Elliptical plasmonic near-field transducer and v-shape waveguide designs for heat assisted magnetic recording

: We proposed a new elliptical near-Ąeld transducer (NFT) and V-shaped waveguide design, which provides multiple pathways to control and optimise the thermal performance of the optical delivery paths for heat-assisted magnetic recording (HAMR). The principle of operation of the design utilises the properties of the localised surface plasmon resonance (LSPR) of the metallic elliptical NFT. We demonstrated a peak temperature in the recording media normalised to the incident laser power ( T Media / P In ) ranging from ∼ 128 K/mW to more than 181 K/mW. We also achieved tunable thermal gradients as high as 23.0 K/nm and 18.7 K/nm in the recording mediaŠs down-track and cross-track directions, respectively. Moreover, we exempliĄed that the inevitable temperature rise in the plasmonic NFT could be tuned to remain under 400 K for maximum heat in the recording media > 700 K. The best thermal performance obtained corresponded to the aspect ratio of the antenna a/b ∼ 0.89 with the minor axis of the antenna a = 85 nm.


Introduction
Plasmonic devices have received a great deal of attention in the past decades due to their ability to concentrate electromagnetic radiation to sub-diffraction limited spots on the order of a few nanometres while enhancing the Ąeld intensity by a few orders of magnitudes [1,2].These remarkable properties have facilitated the development of a wide range of technologies, including near-Ąeld optical microscopy, photodynamic therapy, plasmonic biosensors, and subwavelength waveguides, to name just a few.However, the use of plasmonic systems for high-temperature applications remains mired by the limitations of plasmonic materials, which are mainly due to losses at optical frequencies [3].These have become an urgent bottleneck issue holding back the commercialisation of many plasmonic technologies, particularly heat-assisted magnetic recording (HAMR) in data storage [4,5].Moreover, it set signiĄcant barriers restricting fundamental nanoscale research in a high-temperature environment, such as solar thermophotovoltaics and the burgeoning studies of nanoscale thermodynamics that are fundamental to nanochemistry.
HAMR is a method for encoding information in magnetic media with nanoscale track widths (< 50 nm) to enable high areal densities (ADs) beyond 2 Tb/in 2 in the recording medium of next-generation hard disk drives (HDD) [6].In this technique, the light from a laser (typically at λ = 830 nm) is guided in an optical waveguide and coupled either evanescently [7] or by direct-Ąre approach [8] to an aperture-, or apertureless-based plasmonic antenna (near Ąeld transducer (NFT)) attached to its end.It is designed to focus the electromagnetic power into an area smaller than 50 × 50 nm 2 in a high coercivity material to heat it to above its Curie temperature (∽750 K for bulk L 10 FePt) [9].A range of such devices has been investigated, including C-, E-, and Hshaped apertures [10Ű12], bow-tie apertures [13,14], triangular antenna [15], lollipop antenna [4], droplet antenna [16], and the nanobeak antenna [17].
In such applications, beyond the temperature magnitude, the in-plane temperature distribution (i.e., thermal gradient) of the sub-nanometre conĄned thermal energy is a crucial parameter that needs to be considered.In addition, the heat transfer process makes obtaining a sizeable thermal gradient on a nanoscale region challenging.Furthermore, plasmonic applications have different requirements regarding this metric, which depend on the material and the design of the plasmonic system.For instance, in array-based nano-reactors for plasmonic photocatalysis, a thermal gradient of 1.9 K/nm is obtained [18].In comparison, values as high as 15 K/nm have been reported for antenna-based plasmonic near-Ąeld transducers used in HAMR applications [19], the focus of this work.
The nanofocusing of electromagnetic energy in HAMR applications can be attained straightforwardly using the localised surface plasmon resonances (LSPR) [20] supported by the plasmonic device in use.However, the challenging aspect of this nanofocusing process is the thermal management of the system, for instance, (i) the thermal efficiency of the system, which measures the peak temperature in the media relative to the peak temperature in the NFT for a given incident laser power.This metric should be as large as possible since the largest increase in media temperature for the smallest increase in NFT temperature is desired to prevent the NFT from getting too hot; otherwise, the NFT could deform or melt, degrading its performance.The highest value for this metric was 8.60, obtained in a numerical study using an NFT of an alloy of Au 0.175 Ag 0.875 for a laser power of 4.9 mW [19], (ii) the thermal spot proĄle in the media at the full width at half maximum (FWHM) should maintain its