Proc. SPIE Photonics West Conference, Optical Fibers and Sensors for Medical Diagnostics and Treatment Applications VI, BIOS06, Vol. 6083, p. 116-130, 2006. Invited article.
All-Fiber and Fiber Compatible Acousto-optic Modulators with Potential Biomedical Applications I. Abdulhalim*أ, Israel Gannot** and C.N. Pannell*** *Department of Electro-optic Engineering, Ben-Gurion University of the Negev P.O.Box 653, Beer Sheva 84105, Israel **Department of Biomedical Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel ***Gooch and Housego Group Optronic Laboratories, 4632 36th Street, Orlando, FL, USA (Invited Paper) ABSTRACT All-fiber acousto-optic (AO) devices such as frequency shifters, phase, intensity and polarization modulators, tunable filters and multiplexers have been developed in the last decade mostly for their importance in fiber optic communication systems. However they can equally have potential uses in bio sensing and fiber based biomedical systems. We present the design, construction and performance of a number of all-fiber and fiber compatible acousto-optic modulators that particularly phase and polarization modulators and will address their potential uses in biomedicine. Among these components and devices, an all-fibre phase modulator acts on the phase of optical fields that propagate down the fibre core. To enhance the phase modulation, the acoustic energy is focused into the fiber core using an acoustic lens. Another high efficiency birefringence (or polarization) modulator was demonstrated that is designed to operate at the acoustic resonance frequency of the fiber. Fiber compatible devices were built using gradient index (GRIN) lenses that can couple the light into a fiber or between two fibers. Diffraction based and polarization GRIN modulators were demonstrated and AOMs of in-fiber gratings as well as ones made from glasses that exhibit large AO figure of merit. As a high frequency polarization, phase, intensity or wavelength modulators these devices have a great potential for use in polarimetric imaging, scanning of a fiber-optic OCT system, tuning the wavelengths in miniature hyperspectral imaging systems and sensors or for frequency-domain OCT. Keywords: Fiber sensors, acousto-optics, biosensors, biomedical optics, modulators, optical coherence tomography
1. INTRODUCTION Acousto-optic (AO) devices are based on the interaction between acoustic waves and matter where the stress produces variations in the refractive index and based on that several effects exist1. A uniaxial static stress produces static change in the refractive index in one direction thus produces birefringence, an old effect known as the photo-elastic (PE) effect. An acoustic wave thus produces a phase grating inside the medium which can diffract a light beam, modify its phase, and its frequency; effects that are known as acousto-optic (AO) effects2. When a pulsed laser beam with high enough energy hits a sample and heats it, an acoustic wave is generated due to the thermal gradient, an effect now known as the photoacoustic (PA) effect which is being used for metals thickness measurement, materials science, medical imaging and diagnostics3. The interaction of acoustic wave with matter depends on the geometry of the medium, for example a surface acoustic wave (SAW) can be excited that travels along the surface and a guided acoustic wave (GAW) can be أ
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excited in a horn. A fiber is an interesting geometry for acoustic waves because of its cylindrical shape and flexibility. Flexural and compressional acoustic waves can be excited in fibers to modulate the phase, polarization, wavelength, and frequency of the guided light wave4. One of the most important challenges in fiber acousto-optics is how to enhance the coupling between the acoustic wave and the optical wave guided in the core5. In an optical fiber there are additional effects that contribute to the phase modulation such as the change in the fiber length (strain effect), reduction of the fiber diameter (Poisson effect) in addition to the refractive index variation through the PE effect. Our intention in this article is to review fiber based AOMs and in particular to present fiber AO devices that we developed for telecommunications applications and highlight their potential biomedical optical applications. The paper is organized as follows: in the next section we shall discuss fiber phase modulators with cylindrical geometry then in section 3, AO modulators with planar geometry will be discussed, in section 4 geometries that enhance the acoustic coupling are presented and in section 5 fiber compatible AOMs will be presented and in the last section we shall review the possible potential biomedical applications of fiber based AO devices.
2. CYLINDRICAL AO FIBER MODULATORS 2.1 Fiber around cylindrical piezoelectric transducer: The simplest and most widely used AO fiber phase modulator (AOFPM) is the one that consists of a jacketed optical fiber wound around on the external surface of a hollow cylindrical piezoelectric transducer6. The operation mechanism is a dynamic mechanical stress of the fiber; i.e., the cylinder expands and stretches the fiber when a voltage is applied across the wall of the piezoelectric transducer (see figure 1a). This phase modulator has found widespread applications in such areas as correction of phase drifts in interferometers and numerous fiber-optic sensors including fiber-optic gyroscope. Recently it was used for path length scanning in the reference arm of Michelson-type fiber interferometer optical coherence tomography (OCT) system. Modulation depths of up to 2π rad / V with a dynamic range of more than 1500π rad can be achieved with this modulator at operating frequencies from 1kHz to few tens or more of kHz – the circumferential resonance frequencies of the piezo-cylinder. The resonance frequencies increase as the radius decreases7, however one cannot go down to arbitrary radius due to limitations on the allowed fiber bend.
