Page 1

Polarization control in a He-Ne laser using

birefringence feedback

Ligang Fei, Shulian Zhang, Yan Li and Jun Zhu

The State Key Lab of Precision Measurement Technology and Instruments, Department of Precision Instruments,

Tsinghua University, Beijing, 100084, China

flg02@mails.tsinghua.edu.cn

Abstract: The polarization dynamics of laser subjected to weak optical

feedback from birefringence external cavity are studied theoretically and

experimentally. It is found that polarization flipping with hysteresis is

induced by birefringence feedback, and the intensities of two eigenstates are

both modulated by external cavity length. The variations of hysteresis loop

and duty ratios of two eigenstates in one period of intensity modulation with

phase differences of birefringence element in external cavity are observed.

When the phase difference is π/2, the two eigenstates will equally

alternatively oscillate, and the width of hysteresis loop is the smallest.

©2005 Optical Society of America

OCIS codes: (140.1340) Atomic gas lasers, (260.1440) Birefringence, (260.3160) Interference.

References and links

1.

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52, 918-921 (1984).

G. Ropars, A. L. Floch and R. L. Naour, “Polarization control mechanisms in vectorial bistable lasers for

one-frequency systems,” Phys. Rev. A 46, 623-640 (1992).

G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical,” Phys. Rev. Lett. 55,

703-706 (1985).

W. Xiong, P. Glanzning, P. Paddon, A. D. May, M. Bourouis, S. Laniepce and G. Stephan, “Stability of

polarized modes in a quasi-isotropic laser,” J. Opt. Soc. Am. B 8, 1236-1243 (1991).

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann and R. Michalzik,

“Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-

emitting lasers,” Appl. Phys. Lett. 84, 2763-2765 (2004).

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret and M. Blondel, “Optical feedback

induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545

(2003).

L. G. Fei, S. L. Zhang and X. J. Wan, “Influence of optical feedback from birefringence external cavity on

intensity tuning and polarization of laser,” Chin. Phys. Lett. 21, 1944-1947 (2004).

J. Houlihan, L. Lewis and G. Huyet, “Feedback induced polarization switching in vertical cavity surface

emitting lasers,” Opt. Comm. 232, 391-397 (2004).

10. T. H. Peek, P. T. Bolwijn and T. J. Alkemade, “Axial mode number of gas lasers from moving-mirror

experiments,” Am. J. Phys. 35, 820-831 (1967).

11. J. Brannon, “Laser feedback: its effect on laser frequency,” Appl. Opt. 15, 1119-1120 (1976).

2.

3.

4.

5.

6.

7.

8.

9.

1. Introduction

Single-mode He-Ne laser usually emits linearly polarized light, but its polarization may

abruptly flip between two eigenstates [1]. Floch and co-workers [2,3] observed the

polarization flipping and hysteresis effect by changing the anisotropy values of laser

intracavity. Stephan and co-workers [4,5] experimentally and theoretically studied the

polarization switching induced by optical feedback from a polarizer external cavity. Although

the polarization flipping and hysteresis effect were observed, they could not modify the size of

(C) 2005 OSA 18 April 2005 / Vol. 13, No. 8 / OPTICS EXPRESS 3117

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hysteresis loop, and only one polarization intensity can be modulated. Recently, the

polarization switching induced by optical feedback has attracted considerable interest [6-9].

However, to the best of our knowledge, the polarization control by changing the anisotropic

values of external feedback cavity has not been investigated.

In this letter, we demonstrate the influence of the optical feedback from birefringence

external cavity on the laser polarization states and output intensity. When the length of

external cavity is changed, the polarization flipping with hysteresis between two eigenstates

will occur, and the intensities of the two eigenstates are both modulated. The width of

hysteresis loop decreases when the phase difference of birefringence element in external

cavity increases, and the duty ratios of the two eigenstates in one period of laser intensity

modulation also vary with the phase difference. When the phase difference is π/2, the width of

hysteresis loop is the smallest, and the duty ratios are equal. In this case, the two eigenstates

will equally alternatively oscillate, and the square wave oscillation can be observed. Each

polarization switching corresponds to λ/4 change of the external cavity length.

