# An all-fiber device for generating radially and other polarized light beams

T. Grosjean, D. Courjon, M. Spajer

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T. Grosjean, D. Courjon, M. Spajer. An all-fiber device for generating radially and other polarized light beams. Optics Communications, 2002, 203 (1-2), pp.1-5. 10.1016/S0030-4018(02)01122-7. hal-00093567

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# An all-fiber device for generating radially and other polarized light beams

T. Grosjean*, D. Courjon, M. Spajer

Université de Franche-Comté, Faculté des Sciences, Laboratoire d'Optique P.M. Duffieux, UMR 6603,
Route de Gray, 25030 Besançon cedex, France

## Abstract

Radially polarized beams are beams for which the electric vector is radially distributed along the beam axis. Such beams are interesting for applications in which a total symmetry of the electric field is required. In this paper we propose an all-fiber method allowing the generation of radially, azimuthally, and hybrid polarized light beams in a rapid and simple way.

## 1. Introduction

From both theoretical and experimental works, it is known that the polarization state is particularly important in near-field optical confinement [1–4]. More precisely, it has been shown that the polarization will strongly influence the width of the peak confinement. Therefore, in the framework of immaterial tip use, the knowledge and the choice of the polarization is compulsory. These comments can be generalized to any large aperture imaging systems, such as solid immersion systems [5] although, in that case, the effect of polarization on the focal spot is not so significant.

It turns out that the radial polarization of the incident beam, because of total symmetry, will enhance the $E_z$ component of the field (versus $E_x$ and $E_y$) after beam focusing. Since the component $E_z$ of the field is responsible for the confinement, the diameter of the central spot will decrease consequently. Note that radial polarization has been also proposed for large numerical aperture systems (see [6]).

For more than 30 years, various methods have been developed in order to generate such radially polarized fields. Those methods are based on interferometric systems [7,8], on computer generated holograms [9], or polarization converters using liquid crystals [10]. Annular transverse radially or azimuthally polarized modes have been selected in passive resonant cavities [11] and in laser cavities [12–16]. Such peculiar beams have also been reconstructed by interferometry inside the cavity [17]. Despite the efficiency of such techniques (in terms of polarization purity and energy efficiency)

<footnote>* Corresponding author. Tel.: +33-03-81-66-64-10; fax: +33-03-81-66-64-23.</footnote>

<footnote>E-mail address: thierry.grosjean@univ-fcomte.fr (T. Grosjean).</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic representation in intensity and polarization of the three annular modes *TM*<sub>01</sub> radially polarized, *TE*<sub>01</sub> azimuthally polarized and *HE*<sub>21</sub> with hybrid polarization.</figcaption></figure>

they are generally rather heavy and tricky (mainly
due to problems of stability).

We propose here a simple and cheap technique
allowing the generation of radially polarized
beams. Its principle is based on mode selection
inside an optical fiber rather than inside a laser
cavity. It is well known that a multi-mode optical
fiber (step index fiber) accepts several annular
modes including *TM*<sub>01</sub> mode with radial polariza-
tion, *TE*<sub>01</sub> mode with azimuthal polarization and
*HE*<sub>21</sub> mode with an hybrid polarization state
(combination of radial and azimuthal polariza-
tion) (see Fig. 1). *HE*<sub>21</sub> is named as hybrid mode.
In the case of weak guiding those three modes have
the same cutoff parameters which are smaller than
the cutoff parameters of the other modes (except
the fundamental mode *HE*<sub>11</sub>) [18,19]. Far from
cutoff, they can combine and lead to degenerated
linearly polarized *LP*<sub>11</sub> modes with a two-lobe
structure in intensity.

**2. Experiments**

The problem to solve deals with the way of se-
lectively exciting the purely radial mode, i.e. *TM*<sub>01</sub>
The technique which is presented and described
here is easy to carry out. It uses a precise control
and monitoring (in shift and tilt) of the injection of
a linearly polarized light beam (at the wavelength
λ = 632.8 nm) in a multi-mode fiber. For the three
annular modes, the cutoff diameter is 4.2 µm for a
fiber with an index difference Δn = 0.0045 between
core and cladding. The diameter reaches 6.7 µm
for the next mode *EH*<sub>11</sub> in the cutoff classification.

Since the core diameters of the multi-mode fibers
used here are 5 and 6 µm for approximately the
same Δn, only the fundamental and the three an-
nular modes will be transmitted, the other modes
being filtered. We note that for those fiber widths,
the selected modes propagate far from cutoff.

The light injection is performed by means of a
mono-mode fiber the exit face of which is set in the
vicinity of the entrance face of the multi-mode fi-
ber. First of all, the three annular modes exhibit
similar intensity profiles, they only differ from the
polarization state. Therefore, the shift and the tilt
between the two fibers will be defined according to
the polarization direction of the incident beam.
Moreover, the field distributions of the three
modes show axial symmetry, for they follow the
cylindrical symmetry of the fiber. Consequently,
we can expect that a system which is able to select
such annular modes has to keep the axial sym-
metry given by optical fibers as much as possible.
A priori, tilt between fibers has to be weak or null.
In this work, only shift will be used for filtering the
unwanted modes in the multi-mode fiber.

The setup is shown in Fig. 2. The source is a He–Ne 10 mW laser. An objective allows the light injection in the first mono-mode piece of fiber. The multi-mode fiber is set in such a way that the cleaved extremity be as closed as possible to the extremity of the first fiber. The two faces must be as flat and clean as possible which implies that the cleaning procedure must be carried out very carefully. An index matching liquid can be used to reduce parasitic reflections and to cancel the possible cleavage defects.