Figure 1: Cylindrically symmetric fiber acousto-optic modulators (a) fiber wound around a piezo-cylinder and (b) Piezoelectric transducer thin film is deposited on the fiber circumference.
There are several mechanisms by which the phase between the two orthogonally polarized modes (x and y) is modulated such as bending, tension and lateral pressure. The birefringence induced by the three effects sums together such that the fast axis is perpendicular to the axis of the cylinder and the slow axis is parallel to it. The induced phase difference between the modes is given by the following expression8:
r 2 2 − 3ν p r 4 f ∆φ = CL + s+ πEr 2 R 2 1 − ν p R Where here
(1)
C = πnc3 ( p12 − p11 )(1 + ν p ) / λ which at λ = 633nm it is C ≈ 2.7 x10 6 rad / m , ν p is
7.6 x1010 N / m 2 ), f is the lateral force per unit length (N/m), nc is the core refractive index, r is the fiber radius, R is the cylinder radius, s is the longitudinal strain in the fiber and p12 , p11 (~ 0.270 and 0.121 for silica) are the strain-optic constants of the core. Poisson’s ratio (for silica ~0.17), E is Young’s modulus for the fiber (for silica:
The first term in equation (1) is due to bending, the 2nd term is due to longitudinal strain (tension) and the 3rd term is due to lateral (uniaxial) pressure which is the most dominant term. Since this is the most dominant term then we give here the phase modulation for each mode:
Where ( s x , s y ) =
{
δφ x =
− nc3 k 0 L p11s x + p12 s y 2
}
(2)
δφ y =
− nc3 k 0 L p11s y + p12 s x 2
}
(3)
{
{
}
f (1 + 3ν p ), (3 + ν p ) are the strain components, which when inserted in ∆φ = δφ x − δφ y , πEr
yield the expression for the 3rd term in equation (1). Hence with a polarization maintaining fiber it is possible to excite one mode and get pure phase modulation.
2.2 Fiber along the axis of a cylindrical piezo-transducer: The next important fiber phase modulator is the one where the fiber is lying along the axis of a piezo-cylinder. The fiber can be bonded inside a glass capillary which is in turn fixed inside a piezo-tube. This configuration allows modulation at frequencies up to the low MHz range but it has the disadvantage that the glue layer has unacceptably high acoustic losses at frequencies above this value. For high frequency operation thin film piezo transducers were used9. Another possibility for very high frequency operation is shown in figure 1b which consists of a thin film piezoelectric transducer deposited coaxially on the fiber circumference. In these devices a cylindrical acoustic standing wave is set up in the fiber, and a stress peak appears in the region of the core at a frequency corresponding to an acoustic resonance. Two coaxial electrodes of Cr/Au are usually deposited on the fiber cladding and on top of the piezo layer allowing the application of a voltage. The piezo layer most frequently used these days is sputter-deposited polycrystalline ZnO10 closely followed by aluminum nitride (AlN) and earlier attempts were performed with ferroelectric polymers acting both as a fiber jacket and as a transducer11,12. The advantages of this scheme are that it allows pure phase modulation due to the radial symmetry at frequencies as high as 1GHz due to the small film thickness (few microns thick). The resulting modulator can operate to give high values of peak phase modulation on any one of a comb of resonant frequencies, these are spaced by (typically) ~ 40-50 MHz and in this sense it is not a true broadband device. The phase modulation is expressed as follows: n 2 δφ = k 0 nc L c ( p11 + p12 ) s r − p12 s a − s a (4)
2
[
]
Where here s a , s r , are the axial and radial strains and L is the interaction length (transducer length). For a silica fiber −5 0.1mm, the phase modulation can be as high as 10 rad / V / m / m . When the applied pressure P is considered hydrostatic the phase modulation is given by:
k 0 nc (1 − 2ν p ) LP nc2 δφ = (2 p12 + p11 ) − 1 E 2
(5)
3. FIBER AOMs USING PLANAR TRANSDUCERS 3.1 Linearly stretched fiber: The linear stretcher modulator13 described in figure 2a consists of a piezo-plate operating in the stretching mode. The fiber is glued to the stretcher and frequencies up to few MHz can be achieved. One of the popular uses of this mode is the modulation of fiber gratings14. Stretching the fiber changes both its length and refractive index and for the case of gratings the pitch will be modulated as well, hence spectral tuning is achieved. The relative stretching of a PZT in this mode is given by:
∆L d 31V = L t
(6)
d 31 = 171x10 −12 m / Volt , and for thickness of t = 0.2mm and using V=400 Volts, L=6 cm, one obtains stretching of about 20 µm which gives phase modulation of nearly 60π at λ = 1 µm . Using some special designs this figure can be enhanced by factor of 20 such as with the one developed by Where for PZT, the piezoelectric strain coefficient
NASA Langley Research Center15. Their device is known as Thin Layer Composite Unimorph Ferroelectric Driver and Sensor (THUNDER). Using their device they obtained tuning of fiber grating wavelength by about 5nm.
