Issues of a laser beam: Depolarization, beam quality degradation and it’s transmission system

Yage Zhan1,2, Zhaoqun Du1, Yiping Qiu1 1Key Laboratory of Textile Science & Technology, Ministry of Education, Donghua University, Shanghai 201620, China

Jianqiu Lei2 College of Science, Donghua University

Shanghai 201620, China

Abstract—High power laser has been used widely in industrial and surgical fields for its many advantages. However, the characteristics of the laser beam may evolve when it is transmitted from the laser exit to the application position through a medium, especially through optical fibers. The evolution of polarization and beam quality of the laser beam in large core fiber are investigated theoretically and experimentally. Investigations demonstrate the laser beam suffers depolarization and beam quality degradation when it propagates in optical fiber. The polarization degree (V) of the laser beam shows an exponential function of fiber length. The beam quality factor (M2) of the laser beam shows a composite tanh function of fiber length. The polarization degree decreases and beam quality degrades when the transmission distance in fiber increases. In addition, an optical fiber delivery system for high power laser beam is proposed concerning of the factors such as focusing lens and delivery fiber.

Keywords- Laser beam, polarization, beam quality, optical fiber transmission system

I. INTRODUCTION With the development of laser technology, high power laser

manifests so many advantages in industrial and surgical fields, such as welding, marking, material processing, percussion drilling, tissue ablation, etc. Various characteristics of the laser beam are required in different applications. For example, the degree of polarization (V) of the laser beam should be controlled in a certain range in the industrial material processing; the laser beam quality factor M2 is required ≤30 in many medical tissue ablation (M2 is a numerical expression of beam quality with 1 being a perfect Gaussian beam and higher values indicating poorer quality); the power densities of the laser beam for cutting should be larger than a threshold; the focused spot size of the laser beam should be equal to the diameter of a bore to be drilled, and so on [1,2].

Among the couples of factors, how to delivery the laser beam from laser exit to the application position, is crucial for an efficient and successful application. In another word, how to select a delivery system to maintain the characteristics of the laser beam, is a fundamental problem we should concern. However, it is not easy because of the involvement of many factors such as depolarization, beam quality degradation, energy loss, damage, and so on [3, 4]. In this work, two of them, depolarization and beam quality degradation in large core fiber have been studied theoretically and experimentally. Based on our investigations and other references, some suggestions for designing an optical fiber delivery system for

high power laser beam are proposed. An optical fiber delivery system designed by us has been demonstrated in the end.

II. POLARIZATION AND BEAM QUALITY OF A LASER BEAM IN LARGE CORE OPTICAL FIBER

A single mode (M2=1.005), linear polarization (V=0.999) continuous wave He-Ne (λ=632.8nm) laser was used as light source to measure the values of V and M2 of output beam after propagation in large core fibers. Three types of optical fibers were used as samples, namely a domestic fused silica optical fiber with core diameter of 0.6mm, two types of 3M fused silica fibers with core diameter of 0.4mm and 0.6mm. The numerical aperture (N.A.) of them were 0.34 ± 0.01, 0.40 ± 0.02 and 0.40 ± 0.02, respectively. Each kind of fiber was cut into seven samples with the length of 0.5m, 1.0m, 2.0m, 3.0m, 5.0m, 10.0m, 22.0m, respectively. The entrance and exit surfaces of all segments were prepared by mechanical polishing.

A. Degree of polarization of the laser beam in large core optical fiber

The depolarization of the laser beam should be considered. It is known that, nominally circular fibers do not maintain the polarization state present at the entrance surface for more than a few centimeters, because of birefringence, irregular imperfections and external disturbances along the fiber. When a laser beam with linear polarization (in x direction) is launched into a large core fiber, the output power will be in two polarization directions, marked as xP and yP respectively.

xP and yP are all related to the fiber length (L) and affected by the random perturbations that couple the two polarization. Since each fiber differs in the length and varies with time or environment, the best evaluation should be an average power over the total length of the fibers. The relationship between P and L is described as[5]

( ) exp( ) cosh( )xP L hL hL= − . (1),

( ) exp( ) sinh( )yP L hL hL= − . (2)

where (0) 1xP = and (0 ) 0yP = . The degree of polarization (V) of the laser beam can be defined by the average power in the two orthogonal directions:

[ ( ) ( )] /[ ( ) ( )] exp( 4 )x y x yV P L P L P L P L hL= − + = − . (3)

Supported by National Natural Science Foundation of China (No:50903014/E0307) Supported by Program of Introducing Talents of Discipline to Universities (No.111-2-04)

978-1-4244-4964-4/10/$25.00 ©2010 IEEE

Figure.1 The experimental schematic setup for measuring the degree of polarization (V) of output beam

It is concluded theoretically that V will vary exponentially along with the fiber length. The longer the fiber is, the smaller the degree of polarization (V) it owns. The polarization would degrade severely when the fiber is long enough.

