Filtering the spectrum of multi-longitudinal lasers by using optical retarders

Joel Santos-Aguilar, Misael Santiago-Bernal, Celso Gutierrez-Martínez Instituto Nacional de Astrofísica Óptica y Electrónica (INAOE)

Apdo. Postal 51,72 000 Puebla, Pue., México. e-mail: cgutz@inaoep.mx; jaguilar@inaoep.mx; sbernal@inaoep.mx

Abstract— Design and practical realization of photonic filters using segments of polarization maintaining optical fibers (PMF) are reported in this work. These photonic filters can modify the spectrum of wide-band optical sources (multi-longitudinal laser or broadband LED). An optical delay, when introduced on the emission of a wide-band optical source, modify its optical autocorrelation and hence its optical spectrum. Optical delays can be generated by optical retarders such as segments of PMF’s or birefringent crystals. In the frequency domain, the optical retarders act as photonic filters. The selective optical filtering of multi-longitudinal laser modes, when matching the photonic filters to the laser spectrum is demonstrated in this paper.

Keywords-optical fibers; polarization maintaining fibers; optical delays; lasers; optical spectrum; optical filters; photonic filters

I. INTRODUCTION Optical filtering can be achieved by resonance cavities,

absorption, dispersion, multilayer thin films, Bragg gratings and acousto-optic techniques [1-4]. In a novel approach, a very simple optical filtering scheme, based on the introduction of optical delays on the emission of wide-band optical sources is described. The optical delays modify the optical autocorrelation and consequently the optical spectrum, as stated by the Wiener-Kintchine theorem. An optical delay is implemented by a segment of polarization maintaining optical fiber (PMF). As a practical application, the free spectral range (FSR) of a multi-longitudinal laser is increased by filtering alternate optical modes when matching precise optical delays to the laser optical spectrum. Multi-longitudinal lasers are used for implementing microwave photonic filters and for generating microwave band-pass transmission windows on the frequency response of radio over fiber systems using a dispersive optical channel [6, 7]. The frequency responses of such schemes can be reconfigured when modifying the FSR of the multi-longitudinal laser.

II. PHOTONIC FILTER SCHEME The basic configuration for the photonic filtering employs

a wide band optical source, a photonic filter, which is essentially a classical polarization interferometer scheme, where the PMF is the optical retarder, figure 1. The input optical spectrum is modified by the photonic filter as can be analyzed by the optical spectrum analyzer.

Figure 1. Photonic filter scheme.

An optical delay can be easily generated when a polarized optical field enters a birefringent media and is projected on its orthogonal TE and TM modes. As the orthogonal components travel at different velocities, on depending of the ordinary and extraordinary refractive index, an optical delay is introduced. A very simple optical retarder is a segment of polarization maintaining optical fiber (PMF), as shown in figure 2. In such a structure, polarized light modes propagate in the core fiber; at the end of the fiber segment, an optical delay has been introduced, as shown in figure 2. The optical delay τ or the equivalent optical path-difference ( md ), are determined by the refractive index difference and the length of the fiber length. In this way, ( )m o ed n n L= − where on and en are the PMF ordinary and extraordinary refractive index, L is the fiber length.

Figure 2. A birefringent optical fiber as optical retarder.

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III. PHOTONIC FILTER FUNCTION The laser optical wave ( )U t (either electric or magnetic

field), has a power spectral density ( )P λ in the wavelength domain. At the output of the photonic filter, the transmitted light is composed of two delayed components ( )1

2 U t and ( )1

2 U t τ− as

τ= + −1 1( ) ( ) ( )2 2o t U t U tU (1)

The corresponding optical intensity is given by the optical autocorrelation

{ }{ }

τ τ τ

τ τ

τ

=< − >= + − +

− + −

= +

2 2

0

1 1( ) *( ) ( ) ( ) ( )4 4

1 ( ) * ( ) * ( ) ( )4

1 1 Re ( )2 2

m t t U t U tU UI o o

U t U t U t U t

GP

(2)

Where ( ) * ( ) ( )G U t U tτ τ= − , is the optical autocorrelation, τ is the optical delay.