Figure 2: Planar piezo-plates in two modes (a) stretching mode used as phase modulator with single mode fiber or intensity or wavelength modulator when fiber grating is stretched (b) compressional mode where the piezo-plate is pressed against an aluminum block with U groove of the same diameter as the fiber.
3.2 Diametrically pressed fiber: In this mode the fiber is pressed between a planar piezo-transducer and an aluminum block (figure 2b). Using this mode polarization modulation is achieved16, modulation of fiber gratings17 and using periodic coupling, frequency shifting18 and spectral filtering were demonstrated19. Traditionally a PZT disk is used which usually allows operation frequencies up to few MHz20,21. However in order to operate at higher frequencies a thin transducer is needed. To achieve this goal we have produced a specially designed modulator using very thin LiNbO transducers and bonded them to an aluminum
plate (figure 3a). A U-groove was formed on a polished AL plate (25x20x3mm) so that about half of the fiber diameter is lying inside it by pressing a stainless steel wire having the same diameter half-way into one of the flat sides. The plate was polished again to 0.5 µm flatness. A 250nm layer of Cr/Au electrode was evaporated onto the flat polished bottom surface of the aluminum plate. The piezo-transducer consisted of a 42 µm thick plate of LiNbO3 (36o rotated Y-cut), corresponding to a resonant frequency of 80 MHz, which was indium cold welded onto the Cr/Au layer. The transducer was connected via a matching circuit which was tuned so that the device exhibits a 50 Ohm electrical load. The electrical bandwidth of the transducer was ~2 MHz. The role of the aluminum plate is to provide a hard supporting base onto which a fiber is pressed, to distribute any generated heat efficiently and to transmit the acoustic wave with low attenuation. Aluminum has acoustic impedance close to that of silica, so that backward acoustic reflections are minimized. The phase modulation was measured by having the fiber in one arm of a Mach-Zehnder interferometer Aluminum plate
Fiber in U-groove
Spectrum Analyzer
Modulator
Generated acoustic wave
Detectors
Bottom electrode
Transducer and top electrode (a)
Oscilloscope (b)
Figure 3: (a) Schematic of high frequency planar modulator where the piezo transducer bonded to one side of aluminum plate and the fiber is in U-groove on the other side. (b) The fiber Mach-Zehnder interferometer setup to measure the phase modulation.
