Spatially and spectrally resolved imaging of modal content in large ...

Spatially and spectrally resolved imaging of modal content in large-mode-area fibers J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi OFS Laboratories, 19 Schoolhouse Rd., Suite 105, Somerset, NJ 08873 [email protected]

Abstract: A new measurement technique, capable of quantifying the number and type of modes propagating in large-mode-area fibers is both proposed and demonstrated. The measurement is based on both spatially and spectrally resolving the image of the output of the fiber under test. The measurement provides high quality images of the modes that can be used to identify the mode order, while at the same time returning the power levels of the higher-order modes relative to the fundamental mode. Alternatively the data can be used to provide statistics on the level of beam pointing instability and mode shape changes due to random uncontrolled fluctuations of the phases between the coherent modes propagating in the fiber. An added advantage of the measurement is that is requires no prior detailed knowledge of the fiber properties in order to identify the modes and quantify their relative power levels. Because of the coherent nature of the measurement, it is far more sensitive to changes in beam properties due to the mode content in the beam than is the more traditional M2 measurement for characterizing beam quality. We refer to the measurement as Spatially and Spectrally resolved imaging of mode content in fibers, or more simply as S2 imaging. © 2008 Optical Society of America OCIS codes: (060.2270) Fiber characterization; (060.2320) Fiber optics amplifiers and oscillators

References and links 1. A. E. Siegman, “Defining, Measuring, and Optimizing Laser Beam Quality,” in Proc. SPIE, 2 (1993). 2. H. Yoda, O. Polynkin, and M. Mansuripur, “Beam Quality Factor of Higher Order Modes in a Step-Index Fiber,” J. Lightwave Technol. 24, 1350–1355 (2006). 3. S. Wielandy, “Implications of Higher-Order Mode Content in Large Mode Area Fibers with Good Beam Quality,” Opt. Express 15, 15,402–15,409 (2007). 4. C. R. S. Fludger and R. J. Mears, “Electrical Measurements of Multipath Interference in Distributed Raman Amplifiers,” J. Lightwave Technol. 19, 536–545 (2001). 5. S. Ramachandran, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Measurement of Multipath Interference in the Coherent Crosstalk Regime,” IEEE Photon. Technol. Lett. 15, 1171–1173 (2003). 6. S. Ramachandran, S. Ghalmi, J. Bromage, S. Chandrasekhar, and L. L. Buhl, “Evolution and Systems Impact of Coherent Distributed Multipath Interference,” IEEE Photon. Technol. Lett. 17, 238–240 (2005). 7. M. E. Fermann, “Single-Mode Excitation of Multimode Fibers with Ultrashort Pulses,” Opt. Lett. 23, 52–54 (1998). 8. F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “Intensity-Based Modal Analysis of Partially Coherent Beams with Hermite-Gaussian Modes,” Opt. Lett. 23, 989–991 (1998). 9. C. Rydberg and J. Bengtsson, “Numerical Algorithm for the Retrieval of Spatial Coherence Properties of Partially Coherent Beams from Transverse Intensity Measurements,” Opt. Express 15, 13,613–13,623 (2007).

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Received 19 Feb 2008; revised 2 Apr 2008; accepted 6 Apr 2008; published 5 May 2008

