Wavelength response of ring-type head with arbitrary gap depth

In 1953 Westmijze found analytic solutions for the fields and wavelength responses of ring-type-head models with zero and infinite gap depths and demonstrated that the wavelength responses for these two extreme cases are substantially different. A model two-dimensional electromagnet that is equivalent to a more general ring-type-head model that takes into consideration a final gap-depth value is considered. It is shown that the Westmijze head models are actually two specific cases of this more general model. Using the theory of complex analytic functions, the gap between the two Westmijze models is bridged and an analytic solution for the wavelength response of a ring-type head with an arbitrary gap depth is derived. Graphs of the responses calculated for several gap depths are presented. These graphs illustrate that the gap depth has no practical effect on wavelength response as long as the ratio of pole thickness to gap size exceeds 0.5. However, further decrease of this ratio causes considerable changes in wavelength responses     

绝对测量小距离的波长扫描-光纤双干涉仪系统

介绍了用于测量小位移的波长扫描－光纤法布里－珀罗干涉仪系统。用扫描波长作为“中介”,比较参考腔长和传感腔长,可以“准绝对”地测量传感腔的长度。这个测量与波长扫描的准确度无关,仅依赖于参考腔的长度,而通过将传感腔改变一个已知距离,就可以简单地“自标定”参考腔的长度。     

Side fringing fields and write and read crosstalk of narrow magnetic recording heads

In magnetic recording systems the side fringing fields of magnetic recording heads are responsible for crosstalk from adjacent tracks and eventually for partial erasure of adjacent tracks, thereby limiting the attainable track density. In this paper we derive analytical expressions for the magnetic field near the side of a recording head and calculate the cosine transform of the longitudinal field component, with the head side angle and gap length as parameters. The field of a head of zero width is also considered. Due to the side fringing field the written track is somewhat wider than the geometrical head width; the increase in width being approximately proportional to the maximum field strength in the recording medium and the head-to-medium distance. The amplitudeuof the read crosstalk signal from an adjacent, infinitesimally narrow track is calculated and it appears that it can be approximated byu/u_{0} = 0.5 exp (-2pi x/lambda), where u0is the on-track signal (with zero head-to-medium spacing),xis the distance between track and head side, and λ is the wavelength. Maximum track densities are calculated for a specified crosstalk-to-signal ratio and a given head width and wavelength. For a wavelength of 10 μm, a head width of 5 μm, and a crosstalk of -20 dB, the track density is limited to about 130 tracks/mm, assuming a track width equal to the head width. When the track is taken to be 5 μm wider than the head to account for the effects of the write process, no guardband at all is needed for -20 dB crosstalk and the limit to the track density is 100 tracks/mn.     

Properties of one-sided probe heads on double-layer perpendicular recording media

The perpendicular recording mode is still a candidate for obtaining higher densities. Best recording results on a double-layer (DL) medium must be expected from using a probe head (PH). This contribution provides an analysis of the write-read performance of one-sided PHs that do not use an auxiliary pole on the back of the medium. Analytical as well as numerical models were used to calculate the effects of saturation and medium thickness on the write fields. Experimental verification of the modeling results was obtained by measuring the wavelength response of many W-shaped PHs on DL media. Combining this with the calculated response, we obtained a semi-empirical relation between the pole nulls, pole thickness and the pole-to-backlayer distance. It reveals a PH behaviour very different from a ring head (RH). The pole thickness calculated from the measured pole-null wavelengths showed a very close agreement with the optically determined value. The calculated head efficiencies are very small, as was confirmed experimentally, and need improvement before the PH has an output comparable with a RH.     

High bit density (100 Mb/cm2) with single-layer Co-Crmedia and ring heads in perpendicular magnetic recording

The signal and noise of single-layer Co₇₉Cr₂₁ media are measured with ring heads to estimate the area density that can be achieved. Densities as high as 100 Mb/cm² (1 μm²/bit) are expected when a signal-to-noise ratio sufficient for an error probability less than 10 ^-5 is required. As a comparison, densities estimated from data from metal-evaporated tape and CrO₂ tape are given. In the frequency response of the single-layer media, an additional minimum was observed for a wavelength slightly larger than the gap length. This is probably caused by the bipolar nature of the perpendicular recording field of a ring head     

Dependence of reproducing gap null on head geometry

The spatial frequency response of reproduce heads with infinite depth, but finite pole length, is determined to very good accuracy by superposition of conformal map solutions for simpler geometries. This approach yields closed form approximations of the frequency response which are accurate to better than 7% for any head length-to-gap length ratio and any spatial frequency. In particular, the effect of this ratio on the location of the first gap null in the frequency response spectrum is explored for narrow pole length heads. The results lead to design considerations for extending the useful frequency range of thin film reproduce heads.     

