For　the　first　time,　we　experimentally　and　theoretically　research　about　the　second-order　nonlinear　signal　(SNS)　including　electromagnetically　induced　absorbing　(EIA)　and　electromagnetically　induced　gain　(EIG),　six　wave　mixing　band　gap　signal　(SWM　BGS)　resulting　from　photonic　band　gap　structure　in　an　inverted　Y-type　four　level　system　with　the　electromagnetically　induced　grating.　The　interplay　between　the　SNS　and　SWM　BGS　is　illustrated　clearly　for　the　first　time.　When　we　change　the　frequency　detuning　to　make　the　SWM　BGS　and　SNS　overlap,　the　SWM　BGS　is　suppressed　and　the　intensity　of　SNS　is　strongest　near　the　resonance　point.　We　can　control　the　intensity　of　the　SWM　BGS　and　EIG　caused　by　the　classic　effect　through　changing　the　power　of　coupling　field.　And　the　changes　on　the　EIA　generated　by　the　quantum　effect　are　obtained　by　changing　the　power　of　dressing　field.　Since　the　SWM　BGS　is　the　enhancement　of　the　four　wave　mixing　band　gap　signal　(FWM　BGS),　when　we　set　FWM　BGS　as　the　input　and　SNS　as　the　modulation　role　to　control　the　amplification　amplitude　for　the　FWM　BGS　in　our　scheme,　the　adjustable　optical　amplifier　can　be　obtained.　(C)　2015　Optical　Society　of　America