12 May 2008 / Vol. 16, No. 10 / OPTICS EXPRESS 7233

10. M. Skorobogatiy, C. Anastassiou, S. G. Johnson, O. Weisberg, T. D. Engeness, S. A. Jacobs, R. U. Ahmad, and Y. Fink, “Quantitative Characterization of Higher-Order Mode Converters in Weakly Multi-Moded Fibers,” Opt. Express 11, 2838–2847 (2003). 11. D. B. S. Soh, J. Nilsson, S. Baek, C. Codemard, Y. C. Jeong, and V. Philippov, “Modal Power Decomposition of Beam Intensity Profiles Into Linearly Polarized Modes of Multimode Optical Fibers.” J. Opt. Soc. Am. A 21, 1241–1250 (2004). 12. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete Modal Decomposition for Optical Waveguides,” Phys. Rev. Lett. 94, 143,902 (2005). 13. J. R. Fienup, “Phase Retrieval Algorithms : A Comparison,” Appl. Opt. 21, 2758 (1982). 14. J. M. Fini, “Bend-Resistant Design of Conventional and Microstructure Fibers with Very Large Mode Area,” Opt. Express 14, 69–81 (2006). 15. J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of BendInduced Nonlinearities in Large-Mode-Area Fibers,” Opt. Lett. 32, 2562–2564 (2007).

1.

Introduction

Large-mode-area (LMA) fibers have enabled recent advances in high-power fiber lasers and amplifiers. However, many applications of fiber lasers depend on the quality of the beam profile. While single-mode fibers (SMF) are known for their excellent beam quality, as the effective area (Aeff ) is pushed larger to enable high power operation and mitigate nonlinearities, the fiber begins to support increasing numbers of higher-order-modes (HOMs) which can degrade the output beam quality. A typical measure of the quality of an optical beam is the M2 parameter [1]. Frequently a low value of M2 is considered to be equivalent to single mode operation with a stable beam. However, even when the amount of power contained in a higher-order-mode becomes very large, it is still possible to achieve a low value of M2 [2, 3]. Even worse, changing the relative phase of the modes propagating in the fiber can lead to pointing instabilities in the far field. In the context of optical communications systems, Multi-Path Interference, or MPI, is a well known impairment caused by the beating of signals and weak, delayed replicas generated, for example, by Rayleigh scattering [4]. In the case of few-mode fibers, coherent MPI results from modes that propagate with different group delays and can lead to signal fading on a slow time scale [5]. This fading is analogous to the beam pointing instability that will occur in an LMA fiber as the phases between modes slowly drift. Furthermore, as the number of scattering sites increases, either due to discrete interfaces such as splices between LMA fibers, or distributed scattering inside the fiber, the impairment due to MPI rapidly increases [6]. Consequently, accurate techniques are required to characterize the MPI of optical beams from LMA fibers capable of supporting multiple HOMs. The fraction of power of the output of an optical fiber contained in the fundamental mode can be estimated by measuring the launch efficiency of the beam into single mode fiber [7]. Measurements capable of quantifying the partially coherent, transverse mode content from bulk-optic laser resonators only require measuring the transverse beam intensity profiles [8, 9]. The situation where the modes are coherent requires more information, however. Various deconvolution algorithms have been presented for determining the modal power from transverse beam intensity measurements if the modes of the fiber are already known [10–12]. However for accurate analysis the modes must be known precisely. Furthermore without additional constraints, the solution of modal weights can contain ambiguities in the retrieval [12, 13]. In this paper we propose and demonstrate a new measurement technique capable of simultaneously imaging multiple, coherent, higher-order modes propagating in an LMA fiber. Not only can the types of modes and their MPI levels be quantified, but the measured data can be analyzed to provide the level of Poynting vector instability in the beam caused by fluctuating phases between the modes. Because the method is interferometrically based, it is sensitive to even very small fractions of power contained in HOMs. We refer to this technique as Spatially #92842 - $15.00 USD

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(a)

(b)

(c)

Fig. 1. Calculated mode profiles from a step-index, low NA fiber for the (a) LP01 mode and (b) the LP11 mode. (c) The spatial pattern of the fringe visibility when the LP01 mode and LP11 modes interfere. The LP11 mode was 10 times weaker than the LP01 mode in this calculation.

and Spectrally resolved imaging of fiber modal content, or more simply as S2 imaging. 2.