Overwrite as a function of record gap length

In disk recorders, a common head is used for both recording and reproducing. Old data are not erased but are simply recorded over. The partially erased old data signal appears in the new data as error-producing interference. The amount of erasure of the old data signal is called "overwrite", and 30 dB is typically required. To avoid the reproduce gap null, the head gap is usually chosen to be less than half of the 2F (or bandedge) flux change length. To achieve adequate overwrite using a gap this small, it is necessary to use a very thin recording layer. A simple explanation for this, involving greater depth of penetration for low density signals, is at best incomplete. The data below show that the overwrite phenomenon is complex. Overwrite spectra measured using a thick medium show large resonance peaks whose amplitude and position depend on the record gap, record current, and the densities of the overwriting signal and the signal being overwritten.     

Magnetic field of a ring head on a double layer medium

A simple theoretical model is developed for a Karlquist-type recording head interacting with a two layer recording medium in which the sublayer has a high but finite permeability. During readback the vertical H fields far from the gap are shown to decay exponentially with a characteristic length r given byr = t ast h ast uwhere t is the sublayer thickness, h is the spacing between the head and the sublayer, and u is the relative permeability of the sublayer. The long tails of this field account for observed readback wave forms. The model also predicts that the spatial extent of sublayer saturation during the write process will be twenty to one hundred gap lengths, justifying the assumption that during write one may ignore the sublayer. The write prediction was tested experimentally by making a standstill recording with a Winchester-type head on a double layer medium and measuring the fringing field above the medium with a high-resolution Hall probe. The data were compared to the predictions of an iterative simulation in which the sublayer was either present or absent during write. A significantly better fit was found when the simulated medium contained no sublayer during the write process.     

Effect of secondary gaps in near-saturated metal-in-gap video heads

Secondary gaps between the ferrite bulk and the Sendust (AlFeSi alloy) shim may occur in metal-in-gap (MIG) heads. Finite-element models are used to explore the effect that these gaps have on the read/write characteristics of single- and double-sided MIG heads. The presence of a secondary gap is shown to cause an additional peak in the writing field and oscillations in the magnitude of the response during replay. The field and response of a double-sided MIG head is affected more than those of the corresponding single-sided MIG head     

A theory of digital magnetic recording on metallic films

A theory is presented predicting the performance of thin magnetic tape as a digital storage medium. The NRZ recording properties are discussed with reference to the properties of both the tape and the replay head. Expressions are derived relating the isolated pulse width, the output voltage, and the packing density to the coercivity and thickness of the tape, the head gap length, and the head-to-tape separation. The theoretical predictions are then compared with experimental results measured over a wide range of head and tape properties. The agreement obtained is excellent.     

Optical scanning extrinsic Fabry-Perot interferometer for absolute microdisplacement measurement

We report an optical-scanning, dual-fiber, extrinsic Fabry-Perot interferometer system for absolute measurement of microdisplacement. The system involves two air-gapped Fabry-Perot cavities, formed by fiber end faces, functioning as sensing and reference elements. Taking the scanning wavelength as an interconverter to compare the gap length of the sensing head with the reference-cavity length yields the absolute measurement of the sensing-cavity length. The measurement is independent of the wavelength-scanning accuracy, and the reference-cavity length can be self-calibrated simply by one's changing the sensing-head length by an accurate value.     

Crucial points in perpendicular recording

Since the introduction of perpendicular recording on a floppy disc by IWASAKI in 1977 and its equivalent design on a rigid disc (SPH-like sensor + double-layer medium) in 1981, many tests have been carried out on different R/W sensors. For each test the main goal was the fci record or the improvement of the magnetic layer. Seen from the recording system point of view, the head and the medium are looked at as a unit through a specification, unchanging with increasing area density. For example, a minimum of 26 dB and 70 % must be achieved for the S/N ratio and the resolution respectively. By considering the noise of the best electronic channel (with a thin film head), and ignoring mechanical and medium noises, the output signal must be at least 250 μv pop. For a 50 Kfci application, however, a sensor does not yet exist. Using a ferrite head with a 1.2 μm gap length to write on FeTbGd, the level of the signal will not be high enough to be used. It is improved with a 0.6 μm gap head but then, the field doesn't allow us to write ! Such problems exist also with thin film heads or SPH like sensors on rigid discs. To improve the R/W process, the trend is to use a double layer medium e.g. CrCo/FeNi. The results show that this direction is not necessarily the best. For example, when erasing or over-writing with the head, some domains appear in the FeNi film which create noise from the track or its edge. Another example is the fact that the optimum parameters for a medium such as CrCo are not always compatible with the characteristics of the head (i.e. Hc, the thickness, the crystallographic orientation, the bit stability compared to the write field, the signal, the noise...).     

Long wavelength response of elliptical reproduce heads

Long wavelength response characteristics for the class of elliptical reproduce heads are calculated. Simple series solutions are obtained for a flat recorded medium, and numerical methods are used for a tape wrapped over the head at arbitrary contact angles. Special eccentricities of the ellipse yield classical results. Many geometries lead to low frequency bumps on the response curve.     