2. Experimental setup

Experiments are carried out on a single mode, linearly polarized He-Ne laser with natural

anisotropy. The wavelength λ is 632.8nm. The experimental setup is shown in Fig. 1. The

ration of gaseous pressure in laser is He:Ne=7:1 and Ne20:Ne22=1:1.

W

X

Y

Z

PZT

ME

D2

BS

P

OS

D1

M2

M1

G

F

P

Fig. 1. Experimental setup and coordinates system. M1, M2, ME: mirrors; G: stress

birefringence element; F: force on G; PZT: piezoelectric transducer; W: glass window anti-

reflective coated; BS: beam splitter; D1, D2: photo detectors; P: polarizer; OS: oscilloscope.

M1 and M2 are laser mirrors with reflectivities of R1=99.8% and R2=98.8%, respectively,

and the distance L between them is 150mm. ME is external mirror with reflectivity of R3=10%,

used to reflect laser beams back into the laser. ME, together with M2 and G can form a

birefringence external cavity. The length of external cavity l is 100mm. D1 is used to detect

the laser intensity. D2 is used to detect the variations of laser polarization state. Due to the

stress birefringence effect, when a force is applied on G, the two optical axes of G are parallel

to the two principal stress directions, and the force-induced birefringence phase difference is

proportional to the magnitude of force. According to the coordinates system shown in Fig. 1,

the two optical axes of G are along y-axis and x-axis, respectively.

3. Experimental results

In our experiments, the initial polarization direction of laser is parallel to y-axis. The force-

induced birefringence phase difference δ can be given by

diameter of G, f0 is the fringe value of the optical materials, and F is the force applied on G.

Therefore, the different phase differences between the two principal optical axes of G can be

obtained by changing the magnitudes of force. When the length of external cavity is scanned

by PZT, the intensity modulation curves can be obtained, and different phase differences of G

correspond to different intensity modulation curves as shown in Fig. 2.

In Figs. 2(a)-2(d), the solid lines are the intensity modulation curves that PZT voltage is

increased, i.e., ME moves toward the laser and the length of external cavity is decreased. The

0

8 F

λ

Df

δπ=

, where D is the

(C) 2005 OSA 18 April 2005 / Vol. 13, No. 8 / OPTICS EXPRESS 3118

#6854 - $15.00 USReceived 15 March 2005; revised 5 April 2005; accepted 7 April 2005

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dash lines represent the intensity modulation curves that PZT voltage is decreased, i.e., ME

moves away from the laser, and the length of external cavity is increased.

PZT voltage increase

PZT voltage decrease

Laser intensity (200mV/div)

PZT Voltage (20V/div)

(a)

F

E

B

A

D

C

PZT voltage increase

PZT voltage decrease

Laser intensity (200mV/div)

PZT Voltage (20V/div)

(b)

F

E

B

A

C

D

PZT voltage increase

PZT voltage decrease

Laser intensity (200mV/div)

PZT Voltage (20V/div)

F

E

B

A

(c)

D

C

PZT voltage increase

PZT voltage decrease

Laser intensity (200mV/div)

PZT Voltage (20V/div)

(d)

F

E

B

A

D

C

Fig. 2. Waveforms of laser intensity modulation and polarization flipping with hysteresis

corresponding to the birefringence element phase differences of (a) δ=π/6, (b) δ=5π/18, (c)

δ=7π/18, (d) δ=π/2. Upper traces: without a polarizer, lower traces: with a polarizer.