Experimental implementation of S2 imaging and data analysis

S2 imaging is based on the idea that modes propagating in optical fibers can be identified by both the group delay difference which leads to a spectral interference pattern in a broadband source propagating through the fiber, as well as by a distinct spatial interference pattern between the high-order mode and the fundamental mode. Figure 1 illustrates the situation for calculated mode profiles of a 27 µ m core diameter fiber with low NA. The intensity profiles for the LP01 and LP11 are shown in Fig. 1(a) and Fig. 1(b). When the electric fields of these two modes are added together, the resulting spatial interference pattern is shown in Fig. 1(c). For this particular calculation, the LP11 was assumed to be 10 times weaker than the LP01 . Note that the interference fringe visibility is peaked away from the center of the beam, and the precise shape of the spatial pattern and location of the peak in the interference fringe visibility depends on the MPI of the two modes. It is the spatial dependence of the interference pattern as well as the different group delays for different modes in fibers, which allows for simultaneously imaging multiple modes propagating in the fibers. The S2 imaging setup for measuring the higher-order-mode content of an LMA fiber is shown in Fig. 2(a). Light from a broadband source is launched into the LMA test fiber. At the exit of the LMA fiber the beam is imaged with magnification onto the cleaved end of a single mode fiber which is coupled into an optical spectrum analyzer (OSA). A polarizer ensures that the polarization states of the modes are aligned on the SMF end-face. The probe fiber, single-moded at the measurement wavelength, is placed on automated translation stages to move the fiber end in x and y directions perpendicular to the beam propagation direction. The SMF fiber is rastered in x and y, and at each (x, y) point the optical spectrum is measured. Computer control is used to automate the movement of the single-mode fiber probe and acquisition of the optical spectrum. A typical optical spectrum measured at an arbitrary (x, y) point is plotted in Fig. 2(b). If two different modes overlap spatially at that (x,y) point, they will have a spectral interference pattern due to group delay differences between the modes in the fiber under test. In the plots of the Fourier transform in this work, the x axis of the Fourier transform is scaled by the fiber length to obtain the group delay difference between the modes in units of ps/m. The Fourier transform of the optical spectrum, plotted in Fig. 2(c) shows several different mode beats at different group delay differences. It is this spatially and modally dependent spectral interference pattern that is used to simultaneously image quantify the relative power levels multiple HOMs propagating in the LMA fiber. The multi-path-interference(MPI), is defined as the ratio of powers P1 and P2 of the modes, MPI = 10 log [P2 /P1 ]. In order to calculate the relative power levels of the modes using the #92842 - $15.00 USD

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large-mode-area fiber under test

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Fig. 2. (a) Schematic of the S2 imaging setup. (b) Typical optical spectrum measured at an arbitrary (x, y) point and (c) the Fourier transform of the optical spectrum in (b) showing multiple beat frequencies. Fourier filtering is used to pick out different peaks of interest. The horizontal axis of the Fourier transform is normalized to the fiber length to obtain group delay difference in units of ps/m.

Fourier transform of the measured optical spectra, we assume two modes with spatially and frequency dependent amplitudes, A1 (x, y, ω ) and A2 (x, y, ω ), related by a constant α (x, y), such that I2 (x, y, ω ) = α 2 (x, y)I1 (x, y, ω ), (1) where α (x, y) is assumed to be independent of wavelength. If the group delay difference between the modes is assumed to be independent of frequency, then the spectral intensity caused by interference between the two modes can be written as I(x, y, ω ) = I1 (x, y, ω ) 1 + α 2(x, y) + 2α (x, y) cos(τb ω ) , (2)

where τb is the period of the beat frequency between the two modes caused by their relative group delay difference. The Fourier transform of the spectral intensity is then B(x, y, τ ) = 1 + α 2(x, y) B1 (x, y, τ ) + α (x, y) [B1 (x, y, τ − τb ) + B1 (x, y, τ + τb )] , (3)

where B1 (x, y, τ ) = F {I1 (x, y, ω )} is the Fourier transform of the optical spectrum of a single mode. Although the optical spectra in this work are plotted with respect to wavelength, the Fourier transforms are taken with respect to frequency. The spatially dependent Fourier transform of the optical spectrum is then used to calculate α (x, y). At a given (x, y) point, the ratio f (x, y) is defined as the amplitude of the Fourier transform of the spectral intensity at the group delay difference of interest divided by the amplitude at group delay zero. Assuming that the width of B1 (x, y, τ ) is small compared to τb (see for example Fig. 2(c)), f (x, y) can be written as f (x, y) =