ŠsquarenessŠ to avoid having a long thermal tail in the media in both the cross-track and down-track directions, (iii) the thermal gradient in the media, which must be as large as possible, as having a sharp thermal gradient allows writing sharp transitions that are key to high linear densities, (iv) the normalised peak temperature, which measures the peak temperature in the media normalised by the total power incident on the NFT must also be as large as possible; it determines how much laser power is needed to deliver to excite the NFT and is also helpful for characterising the effects of laser intensity noise on the recording system [21], (v) and indeed the most problematic and central to all the aforementioned requirements is the reliability of the plasmonic near-Ąeld transducer itself, which is generally made of gold and must withstand the inevitable high temperature within the HAMR system.
Advantageously, in most high-temperature plasmonic applications, including HAMR, the plasmonic nanostructure in question does not have to be at a speciĄc temperature but rather should be illuminated until a speciĄc optical output is reached [22].For instance, the use of alternative plasmonic materials that have very high melting points, like titanium nitride, zirconium nitride, tungsten, etc. [23,24], is not necessarily the best option for making better plasmonic NFTs for high-temperature applications.As these materials have high optical absorption and require much more incident power in order to produce the same strong near-Ąeld enhancement that is produced by noble plasmonic materials like gold or silver.This causes a signiĄcant self-heating effect [25] in these materials, which severely affect the performance of nearby devices in the system, such as the write pole in the case of HAMR, hence, affecting the thermal performance of the whole system.To a large extent, this means that we could alleviate the self-heating burden and side-step the limitations of using noble plasmonic materials for high-temperature applications via engineering the architecture of the plasmonic nanostructures and the optical delivery path to optimise the optical output and the near-Ąeld enhancement.
A "wired" conĄguration, in which a surface plasmon polariton (SPP) is excited and propagated along a plasmonic waveguide of many micrometres long (∽ 6 µm), achieved a thermal efficiency of 5.91% in [26]; outperforming other contending optical antenna designs (Lollipop and Caperture) used for HAMR.Furthermore, the long tapered structure is also found to be most efficient for converting the plasmonic mode in the NFT to thermal energy in the recording media, even without optimisation [22], as it can efficiently match its radiation resistance impedance (a quantity that depends on the length of the antenna) to the impedance of the recording medium [8].On the other hand, "wireless" conĄgurations have demonstrated outstanding potential for managing the optical and thermal performance of the HAMR plasmonic systems.The plasmonic antennas are located far from the laser sources in such designs.The localised surface plasmons resonance (LSPR) is excited via an evanescent coupling approach for an antenna with a tapered structure [27] and via a direct-coupling method in a design that uses a metal-insulator-metals (MIM) conĄguration and reĆection coatings in the waveguide [19].
This work proposes a novel design of an optical delivery system consisting of an elliptical plasmonic antenna (NFT) and a V-shaped waveguide.We adopt the "wireless" conĄguration where the light from the laser is coupled evanescently to the NFT at the end of the V-shaped waveguide.The optical properties of the elliptical geometry and its usage in plasmonic applications have been investigated thoroughly in [4].Here we study its use as a near-Ąeld transducer in an optical delivery path for HAMR.The geometrical parameters of the elliptical antenna provide means to control the near Ąeld enhancement and to support higher-order plasmonic modes, which help match its radiation resistance impedance to the impedance of the recording medium [8].On the other hand, the V-shaped waveguide could also be controlled to optimise the light coupling to the elliptical plasmonic antenna for the chosen elliptical antenna parameters.The proposed system provides Ćexibility and several degrees of freedom to manage the optical and thermal performance of the HAMR optical delivery path and an optimal photonic-plasmonic-thermal conversion yield.The study was performed numerically using (COMSOL Multiphysics software) [28].MaxwellŠs equations are initially solved to determine the power dissipated due to resistive losses in the computational region, which is then applied to the heat transport equations as a heat energy transfer rate.The software discretises and solves the coupled heat transport and electromagnetic equations on a Ąnite-element mesh in three dimensions.