Fig.1 is a diagram of experimental setup. A lens (L1) was used to focus the laser beam to a waist coincident with the size of entrance face of the fiber. The output beam from the fiber was focused into the Rochon prism by the second lens (L2). With rotating the prism, Px and Py in the two orthogonal orientations (x and y) were measured by a photo-power meter behind the prism. Therefore, V can be calculated according to Eq.3.

The experimental results are shown in Fig.2. The data in Fig.2 confirms that linear polarization laser beam launched into a large core fiber suffers depolarization. The V of output beam shows an exponential function of the fiber length for each fiber. The data in Fig.2 can be fitted by Eq.4,

exp( )V Lβ= − . (4) where L is the fiber length and β is the fitting variance. β was determined by the fiber’s material and configuration. For example, β are 0.29, 0.21, 0.17 for the domestic fiber with core diameter of 600 mμ , the 3M fiber with core diameter of 600 mμ and the 3M fiber with core diameter of 400 mμ , respectively. Compared with Eq. 3, we found that β is equivalent to 4h. Therefore, the experimental results are in accordance with the theoretical analysis expressed by Eq.3.

B. Beam quality factor of the laser beam in large core optical fiber

Beam quality factor ( 2M ) describes the beam quality and how well a laser beam can be focused. The definition of it is based on a Gaussian beam and the 86% energy enclosure beam waist. 2M is defined as [6]

2

4 /DM θλ π

= . (5)

Figure.2 V (the degree of polarization) of the output laser beam versus fiber lengt

where D , θ and λ are the beam waist, the full far-field divergence angle of the laser beam and the wavelength of the laser, respectively.

Larger values of 2M indicates poorer beam quality. There are two causations to the beam quality degradation. One is the transverse spreading due to the dispersion and imperfection of fiber material, and the other is mode coupling which increases the far-field divergence angle of output beam. It has been approved that when a laser beam with steady power distribution is launched into a fiber, the far-field divergence angle of output beam can be expressed by [7]

2 222 0

2 20

tanh( )(z)=tanh( )

LL

σθ θ σαθθσ θ σθ σα

∞∞

∞

⎡ ⎤+⎢ ⎥+⎣ ⎦

. (6)

Here, 0θ is the divergence angle of incident beam; L is the length of fiber; θ∞ is the stabilization divergence angle of output beam when the fiber is infinite long; α is a coefficient determined by the fiber’s material and configuration. When the modes in the fiber are excited by continuous wave laser, 1σ = , and the expression of Eq.6 can be simplified as

2 202 2

0

tanh( )(z)=tanh( )

LL

θ θ αθ θθ θ α

∞∞

∞

++

. (7)

Such a result indicates that the far-field divergence angle θ varies with the fiber length, and it approaches a stabilization value if the fiber approximates to be infinite long.

The experimental studies on the beam quality of output laser beam from the fiber were accomplished with the setup shown in Fig.3. A lens (L1) was used to focus the laser beam to form a waist coincident with the size of entrance face of the fiber. The waist diameter of output beam is indirectly measured, by imaging the end surface of the fiber onto a CCD. The lens L2 (f2=30cm) collimated the output beam and the lens L3 (f3=100cm) focused the collimated beam onto the CCD. The oscillograph connected to the CCD was used to obtain an intensity distribution and the waist diameter (D3) of the output beam reaching the CCD could be measured. The lens combination (L2+L3) led to a magnification of beam waist and made the related measurement more practice. The full far-field divergence angle 3θ in the plane of L3 was calculated by

3 3 3/D fθ = . (8) The full far-field divergence angle 2θ in the plane of L2 was

equal to 3θ . The product of the values of the waist diameter and the full far-field divergence angle was a constant, namely,

0 2 2D Dθ θ= . (9)

L: Lens, f: focus length, CCD: Charge coupled device

Figure.3 The experimental schematic setup for the measurement of the beam quality factor (M2)

Laser

Variable attenuator L1

L2 L3 Fiber

CCD

f2 f3 Oscillograph

Laser

Variable attenuator

Fiber Photo-power meter

Rochon prism L2

L1

0 5 10 15 20 250.0

0.2

0.4

0.6

0.8

1.0

3M 400μm 3M 600μm domestic 600μm

Pola

rizat

ion

(V)

Fiber length (m)

0D was the beam waist diameter at the fiber exit surface, and θ was the full far-field divergence angle at the same position. It was considered that the position of the beam waist of output beam was at the fiber exit surface and the waist diameter was approximately equal to the fiber core diameter. Thus the energy distribution would broaden to the entire core diameter of the fiber. Therefore, the beam quality factor was calculated according to the Eq.5.