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B(x, y, τ = τb ) α (x, y) = . B(x, y, τ = 0) 1 + α 2(x, y)

(4)



Thus, α (x, y) is simply related to f (x, y) by

α (x, y) =

1−

p 1 − 4 f 2(x, y) . 2 f (x, y)

(5)

Because the wavelength range over which the measurement is made covers many beat periods, the total intensity of the two modes measured in the OSA at a given (x, y) point integrated over the measurement bandwidth is just the incoherent sum of the individual mode intensities. The intensities of modes then are given by I1 (x, y) = IT (x, y)

1 α 2 (x, y) , and I (x, y) = I (x, y) , T 2 1 + α 2 (x, y) 1 + α 2(x, y)

(6)

where IT (x, y) = I1 x, y)+ I2 (x, y) is the integrated optical spectrum at a given (x, y) point. Therefore, at each (x, y) point, I1 (x, y) and I2 (x, y) can be calculated via Eq. 5 and Eq. 6, and then the total MPI calculated from RR I2 (x, y) dx dy . (7) MPI = 10 log R R I1 (x, y) dx dy 3.

Experimental results of S2 measurements

For these experiments a 20 m length of LMA fiber with 0.065 NA and 27 µ m core diameter was characterized. Taking into account the 13 cm bend radius that was used when coiling the fiber, the Aeff was approximately 370 µ m2 [14,15]. The broadband optical source used in these experiments was an Yb ASE source that was first polarized and then amplified. The single mode output fiber of the Yb ASE source was spliced with a mode-matching splice to the LMA fiber. Figure. 3(a) shows the beam profile obtained by integrating the measured spectrum at each (x,y) point. A sum of the Fourier transforms of all the measured optical spectra from each spatial point is shown in Fig. 3(b). There are clearly several different beat frequencies visible, corresponding to interference between the primary LP01 mode and different higher order modes. Because the HOMs are weak compared to the LP01 mode, interference between two different HOMs is considered negligible. Figures 3(c) through (f) show the result of the data analysis described in Section 2 applied to the various peaks observed in the Fourier transform of the optical spectra in Fig. 3(b). A variety of higher order modes were observed, clearly identifiable by their spatial patterns as LP11 , LP12 , LP21 , and LP02 . The strongest higher-order-mode, the LP11 , was 21.7 dB weaker than the LP01 . The peaks of the Fourier transform were identified by the mode image obtained from the data analysis. In order to confirm the mode identification, the measured index profile of the LMA fiber was used to calculate the expected group delays of the modes, and the group delay difference at which the beat frequencies are expected. The expected beat frequencies obtained from the calculation between the LP01 and the various higher order modes are indicated in Fig 3(b) by dashed lines. The beat frequencies obtained from the calculation based on the measured index profile agree well with the identification of the beat frequencies based on the obtained mode images. In order to ascertain the accuracy of the MPI levels obtained from the calculation of the mode images, a higher-order mode fiber with a long-period grating (LPG) designed to couple from the LP01 mode to the LP02 mode was characterized. The transmission loss of the LP01 through the LPG is approximately equal to the LP02 /LP01 MPI. The measured transmission loss of the LP01 through the LPG is shown in Fig. 4(a). #92842 - $15.00 USD

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(a) amplitude (dB)