placed in the U-groove of the modulator and pressed on top with a flat aluminum block (figure 3b). The signal of the photodiode was analyzed with an electrical spectrum analyzer where we measured the ratio between the 2nd harmonic peaks at 160 MHz to the 1st peak at 80 MHz. Assuming a linear change in the modulated phase: φ (t ) = φ0 + φ m sin ωt , with the amplitude of the applied sinusoidal electrical signal, the ratio between the maximum heights of the 2nd harmonic to the fundamental corresponds to
J 2 (φ m ) / J1 (φ m ) 22. Here φ0 , φ m , J1 , J 2 is the
static phase, modulated phase, 1st order and 2nd order Bessel functions respectively. Figure 4 shows the measured phase modulation as a function of the RF power for two wavelengths 600nm and 1550nm. Using this phase modulator we were able to mode lock an erbium doped fiber laser operating at 1550nm23. The mode locked pulses had a width of 300 ps at a repetition rate of 160 MHz, twice the modulation frequency. The fact that we get such high modulation at relatively low power is because of two possible reasons: first the LiNbO3 transducer was properly tuned so that its conversion efficiency was high and secondly the fact we used U-groove in the aluminum plate caused some focusing of the acoustic energy into the fiber core because the sound velocity in aluminum is higher than in silica. In addition to the phase modulation there is a modulated birefringence as one expects from the lateral pressure effect on the phase difference between the two orthogonal modes. In order to measure this we launched a HeNe laser beam into single mode fiber at 633nm, 70 cm long after passing through a polarizer and half waveplate. A quarter pitch gradient index lens (GRIN) was used to collimate the output beam, which passed through an analyzer and onto the detector. The modulation versus the RF power is shown in figure 4 showing M = ( I max − I min ) / I max = 17% modulation depth at 0.8 W RF power. To understand this further, the applied compressive force to the fiber is estimated from P=FV where V=6.42 Km/s is the acoustic velocity in aluminum, giving F=1.24x10-4 N. From the 3rd term of equation (1):
∆φ = 4CF / πEr where F is now the compressive force, using λ = 0.633 µm; r = 62.5 µm we get
∆φ ≈ 10 −4 rad , which cannot explain the 17% modulation. Therefore there must be additional induced birefringence associated with this modulation. Our main suspect is that due to some anisotropy in the radial strain along the acoustic wave direction and perpendicular to it. Using the part that depends on the radial strain from equation (4) we can write: ∆φ = πnc3 L( p11 + p12 )∆s r / λ ≈ 1.5 x10 5 ∆s r . Since for a waveplate with optic axis at 45o with respect to −5 2 incident polarization we can write: M = sin ( ∆φ / 2) ≈ 0.17 , then we should have ∆s r ≈ 0.56 x10 . 25 633nm
0.6
20
0.5 633nm
0.4
15
1550nm
0.3
10
0.2 5
0.1 0
Intensity Modulation (%)
Phase Modulation (Rads.)
0.7
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
RF Power (W) Figure 4: Plot of phase and intensity modulation at a frequency of 80MHz using the planar modulator at the wavelengths indicated.
Using
fiber
∆r ≈ 0.56 x10
diameter −5
of
125µm, −5
x125 = 70 x10
then
the
absolute
radius
anisotropy
is
of
the
order
of
µm
or less than 1 nm which is certainly feasible since the total absolute strain is only few nm. This amplitude modulation was used to stabilize femto-second soliton pulses generated in passively mode locked erbium doped fiber laser23. The repetition rate of the pulses was 160 MHz, twice the frequency of modulation as expected from the theory of active mode-locking.
4. FIBER AOMs WITH ENHANCED ACOUSTIC COUPLING 4.1 Enhancement using acoustic cylindrical mirror: The planar modulators suffer from low fiber acoustic coupling efficiency due to the small core diameter with respect to the dimensions of the transducer, a fact that poses problem in particular at large frequencies. The geometry described in section 2 where a thin film piezo transducer is deposited directly on the fiber circumference is an elegant solution but it is costly and also limited to high frequencies. In order to resolve this problem we have used a simplified inexpensive configuration where a cylindrical acoustic lens focuses the acoustic energy from a planar transducer into the fiber core24. A schematic of the device is shown in figure 5. An aluminum cylindrical rod 20mm diameter and 20mm length was cut along its length parallel to its axis of symmetry such that the maximum thickness was equal to one quarter of the diameter. We refer to this section as the quarter cylindrical rod (QCR). A U-groove was formed along the symmetry axis of the planar side by pressing into it a stainless steel wire of 125 µm diameter. The optical fiber used was aluminum jacketed and single mode at 1550nm obtained from Fiberguide Inc. A short section of the aluminum coated fiber and the flat surface of the QCR were nickel plated using electroless sulphate bath process until a nickel layer several µm thick
was formed on the aluminum. The fiber was then soldered on the U-groove using an indium based alloy solder leaving ~50 cm pigtail. The solder side acts as a strong metallic thermally stable and acoustically transmitting joint. After depositing the 250nm thick Cr/Au electrode layer, the piezo-transducer which is 42 µm thick plate of LiNbO3 (36o rotated Y-cut) corresponding to 80 MHz resonant frequency, was indium cold-welded onto the flat polished surface of the QCR. The top electrode was Cr/Au in the form of two stripes 2mmx8mm each aligned directly above the soldered fiber (figure 5b). The two stripes were connected electrically in series and the transducer was connected via a matching circuit which was adjusted so that the device presented a 50 Ohm load. The generated longitudinal acoustic wave traveled through the QCR and was reflected from its cylindrically curved surface and focused back onto the fiber and transducer. This gave a standing wave device with a series of resonances around 80 MHz separated by approximately V / 2l ≈ 0.6 MHz , where V=6420m/s is the acoustic velocity in aluminum and l=5mm is the maximum distance from the transducer to the curved radius, that is one half of the radius of the cylinder from which the QCR was cut. The QCR material was selected from aluminum because its acoustic impedance (17.3x106kg/m2s) is close to that of silica
Figure 5: (a) Schematic showing the way the quarter cylinder was cut from the whole cylindrical rod of radius R and the focusing action of the resulted cylindrical mirror. (b) Top view of the QCR with the two stripe transducer on the flat side.
