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We report progress towards the realization of optical modulators based on electro-optic effects in soft glass fibres. A hybrid fabrication procedure was developed for producing microstructured lead silicate glass fibres with internal electrodes. Electro-optical characterization confirms experimentally that the enhanced nonlinear properties and superior isolation between the optical field and the electrodes make these fibres an ideal candidate platform for efficient electro-optical devices.
© 2013 Optical Society of America
1. Introduction
The prospect of low cost, high efficiency electro-optic (EO) fibre devices has long driven researchers to find methods for inducing permanent second order nonlinearities (SON) in glass. To date several such methods have been discovered, such as thermal and optical poling and e-beam irradiation [1, 2]. Silica, while an ideal material for integration into existing optical fibre systems, places a fundamental limitation on the efficiency of these devices as it has a relatively small intrinsic third order nonlinearity. This, in turn, has limited the magnitude of the induced second order nonlinearities to values around 1 pm/V.
Lead silicate glasses show great promise as they have comparable physical and optical properties to silica while possessing intrinsic nonlinearities an order of magnitude larger [3]. Importantly, results indicate that this translates into larger attainable induced second order nonlinearities [4–9].
We present herein the fabrication of a lead silicate microstructured optical (MOF) with internal electrodes. MOFs are well known to be superior in their ability of dispersion tailor [10]. This dispersion tailoring property can be crucial for SON applications such as second harmonic generations [11,12]. Furthermore, we have demonstrated amplitude modulation via the intrinsic third order nonlinearity with an external electric field in a Mach-Zehnder interferometer. This marks the first step towards a EO parametric switching device or a passive device by inducing permanent second order nonlinearities into the fibre through thermal poling.
2. Motivation
To compare the relative EO performance of lead silicate fibres with respect to what is achievable in silica we derive an expression for the relative switching performance.
The change in refractive index of a material in the presence of a large DC bias field EDC and a small modulating field E(t) can be approximated by:
where χ(3) is the intrinsic third order nonlinearity and n is the refractive index.If we have an interferometer with an EO fibre of length L in one of the arms, then the altered refractive index will produce a phase difference between the two beams equal to:
For complete amplitude switching a phase shift of π is required. The applied voltage at which this occurs is thus Vπ for a given VDC, where For the sake of simplicity we consider a fibre modulator that uses only the third order nonlinearities, a so called Kerr modulator. If we compare two geometrically identical devices made from two different materials one can use Eq. (3) to obtain a relative criterion for complete switching: where deff1 and deff2 are the effective distance between the electrodes. The subscripts refer to materials 1 and 2.The reason we use effective distances deff instead of the direct distances between the electrodes is that the space between the electrodes may contain structure such as in a microstructured optical fibre (Fig. 1). The electric field between the electrodes is influenced by the air holes within that region. Since the fibre core sits at the middle of the geometry, we can approximate the effective distance between the electrodes using as following. We approximate the air holes around the core as an uniform air gap, i.e., ignore the thin struts around the core in Fig. 1. We define the thickness of the gap as and the distance from the electrode hole to the gap as . If the core diameter is dcore, the voltage between the electrodes can be written as
where , dglass = dglassclad + dglasscore, εr is the static dielectric constant of the glass. Comparing Eq. (6) with the case of homogeneous fibre, we can define the effective deff as deff = dglass + εrdair.
Fig. 1 Diagram of proposed fibre geometry. Electrode holes left and right, wagon wheel microstructure in center.
Using literature reported values for silica and commercial lead silicate glass SF57 [13, 14] we calculate that a SF57 EO modulator would require 1/16 the switching voltage of silica if deff’s are the same. For example, a silica Kerr switch has been reported to operate with a bias of 3.8 kV and Vπ = 100 V [15], the equivalent SF57 device would have Vπ ≈ 6 V, putting it within the desirable realm of transistor-transistor logic (TTL) driven signals.
The comparison becomes more complex for a second order nonlinear device as the magnitude of the SON is highly dependent on the processing technique. However, it is reasonable to extrapolate from the reports of proportionally higher values of χ(2) [4, 8] that a similar improvements would be possible.
A glass normally does not exhibit SON, but by introducing an external electric field EDC, a non-equilibrium space charge configuration can be formed within the glass, which acting effectively as SON.
Silica fibre modulators with an induced SON have been reported to have switching voltages in the order of 100 V [16]. Given the calculated relative improvement promised by SF57, it should be possible to produce EO fibre modulators with TTL switching requirements from lead silicate glasses.
3. Fabrication
3.1. Fiber design
Several important considerations were made for the design of the EO MOF. We require a light guiding region, which in a MOF typically means some configuration of air holes around a glass core. The fibre also needs holes for the subsequent introduction of electrodes. The electrodes should be as close to one another as possible to maximize the electric field between them. Finally, the electrodes need to be isolated from the light so as to minimize attenuation. The last two points appear at first to be contradictory, however, by choosing a suspended core type structure the optical field is tightly confined to the core [17]. Accordingly, the optical field is almost nil at the electrodes, allowing for close placement of the electrodes to the core. The geometry we propose is illustrated in Fig. 1.