From the Fig. 2, we can find that there are dips on the intensity modulation curves, which

is different from the conventional optical feedback intensity curve whose profile is similar to

sine wave. If observe the laser output through a polarizer, we can find that the polarization of

laser hops at the dip points, and the intensities of two eigenstates are both modulated by the

length of external cavity. When PZT voltage is increased, the position of polarization flipping

from y-polarization (Py) to x-polarization (Px) is at point D. If PZT voltage is decreased, the

position of polarization flipping from Px to Py is at point C. From Figs. 2(a)-2(d), we can find,

if the phase difference of G is changed, the position of polarization flipping is also different.

This indicates that the duty ratios of the two eigenstates in a period of intensity modulation

curve vary with the phase difference. The relationship between the duty ratios of the two

eigenstates and the phase difference are shown in Fig. 3(a). Meanwhile, for a certain phase

difference of G, when the moving direction of feedback mirror (ME) is different, the

polarization flipping points C and D are not superposition. This indicates the hysteresis effect

of polarization flipping. When the phase difference is changed, the width of hysteresis loop is

also changed. Using this result, we can control the polarization switching outside the laser. As

known, the length variation of external cavity is proportional to the voltage applied on PZT,

so the voltage increments on PZT can be used to represent the width of hysteresis loop shown

by the space between point C and D. The relationship curve of the hysteresis loop width and

the phase difference is shown in Fig. 3(b). When δ=π/2, the width of hysteresis loop is the

smallest.

When δ=π/2, the curve of intensity modulation is similar to the full wave rectification of

sine wave, as shown in Fig. 2(d). Observing the output intensity through a polarizer, we can

find that the duty ratios are nearly equal and the profile of intensity curve is similar to a square

wave due to the existence of the laser initial intensity. Because λ/2 change of the external

cavity length corresponds to one period of intensity modulation, in this case, each polarization

switching will correspond to λ/4 change of the external cavity length.

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Page 4

0.40.60.81.01.21.41.6

0.2

0.4

0.6

0.8

Px

Py

(a)

The duty radio

Phase difference of birefringence element(rad)

0.40.6 0.81.01.2 1.41.6

0

5

10

15

20

25

Phase difference of birefringence element(rad)

(b)

The width of hyteresis loop (V)

Fig. 3. Measurement curves. (a) Duty ratios of two eigenstates versus the phase difference. (b)

The width of hysteresis loop versus the phase difference.

4. Theoretical analyses

The eigenstates polarizations depend on the active medium, on a linear phase anisotropy and

on a loss anisotropy. For smaller phase anisotropy of intracavity, the polarization flipping

conforms to the rotation mechanism [2]. Let initial polarization direction of laser be parallel to

y-axis. When the following inequality is satisfied [3], the polarization flipping from Py to Px

will occur

11

[] [ ] [ (

24

L

β α θβ

−

where α is laser net gain, β and θ are self and cross saturation coefficient, ρ is self pushing

coefficient, ∆Φxy is the phase anisotropy in internal cavity, tx and ty represent the transmission

coefficients of Px and Py respectively. The first term of Eq. (1) represents the effect of the

active medium, the second term represents the effect of the phase anisotropy of intracavity

and the third term represents the effect of the loss anisotropy.

In the presence of optical feedback, due to R3<<R2, according to the model [10] of

equivalent cavity of Fabry-Perot interferometer, when the length of external cavity changes,

the equivalent mirror reflectivities along y-axis and x-axis can be given by

1 2

2232

2() (1

y y

RR R RR

RR

−

=

where ϕf =4πl/λ represents the phase of external cavity. Due to Ry-y≠Ry-x, the two eigenstates

of one laser mode will subject to different losses. Substitute Eq. (2) into Eq. (1), we can get

the condition of polarization flipping from Py to Px

c

L

βαθ

where κ=(R3/R2)1/2(1-R2). Because the frequency shift caused by optical feedback and the

intracavity anisotropy are very small [11], if we neglect saturation effects, Eqs. (2) and (3)

show that the azimuth of polarization will be along the larger reflectivity axis, and the right

term in Eq. (3) can be assumed as zero. In this case, the light will be polarized along y-axis