(13.1x106kg/m2s) yielding an acoustic transmission of 98% at the aluminum/fiber interface. In addition, aluminum is a good thermal conductor which distributes efficiently any generated heat. Characterization of the phase modulation was performed using a setup similar to the interferometric setup shown in figure 3b. Figure 6a is a graph of the traces from the spectrum analyzer showing both a peak which corresponds to the fundamental frequency (86.864MHz) and a peak at twice this frequency showing that their ratio between the two peaks is ~1 which corresponds to a phase modulation of φ m ≈ 2.63 radians at the wavelength 1550.3nm and 1W RF power. The variation of the phase modulation with the RF power is shown in figure 6b. As compared to the phase modulation obtained with the planar modulator (figure 4) using similar transducer we get here an enhancement by factor of ~11. To estimate the quality of the acoustic focusing 3 we use the following expression for the acoustic Poynting vector1: I a = ρV S e / 2 where ρ is the density, V is the acoustic velocity and
S e is the strain. The change in the refractive index is: δn = − nc3 p e I a / 2 ρV 3 where pe is
the effective photo-elastic constant given by:
φ m = 2πdδn / λ .
pe = nc2 ( p12 − ν p ( p11 + p12 )) / 2 and the phase modulation is then:
Using the data for silica fiber:
nc = 1.46; ρ = 2.2 x10 3 kg / m 3 ;V = 5950 m / s; p e ≈ 0.2 ,
we get:
δn ≈ 2 x10 −8 I a [ MKS ] .
Using
φ m ≈ 2.63 radians
at 1550nm and d=16mm we get:
I a ≈ 4 x10 6 W / m 2 while the estimated value from the transducer area of 16x2mm and 1W acoustic power is I a ≈ 3 x10 4 W / m 2 using transducer efficiency of 85%. This gives an enhancement of the index modulation in the fiber core by factor of ~11.5 as compared to the case of direct contact transducer without focusing. This is very close to the value we obtained (~11) by comparing the phase modulation for the focused case to that of the non-focusing device. This is not far from the ideal value
H / rc ≈ 14.5 , that one expects from focusing the whole acoustic energy from a
transducer with width H=1mm into a fiber with core radius rc = 4.75µm .
Figure 6: (a) Spectral analysis of the signal from the interferometer showing the fundamental peak at 86.864MHz and its 2nd harmonic. (b) Measured phase modulation from the ratio between the two peaks in (a) versus the RF power. 4.2 Enhancement using fiber transverse acoustic resonance: Another way to enhance the acoustic coupling to the fiber core is using a piezo-transducer that is operating at the fundamental transverse acoustic resonance (FTAR) frequency of the fiber25. The FTAR for silica fiber with a diameter D = 125µm is given by f r = V / 2 D = 23.8MHz . This mode of operation is known26 from bulk photo-elastic
Figure 7: (a) Front view of the FTAR modulator with aluminum block pressing on top and controlling the load. (b) Schematic of the experimental setup used to measure the intensity modulation.
modulation (PEM) as the half-wave resonance condition; however in bulk glass blocks the modulation frequency is much smaller up to few tens of kHz. A schematic of the FTAR-PEM is shown in figure 7a, basically with similar fabrication procedure as with the 80MHz planar modulator shown in figure 3a except that the transducer thickness that produces the acoustic wave with the correct desired frequency is 140 µm of LiNbO3 (36o Y cut) and its lateral dimensions are 1mmx22mm. The experimental setup used to test its intensity modulation capabilities is shown in figure 7b where the HeNe laser beam at 633nm is launched into 50cm long single mode fiber positioned on the top polished aluminum side of the modulator parallel to the transducer and pressed with a flat silica block. A good acoustic joint between the fiber and the modulator was achieved by varying the pressure of the top silica block. A half waveplate (HWP) is used at the input to control the incident polarization so that it makes 45o with the optic axis. A quarter-pitch GRIN lens was used to collimate the beam at the output which passed through an analyzer and onto the detector. The HWP and analyzer are adjusted such that extinction is obtained at zero power. Figure 8a shows the modulated signal exhibiting a modulation depth of 90% using 0.7W RF power at 22.9MHz and the modulation versus the RF power is shown in figure 8b. The modulation was found to be the highest in the range 22.2-23.2 MHz corresponding to the actual transverse resonance frequency for the fiber. The expression for the induced birefringence is given by:
1 +ν p ∆n = 4nc3 ( p12 − p11 ) 3 +ν p Which for silica yields:
Ia ρV 3
(6)
∆n = 3.19 x10 −8 I a [SI], and using an acoustic power of 0.7W and transducer dimensions
−6 HxL=1mmx22mm we get ∆n = 5.69 x10 giving phase retardation of ∆φ = 0.39π leading to 89% modulation. To the best of our knowledge this is the highest frequency birefringence modulator exhibiting such high modulation.