3.2. Preform fabrication
The optical fibre preform was fabricated from the commercial lead silicate glass, SF57 (Schott Glass Co.) via the extrusion technique [18]. We produced a three spoke wagon wheel structure and cladding tube. The dimensions of the wagon wheel preform were approximately 10 mm diameter and 150 mm length. The cladding tube had an outer diameter of 12 mm, an inner diameter of 1 mm and 150 mm in length.
Initially, we investigated the possibility of extruding the jacket preform with the central hole and the two electrode holes. The resulting preforms had significant distortion of the holes. From our experience in extruding asymmetric structures we interpret this as being due to unbalanced flow in the extrusion die, and that it should be possible to reduce it with more sophisticated die designs.
As a more immediate alternative, we elected to use an ultrasonic drill instead of the extrusion technique to make two 3.4 mm diameter holes that ran either side of the cladding tube hole. These were separated from the inner hole by 1 mm. Holes created via ultrasonic drilling have a relatively high degree of surface roughness; however, this is not deleterious to the operation of the fibre as it is not in the light guiding region and heat during fibre drawing process smoothens the rough surface. Thus drilling is a viable alternative to extrusion for the production of holes used for the insertion of the metal electrodes.
3.3. Fiber fabrication
The wagon wheel preform was loaded into a fibre draw tower and caned down to 1 mm diameter to enable an interference fit into the cladding tube. Self pressurization was achieved in the holes by flame sealing the cane and gluing scraps of SF57 glass over the openings of the electrode holes.
The preform assembly was drawn into fibre with an outer diameter of approximately 350 μm (Fig. 2 top left). We note that there was incomplete fusion between the cane and cladding. The fibre geometry exhibited significant distortions of the electrode holes for fibre diameters below 180 μm. Future trials will include active pressurization of the preform to mitigate these distortions and aid in the fusion of cane and cladding.
Fig. 2 Top Left: optical micrograph of fibre cross section. Top Right: image of fundamental mode as imaged on a CCD. Bottom: fibre with electrodes inserted.
3.4. Device fabrication
Sections of fiber of approximately 29 cm in length were provided with electrodes by manually inserting 50 μm diameter, gold coated tungsten wire into the electrode holes (Fig. 2 bottom). One wire was inserted from each end of the fibre to guard against electrical arcing between them. The wires were then set back from the fibre ends to prevent arcing between the electrode and the focusing optics used to couple light in and out of the fibres.
4. Experiment
We assessed the EO performance of the prepared fibre by monitoring the switched output of a Mach-Zehnder interferometer. Figure 3 is a schematic illustration of the experimental setup. The 1mW output of a 1550 nm DFB laser diode is polarized by a fibre in-line linear polarizer (FP) and then split by a 50/50 polarization maintained (PM) fibre coupler, producing two beams with same amplitude, phase and polarization. One beam is sent through free space as a reference, the other is sent through the fibre-under-test (FUT) to be modulated. The FUT is highly birefringent due to the asymmetric geometry of the structure caused by fabrication distortion. One of its principle axes is aligned to the holes for the electrodes. A half wave plate (HW2) is used to rotate the polarization of the incoming beam to this axis. Another two half wave plates (HW1 & HW3) are used to rotate the polarization of the beams before they recombined in the second PM fiber coupler. The combined light is then sent to be detected by a photo detector (PD) where the optical signals are converted into electric signals.
Fig. 3 Mach-Zehnder interferometer characterization setup. L1 4: lens. FP: fiber inline polarizer. Ref.: free space reference arm. FUT: fiber under test. PD: photo detector. HW1 3: half wave plates. HV: high power supply. MOD: modulator. Black lines: polarization maintaining fibers. Green lines: electrical wires.
The coupling of the light into the test fibre was carefully arranged to maximally excite the fundamental mode (Fig. 2 top right). This was necessary to minimize the phase noise induced by the excitation of the other fibre modes.
Bias DC voltages up to 4 kV were supplied by a high voltage power supplier (HV) and applied across the electrodes. The switching was provided by a pulsed voltage modulator (MOD) with peak voltages switching between 0 to 200 V. HV and MOD shared a common ground (GND).
5. Data processing
In the experiment, we noticed a low frequency phase fluctuation between the reference arm and the test arm. To remove this effect, we derived the following relations.