Results and discussion
The proposed optical delivery path consists of a V-shaped waveguide (Fig. 1(a)) that evanescently couples a photonic mode from a semiconductor laser to a plasmonic mode supported by an elliptical antenna (Fig. 1(b)) positioned 10 nm above the core at the end of the waveguide (Fig. 1(a) -insets (i) and (ii)).Each of the two arms of the waveguide is designed for single-mode excitation at a continuous wavelength of 830 nm.The injected modes are TE 10 -modes, and they are 180• out of phase to allow for the excitation of the quadrupole or higher-order modes based on the size of the plasmonic NFT.The angle ϕ between the arms of the waveguides was adjusted until maximum coupling to the plasmonic mode was achieved at ϕ = 54 • .It should be noted here that all the parameters of the design are tied together; for instance, changing the dimensions of the elliptical antenna changes the plasmonic mode supported and hence requires a new coupling conĄguration, which also requires a change of the waveguide angle ϕ.
The choices of waveguide materials for the magnetic head industry are limited since these materials must have long-term stability.The core of the waveguide usually is tantalum oxide (Ta 2 O 5 ), and the cladding materials could be either aluminium oxide (Al 2 O 3 ) or silicon dioxide (SiO 2 ) [29].Recently, other materials such as silicon nitride (Si 3 N 4 ) [19,30] and silicon (Si) [27] have also been investigated.The core material in the proposed design in this work is silicon (Si) fully embedded in silicon dioxide (SiO 2 ) cladding.The reason for this choice is the high refractive index of silicon which provides better light conĄnement and coupling to high     effective index plasmon modes.More importantly, the much higher thermal conductivity of Si (k = 130 W/(m.K)) compared to Ta 2 O 5 (k = 0.45 W/(m.K)), which would help markedly lower the steady-state temperature of the NFT given equal amounts of dissipated power [27].Notwithstanding, Silicon Nitride material, for example, could have been chosen in this work instead.In this case, the waveguide height (h) should be increased from 120 nm to 180 nm, and the gap (g) between the antenna and the waveguide should also increase from 10 nm to 188 nm for best evanescent coupling of the photonic mode in the waveguide to the plasmonic mode in the antenna as shown in a previous study [31].Therefore, the Ćexibility of the design allows for various choices of materials and dimensions to be investigated.The NFT used in the proposed optical delivery path for HAMR has elliptical geometry (Fig. 1(b)).All the dimensions shown in this diagram can be manipulated to optimise the performance of the antenna.a and b are the minor and major axes of the antenna, respectively.Tuning these two dimensions independently provide more control on the NFT performance than the conventional lollipop NFT.Varying the lengths a and b generate different charge distributions; consequently, different order plasmonic modes could be supported according to their resonance with the incident wavelength.This will have a signiĄcant inĆuence on the thermal performance of the HAMR system.
The tip is designed with rounded corners with a radius of 5 nm to evade large Ąeld enhancement at perfectly sharp edges, which are not easy to make practically, for instance, because of the proximity effect [32], which limits the achieved resolution in electron-beam lithography in the nanofabrication process.Its width d 1 controls the cross-track length of the heated region in the recording medium.The height d 2 should be minimised to mitigate the propagation of the surface plasmon along the tip at the Air Bearing Surface (ABS) [27] (see Fig. 1((c) and (f)) and to reduce the down-track size of the hot spot.It should also be noted here that the surface plasmon in this design is generated at the bottom surface of the antenna at the interface between the plasmonic and the dielectric spacer layer (the H x component of the plasmonic mode is shown in Fig. 1(b) inset (ii)).However, the top part of the elliptical body (the gold material present above the height d 2 ) could be extended ( Fig. 1(b) -inset (i)) to act as a heatsink for the NFT at no cost to the optical performance [27].
The gap between the antenna and the waveguide has a thickness g ( Fig. 1(a) -inset (ii)) which is also important to match the photonic-plasmonic modes coupling [27,33].d 3 and d 4 deĄne the extension of the tip and the height of the back end of the antenna, respectively, which are also needed to optimise the coupling of power from the waveguide to the antenna and from the antenna to the recording medium.The angle θ is adjusted to keep the write pole away from the body of the antenna, so it does not interfere with the plasmon mode while maintaining a close distance of 30 nm of the tip in the front side to enable easy data encoding.Figures 1((c), 1(d), 1(e), and 1(f)) show a schematic of the complete optical delivery path proposed in this work.The various components are labelled on the diagram.
The dimensions of the tip d 1 and d 2 are set for the desired hot spot size in the recording media.The gap g is set to optimise the photonic mode coupling from the waveguide to the plasmonic mode of the NFT.d 3 is adjusted to optimise the conĄnement of the near-Ąeld and hence, the conversion process of the plasmonic mode to a hot spot in the recording media.d 4 is the height of the backside of the top part of the antenna, which acts as a heatsink.The minor and major axes dimensions of the antenna a = b = 85 nm that corresponds to the conventional circular shape of the antenna are the initial values that produced the maximum photonic to plasmonic coupling; then a is kept Ąxed while b varied during the study.Here, the role of the V-shaped design of the waveguide comes into play as it could easily modify the coupling arrangement for the guided photonic mode to the supported plasmonic mode based on the chosen parameters of the NFT.The chosen material for the elliptical NFT was gold for its superior plasmonic performance compared to other plasmonic materials [34].An in-depth discussion of HAMR plasmonic materials can be found in [6].