Figure 8: (a) Oscilloscope traces of the modulated light, the electrical signal, the zero level and maximum level. (b) Measured modulation depth versus the applied RF power.
5. FIBER COMPATIBLE AO MODULATORS
5.1 GRIN based diffractive AOM: In parallel to in-fiber modulators, the possibility of building fiber compatible modulators has been considered in particular the use of GRIN lenses as the interaction medium. One of these modulators27 is a traveling wave modulator to operate based on diffraction as a fast switch or frequency shifter. The GRIN medium is essentially different to the conventional bulk-optic AOM in that a radial inhomogeniety of refractive index is introduced during manufacture in order to provide imaging properties. It is the imaging property that has been exploited here in order to provide a truly fiber compatible device. The use of GRIN lenses as AOMs has several advantages over conventional devices in the context of fiber systems such as their small size, inherent compatibility and cylindrical geometry. A single mode fiber can be butted against the input face of a quarter-pitch GRIN lens in order to obtain collimated output beams. Alternatively, a half-pitch lens can be used for simultaneous fiber-fiber coupling. Due to the cylindrical symmetry, an acoustic transducer deposited directly onto the curved surface produces a converging cylindrical acoustic wave. This can be used to match optical and acoustic beam divergence in order to obtain high switching speeds without sacrificing diffraction efficiencies. The GRIN AOM is shown schematically in figure 9 where a Nippon sheet glass quarter-pitch 2 lens is used having a quadratic profile n( r ) = n0 (1 − Ar / 2) with on-axis index n0 = 1.6075 at λ = 633nm , A = 0.339mm −1 , and NA=0.46. The length of the lens was 4.63mm and its diameter 1.8mm. The lens was supplied with Cr/Au layer on its cylindrical surface (700nm thick) and anti-reflection coated. The lens was soldered into a suitably drilled brass block, using an indium based solder. The soldering is particularly useful in creating a hermetic seal or simply a stable bond that will withstand higher temperatures than epoxy bonding. A metallic bond also has the advantage of approximately having the same acoustic impedance as that of the glass, so that backward acoustic reflections are minimized. The block was then carefully lapped until approximately 0.125mm of glass had been removed and the glass was visible as a 0.9mm wide stripe in the brass block.
Figure 9: Schematic of the GRIN AOM. (a) One of the faces of the lens inside a brass block. (b) Side view of the AOM along the length of the lens showing the plane acoustic wave, the light beam inside the lens and the diffracted beams.
A 250nm layer of Cr/Au was next evaporated onto the side of the block containing the exposed lens. The piezotransducer consisted of a 42µm thick plate of LiNbO3 (36o, Y-cut), corresponding to the resonant frequency of 80MHz and indium cold-welded onto the flat polished surface. The top electrode was Cr/Au in the form of a stripe 0.5mmx4.5mm aligned directly above the exposed flat portion of the lens. The transducer was connected via a matching circuit which was adjusted so that the device presented a 50 Ohm electrical load. To characterize the device, a single mode fiber guiding light from a HeNe laser was butted up against the lens. The far field light distribution of the diffracted pattern upon applying a CW RF signal is shown in figure 10a. The central spot appears larger as it is overexposed, but measurements indicate that the m=-1 and +1 first order beams were indistinguishable in shape from the zero order beam. The diameters of the emerging beams were measured at various distances from the device using a
scanning knife-edge technique showing that the diffracted beams and the zero order beam have the same Gaussian radius. These facts indicate that the diffraction process is not appreciably distorting the beam profile and the imaging property of the GRIN lens is preserved. This is particularly important for fiber systems in order to maintain high launch efficiency. The measured diffraction angle was 2θ B = 8.9mrad where θ B is the Bragg angle which gives an acoustic wavelength of Λ = λ / 2θ B ≈ 71.1µm in agreement with the expected one (70.9µm) calculated from the acoustic velocity of BK7 glass 5672m/s at 80MHz. The measured diffraction efficiency was 3% into each of the first order beams at RF power of 0.5W. This low diffraction efficiency is due to the low value of the acoustic figure of merit M2 for borosilicate glass, of the order of 0.06 relative to water against 0.22 for lead molybdate. The device described here is clearly operating in the Raman-Nath regime. This can be seen because altering the position of the input fiber away from the lens axis in order to achieve the Bragg condition has little effect on the relative intensities of the two first 2 order spots. In order to distinguish between the two regimes of operation, the parameter Q = 2πλL / nΛ is used, where L is the interaction length (4.5mm) and n is the refractive index. The limit Q >> 1 places the device in the Bragg regime, while in our case Q~2.4 and hence it is operating in the Raman-Nath regime where multiple scattering of the optical beam is occurring, however we see only the 1st orders due to the low efficiency. Higher orders were observed but they were weak.
