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Compensation for depolarisation by a fibre coil in the presence of self-phase modulation
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Optics & Laser Technology 35 (2003) 381 – 383 www.elsevier.com/locate/optlastec
Compensation for depolarisation by a %bre coil in the presence of self-phase modulation Damian Bird, Min Gu∗ Centre for Micro-Photonics, School of Biophysical Sciences and Electrical Engineering, Swinburne University of Technology, P.O. Box 218, Hawthorn Vic. 3122, Australia Received 1 October 2002; accepted 4 February 2003
Abstract We report on the dependence of the degree of polarisation of an 80 fs pulsed laser beam propagating through a length of a single-mode birefringent %bre on the illumination power. Due to the birefringence and the nonlinear e2ect of self-phase modulation, the measured depolarisation dependence is oscillatory. It is, however, demonstrated that the oscillatory depolarisation can be compensated for by introducing a loop into the %bre geometry, which maintains the degree of polarisation of the pulsed beam as high as 90%. ? 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nonlinear %bre optics; Depolarisation; Self-phase modulation (SPM)
1. Introduction The presence of intense light pulses in an optical %bre gives rise to a number of nonlinear phenomena [1]. Self-phase modulation (SPM) is one of the e2ects, which manifests as a consequence of the intensity dependence of the refractive index and causes broadening of the optical pulse. In the presence of birefringence in a single-mode %bre, SPM leads to a phase mismatch between two orthogonal polarisation components as the pulse evolves within the core. Consequently, polarisation instability such as symmetry breaking bifurcation occurs [2,3], which limits the performance of a %bre-optical system that is reliant on the polarisation property of a pulsed beam. Recently, a single-mode %bre has been used to deliver a femtosecond pulsed laser beam for two-photon @uorescence microscopy [4,5]. While the pulse broadening caused by SPM is an important e2ect on imaging performance in %bre-optical two-photon @uorescence microscopy [5], the degree of polarisation of a femtosecond pulsed beam directly a2ects the applicability of this technique in single molecule detection. In this letter we present an experimental investigation into the polarisation property of a femtosecond pulsed ∗ Corresponding author. Tel.: +61-3-9214-8776; fax: +61-3-92145435. E-mail address: [email protected] (M. Gu).
beam propagating through a single-mode birefringent %bre and a method for compensation of the depolarisation e2ect in the presence of SPM. 2. Experiment The schematic diagram of the experimental setup used for the measurement of the polarisation characteristics is shown in Fig. 1. Three illumination modes were investigated in our experiments in order to understand the e2ect of the femtosecond pulsed beam on depolarisation. First a femtosecond pulsed beam was coupled into a length of a single-mode %bre and second, a continuous wave (CW) beam was coupled into the %bre for comparison. In both cases, the %bre was arranged to be straight (solid line in Fig. 1). It has been shown that the polarisation state of a CW beam can be controlled using a %bre loop [6]. To demonstrate the e2ect of a %bre loop on the polarisation state of a femtosecond pulsed beam in a %bre, in the third case, a femtosecond pulsed beam was coupled into a %bre with a single 20 cm diameter loop (dotted line in Fig. 1). Multiple %bre lengths of 1, 2 and 3 m were investigated. The optical %bre used was single-mode (Newport) having a core/ cladding diameter ratio of approximately 4/125, numerical aperture 0.16 and an operating wavelength of 785 nm. For femtosecond illumination, an 800 nm pulsed beam generated from a Ti: sapphire laser (Spectra-Physics:
0030-3992/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0030-3992(03)00032-X
D. Bird, M. Gu / Optics & Laser Technology 35 (2003) 381 – 383
λ /4 GTP O1
1
Fibre Chuck
Power Meter
O2
A
Fig. 1. Schematic diagram of the experimental setup used for measuring the degree of polarisation of a femtosecond pulsed beam through a single-mode optical %bre.
Tsunami) with a repetition rate of 80 MHz was coupled through a microscope objective O1 into the %bre core. The temporal full-width at half-maximum of the pulse as measured with a commercial autocorrelator (Femtochrome Research, FR-103XL) was approximately 80 fs. In the case of CW illumination, the mode-locking function of the laser was tuned o2. The polarisation direction of the beam at the entrance end of the %bre matched one of the birefringent axes of the %bre by the rotation of the =4 plate and the GlanThompson polariser (GTP). A neutral density %lter placed in the beam path just before the coupling objective O1 allowed the variation of the input power up to 600 mW. The average coupling ratio for a given input power to the %bre was approximately −5:53 dB. The maximum (Imax ) and minimum (Imin ) power of the emerging beam after the collimating objective O2 , was measured through the rotation of the analyser (A).