The experiments were accomplished to study the relationship between the laser beam quality factor and the fiber length. The results are shown in Fig. 4. The data in Fig.4 show that M2 increases with the fiber length increasing. The data can be fitted by Eq.10,

2 22 22 2 0

2 22 20

) ( ) tanh( )( )

) ( ) tanh( )

((

LM L M

L

M MM M

α

α∞

∞

∞

+=

+

. (10)

20M (=1.005) is the beam quality factor of the incident laser

beam in experiments; 2M∞ is the beam quality factor when the fiber approximates to be infinite long; α is the fitting parameter determined by the fiber’s material, configuration and bend state. 2M∞

and α of these three types of fibers are listed in Table 1.

Based on the definition of 2M expressed by Eq.5 and the equivalency of the waist diameter of output laser beam and the fiber core diameter, the calculation of 2M should be similar with that of far-field divergence angle θ shown in Eq.7 in expression. The fitting equation of experimental data confirms this as Eq.10. As a consequence, our experimental results agree with the theoretical analysis. Firstly, according to Eq.10, 2M becomes larger and the beam quality degrades with the fiber length increasing. For example, when the fiber length is 15m,

2M is almost steady and approaches to a maximum value gradually. Secondly, according to Table 1, 2M of the output laser beam from the larger-core fiber is larger than that from the smaller-core fiber. It is predicted that the shorter fiber makes less beam quality degradation of the laser beam propagating in it and also the fiber with smaller core diameter makes less beam quality degradation of the laser beam propagating in it. In other words, the fiber should be as short as possible and its core should be as small as possible in practice, so long as it satisfies application requirements.

Figure.4 The beam quality factor (M2) of the output laser beam versus the fiber length

Table 1 2M ∞ and α for the three types of fibers

Fiber type Domestic fiber

(600 mμ ) 3M fiber

(600 mμ ) 3M fiber

(400 mμ ) 2M ∞

155 151 131 α 0.130 0.125 0. 118

III. DESIGNS OF THE OPTICAL FIBER TRANSMISSION SYSTEM

To our knowledge there are two kinds of laser beam transmission system: spatial transmission system and optical fiber transmission system. Spatial transmission system is based on mirrors and lens, with the prominent advantage of best capability of beam quality and polarization maintenance. However, the flexibility and safety of optical fiber transmission system is especially beneficial when it is used in a complex three-dimensional work piece, as it is much easier to manipulate compact fiber-coupled effectors optics than to manipulate the work piece itself [8]. It was reported that the large core (0.2mm-1.5mm) high N.A. fibers are used in flexible delivery systems for high-power lasers successfully [9]. In fact, it’s true for many applications as the spatial flexibility of optical fiber transmission system has been proved popular and convenient.

A. Focusing lens Focusing lens, the important optics component, couples a

laser beam to a transmission fiber. The focusing lens must be placed coaxial with the fiber to avoid the damage on the entrance surface of the fiber. Moreover, misalignment makes energy leak into the fiber cladding and emit in the form of heat. The numerical aperture of a common spherical lens (N.A.(lens)) for beam focusing is given by,

( ). . = sin2

Llens o m

dN A nf

θ ≈ . (11)

where Ld and f are the aperture and the focal length of lens. The N.A. of the laser beam ( ( ). . beamN A ) and the focused spot size of laser beam ( D ′ , focused by the lens) are defined as,

( ) ( ). . . . sin2

Lbeam lens o m

dN A N A nf

θ≤ = ≈ . (12),

0D f θ′ = . (13) where 0θ is the divergence of incident beam after focus.

( ). . le n sN A varies with the fluctuations of Ld and f . A larger f leads to a smaller

( ). . len sN A , but the focused spot size increases and the aberration becomes larger accordingly.

When a focusing lens is determined, the following aspects should be satisfied:

(1) The focused spot size ( D′ ) at the fiber entrance surface is constrained by,

0

0.7 600 '

200 600 f f

f f

d d mD f

d d mμ

θμ

≤⎧⎪= = ⎨ − >⎪⎩

（ ） （ ）

（ ） （ ）

. (14)

where fd and D′ are the fiber core diameter and the focused spot size at fiber entrance surface.