Figure 10: (a) Diffraction pattern from the GRIN AOM under 0.5W of RF power at 80MHz showing the zero order and the first order diffraction orders. (b) Transient response (lower trace) to a 50ns pulse showing a rise time of about 14ns.
At higher frequencies the AOM tends towards the Bragg regime and higher efficiencies should be obtainable. The transient response of the device upon applying an RF pulse is shown in figure 10b. The measured rise time is 14ns, faster than many commercially available bulk-optic AOMs by a factor of 2-3. Inside the lens, the guided optical beam radius starts at 3µm and attains a maximum value of approximately 120µm radius at the output face calculated from the known parameters of the GRIN lens. Using Maydan’s formula28 which relates the rise time to the Gaussian beam radius and the acoustic velocity τ = 1.3ωb / V , we found an effective beam radius of 61µm. Note that the average RF power for short RF pulses is less than a mW for repetition rates of few kHz. Hence, heating problems are avoided and it is possible to apply higher RF powers under these conditions to get higher diffraction efficiencies. One of the most promising approaches for this modulator concept is to use GRIN lenses made of glasses with high figure of merit. During our search for fiber glasses for the infrared range we have found that the chalcogenide29 glass Ga2S3-La2S3 (GLS glass) and the chlorotellurite30 glasses are suitable candidates and fibers were drawn from them. 5.2 GRIN based birefringence PEM: Photo-elastic modulators (PEMs) exist in bulk form and being used for applications in polarimetry and ellipsometry over a wide range of frequencies (10-300kHz)31. As the frequency is determined by the thickness and acoustic velocity of the photoelastic medium, the FTAR modulator described in section 4.2 is an extension to high frequencies using a 0.125mm diameter single mode fiber as the photoelastic medium. A GRIN lens is used here32 as a fiber compatible PEM that can
operate up to few MHz. For a BK7 GRIN lens with 1.8mm diameter the FTAR is 1.57MHz and because GRIN lenses and GRIN fibers can be made with smaller diameter, one can design such a modulator with almost any desired frequency. One of the fortunate properties of existing GRIN lenses made from borosilicate glasses, is that they posses relatively high stress-optic coefficient. A schematic of the setup is shown in figure 11. The GRIN lens was pressed directly on top of a PZT disc using an aluminum block. The PZT disc is of type 5A (Vernitron-U.K. Ltd.), having the dimensions 22mm diameter and 1.8mm thickness, designed to resonate at 1MHz in thickness mode. Light from a HeNe laser at 633nm was launched into 85cm long single mode fiber after passing through a polarizer and a half waveplate (HWP). The end of the fiber was butted to one face of the GRIN lens. For the case of quarter pitch GRIN lens (QPL) the diameter was 1.8mm and its length is 4.6mm, AR coated on its faces and gold coated on its cylindrical surface. The collimated beam passed through an analyzer and to the detector. In the half pitch case, a GRIN lens of 8mm length and 2mm diameter was used. On the output face of the lens a second identical fiber was butted to receive the light coupled to the lens from the input fiber. The fiber to fiber coupling efficiency to the 2nd fiber was approximately 50%. In the case of half-pitch lens (HPL) there are two modes of operation. The first mode is based on the birefringence modulation (BM) similar to that due to the stress distribution in the GRIN medium. This modulates the coupling efficiency to the output fiber with no need for an analyzer. This latter mode is called the launch efficiency modulation (LEM). Results of the modulation in each mode are shown in figure 12. Since the HPL is longer the modulation is higher than the QPL case. In the LEM mode the analyzer was removed and the light coming directly from the output was detected. In figure 12c the LEM modulation is 15%. For further details the reader is referred to our previous publications.