Degree of Polarisation (γγ )
Fibre Chuck
Pulsed or cw laser λ = 800 nm
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
cw - Straight Fibre Pulsed - Straight Fibre
0.1
Pulsed - Coiled Fibre
0 0
100
(a)
200
300
400
500
600
Input Power (mW) 1
Degree of Polarisation (γγ )
382
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
cw - Straight Fibre
0.1
Pulsed - Straight Fibre Pulsed - Coiled Fibre
0 0
100
(b)
200
300
400
500
600
Input Power (mW)
3. Results To characterise the output polarisation state under the three illumination conditions, we introduced the degree of polarisation de%ned as = (Imax − Imin )=(Imax + Imin ). The dependence of on the input power for three %bre lengths is shown in Fig. 2. It is observed that in the case of CW illumination, the depolarisation e2ect introduced by the %bre birefringence remains constant with increasing the input power but increases with the %bre length. This result was expected since the power of the input illumination is not high enough to induce nonlinear e2ects. The value of is determined by the birefringent refractive indices along the two principal axes, n0x and n0y , and by the length of the %bre [1]. The pulsed illumination however gives rise to a nonlinear depolarisation response that varies signi%cantly with the input power. It should be pointed out that the temporal pulse shape remains approximately Gaussian after propagation through the single-mode %bre [7]. It is observed from the data that when the illumination power is low, the degree of polarisation becomes better than that under CW illumination. As the input power increases, the degree of polarisation exhibits an oscillatory behaviour. The maximum depolarisation appears at an input power of approximately 500, 250 and 150 mW for %bre lengths of 1, 2 and 3 m, respectively. This observation suggests that is proportional to the product of the input power and the %bre length. These features may be caused by the combined e2ects of birefringence and
Degree of Polarisation (γγ )
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
cw - Straight Fibre Pulsed - Straight Fibre
0.1
Pulsed - Coiled Fibre
0 0
(c)
100
200
300
400
500
600
Input Power (mW)
Fig. 2. Degree of polarisation through a length of a single-mode %bre as a function of the input power: (a) 1 m, (b) 2 m and (c) 3 m.
SPM under femtosecond pulsed illumination, in which case, the principal refractive indices nx and ny can be expressed as nx = n0x + I; ny = n0y + I;
(1)
where the %rst term is caused by linear birefringence and the second term results from SPM [1]. Here is the nonlinear coeLcient. This power dependent phase di2erence between two orthogonal polarisation
D. Bird, M. Gu / Optics & Laser Technology 35 (2003) 381 – 383
states leads to the rotation of the polarisation ellipse [2]. It is interesting to see that the introduction of a loop in the %bre results in the reduction of depolarisation and suppresses the oscillatory nature of depolarisation. In fact, the degree of polarisation can be maintained at approximately 90% over the entire power range. The quantitative understanding of the dependence depicted in Fig. 2 may be achieved by numerical simulation of the propagation of a femtosecond pulsed beam in a birefringent %bre [1]. 4. Conclusion We have demonstrated that in the presence of birefringence and nonlinear e2ects such as SPM, the degree of polarisation is oscillatory as the power of the femtosecond pulsed beam increases. Introducing a loop into the %bre however can compensate for the depolarisation e2ect and maintain the degree of polarisation of the pulsed beam as high as 90%.
383
Acknowledgements The authors thank the Australian Research Council for its support. References [1] Agrawal GP. Nonlinear %bre optics. California: Academic Press, 1989. [2] Winful HG. Polarisation instabilities in birefringent nonlinear media: application to %ber-optic device. Opt Lett 1986;11:33–5. [3] Trillo S, Wabnitz S, Stolen R, Assanto G, Seaton CT, Stegeman G. Experimental observation of polarization instability in a birefringent optical %ber. Appl Phys Lett 1986;49:1224–6. [4] Wolleschensky R, Feurer T, Sauerbrey R, Simon U. Characterisation and optimisation of a laser-scanning microscope in the femtosecond regime. Appl Phys B 1998;67:87–94. [5] Bird D, Gu M. Resolution improvement in two-photon @uorescence microscopy using a single-mode %bre. Appl Opt 2002;40:1852–7. [6] Lefevre HC. Single-mode %bre fractional wave devices and polarisation controllers. Electron Lett 1980;16:778–80. [7] Bird D, Gu M. Fibre-optic two-photon scanning @uorescence microscopy. J Micros 2002;208:35–48.