(cos0

f

ϕ > ) or x-axis (cos0

f

ϕ <

). When polarization direction of laser is along y-axis, the

intensity variation can be obtained by ∆Iy=ηcosϕf [8], where η represents optical feedback

factor. Similarly, when the polarization direction of laser is parallel to x-axis, the equivalent

mirror reflectivities along x-axis and y-axis are given by

1 2

2232

2() (1

x x

RR R RR

RR

−

=

2

1

2

1)]0

xyxyyx

c

tt

ρθβ+

∆Φ+ ∆Φ−−>

, (1)

2

)cos

f

y x

ϕ

−

=+−

, (2)

2

cos

2

f xyxy

ρθβ

β

κϕ

+

−

<∆Φ + ∆Φ

, (3)

2

)cos( 2 )

δ

f

x y

ϕ

−

=+−−

, (4)

(C) 2005 OSA18 April 2005 / Vol. 13, No. 8 / OPTICS EXPRESS 3120

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where δ is the phase difference between two principal optical axes of G. The Px to Py flip

condition is similar to Eq. (1), and only the signs of the first and third terms are changed. The

condition of polarization flipping from Px to Py can be written as

ρ

κϕδ

β

The light will be polarized along x-axis (cos(ϕf -2δ)>0) or y-axis (cos(ϕf -2δ)<0). If

polarization direction of laser is along x-axis, the intensity variation is ∆Ix=ηcos(ϕf -2δ).

When the length of external cavity is changed, the dependence of laser intensity and

polarization flipping on δ can be illustrated in Fig. 4. The horizontal dot lines in Fig. 4

represent the right-hand sides of Eqs. (3) and (5), which are nearly equal to zero.

2

cos( 2 )

2

fxy xy

c

L

θ

θ

β

βα

+

−

−< ∆Φ − ∆Φ

. (5)

1.53.0

External cavity phase(rad)

4.5 6.07.5 9.010.5

x

P

y

P

x

y

∆I

Laser intensity (200mV/div)

K

J

(a)

I

H

∆I

F

E

D

C

B

A

1.53.0

External cavity phase(rad)

4.56.07.59.010.5

∆I

Laser intensity (200mV/div)

K

J

(b)

x

y

P

P

I

H

x

y

∆I

F

E

D

C

B

A

1.5 3.0

External cavity phase(rad)

4.56.0 7.5 9.010.5

Laser intensity (200mV/div)

∆I

K

J

(c)

I

H

x

y

P

P

xy

∆I

F

E

DC

B

A

1.53.0

External cavity phase(rad)

4.56.07.59.010.5

Laser intensity (200mV/div)

∆I

C

B

A

(d)

P

P

x

y

x

y

∆I

Fig. 4. Illustrations of laser intensity modulation and polarization flipping with hysteresis

corresponding to the birefringence element phase differences of (a) δ=π/6, (b) δ=5π/18, (c)

δ=7π/18, (d) δ=π/2. Lower traces: hysteresis loop.

Firstly, we decrease the length of external cavity. Because the initial polarization direction

of laser is Py, the intensity variation is ∆Iy shown by solid lines in Fig. 4. In Figs. 4(a)-4(c),

when starts from point A to the right and reaches point D, the condition of polarization

flipping from Py to Px is satisfied from Eq. (3). The polarization direction of laser jumps from

Py to Px, i.e., from point D to point E, and the intensity turns into ∆Ix shown by dash lines. At

point F, the polarization should jump from Px to Py from Eq. (5). However, due to Rx-x>Ry-y, Py

will subject to more losses and be suppressed. The polarization still remains Px. Once reaches

point H, due to Ry-y>Rx-x, from Eq. (5), the polarization will jump back to Py. The intensity

becomes ∆Iy again till point I, and then begins another period. The trace of intensity

modulation within a period is ADDEEFHHI

?????????