Frequency response function of a gapped infinite length pole piece recording head

The frequency (wavelength) response function of a gapped infinite length, infinite permeability magnetic reproduce head is calculated analytically.     

Wavelength response of perpendicular magnetic recording

From the measurements of the surface field of a recording medium, it was obtained that an almost ideal step change distribution of magnetization is formed in perpendicular recording for digital signals. The fact represents that the upper limit of usable recording density is determined only by the resolution of a reproducing head. Therefore, the reproduction by a perpendicular head was successfully analyzed by using the reciprocity theorem. By introducing thickness loss of main pole of the head, the satisfactory coincidence was obtained between the calculated and the measured results in the wavelength response even at the densities of more than 150 kMRPI. In reproducing process, the magnetic interaction between the main pole and the medium acts so as to decrease the effective spacing between them.     

Analytic 3-D Read Head Model With Finite Shields

This paper presents an analytic model of a read head with shields of finite length and width, suitable for replay at 1 Tb/in $^{2}$. The model determines the shield potential by iterative solution of the equations governing the Fourier coefficients, given an initial guess. The model is used to demonstrate the effect of varying the length and width of the shields. The paper gives results for the shield potential, equipotentials, vertical head field, and spectral response function. A head with shields that are the same length as the semi-shield—shield gap offers an almost constant magnitude response over a broad range of along-track frequencies, and the use of sufficiently wide side shields is advantageous.      

Wavelength response of harmonic distortion in AC-bias recording

Wavelength response of harmonic distortion in ac-bias recording is analyzed. The wavelength response is affected in both the record and playback processes. In the record process tape nonlinearity and magnetization phase shift, which is dependent on signal-field intensity, are taken into account. In the playback process, tape thickness, tape-to-head spacing, gap length, etc. axe taken into account. An approximate expression for the third-harmonic distortion is derived. The experimental data show quantitative agreement with theory.     

Modeling of diffuse-diffuse photon coupling via a nonscattering region: a comparative study

It is well established that diffusion approximation is valid for light propagation in highly scattering media, but it breaks down in nonscattering regions. The previous methods that manipulate nonscattering regions are essentially boundary-to-boundary coupling (BBC) methods through a nonscattering void region based on the radiosity theory. We present a boundary-to-interior coupling (BIC) method. BIC is based on the fact that the collimated pencil beam incident on the medium can be replaced by an isotropic point source positioned at one reduced scattering length inside the medium from an illuminated point. A similar replacement is possible for the nondiffuse lights that enter the diffuse medium through the void, and it is formulated as the BIC method. We implemented both coupling methods using the finite element method (FEM) and tested for the circle with a void gap and for a four-layer adult head model. For mean time of flight, the BIC shows better agreement with Monte Carlo (MC) simulation results than BBC. For intensity, BIC shows a comparable match with MC data compared with that of BBC. The effect of absorption of the clear layer in the adult head model was investigated. Both mean time and intensity decrease as absorption of the clear layer increases.     

An effective medium model for elastic waves in microcrack damaged media

Direct numerical simulations of waves traveling through microcrack-damaged media are conducted and the results are compared to effective medium calculations to determine the applicability of the latter for studying wave propagation. Both tensile and compressive waves and various angular distributions of randomly-located cracks are considered. The relationships between the input wavelength and the output wave speed and output signal strength are studied. The numerical simulations show that the wave speed is nearly constant when 1/ka > 60 for tensile waves and 1/ka > 10 for compressive waves, where k is the wave number and a is the average half-crack length. The direct simulations also show that when the input wavelength is much longer than the crack length, 1/ka > 60, the wave can pass through the damaged medium relatively unattenuated. On the other hand, when the input wavelength is shorter than a “cut off” wave length, the output wave magnitude decreases linearly with the input wavelength. The effective medium wave speed and magnitude calculations are not dependent on the input wavelength and therefore the results correspond well with the numerical simulations for large 1/ka. This suggests a minimum wavelength for which the homogenized methods can be used for studying these problems.     

Narrow track readout with magnetic garnet film

A novel magneto-optic readout head, which utilizes the modulation of width of straight domains in a garnet film in response to the fringing field from the recording medium, was evaluated from the viewpoint of narrow track readout. In a static transfer experiment with a garnet film having a domain width of 2.25 μm, a definite transfer to the garnet film with track widths of 3 μm or less was confirmed. An expression for the modulation degree of the domain width was derived, and its predictions agreed well with the experimental results. In the dynamic readout experiment, a carrier-to-noise ratio of 50 dB was obtained for a trackwidth of 4 μm and a wavelength of 10 μm. The cross-talk was -30 dB when the track-to-track spacing and track width were 10 μm and 5 μm, respectively. From these results the feasibility of narrow track readout based on this head was demonstrated. The readout performance, including the decrease of readable track width, the wavelength and crosstalk, can be greatly improved if a garnet film, having a domain width narrower than that used in this experiment is used together with a high-density recording medium.