Photonic − → plasmonic − → thermal conversion processes
The efficiency of the photonic − → plasmonic − → thermal conversion processes depends on the geometries and materials of the transducer, waveguide [6], and the dielectric spacer layer between them [33].And it is also affected by the presence of any metal in proximity (e.g., write pole, heatsink, recording media, etc.).These processes are illustrated in (Fig. 2).First, the photonic TE 10 -mode is launched and propagates on both sides of the waveguide arms with a π-phase shift to allow exciting a quadrupole or higher-order localised surface plasmon resonance (LSPR) mode, according to the size of the NFT [7].We highlighted the magnetic Ąeld component, H x of such a mode at the bottom surface of the antenna for an incident laser power of 7.25 mW; the same laser power that is used in the comparative study in section 2.3.The plasmonic mode concentrates the light at the tip due to the lightning rod effect [35].Finally, the energy dissipates in the lossy magnetic material, creating the required hot spot where the dimensions of the tip determine its proĄle.The smaller the tip, the higher the systemŠs ADC; however, the frailer the NFT would be, and a careful trade-off needs to be made.
The maximum temperature generated in the media was 932 K, achieved with an antenna with the tapered angle (θ = 30 • ) and a minor and major axes of sizes (a = 85 nm) and (b = 95 nm), respectively, as shown in Fig. 2.However, it is expected that increasing the size of the antenna, which is desired for fabrication tolerance, would require re-optimising all the other parameters in the design to optimise the photonic − → plasmonic − → thermal conversion processes.

Thermal behaviour of the system
Based on the structural, optical and thermal properties of the different devices and stack materials shown in Table 1, we analysed the thermal performance within the system.Figure 3(a) demonstrates the overall temperature proĄle within the different components.The maximum temperature recorded in a plane at the middle of the magnetic recording layer reached 932 K for a total laser power of 7.25 mW, indicating efficient heating.Figure 3(b) shows a close up of the generated hot spot concentrated within < 50 x 50 nm 2 in the FePt recording layer.Such an area meets industry standards of storage densities of 1 Tb/in 2 or larger.It is determined by and large by the dimensions of the elliptical antenna tip at the ABS and the thermal gradient magnitude within the media.The recording medium layer FePt has a ∽ 750 (K) Curie temperature.The necessary quantities for qualitative and quantitative analysis of the systemŠs thermal behaviour are presented in Figs.4(aŰc).Figure 4(a) compares the maximum temperature in the media, NFT and the write pole as a function of the eccentricity of the NFT.While the temperature in the HAMR media needs to be maximised to above its Curie temperature, it needs to be minimised in the other components to ensure devices reliability and durability, the task that is demonstrated in section 2.3.But in general, the typical speciĄcation is that the electromagnet must be under 450K to avoid a substantial deterioration of the magnetic Ćux output from the write head [22].On the other hand, the temperature of the NFT must remain under 400 K if it is made of gold, as it is known to become signiĄcantly malleable at this point.
The down-track and cross-tack thermal gradients of the hot spot are highly important too.These quantities must be above 10 K/nm for high areal densities and to not overwrite adjacent bits with parasitic heating [19].The thermal gradient is strongly affected by multiple factors, including the shape of the antenna [18,36], the dimensions of the various layers in the recording Ąlm stack [22], and the power of the laser, to name a few. Figure 4(b) depicts the change of the down-track (black marks) and cross-track (red marks) thermal gradients, with maximum values of 23.2 K/nm and 17.7 K/nm, respectively, for the aspect ratio of the antenna a/b ∽ 0.89.Fig. 2. The diagram demonstrates the coupling of photonic to plasmonic mode and the coupling of plasmonic to hot spot in the recording media.The TE 10 guided mode in the waveguide, E y , excites the antennaŠs localised surface plasmon resonance (LSPR) mode, the H x component of which is plotted at the NFT-spacer layer interface, and which in turn concentrates the light and dissipates the energy in the lossy magnetic material creating the hot spot in the recording medium.Due to the tapered angle (θ = 30 • ) and the size of the minor (a=85 nm) and major (b=95 nm) axes of the elliptical antenna, the tapered write pole is 216 nm high above the NFT-dielectric interface at the back-end of the NFT and 30 nm from its tip for easy data encoding.This arrangement prevents the write pole and heatsinks from affecting the photonic-plasmonic modes coupling.
Au NFT b = variable, a = 85 nm, 0.17 5.17   Figure 4(c) shows the results for two Ągures of merits (FOMs) that quantify the systemŠs thermal performance.The Ąrst is the thermal efficiency (∆T Media /∆T NFT ) (red marks), which measures the peak temperature in the media relative to the peak temperature in the NFT for a given incident power.This metric should be as large as possible to achieve the largest increase in temperature in the recording media for the smallest increase in the temperature of the NFT.The other is the normalised peak temperature (T Media /P In ) K/mW (blue marks) which measures the peak temperature in the media normalised by the incident laser power.It indicates how much laser power is needed to be delivered to the NFT for a speciĄc output which is useful for characterising the effects of laser intensity noise on the recording system [21].The curves in Figs.4(aŰc) demonstrate the tunability of the thermal performance with the aspect ratio of the elliptical antenna, which shows peaks at a ratio of ∽0.89.