(a)
(b)
Figure 11: Schematic of the GRIN-PEM modulator setups for the quarter pitch lens case (a) and for the half-pitch lens case.
Figure 12: Oscilloscope traces of the intensity modulation in the birefringence mode at 1.078MHz (a) for QPL case and (b) HPL case. (c) Modulation in the launch efficiency mode of HPL at 1.089MHz. RF power is 2.5W.
One of the questions that were raised by Su and Gilbert33 is whether the shear stress component
τ xy
needs to be taken
into account. In our previous work we have neglected it because it is small compared to the tensile stress components along x and y. Since the contribution to the induced birefringence due to the tensile stress alone is proportional to (σ x − σ y ) while that due to the shear stress is proportional to τ xy we have plotted in figure 13 the ratio between the two as a function of x and y (normalized to the lens radius). Figure 13 shows that within an area around the lens axis within about half the radius from the axis the shear stress is small compared to the anisotropy (σ x − σ y ) . Because the
xy/( x- y)
maximum optical beam radius inside the lens is 120um, we conclude that the effect of the shear stress on the induced birefringence modulation is negligible.
1 0.5 0 - 0.5 -1 -1
1 0.5 0 - 0.5 - 0.5
0
x/r
y/r
0.5 1 -1
Figure 13: Plot of the ratio between the induced birefringence contributions from the shear stress and the anisotropy of the lateral stress components showing that the shear stress contribution is much smaller near the center where the optical beam exists.
6. POTENTIAL BIOMEDICAL APPLICATIONS As phase and polarization modulators, fiber based AOMs can be used in many fiber based biomedical optical systems such as optical coherence tomography (OCT), endoscopy and other fiber based sensors. The use of AOMs in OCT systems has been shown to be promising recently for high speed scanning34, for Doppler-OCT35, and for dispersion compensation36. In OCT systems there is a need for fast scanning mechanism of the path-length with high enough dynamic range to cover the whole axial range of interest usually up to a mm or more inside the tissue. Each mm of pathlength difference corresponds to about 1500 wavelengths equivalent to 1500π, which is achievable using a fiber wound
around a cylindrical piezo transducer as explained in subsection 1.1. Polarization insensitive frequency shifting has been achieved37 using two AOMs, which can equally be achieved using the GRIN based AOM described in subsection 5.1, although the diffraction efficiency needs to be improved using glasses with higher figure of merit29,30. A combination of GRIN PEM with the GRIN based OCT system reported recently38 is straightforward thus allowing for polarization sensitive GRIN based OCT system. The high frequency phase and intensity modulators described in sections 4.1 and 4.2 can be used for AC modulated schemes usually used to enhance the signal to noise ratio. Fiber based biosensors based on surface plasmons and ITO deposited at the end of the fiber usually detect weak signals, hence modulation of the optical phase and polarization will allow enhancement of the signal to noise ratio using phase or amplitude locking techniques. The intensity modulators can be used for polarization based fiber optic devices. Consider for example the high frequency FTAR modulator which can be used for phase modulated polarimetry or ellipsometry using a fiber probe. A GRIN PEM can be combined with a polarization maintaining single mode fiber where the fiber is attached to one of its faces with a thin film polarizer integrated into the 2nd face. Combination of polarimetry and tunable filtering has been shown recently to be possible with potential biomedical applications39. Acoustic tunable filtering based on fiber null coupler was demonstrated recently40. Combination of this concept with the birefringence and phase acoustic modulation capabilities presented in this article should allow spectral polarimetric medical diagnostic methods. A note should be added on the possible modulation of fiber lasers as sources of short and high power pulses. Recently an all-fiber acousto-optic Q-switch of Er fiber laser has been demonstrated using a flexural acoustic wave excited with a horn and pulses of 150ns width, 3µJ energy at 5kHz were achieved41. Using a specially designed TeO2 AO modulator we have demonstrated42 Q-switching of 1% doped Nd+3 fiber laser obtaining 2.8ns width pulses with 0.7kW peak power at 1kHz repetition rate and 1.4ns, 2kW pulses from 3% Nd+3 doped fiber. Using cavity dumping we obtained higher frequency train of pulses having greater width43. Such miniature fiber sources can be used in photodynamic therapy, photoacoustic medical imaging and other sensing schemes.
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