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MPI = -35.6dB

LP02

Fig. 3. Measurement results on a 20m length of 27 µ m core diameter fiber with 0.065 NA. (a) The beam profile obtained by integrating the optical spectrum at each pixel. (b) The Fourier transform of the optical spectra showing the beat frequencies of interest. Also shown as dashed lines are group delay differences between the higher order modes and the LP01 obtained from a calculation based on the measured index profile. (c)-(f) The results of the calculation to obtain the higher-order modes images and MPI levels corresponding to the indicated peaks in (b). -20

0

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Fig. 4. (a) MPI due to an LPG measured via the transmission loss of the LP01 through the LPG. (b) Beam profile out of the HOM fiber. (c) Fourier transform of the optical spectra, modes associated with the Fourier peaks, and their MPI levels, measured at 1050 nm.

After the LPG was characterized with the loss measurement it was then measured using the S2 imaging setup. Becuase of the frequency dependance of the LPG, the mode content was characterized at 1055 nm with a 10 nm bandwidth in the OSA, where the LPG spectrum was relatively flat. The beam profile measured after the LPG was an LP02 , as shown in Fig. 4(b). The Fourier transform of the optical spectra and the modes obtained that correspond to the peaks observed in the Fourier transform are shown in Fig. 4(c). The traditional loss measurement gave an MPI value for the LP01 mode of -17.5 dB at 1055 nm. This number compared very well with the value of -18.3 dB obtained from the S2 measurement. In addition to the LP01 MPI the S2 image also showed -31.4 dB of the LP11 was excited by the LPG, which was not observed by the simple loss measurement of the LP01 . Consequently the S2 imaging not only compared very well with the loss based measurement of MPI, but also gave additional information unavailable from the more traditional technique.

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(b)

y (normalized units)

0.3

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LP11 MPI = -21.7 dB 2

0.2 M = 1.04 0.1

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0.0 -0.1 LP11 MPI = -14.8 dB

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Fig. 5. (a) (3.6 MB) and (b) (3.9 MB) Movies of the beam profile vs. wavelength for two different 27 µ m core diameter fibers. (c) and (d) Change in beam center of mass and beam diameter vs. wavelength obtained from the data in (a) and (b). For comparison the center of mass movement and beam diameter change for a single mode fiber was also measured. Curves in (c) and (d) have been offset horizontally for clarity.

4.

Beam pointing instabilities due to higher-order modes

The S2 imaging data is capable of measuring the number, type, and MPI of the higher order mode propagating in a large-mode area fiber. Because these modes are coherent, they beat together and cause changes in beam shape and lead to beam pointing instabilities as the phases between the various modes drift. The implications of higher order mode content on beam pointing instabilities were calculated theoretically in Ref. [3]. In addition, it was pointed out in [3] that the traditional measure of beam quality, M2 , is relatively insensitive to such impairments, and low values of M2 can be obtained even for a large fraction of power in HOMs. Because the S2 imaging data contains information about all of the higher-mode content propagating in the fiber, the effect of phase changes between the modes can be extracted from the S2 data set be analyzing the data in an alternate way. Rather than analyzing the data in the Fourier domain, it can be appreciated that a unique beam profile is being measured at each wavelength, and because the different modes in the fiber have different group delays, varying the measurement wavelength effectively samples possible relative phases between the modes. Analyzing the data in this manner allows the MPI levels of the higher order modes calculated in the spectrum’s Fourier domain to be correlated with the level of Poynting vector instability in the spatial domain. The level of MPI in few mode fibers has been previously measured by measuring the change in interference versus wavelength [5]. However, such an approach underestimated the MPI. Consequently the measurement of beam pointing instabilities obtained in this manner could also underestimate the impact of drift in mode phases and only provides a lower bound on movement of the beam center of mass. Figure 5(a) shows a movie of the measured beam profile versus wavelength for the 27 µ m core diameter fiber. This movie was generated from the same data used to calculate the mode images shown in Fig. 3. Even though the MPI of the individual higher-order modes was measured to be less than -20 dB, significant changes in the beam center of mass and width are observed. Using a narrowband (