Optics & Laser Technology 35 (2003) 381 – 383 www.elsevier.com/locate/optlastec
Compensation for depolarisation by a %bre coil in the presence of self-phase modulation Damian Bird, Min Gu∗ Centre for Micro-Photonics, School of Biophysical Sciences and Electrical Engineering, Swinburne University of Technology, P.O. Box 218, Hawthorn Vic. 3122, Australia Received 1 October 2002; accepted 4 February 2003
Abstract We report on the dependence of the degree of polarisation of an 80 fs pulsed laser beam propagating through a length of a single-mode birefringent %bre on the illumination power. Due to the birefringence and the nonlinear e2ect of self-phase modulation, the measured depolarisation dependence is oscillatory. It is, however, demonstrated that the oscillatory depolarisation can be compensated for by introducing a loop into the %bre geometry, which maintains the degree of polarisation of the pulsed beam as high as 90%. ? 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nonlinear %bre optics; Depolarisation; Self-phase modulation (SPM)
1. Introduction The presence of intense light pulses in an optical %bre gives rise to a number of nonlinear phenomena [1]. Self-phase modulation (SPM) is one of the e2ects, which manifests as a consequence of the intensity dependence of the refractive index and causes broadening of the optical pulse. In the presence of birefringence in a single-mode %bre, SPM leads to a phase mismatch between two orthogonal polarisation components as the pulse evolves within the core. Consequently, polarisation instability such as symmetry breaking bifurcation occurs [2,3], which limits the performance of a %bre-optical system that is reliant on the polarisation property of a pulsed beam. Recently, a single-mode %bre has been used to deliver a femtosecond pulsed laser beam for two-photon @uorescence microscopy [4,5]. While the pulse broadening caused by SPM is an important e2ect on imaging performance in %bre-optical two-photon @uorescence microscopy [5], the degree of polarisation of a femtosecond pulsed beam directly a2ects the applicability of this technique in single molecule detection. In this letter we present an experimental investigation into the polarisation property of a femtosecond pulsed ∗ Corresponding author. Tel.: +61-3-9214-8776; fax: +61-3-92145435. E-mail address: [email protected] (M. Gu).
beam propagating through a single-mode birefringent %bre and a method for compensation of the depolarisation e2ect in the presence of SPM. 2. Experiment The schematic diagram of the experimental setup used for the measurement of the polarisation characteristics is shown in Fig. 1. Three illumination modes were investigated in our experiments in order to understand the e2ect of the femtosecond pulsed beam on depolarisation. First a femtosecond pulsed beam was coupled into a length of a single-mode %bre and second, a continuous wave (CW) beam was coupled into the %bre for comparison. In both cases, the %bre was arranged to be straight (solid line in Fig. 1). It has been shown that the polarisation state of a CW beam can be controlled using a %bre loop [6]. To demonstrate the e2ect of a %bre loop on the polarisation state of a femtosecond pulsed beam in a %bre, in the third case, a femtosecond pulsed beam was coupled into a %bre with a single 20 cm diameter loop (dotted line in Fig. 1). Multiple %bre lengths of 1, 2 and 3 m were investigated. The optical %bre used was single-mode (Newport) having a core/ cladding diameter ratio of approximately 4/125, numerical aperture 0.16 and an operating wavelength of 785 nm. For femtosecond illumination, an 800 nm pulsed beam generated from a Ti: sapphire laser (Spectra-Physics:
0030-3992/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0030-3992(03)00032-X
D. Bird, M. Gu / Optics & Laser Technology 35 (2003) 381 – 383
λ /4 GTP O1
1
Fibre Chuck
Power Meter
O2
A
Fig. 1. Schematic diagram of the experimental setup used for measuring the degree of polarisation of a femtosecond pulsed beam through a single-mode optical %bre.
Tsunami) with a repetition rate of 80 MHz was coupled through a microscope objective O1 into the %bre core. The temporal full-width at half-maximum of the pulse as measured with a commercial autocorrelator (Femtochrome Research, FR-103XL) was approximately 80 fs. In the case of CW illumination, the mode-locking function of the laser was tuned o2. The polarisation direction of the beam at the entrance end of the %bre matched one of the birefringent axes of the %bre by the rotation of the =4 plate and the GlanThompson polariser (GTP). A neutral density %lter placed in the beam path just before the coupling objective O1 allowed the variation of the input power up to 600 mW. The average coupling ratio for a given input power to the %bre was approximately −5:53 dB. The maximum (Imax ) and minimum (Imin ) power of the emerging beam after the collimating objective O2 , was measured through the rotation of the analyser (A).