The fields in the x and y polarizations of the beams from the two arms can be written as
where 1 denotes reference arm, 2 denotes the arm with fibre. E and P denote the field and power at the photo detector. ψ is the phase induced by the 200V modulation, and ϕ denotes all other phases. The polarization of the input beam is aligned in x direction, therefore Ey1 ≈ 0. The total power in the x and y polarizations can be written as where Δϕ = ϕx2 − ϕx1, Δψ = ψx.We measured less than 10% of the total power in the y direction at the output of the fibre. Therefore, Py2 ≈ 0.1Px2. Also, when the modulation voltage is 0, Δψ = 0. Now we can have the total power that reaches the photo detector for modulation voltage on and off as following,
Reorganize the equation, we can haveThe phase of interest, Δψ, can be solved numerically. It’s worth mentioning that y = cos(x) is in the range of [−1, 1], but x′ = cos−1(y) is in the range of [0, π]. x′ and x do not have one to one relation. However, when Δϕ in the range of [nπ, (n + 1)π − Δψ] where n is an integer, the absolute value |cos−1(Δϕ + Δψ) − cos−1(Δϕ)| is equal to |Δψ|. We take many 1-minute measurements and average the maximum |Δψ| of each measurement to obtain the modulated phase.
6. Results
We observed EO amplitude modulation at a series of bias DC voltages ranging from 0 to 4 kV with a 200 V peak voltage modulation. Shown in Fig. 4 is modulated phase Δψ as a function of bias voltage VDC, where
It’s worth mentioning that the electrodes are rather sloppy inside the holes. The position of the electrodes with respect to the holes also varies along the fibre. However, we assumed that when high voltage was applied onto the electrodes, the static charges on the electrodes pull the electrodes close to each other, hence close the gaps in the electrode holes. The distance between the two electrode holes is approximately 85 μm, the air holes around the fibre core is approximately 8 μm. We measured the static dielectric constant of the SF57 glass using a parallel plate method. A 39.9 × 40.1 × 4.06 mm glass plate was coated with silver on the two sides. A capacitance of 49±1 pF was measured. We extract the static dielectric constant εr using the following equation, where C is the capacitance, ε0 = 8.85 × 10−12 F/m is the permittivity of vacuum, A is the area of the plate and d is the thickness of the plate. We calculated εr = 14 ± 0.3 from the equation. Therefore, the estimated deff is equal to deff = 85 − 8 + 8 × 14 = 189 μm.Fig. 4 Experimental confirmation of the nonlinear phase change as a function of bias voltage with 200 V modulation.
The red circles in Fig. 4 are experimental measured data, the blue line is the theoretical prediction using the χ(3) = 5.02 × 10−21 m2/V2, refractive index n = 1.8. The nonlinear phase change Δψ is inversely proportional to the square of the separation distance deff. The 190 μm separation of this fibre limited the switching performance in this experiment. However, the match between theoretical and experimental data demonstrate that our hybrid fabrication technique imposes no deleterious effects on the achievable EO performance and further indicates that soft-glass MOF is a promising platform for efficient EO switching devices because of the high χ3 of soft-glasses and the potential of dispersion engineering through the structures around the fibre core.
7. Future work
The current fibre can be further improved. In principal, the distance between the electrodes can be reduced to approximately 20 μm by drilling closer to the preform central hole and reducing the overall diameter of the fibre. It is possible to introduce the electrodes in more sophisticated way to ensure no air gaps between metal and glass, thus providing a stronger, more homogeneous electric field [19]. These improvements can potentially increase the nonlinear phase modulation by approximately 5 times taking the dielectric constant of silica (εr = 3.9) into account. However, the air gaps around the fibre core dramatically reduce the effectiveness of modulation due to the high dielectric polarization field, but it provides the opportunity of tailoring fibre dispersion, which is also an important characteristic for nonlinear applications such as the generation of second harmonic waves. With the ability to tailer dispersion, the effectiveness of nonlinear process can be greatly enhanced. This have been demonstrated in many third order nonlinear application, especially in supercontinuum generation. The second order nonlinear processes are much more efficient than their third-order counterpart. With proper dispersion engineering and the increase of due to high χ(3) of the material, the potential of soft-glass based thermally poled devices are worth further investigation.
8. Conclusion
We have demonstrated the feasibility of our hybrid fibre fabrication approach and fabricated the first lead silicate microstructured optical fibre with internal electrodes. Electro-optic amplitude modulation was demonstrated with a Mach-Zehnder interferometer with bias and modulation voltages significantly below what would be feasible in an equivalent silica fibre. These results indicate that lead silicate EO MOFs can outperform the equivalent silica counterparts and may pave the way towards low cost, high efficiency EO fibre modulators.
Acknowledgments
This work was undertaken under ARC Discovery project DP0987056. This work was performed in part at the OptoFab node of the Australian National Fabrication Facility utilizing Commonwealth and SA State Government funding. Tanya Monro acknowledges the support of a Federation Fellowship. The authors thank Walter Margulis for helpful discussions. The Authors thank Roger Moore for the fabrication of the optical fibres.
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