The autocorrelation function and the power spectral density form a Fourier transform pair τ λ⇔( ) ( )G P , as stated by the Wiener-Kintichine theorem. The Fourier transform of the autocorrelation function gives the power spectral density and vice-versa. The real part of the optical autocorrelation can be easily measured by Michelson interferometry, and a fringe pattern is obtained. Such a fringe pattern is given as

{ } 2Re ( ) ( ) cos( )vG G

π ττ τλ

= (3)

Where v is the light velocity, λ is the optical wavelength. From such a measurement the corresponding power spectral density ( )S λ can be determined. At the output of the photonic filter, the power spectral density is given as

λ λ λ= *( ) ( ) ( )ooS UU (4) From expressions (1) and (4)

( ) ( ) ( )

( ) ( )

* *1 exp 22

1 exp 22

vS jU U

vU U j

λ λ λ π τλ

λ λ π τλ

= + ×

+ − (5)

This expression can be stated in terms of the optical path-difference md vτ= , as

( ) ( )1 11 cos 22

mS P dλ λ πλ

= + (6)

Where ( )S λ is a filtered spectrum, as shown in figure 3.

Figure 3. A birefringent optical fiber as optical retarder.

The optical filtering only occurs if the introduced optical path-difference is longer than the coherence length of the optical source [5]. The coherence length and the optical delays can be determined by measuring the autocorrelation of the transmitted light.

To show experimental results, fiber photonic filters can be used to eliminate longitudinal modes on the spectrum of a multi-longitudinal laser. Based on the optical path-differences, it is possible to match photonic filters in order to modify the laser spectrum. A particular filtering consists in modifying the spectrum by eliminating alternate modes in a way to increase the laser free spectral range. This filtering process is demonstrated in this work.

IV. PHOTONIC FILTER DESIGN In this section, the optical spectrum parameters of a real

multi-longitudinal laser is used for matching photonic filters in order to eliminate alternate longitudinal modes. The optical parameters are listed in table 1.

TABLE I. MULTILONGITUDINAL LASER PARAMETERS

Laser parameters Value Units

Center wavelength 1546 nm

Spectral width 10 nm

Free Spectral Range 0.5 nm

A first filter allows the cancellation of one mode when a 2.2 mm optical path-difference is introduced, figure 4a. This photonic filtering doubles the FSR to 1 nm. A second optical path-difference of 1.48 mm eliminates two optical modes and the free spectral range is increased to 1.5 nm, as illustrated in figure 4b.

(a)

(b)

(a)

(b)

Figure 4. (a) Photonic filter for one mode cancellation; (b) photonic filter for two modes cancellation

The matched optical filters in figures 4a and 4b ensure a regular cancellation of modes; otherwise the filtering is not regular.

V. EXPERIMENTAL PHOTONIC FILTERING From the filtering function in (6), it is possible to realize

the photonic filters for modifying a real optical spectrum. As described in the previous section, the filtering can be achieved by matching an optical path-difference, which is introduced by a PMF segment. The optical autocorrelation and optical path-differences can be measured by an automated Michelson interferometer [5]. The measuring set-up is depicted in figure 5.

The original autocorrelation of a real multi-longitudinal laser emission is shown in figure 6a. The optical parameters correspond to those given in table I.

A fiber photonic filter modifies the autocorrelation and the spectrum of the laser emission. The optical correlation when an optical path-difference of 2.2 mm is introduced is shown in figure 6b. The autocorrelation shows new fringe packets at half distance of the original ones. The modified autocorrelation means that in the frequency domain, the laser

spectrum is now modified and the free spectral range now doubles. This means that the cancellation of alternate modes was achieved.

Figure 5. Optical delay measurement setup

Figure 6. (a) laser original autocorrelation; (b). Modified autocorrelation for

a 2.2 mm optical path-difference.

After the description of the filtering function in section 4, the spectral filtering for selective cancellation of modes was realized. This is achieved when the optical delay matches to the spectral characteristics for the elimination of specific modes.

(a)

(b)

Two photonic filters were realized for cancelling one and two modes on the original spectrum. The cancellation of one alternate optical mode is achieved for a 2.2 mm optical path-difference. A second filter that eliminates two optical modes is based on an optical path-difference of 1.48 mm. The modified optical spectra are shown in the figures 7(a) and 7(b).

VI. CONCLUSIONS The photonic filters based on PMF segments are simple

elements that can be easily realized and adapted to complex optical and optoelectronic schemes. The photonic filters are designed as optical retarders and the optical delay is determined by measuring the optical autocorrelation. In this work, the selective filtering of one and two modes on the spectrum of a longitudinal laser has been experimentally demonstrated. The selective optical filtering increased the FSR of the laser. An increased FSR can reconfigure the frequency response of either microwave photonic filters or radio over fiber systems using a dispersive optical channel.

One important issue of this work is to improve the thermal sensitivity of a PMF when used in a polarization interferometer scheme. This subject is in study in our work. The use of less sensitive temperature birefringent crystals can be used to introduce optical delays and can also be used as photonic filters. However this possibility is under investigation.

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Figure 7. (a) laser original autocorrelation; (b). Modified autocorrelation for a 2.2 mm optical path-difference.