shown in Figs. 4(a)-4(c). Then, we increase the

length of external cavity. For conveniently, we start from point F to the left. Because the

polarization direction of laser at point F is Px, the intensity variation is ∆Ix shown by dash

lines. In Figs. 4(a)-4(c), when reaches point C, from Eq. (5), the polarization will jump from

Px to Py, i.e., from point C to point B. At point J, the polarization will jump back to Px. The

intensity becomes ∆Ix again till point K, and then begins another period. The trace of intensity

modulation within a period is FCCBBAJJK

??????

??? ?????? ???. If δ=π/2, Fig. 4(d) shows, the length of external

(C) 2005 OSA 18 April 2005 / Vol. 13, No. 8 / OPTICS EXPRESS 3121

#6854 - $15.00 US Received 15 March 2005; revised 5 April 2005; accepted 7 April 2005

Page 6

cavity whether is increased or is decreased, the positions of polarization flipping are both at

point B. The intensity modulation curve is ABBC???

??? or CBBA???

of sine wave. From the conditions of polarization flipping Eqs. (3) and (5), the duty ratios of

the two eigenstates can be written by

2(

y

D

=

that the duty ratios vary with δ are shown in Fig. 5(a).

???

, which is full wave rectification

)

πδ−

and

2

x

D

δ

=

. The normalized curves

0.00.20.4 0.60.8 1.0 1.21.4 1.6

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

(a)

The duty radio

Phase difference of birefringence element(rad)

x- pol ar i zat i on

y- pol ar i zat i on

0.00.20.40.6 0.81.0 1.21.4 1.6

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

(b)

Width of hyteresis loop (rad)

Phase difference of birefringence element(rad)

Fig. 5. Theoretical curves. (a) Duty ratios of two eigenstates versus the phase difference. (b)

The width of hysteresis loop versus the phase difference.

The stabilities Eqs. (3) and (5) can also be used to explain the hysteresis loop apparent in

Fig. 2 and the fact that we have observed a decrease in the size of the loop with increasing δ.

The relationship between the width of hysteresis loop and the phase difference of

birefringence element can be given by

H

W

π

=

loop varies with δ is shown in Fig. 5(b).

Above analyses show that the intensities of the two eigenstates are both modulated by the

length of external cavity, and there is a hysteresis loop between Py→Px and Px→Py. The width

of hysteresis loop CD shown by lower traces in Figs. 4(a)-4(d) decreases with increasing the

phase difference of birefringence element. If δ=π/2, the width of hysteresis loop is the

smallest, and nearly equal to zero. Meanwhile, in a period of laser intensity modulation, the

duty ratios of two eigenstates also vary with the value of phase difference. The greater phase

difference the smaller difference of duty ratios. When δ=π/2, the duty ratios of two

eigenstates are equal. The theoretical analyses are in good agreement with the experimental

results.

2

δ

−

. The curve that the width of hysteresis

5. Conclusions

We have demonstrated the polarization control outside the laser. By adjusting the phase

difference of birefringence element in the external feedback cavity, we can change the width

of hysteresis loop and the duty ratios of two eigenstates. When δ=π/2, the duty ratios are

equal, and intensity curve is similar to the full wave rectification of sine wave. If we observe

the laser intensity through a polarizer, the square wave can be output. In this case, the width of

hysteresis loop is the smallest, and each polarization switching corresponds to λ/4 change of

the external cavity length. Our results are promising for applications in optical switching,

optical bistability, and precision measurements of some physical quantities.

Acknowledgments

The Nature Science Foundation of China supported this work.

(C) 2005 OSA18 April 2005 / Vol. 13, No. 8 / OPTICS EXPRESS 3122

#6854 - $15.00 USReceived 15 March 2005; revised 5 April 2005; accepted 7 April 2005