Comparison with other NFTs
Here, we perform comparative studies of the thermal behaviour of the proposed optical delivery path for HAMR featuring the elliptical antenna and the V-shaped waveguide with other near-Ąeld transducers designs.The studies compare conventional [36] and high-performance [19] designs.The thermal performance of a triangular antenna, E-antenna, and a lollipop antenna from [36] is plotted along that of the elliptical antenna (Fig. 5) with red, yellow, blue and green colours bars, respectively.All the antennas are excited with the same laser power of 5 mW, which is the power used in [36].Here, the elliptical antenna has a major axis b = 95 nm and a minor axis a = 85 nm.From a glance at the Ągures, the superiority of the elliptical antenna design performance is apparent.The Ągures of merits used here are the same as those discussed in the previous section.Figure 5(a) is the maximum temperature in the media normalised to the laser power, which indicates the efficiency of the photonic to plasmonic, and the plasmonic to thermal conversion processes.The elliptical antenna produced the highest normalise peak temperature with a value of ∽ 150 K/mW. Figure 5(b) is the thermal efficiency (∆T Media /∆T NFT ) which quantiĄes the ratio of the temperature rise in the media to the temperature rise in the NFT.The thermal efficiency of the elliptical antenna (green bar) is almost twice that of the best of the other three antennas (yellow bar).Figures 5(c) and 5(d) are the mediaŠs cross-track and down-track thermal gradients, respectively.The values presented here are greater than the other antennas in this comparative study and close to or even better than values obtained from different designs ( [18,19,37Ű39].It is also worth mentioning that the analysis in [36] did not ponder the presence of any nearby metallic components such as the write pole or heatsinks to the NFT, which would have undoubtedly affected the performance of these antennas. The results of another comparison with the optical delivery path design using metal-insulatormetal (MIM) NFT design [19] is presented in (Table 2).This MIM design demonstrated a high standard of thermal performance and considered all the devices close to the NFT in the HAMR head.The elliptical antenna design (1) compared the case in Ref. [19] for the incident laser power of P In = 7.25 mW, where we used similar optical and thermal properties of the materials in the simulations with slight changes in the thicknesses of a few layers in the recording media stack (Table 1).The best performance in each metric is highlighted in green.The elliptical antenna resulted in signiĄcantly improved values of 23.0 K/nm and 18.7 K/nm for both the down-track and the cross-track thermal gradients, respectively, and in higher temperature rise in the recording media per milli-watt of laser power T Media /P In ∼ 134 K/mW.However, the temperature of the NFT increased signiĄcantly to 495 K.This is an unwanted result for the HAMR application, where the NFT has to remain under 400 K if it is made of gold, as discussed previously.Notwithstanding, the temperature of the NFT and the metric (∆T Media /∆T NFT ) for the elliptical antenna could be improved, for instance, by reducing the power of the laser, by changing the aspect ratio of the antenna, or by varying any of the parameters shown in Fig. 1.We showed improved performance in the elliptical antenna design (2) by reducing the laser power to 3.9 mW and made θ = 25 • .Figure 6 shows the arrangement used in this comparative study, where it also shows that the spot proĄle indeed has the shape and dimensions of the tip of the antenna.Therefore, its size could be controlled by changing the cross-section of the tip facing the Air-Bearing surface.2. ( 1) is the heatsink of the write pole (2), ( 3) is the elliptical antenna, (4) is the hot spot, (5) is the waveguide, and ( 6) is the surrounding cladding .

