imaging system provide higher optical attenuation at specific Δf values. In addition, the change in the optical beam waist wR rather than the radius of curvature RR plays a very important role in achieving high optical attenuation values. Based on the above analysis, very-compact high-dynamic-range VFOAs can be realized via longitudinal motion of the lens used in the imaging system.

V. CONCLUSION In this work, we show for the first time that a longitudinal

misalignment between two fiber-optic collimators can provide high optical attenuation. Specifically, the key idea is to tremendously alter the optical beam waist at the receiving fiber-optic collimator via movable lenses of the imaging system. Based on our analysis, shorter focal-length lenses offer higher optical attenuation. Additional key features include compactness, low components count, and ease of implementation. Future work relates to the implementation and demonstration of our proposed moving-lens based VFOA.

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