Asymmetry in density peaks on either side of an m = +1 half helical antenna is observed both in terms of peak position and its magnitude with respect to magnetic field variation in a linear helicon plasma device [Barada et al., Rev. Sci. Instrum. 83, 063501 (2012)]. The plasma is produced by powering the m = +1 half helical antenna with a 2.5 kW, 13.56 MHz radio frequency source. During low magnetic field (B < 100 G) operation, plasma density peaks are observed at critical magnetic fields on either side of the antenna. However, the density peaks occurred at different critical magnetic fields on both sides of antenna. Depending upon the direction of the magnetic field, in the m = +1 propagation side, the main density peak has been observed around 30 G of magnetic field. On this side, the density peak around 5 G corresponding to electron cyclotron resonance (ECR) is not very pronounced, whereas in the m = −1 propagation side, very pronounced ECR peak has been observed around 5 G. Another prominent density peak around 12 G has also been observed in m = −1 side. However, no peak has been observed around 30 G on this m = −1 side. This asymmetry in the results on both sides is explained on the basis of polarization reversal of left hand polarized waves to right hand polarized waves and vice versa in a bounded plasma system. The density peaking phenomena are likely to be caused by obliquely propagating helicon waves at the resonance cone boundary.