Degree of Polarisation (γγ )
Fibre Chuck
Pulsed or cw laser λ = 800 nm
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
cw - Straight Fibre Pulsed - Straight Fibre
0.1
Pulsed - Coiled Fibre
0 0
100
(a)
200
300
400
500
600
Input Power (mW) 1
Degree of Polarisation (γγ )
382
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
cw - Straight Fibre
0.1
Pulsed - Straight Fibre Pulsed - Coiled Fibre
0 0
100
(b)
200
300
400
500
600
Input Power (mW)
3. Results To characterise the output polarisation state under the three illumination conditions, we introduced the degree of polarisation de%ned as = (Imax − Imin )=(Imax + Imin ). The dependence of on the input power for three %bre lengths is shown in Fig. 2. It is observed that in the case of CW illumination, the depolarisation e2ect introduced by the %bre birefringence remains constant with increasing the input power but increases with the %bre length. This result was expected since the power of the input illumination is not high enough to induce nonlinear e2ects. The value of is determined by the birefringent refractive indices along the two principal axes, n0x and n0y , and by the length of the %bre [1]. The pulsed illumination however gives rise to a nonlinear depolarisation response that varies signi%cantly with the input power. It should be pointed out that the temporal pulse shape remains approximately Gaussian after propagation through the single-mode %bre [7]. It is observed from the data that when the illumination power is low, the degree of polarisation becomes better than that under CW illumination. As the input power increases, the degree of polarisation exhibits an oscillatory behaviour. The maximum depolarisation appears at an input power of approximately 500, 250 and 150 mW for %bre lengths of 1, 2 and 3 m, respectively. This observation suggests that is proportional to the product of the input power and the %bre length. These features may be caused by the combined e2ects of birefringence and
Degree of Polarisation (γγ )
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
cw - Straight Fibre Pulsed - Straight Fibre
0.1
Pulsed - Coiled Fibre
0 0
(c)
100
200
300
400
500
600
Input Power (mW)
Fig. 2. Degree of polarisation through a length of a single-mode %bre as a function of the input power: (a) 1 m, (b) 2 m and (c) 3 m.
SPM under femtosecond pulsed illumination, in which case, the principal refractive indices nx and ny can be expressed as nx = n0x + I; ny = n0y + I;
(1)
where the %rst term is caused by linear birefringence and the second term results from SPM [1]. Here is the nonlinear coeLcient. This power dependent phase di2erence between two orthogonal polarisation
D. Bird, M. Gu / Optics & Laser Technology 35 (2003) 381 – 383
states leads to the rotation of the polarisation ellipse [2]. It is interesting to see that the introduction of a loop in the %bre results in the reduction of depolarisation and suppresses the oscillatory nature of depolarisation. In fact, the degree of polarisation can be maintained at approximately 90% over the entire power range. The quantitative understanding of the dependence depicted in Fig. 2 may be achieved by numerical simulation of the propagation of a femtosecond pulsed beam in a birefringent %bre [1]. 4. Conclusion We have demonstrated that in the presence of birefringence and nonlinear e2ects such as SPM, the degree of polarisation is oscillatory as the power of the femtosecond pulsed beam increases. Introducing a loop into the %bre however can compensate for the depolarisation e2ect and maintain the degree of polarisation of the pulsed beam as high as 90%.
383
Acknowledgements The authors thank the Australian Research Council for its support. References [1] Agrawal GP. Nonlinear %bre optics. California: Academic Press, 1989. [2] Winful HG. Polarisation instabilities in birefringent nonlinear media: application to %ber-optic device. Opt Lett 1986;11:33–5. [3] Trillo S, Wabnitz S, Stolen R, Assanto G, Seaton CT, Stegeman G. Experimental observation of polarization instability in a birefringent optical %ber. Appl Phys Lett 1986;49:1224–6. [4] Wolleschensky R, Feurer T, Sauerbrey R, Simon U. Characterisation and optimisation of a laser-scanning microscope in the femtosecond regime. Appl Phys B 1998;67:87–94. [5] Bird D, Gu M. Resolution improvement in two-photon @uorescence microscopy using a single-mode %bre. Appl Opt 2002;40:1852–7. [6] Lefevre HC. Single-mode %bre fractional wave devices and polarisation controllers. Electron Lett 1980;16:778–80. [7] Bird D, Gu M. Fibre-optic two-photon scanning @uorescence microscopy. J Micros 2002;208:35–48.