Conclusion
We proposed an optical delivery system for HAMR consisting of an elliptical plasmonic antenna and a V-shaped waveguide design.The dimensions of the elliptical antenna allow tuning the optical and thermal performance of the system.We demonstrated in various examples the ability of the elliptical antenna design to tune the normalised peak temperature metric, which indicates how much laser power is needed to be delivered to the NFT for a speciĄc output; we generated values ranging from ∼ 128 K/mW (Fig. 2) to more than 181 K/mW (Table 2, elliptical antenna design (2)).
Such Ćexibility provides reasonable control to maintain a suitable trade-off between the normalised peak temperature and the thermal efficiency (∆T Media /∆T NFT ).In addition, comparative studies with many other NFT designs showed that the thermal gradients in the down-track and the cross-track directions of the recording media produced by the elliptical antenna outperformed those designs.On the other hand, increasing the size of the elliptical NFT will cause the antenna to support higher-order plasmonic modes, which will require considering a new coupling arrangement.Here, the V-shaped waveguide comes into play; its design offers agile coupling between photonic and plasmonic modes by changing the angle between its arms.
Furthermore, as any metallic component such as the write pole near the plasmonic antenna would affect its performance severely, placing the write pole 30 nm above the antenna is challenging.Nevertheless, the tapered antenna, write pole, and the various heatsinks allow dealing with this problem efficiently.It keeps these metallic components far from the bottom surface of the antenna where the plasmonic response occurs, while they are only 30 nm distant above the tip at the front, allowing easy data encoding.Practically, it could also be fabricated inside the gap of the V-shaped waveguide.Such tapered features enhance the thermal performance and offer Ćexibility in different engineering designs and allow the investigation of complete optical delivery systems for HAMR with the essential metallic components near the NFT.
In general, the proposed system demonstrated tunability and high photonic-plasmonic-thermal conversion efficiency.These results offer multiple pathways for engineering plasmonic NFTs and waveguides to optimise and manage the thermal output in heat-assisted magnetic recording.They also provide important insight for designing effective optical delivery systems for a wide range of other plasmonic applications with different temperature requirements.
(a) V-shaped waveguide (b) Elliptical antenna (c) 3D view (d) Top view (e) ABS view (f) Side view

Fig. 1 .
Fig. 1.(a) is the V-shape waveguide design.w and h are the width and height of the waveguide arm, respectively, w out is the width of the waveguide exit port, ϕ is the angle between the two arms.(b) is schematic of the proposed elliptical NFT.The dimensions a and b are the minor and major axes of the antenna, respectively.d 1 is the width of the tip, d 2 is the height of the main body of the antenna, d 3 is the extension of the tip from the body of the NFT, d 4 is the height of the back end of the antenna, and θ is the angle of the taper of the top section of the NFT which also acts as a heat sink.(c), (d), (e), and ( f) are labelled schematics of the complete optical delivery path.The Initial dimensions and materials properties are listed in (Table1).The Si-waveguide is cladded in SiO 2 .ABS-air bearing surface.

Fig. 3 .
Fig. 3. (a) is an overall view of the temperature distribution in the proposed HAMR optical delivery system elements, (b) a close-up of the hot spot in the media.

Fig. 4 .
Fig. 4. The Ągures show the thermal performance as a function of the aspect ratio of the elliptical antenna.(a) is the highest temperature recorded in the different components, (b) thermal gradients, and (c) is the Ągures of merit recorded as a function of the aspect ratio of the elliptical antenna.

Fig. 5 .
Fig. 5.The Ągures compare the thermal performance at the steady-state for various antenna designs reported in [36] with the elliptical antenna proposed in this work.(a) is the normalised peak temperature (T Media /P In ) K/mW, (b) is the thermal efficiency (∆T Media /∆T NFT ), (c) is the cross-track, and (d) is the down-track thermal gradients.

Fig. 6 .
Fig.6.The Ągure shows ABS view for the system used in the comparative study presented in Table2.(1) is the heatsink of the write pole (2), (3) is the elliptical antenna, (4) is the hot spot, (5) is the waveguide, and (6) is the surrounding cladding .