The mono-mode fiber length is about 1 m. It is
equipped with a polarization controller allowing
the choice of the direction of the linearly polarized
field. The multi-mode fiber is shorter (less than
1 m). It is mounted on an optical bench and, by
means of precision actuators it can be shifted and
tilted versus the mono-mode fiber position at will.
The proposed setup allows the positioning and the
setting of the two fibers in a simple, precise and
reproducible manner. By using a binocular, the
two-fiber alignment can be better than 5 min arc.

When the two fiber axis are superposed only
the fundamental mode can be visualized. When
the two fibers are shifted in the direction of the
<figure><img src="image_3.png" /><figcaption>Fig. 2. Experimental setup. By performing the proper light injection in the bi-mode fiber (shorter than 1 m) by means of the mono-mode fiber (length of 1 m), either radially, azimuthally or hybrid polarization beam can be created at the output of the system.</figcaption></figure>

incident beam, the *TM*<sub>01</sub> mode is selected. When the shifting is performed along the perpendicular direction, the *TE*<sub>01</sub> mode is selected instead. Although the rotation of the incident field direction would not affect the filtering behavior of the system, because of symmetry, we have observed in our case that the *HE*<sub>21</sub> mode is obtained whatever the shifting between the two fibers, by rotating the polarization of the incident beam or the holder of the second fiber of 90°. The residual dissymmetry is probably due to a <5 min arc residual tilt or some birefringence effects due to the fiber clipping on the translation stage. The maximum value for the shift is about 7 µm. The precise setting can be achieved in a few minutes only.

Two types of multi-mode fibers characterized by cutoff wavelengths (for the fundamental mode) of 820 and 980 nm have been used. In the two cases, the characteristics of the fibers are far from the cutoff parameters of the annular modes. Moreover, the possible effect of the fiber length has been considered (50 and 100 cm). Whatever the chosen configuration for the multi-mode fiber, the results are similar.

From several experiments in various conditions we can assert that the modal selection is strictly due to the injection of light in the multi-mode fiber. According to its cutoff characteristics, the multi-mode fiber (which must be free from mechanical stresses) generate the expected mode from

the field distribution on its entrance face. Because of short fiber lengths, some more complex effects described for instance by coupled mode theory can be neglected.

### 3. Results

The field intensity distribution of the radially polarized beam in the multi-mode fiber exit plane is shown in Fig. 3. To comfortably observe the field behavior, the out-coming light beam is projected onto a rotating glass diffuser, in order to break down the light speckle. Pictures have been recorded by means of a CCD camera. The field distributions shown in Fig. 4 have been recorded

<figure><img src="image_4.png" /><figcaption>Fig. 3. Annular radially polarized *TM*<sub>01</sub> mode.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Intensity distributions after crossing a polarizer whose axis is oriented along the arrows. (d) The two-lobe structure is spoiled by residual annular shaped light due to the partial cancellation of the fundamental mode in the bi-mode fiber.</figcaption></figure>

by setting a polarizer between the fiber and the
diffuser. The polarizer directions are indicated by
arrows on the pictures.

In order to estimate the energy coupling be-
tween the two fibers, we have calculated the
overlap integrals between the single mode of a
mono-mode planar waveguide (at $\lambda = 632.8$ nm)
and the two modes of a bi-mode planar waveguide
transversally shifted relatively to the first one. For
a 4 µm shift, 16.3% of the incident energy is pre-
sent in the higher mode whereas only 4.4% is
transferred in the fundamental one. It appears that
such a filtering process is not optimal since the
cancellation of the fundamental mode is only
partial. Experimentally, the fundamental mode
residue can only be detected on the polarization
purity. When the polarizer is oriented in the po-
larization direction of the incident beam, the spu-
rious effect is significant (see Fig. 4(d)).

However, by increasing the mismatch between
the two fibers (by simply increasing the shift) the
fundamental mode can be greatly reduced ensur-
ing a better polarization purity. Unfortunately,

purity is accompanied by energy efficiency losses
which can increase dramatically. As an example,
the efficiency measured in the case of Fig. 3 is
about 1% (few percents is, however, realistic). In
the case of $HE_{21}$ mode, a high purity can be
achieved with about 10% efficiency. Note that
weak efficiency is largely compensated by the
simplicity and the stability of the device and that
the use of pulsed laser sources can make it suitable
for imaging applications.

4. Conclusion

We have shown that a linear polarized light
beam can be easily converted into three quasi-
perfectly rotationally polarized light beams by
means of a very simple all-fiber device. Such a
device is easy to realize and remarkably stable.
However, two drawbacks have been pointed out:
first, the residual fundamental mode spoils more or
less the emerging field, second, the available in-
tensity in the output of the multi-mode fiber is
weak (often less than 1%). Therefore, a compro-
mise has to be found between polarization purity
and energy efficiency; it will depend on the type of
application. As already mentioned, in applications
where power is not compulsory, the method is very
valuable. When high intensities are necessary, the
use of a pulsed laser is a good solution. The non-
linear effects induced in that case (self-phase
modulation, white light continuum generation) are
negligible for the short pieces of fiber used. Few
solutions can be found to increase the efficiency of
our setup. It has been noted first that in addition
to the mismatch between the fibers, a slight twist of
the end part of the multi-mode fiber permit the
system rising more than 5% in efficiency for the
$TM_{01}$ mode selection. The fabrication of discon-
tinuous phase elements onto the faces of the fibers,
by focusing ion beam (FIB) etching for example,
could also be a good alternative to improve the
efficiency despite the complexity of the microma-
chinery. Finally, it seems to be the first time to our
knowledge that a beam with hybrid polarization is
created in a so simple way. Its particular polar-
ization properties could be valuable in various
imaging systems.
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