(2) The N.A. of incident laser beam (( ). . b ea mN A ) is

constrained by

0 5 10 15 20 25-20

0

20

40

60

80

100

120

140

160

3M fiber (400μm) 3M fiber (600μm) Domestic fiber (600μm)

Bea

m q

ualit

y fa

ctor

(M2 )

Fiber length (m)

( ) ( ) ( )0.3 . . . . 0.9 . .fiber beam fiberN A N A N A≤ ≤ . (15) According to formula 15, formula16 is true

( ) ( )0 .3 . . 0 .9 . .2

Lfib e r fib e r

dN A N Af

≤ ≤ . (16)

Too small ( ). . b ea mN A may result in surface damage or bulk

damage at a certain distance from the entrance surface. Alternatively, too large ( ). . beamN A may lead to overfilling and leakage of laser power into the cladding of the fiber. If

( ). . beamN A is constrained by formulas 15 and 16, both of damage and leakage can be effectively avoided. The

( ). . fib erN A can always be informed by fiber suppliers.

B. Selections for fiber a) Fiber type

Propagation of a laser beam in step-index fibers differs from that in gradient-index fibers. Total internal reflection in step-index fiber occurs at the core/cladding interface for all modes. When all modes are filled, the output profile on the end surface of the fiber will be relatively homogeneous. The intensity distribution is relatively uniform and a stable spot size would be obtained.

However, in gradient-index fiber, each mode of the beam is refracted gradually as it traverses the fiber as different mode characterizes a unique mode radius. Except for the evanescent components, only the highest order modes, reaches the core/cladding interface. The output profile (on the fiber end surface) resembles a Gaussian distribution. For the same fiber diameter, the 86% radius is smaller. The peak intensity is often about five times bigger than that in a step-index fiber. Thus the fiber is capable of significantly modifying the properties of an optical-fiber delivered laser beam. It indicates that the fiber type should be determined according to the intensity demands.

b) Fiber core size Fiber core size is an important consideration in deploying a

transmission beam quality. Smaller fibers lead to less degradation of beam quality and less depolarization, so they are preferred in real applications. However, the laser beam itself constrains on the appropriate (smallest) fiber can be used. The size of the fiber core has to be larger than the focused spot size of the laser beam to avoid heat effects and allow for the mechanical tolerances of the optical fiber connectors. There are important limitations to the selection of the fiber core size.

The worst beam quality from a large core fiber, which can be estimated by the definition of M2, is shown in Eq.5. Working from the equation for the focused spot size for an M2-times-diffraction-limited beam, the worst case beam quality from a fiber can be estimated by Eq.17[2],

2 a r c s in ( . . )f ib e rM H R N A πλ∞ = ⋅ . (17)

H is determined by fiber itself (scattering, absorption, N.A.) and the status during transmission (bend, distortion and stress). H equals the uppermost value (0.86) in the conditions of smallest bend diameter, biggest stress, biggest distortion, worst misalignment. Under normal conditions, H is 0.5 or so. From above discussion, we also concluded the smaller fiber core size maintains better beam quality. But the smallest size

of the fiber core is limited by beam quality, focusing optics, N.A. and power transmission capability. Generally speaking, the fiber diameter, d , can be determined by Eq.18,

2 2tan(arcsin( . .))

abd M Kc N A

λπ

=⋅

. (18)

where K is the aberration multiplier of the optics (K=1 for a perfect lens); λ is the wavelength of laser; a is the ration of 86%-100% radii in the collimated beam; b is ratio in the focused beam on the fiber surface; c is the desired fiber fill factor.

IV. CONCLUSIONS The current work shows that: 1). the degree of polarization

(V) of the laser beam decreases exponentially with the fiber length when the laser beam propagates in an optical fiber; 2). the laser beam quality degrades when the laser beam transmits in an optical fiber and the beam quality factor (M2) could be described as a composite tanh functional of fiber length. Therefore, it can be concluded that the shorter fiber maintain the polarization and beam quality better than the longer fiber. The experiments demonstrate that the optical fiber with smaller core preserves the beam quality better than the optical fiber with larger core. Based on the experimental results and references, some suggestions of optical fiber transmission system for high power laser beam design have been proposed. Moreover, we concluded the fiber length as well as fiber core size should be as small as possible in the optical fiber delivery system, so long as the application requirements can be satisfied.

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