632.8nm激光下渐变光纤模式传播研究

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本文主要研究了632.8纳米激光在锥形光纤中的模式传播特性。锥形光纤是一种特殊的光纤结构，其材料色散可以通过Sellmeier方程进行描述，该方程考虑了折射率随波长和掺杂浓度的变化。实验中，研究者利用了输出波长为632.8纳米的氦氖激光，这一波长通常用于可见光范围，不同于常规的单模光纤工作在电信号波段，如1550纳米。当锥形光纤的截止频率低于激光频率时，情况发生了变化。由于632.8纳米的波长小于1550纳米的单模光纤的工作波长，原本设计为在1550纳米处保持单一模式传输的光纤，在这种情况下转变为一个多模波导。这意味着在锥形部分，光的传播模式不再局限于单一模式，而是支持多种模式同时传播，这与传统的单模光纤设计形成了对比。论文详细探讨了光在锥形区域的传播和模式耦合。通过控制光纤锥尖的尺寸，研究人员能够调控多模光束的转换和模式之间的相互作用。这样的控制对于理解光纤设计对光路性能的影响至关重要，特别是在光通信、光学测量或光信号处理等领域，锥形光纤的多模行为可能被用来实现特定的功能，如光分束、模式整形或非线性效应的增强。此外，这项研究还可能涉及到光纤传感技术，因为多模光的出现可能会影响传感器的灵敏度和响应特性。锥形光纤的设计优化对于提高这些应用的性能具有重要意义。总结来说，这篇论文不仅提供了对锥形光纤色散行为的新见解，也为未来在短波长光通信和光子学应用中利用锥形光纤的设计和优化提供了理论依据。

September 10, 2009 / Vol. 7, No. 9 / CHINESE OPTICS LETTERS 771

Study of mode propagation with 632.8-nm laser

in tapered fiber

He Chen (陈陈陈和和和)

, Junliang Lu (陆陆陆均均均良良良)

, Chengliang Zhao (赵赵赵承承承良良良)

Botao Cheng (程程程波波波涛涛涛)

, and Xuanhui Lu (陆陆陆璇璇璇辉辉辉)

1∗

Optical Institute, Physics Department, Zhejiang University, Hangzhou 310027, China

Scho ol of Management, Zhejiang University, Hangzhou 310058, China

∗

E-mail: xhlu@zju.edu.cn

Received December 26, 2008

The material dispersion of a tapered fiber is described by Sellmeier’s equation. The dependence of refractive

index on wavelength and doping concentration is discussed. A He-Ne laser with the output wavelength of

632.8 nm is used in the experiment. When the cutoff frequency of the fiber is less than the laser frequency,

the guiding modes of a single-mode fiber (at 1550 nm) are investigated. The results show that the original

single-mo de fiber becomes a multi-mode waveguide. The propagation and mode coupling of the light in

the taper region are analyzed. By controlling the taper end size of the fiber, the unique tapered fiber can

convert a multi-mode b eam into a single-mode one.

OCIS codes: 060.2310, 060.2430, 140.3300.

doi: 10.3788/COL20090709.0771.

In recent years, tapered optical fiber has been widely

studied and applied in many fields such as biochemi-

cal sensor

[1]

, near-field scanning optical microscope

[2]

laser coupling devices

[3,4]

, and fiber lasers

[5]

, because it

has linear characteristics in evanescent field interaction,

mode coupling, mode filtration, and transformation. It

also has great p otential values in applications for optical

coherent photography and frequency measurement since

it can form supercontinuum spectrum

[6]

due to its big

nonlinear coefficient when the size of the fiber is reduced.

In this letter, we get image scanning using fiber arrays

and the light source of a He-Ne laser, whose wavelength

(632.8 nm) is shorter than the cutoff wavelength of the

fiber. Under this condition, original single-mode fiber at

1550 nm is turned to multi-mode fiber in that wavelength

band, but in practical application single mode operation

is desired. Single-mode operation can be obtained by

designing and fabricating a tapered fiber properly.

For the tapered fiber that achieves single-mode opera-

tion, the mode conversion when the radiating field wave-

length is larger than the cutoff wavelength have already

been reported

[7−9]

. If the tapered fiber is adiabatic

[8]

, the

mode ﬂuctuation caused by the change of fiber size can

be considered small enough that the induced power loss

in the mode conversion from fundamental mode to high-

order modes can b e ignored. The conversion process for

the light propagation in the tapered fiber can be simply

described as follows. At the beginning, light propagates

in the fiber core, and most of the energy is concentrated

in the core. In the tapered part, the core diameter re-

duces gradually, and as the refractive index difference

between the core and the cladding is so small, the fibers

can no more support the mode propagation in the core.

Light leaks to the cladding layer and propagates as the

radiating mode. We call the point where the propagating

mode is turned from core mode to cladding mode as a

critical point, or the cutoff point of core mode. For a

given tapered fiber, the transmission coefficient V

from

the core mode to the cladding mode can be expressed

[10]

≈

2/ln s (1 + 0.26/ln s)

1/2

, where s is the

ratio of the cladding diameter to the core diameter, in-

dependent of wavelength, and is considered invariable in

the tapered part. The unitary frequency V at a point z

of the fiber core which is related to the wavelength λ can

be written as

core

(z) =

2π · r

core

(z)

− n

, (1)

where r

core

is the core radius, n

and n

are refrac-

tive indices of the fiber core and cladding, respectively.

When V

core

(z) > V

, light propagates in core mode. At

the critical point, V

core

(z) = V

. If the local unitary fre-

quency V

core

(z) is too small to restrict the core mode,

core

(z) < V

, the cladding will become the new waveg-

uide medium and light will propagate in cladding mo de.

If a radiating source whose wavelength is shorter than

the fiber’s cutoff wavelength is used, Rayleigh scatter-

ing will increase and make the propagating loss increase

rapidly. On the other hand, the material dispersion in-

duces the change of refractive index of the dop ed fiber,

thus, it redistributes the propagation energy. In the ex-

periment, propagation distance l is very short (l < 1 m).

In real applications, we only consider the inﬂuence of dis-

persion. Usually, quartz optical fiber is manufactured by

doping different materials in SiO

to form the core and

cladding with a small refractive index difference. The re-

fractive index will increase when GeO

or P

is doped

and decrease when B

is doped. Here we consider

a special situation that the cladding is pure SiO

and

the core is SiO

with a small amount of GeO

dopant.

The dependence of the refractive index n on wavelength

and doping concentration can be expressed by Sellmeier’s

equation

[11]

= 1 +

i=1

× λ

− b

. (2)

In Eq. (2), the unit of wavelength λ is micron, and

0.21 µm< λ <3.71 µm, a

and b

(i = 1,2,3) are related

to the materials. According to Refs. [11,12], Table 1

gives the values of a

and b

for some materials.

1671-7694/2009/090771-04

° 2009 Chinese Optics Letters

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